Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Werner, Maxwell
Master of Science - MSc
University of British Columbia
The field of two dimensional materials is growing rapidly, with monolayer transition metal dichalcogenides (TMD) showing promise for applications in electronics and optoelectronics. Multidimensional coherent spectroscopy (MDCS) is a nonlinear technique which offers a significant advantage over commonly used linear spectroscopy, allowing for the direct determination of homogeneous linewidths and coherent coupling between states. These capabilities also allow for identification of decoherence mechanisms. Moreover, collinear MDCS allows for hyperspectral imaging which could be leveraged to characterize and improve sample fabrication, a key concern for monolayer systems and heterostructures. Towards this end, we have developed an ultrafast light source which, when combined with a commercial MDCS system, can be utilized to study a variety of 2D semiconductors with optical bandgaps in the visible to near infrared. The light source is a synchronously pumped Optical Parametric Oscillator (OPO), capable of producing optical pulses with approximately 50nm bandwidths and a center wavelength tunable from 650nm to 900nm through adjustment of the cavity length and lithium triborate (LBO) crystal temperature. The design, characterization and operation of this OPO is presented for the benefit of future system users. Additionally, cavity simulations indicate that bandwidth limitations are ultimately imposed by the cavity mirror dispersion. Suggestions are made to overcome these limitations in the future using alternative dispersion compensation methods or single-pass nonlinear broadening. To measure multi-dimensional spectra, we utilized the MONSTR Sense Technologies BIGFOOT Ultrafast Spectrometer. Using monolayer MoSe₂ samples as a benchmark, we worked to verify the operation of the spectrometer. Two prominent artifacts were observed in the measured spectra – a narrow peak along the diagonal and a vertical stripe extending across the excitation energy axis. The source of the narrow diagonal feature was determined to be a stray retro-reflection. We were unable to definitively identify the source of the vertical feature; however, our troubleshooting efforts are catalogued, and additional considerations are presented for future testing. Despite the remaining artifact, we present a low temperature 2D spectra obtained from unencapsulated MoSe₂, with exciton and biexciton energies showing good agreement with the literature.
Design and Operation of a Multi-dimensional CoherentSpectroscopy SystembyMaxwell WernerB.Sc., Bethel University, 2018A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University of British Columbia(Vancouver)August 2024© Maxwell Werner, 2024The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Design and Operation of a Multi-dimensional Coherent SpectroscopySystemsubmitted by Maxwell Werner in partial fulfillment of the requirements for thedegree of Master of Science in Physics.Examining Committee:David Jones, Professor, Physics and Astronomy, UBCSupervisorZiliang Ye, Associate Professor, Physics and Astronomy, UBCSupervisory Committee MemberiiAbstractThe field of two dimensional materials is growing rapidly, with monolayer Transi-tion metal dichalcogenides (TMD) showing promise for applications in electronicsand optoelectronics. Multidimensional coherent spectroscopy (MDCS) is a non-linear technique which offers a significant advantage over commonly used linearspectroscopy, allowing for the direct determination of homogeneous linewidths andcoherent coupling between states. These capabilities also allow for identificationof decoherence mechanisms. Moreover, collinear MDCS allows for hyperspectralimaging which could be leveraged to characterize and improve sample fabrication,a key concern for monolayer systems and heterostructures. Towards this end, wehave developed an ultrafast light source which, when combined with a commercialMDCS system, can be utilized to study a variety of 2D semiconductors with opti-cal bandgaps in the visible to near infrared. The light source is a synchronously-pumped Optical Parametric Oscillator (OPO), capable of producing optical pulseswith ≈ 50nm bandwidths and a center wavelength tunable from 650nm to 900nmthrough adjustment of the cavity length and lithium triborate (LBO) crystal tem-perature. The design, characterization and operation of this OPO is presented forthe benefit of future system users. Additionally, cavity simulations are indicatedthat bandwidth limitations are ultimately imposed by the cavity mirror dispersion.Suggestions are made to overcome these limitations in the future using alterna-tive dispersion compensation methods or single-pass nonlinear broadening. Tomeasure multi-dimensional spectra, we utilized the MONSTR Sense TechnologiesBIGFOOT Ultrafast Spectrometer. Using monolayer MoSe2 samples as a bench-mark, we worked to verify the operation of the spectrometer. Two prominent ar-tifacts were observed in the measured spectra – a narrow peak along the diagonaliiiand a vertical stripe extending across the excitation energy axis. The source of thenarrow diagonal feature was determined to be a stray retro-reflection. We wereunable to definitively identify the source of the vertical feature; however, our trou-bleshooting efforts are catalogued, and additional considerations are presented forfuture testing. Despite the remaining artifact, we present a low temperature 2Dspectra obtained from unencapsulated MoSe2, with exciton and biexciton energiesshowing good agreement with the literature.ivLay SummaryAtomically thin two dimensional materials provide an exciting platform to studyhighly correlated systems, with many materials exhibiting distinct properties in the2D limit due to reduced dimensionality and the resulting strong electronic inter-actions. These 2D layers can also be stacked and bonded together via the van derWaals force, enabling the fabrication of materials with new and tunable properties,and motivating studies towards industrial applications. We have developed a lightsource to study 2D materials, leveraging a commercial MDCS system to measureinhomogeneities in the sample, ultrafast time dynamics, and interactions betweenexcitations. In this thesis, we present the design and operational details of the lasersystem developed for these studies and suggest possible improvements towardsbroader bandwidths and stable operation. In addition, initial measurements andtroubleshooting of the multi-dimensional spectrometer are presented along withpromising material systems for study with MDCS.vPrefaceInitial designs of the OPO presented in this thesis were developed with input fromProf. Giulio Cerullo and the Ultrafast Spectroscopy Group at Politecnico di Mi-lano.Detailed cavity design and optomechanical design was performed by me. Thecavity alignment procedure was developed by me, with troubleshooting assistanceprovided by Dr. Evgeny Ostroumov.A majority of the characterization of the OPO system was performed by me, withprocedures leveraging the MONSTR Sense Technologies BIGFOOT Ultrafast Spec-trometer developed in collaboration with Dr. Evgeny Ostroumov, and Dr. EricMartin of MONSTR Sense Technologies. Stabilization schemes for the OPO wereimplemented by me with significant input from Dr. Arthur Mills and Dr. DavidJones.Simulations of the OPO cavity were developed by me, in collaboration with Dr.Arthur Mills.Commissioning of the BIGFOOT Ultrafast Spectrometer was performed by me andDr. Evgeny Ostroumouv, with assistance provided by Dr. Eric Martin. The MoSe2samples used for this commissioning were generously provided by Dongyang Yang.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 OPO Theoretical Background and Cavity Design . . . . . . . . . . . 42.1 Gaussian Beam Propagation . . . . . . . . . . . . . . . . . . . . 52.2 Dispersion and Dispersion Compensation . . . . . . . . . . . . . 72.3 Nonlinear Optics . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 Broadband OPO Cavity Design . . . . . . . . . . . . . . . . . . . 122.4.1 Cavity Geometry . . . . . . . . . . . . . . . . . . . . . . 132.4.2 Cavity Dispersion . . . . . . . . . . . . . . . . . . . . . . 153 Characterization of OPO System . . . . . . . . . . . . . . . . . . . . 18vii3.1 Pump Charcterization . . . . . . . . . . . . . . . . . . . . . . . . 203.1.1 Transverse Mode . . . . . . . . . . . . . . . . . . . . . . 203.1.2 Spectrum and Temporal Characteristics . . . . . . . . . . 223.1.3 SHG Conversion Efficiency . . . . . . . . . . . . . . . . 253.2 Signal Characterization . . . . . . . . . . . . . . . . . . . . . . . 283.2.1 Transverse Mode . . . . . . . . . . . . . . . . . . . . . . 283.2.2 Spectral and Temporal Characterization . . . . . . . . . . 293.2.3 Output Power . . . . . . . . . . . . . . . . . . . . . . . . 353.2.4 Spectral Stability . . . . . . . . . . . . . . . . . . . . . . 353.3 Towards Broader Bandwidths . . . . . . . . . . . . . . . . . . . . 403.3.1 Passive Cavity Simulations . . . . . . . . . . . . . . . . . 403.3.2 Alternative Dispersion Compensation and Single Pass Broad-ening . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454 Multidimensional Coherent Spectroscopy: Towards Studies of Exci-tonic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.1 MonstrSense Bigfoot Spectrometer - Collinear MDCS . . . . . . 504.2 Future Studies: MDCS for Ultrafast Studies of 2D Materials . . . 584.2.1 NiPS3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.2.2 Transition Metal Dichalcogenides . . . . . . . . . . . . . 605 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65A OPO Alignment Procedure . . . . . . . . . . . . . . . . . . . . . . . 70A.1 Initial Optics Placement . . . . . . . . . . . . . . . . . . . . . . . 70A.2 IR Cavity Alignment . . . . . . . . . . . . . . . . . . . . . . . . 72A.3 Overlap Pump with Cavity Mode . . . . . . . . . . . . . . . . . . 74viiiList of TablesTable 2.1 Summary of relevant two-dimensional TMD electronic proper-ties. In terms of optical excitation, these bandgaps are in the vis-ible and near infrared, ranging from 590nm to 730nm. The exci-ton binding energies represent experimentally measured values.Reproduced with permission from Springer Nature [1] . . . . . 4Table 2.2 Summary of specifications for OPO cavity optics. . . . . . . . . 16ixList of FiguresFigure 2.1 A schematic of the OPO cavity layout. The curved mirrors,CM1 and CM2, form a cavity focus centered in the LBO crys-tal. The green arrow represents the pump beam coupled inthrough CM1. The yellow lines trace out the propagation ofthe signal beam inside the cavity. . . . . . . . . . . . . . . . . 12Figure 2.2 Plot of OPO Cavity Stability Region. The blue and orange linesrepresent the transverse vertical and horizontal axes, respec-tively. Outside of these plotted curved mirror separations, thecavity is unstable. . . . . . . . . . . . . . . . . . . . . . . . . 14Figure 2.3 Plot of OPO Cavity Mode over one full round trip. The or-ange trace represents the transverse horizontal mode, while theblue represents the transverse vertical mode. The mode passesthrough a tight cavity focus twice on each round trip, comingto a loose secondary focus on each end mirror. . . . . . . . . 15Figure 3.1 CAD model of the pump beam path and OPO cavity. Col-ored lines designate the beam paths with red representing the1035nm pump light, green the 517nm doubled pump light, andorange the tunable signal output. These optics are mounted ona watercooled breadboard which helps to minimize the impactof environmental changes on the OPO operation. . . . . . . . . 18xFigure 3.2 Schematic of the full OPO setup. Colored lines designate thebeam paths with red representing the 1030nm FLINT beam,green the 515nm pump light, and orange the tunable signaloutput. In addition to the pump laser and OPO cavity, a gratingcompressor is used at the output to compenesate linear chirpand generate high peak intensities at the sample of interest. . . 19Figure 3.3 Measurement of the transverse mode of the FLINT. Similarmeasurements at varying distances from the laser output showthat the beam is well collimated. . . . . . . . . . . . . . . . . 20Figure 3.4 Measurements and fits of the 517nm transverse mode follow-ing a weak focusing lens with f = 200mm. The solid linesshow a fit of a theoretical Gaussian beam propagation to themeasured data. In addition to the waist shown in the legend,this fit produces M2 ≈ 1.15. . . . . . . . . . . . . . . . . . . 21Figure 3.5 Overlap of pump and cavity mode. The dashed line shows thesimulated cavity mode near the LBO crystal. The solid coloredlines show the simulated propagation of the pump beam. Thedata points show measured beam waists of the pump. . . . . . 23Figure 3.6 Typical optical spectrum of the Light Conversion FLINT Fem-tosecond Laser. The spectral widths listed in the figure are ex-tracted from fits of Gausian and Sech2 pulse shapes, and repre-sent the full-width at half-maximum of the fitted curve. Fromthe fits we can also extract a center wavelength of 1030.9nm. . 25Figure 3.7 Typical intensity autocorrelation of the Light Conversion FLINTFemtosecond Laser. The temporal widths listed in the figureare extracted from fits of Gausian and Sech2 pulse shapes, andrepresent the full-width at half-maximum pulse width, not thefitted autocorrelation width. The transform limited (TL) pulseis obtained by Fourier transforming the spectrum. . . . . . . . 26xiFigure 3.8 Typical optical spectrum of the second harmonic generatedfrom the Light Conversion FLINT Femtosecond Laser utiliz-ing a LBO crystal. The spectral widths listed in the figure areextracted from fits of Gausian and Sech2 pulse shapes, and rep-resent the full-width at half-maximum of the fitted curve. Fromthe fits we can also extract a center wavelength of 514.9nm. . 27Figure 3.9 Measurement of the second harmonic power and conversionefficiency for the frequency doubled FLINT beam. The sec-ond harmonic power grows quadratically at low pump powersbefore becoming approximately linear as the pump power issignificantly depleted. . . . . . . . . . . . . . . . . . . . . . 28Figure 3.10 OPO Signal Spectra obtained at varying cavity length and crys-tal temperature with two pairs of Dispersion compensating mir-rors (DCM). The temperatures listed represent the setpoint ofthe crystal oven. Additionally, a pair of fused silica wedgeswere used inside the cavity to tune closer towards zero GDD. . 31Figure 3.11 OPO signal spectra obtained at varying cavity length and crys-tal temperature with a single pair of DCM.The temperatureslisted represent the setpoint of the crystal oven. The singleDCM pair resulted in slightly negative GDD, with reducedresidual group delay dispersion (GDD) oscillations at longerwavelengths. . . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 3.12 (a) and (b) show second harmonic generation (SHG) frequencyresolved optical gating (FROG) traces of the OPO spectrum mea-sured after the Bigfoot spectrometer for two grating compres-sor settings, with (a) showing a strongly chirped pulse. (c) and(d) show the autocorrelation and spectra obtained by integrat-ing over the wavelength and delay axes, respectively. The OPOspectrum and transform limited temporal pulse envelope arealso shown. Limited SHG bandwidth results in some narrow-ing of the FROG spectra. . . . . . . . . . . . . . . . . . . . . 33xiiFigure 3.13 Characterization of the OPO Signal pulse after passing throughthe Bigfoot spectrometer and objective lens. The autocorre-lation trace measured utilizing the Bigfoot lock-in detectionis shown on the right, along with the transform limited pulseshape produced by assuming a flat spectral phase and Fouriertransforming the spectrum. . . . . . . . . . . . . . . . . . . . 34Figure 3.14 Measurements of the OPO output power as a function of centerwavelength for varying LBO crystal temperatures. One can seethe peak parametric gain shifts to longer wavelengths as thecrystal temperature is increased. . . . . . . . . . . . . . . . . 36Figure 3.15 Spectral Stabilization Scheme. A reflection off of the first com-pressor grating is used to monitor the OPO output spectrum. Areflection grating is used to spatially disperse the spectrum. Anadjustable slit is used to isolate one edge of the spectrum to bemeasured by a photodiode. This photodiode signal is then usedas feedback to adjust the cavity length. . . . . . . . . . . . . . 37Figure 3.16 Long term OPO stability. The spectrum is actively stabilized,exhibiting a slow drift due to the decreasing output power. Wesee a similar drift in the output pointing, suggesting that thepower drift is due to changing cavity alignment as the cavitylength is adjusted to compensate environmental changes. . . . 38Figure 3.17 Short term spectral stability with the OPO free-running andlocked.The OPO spectrum is measured with the Thorlabs CCS175Spectrometer with a scan rate of 100Hz, resulting in a Nyquistfrequency of 50Hz. Each spectrum is fit to a Gaussian curveto determine the center wavelength. A prominent 30Hz peakis observed when the OPO is free-running. When locked, thepower spectrum drops by a factor of 10 across the FFT band-width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41xiiiFigure 3.18 Simulated cavity enhancement as a function of relative cavitylength and wavelength. The simulation includes dispersion dueto two DCM pairs, the LBO crystal, fused silica wedges, and air.The fused silica wedges are used to bring the average cavityGDD closer to zero. This map can be compared with measuredspectra obtained utilizing the same cavity configuration, shownin Fig. 3.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 3.19 Simulated cavity enhancement as a function of relative cav-ity length and wavelength. The simulation includes dispersiondue to one DCM pair, the LBO crystal, fused silica wedges, andair. The fused silica wedges are used to raise the average cavityGDD to avoid unstable operation. This map can be comparedwith measured spectra obtained utilizing the same cavity con-figuration, shown in Fig. 3.11. . . . . . . . . . . . . . . . . . 46Figure 3.20 Plot of the OPO free spectral range (FSR) as a function ofwavelength with average zero GDD cavity configuration. Theresonance map simulations rely on the single-valued determi-nation of the synchronous wavelength, the wavelength for whichthe cavity FSR is equal to the pump repetition rate. Near zeroGDD there exist multiple synchronous wavelengths. . . . . . . 47Figure 4.1 A schematic of the MDCS system constructed at Stewart Blus-son Quantum Matter Institute (SBQMI). Pulses from the OPOare split and delayed in the spectrometer before being focusedonto the sample of interest. The four wave mixing (FWM) sig-nal reflected from the sample is then measured on a photode-tector and isolated using lock-in detection. . . . . . . . . . . . 49xivFigure 4.2 Rephasing 2D spectrum of MoSe2 generated with pulses hav-ing alternating σ+ and σ− polarization. The diagonal peaksrepresent the exciton (X) and trion (T). The off-diagonal peaksare identified as bound charged (XT b,T Xb) and neutral (XX)biexcitons. Due to valley-selective optical excitation, the alter-nating polarizations generate excitons in both the K and K’ val-leys, highlighting these intervalley interactions. Reproducedwith permission from Springer Nature [2]. . . . . . . . . . . . 53Figure 4.3 Hyperspectral MDCS measurements obtained on an hBN en-capsulated monolayer MoSe2 sample. (a) and (b) show spatialmaps of the homogeneous (γ) and inhomogeneous (σ ) excitonlinewidths, with (c) highlighting correlations between γ and σfor different regions of the sample. (d) shows the exciton res-onance energy measured at different points across the sample.Reprinted from [3] with the permission of AIP Publishing. . . 54Figure 4.4 2D rephasing spectrum obtained from an unencapsulated mono-layer MoSe2 sample at room temperature. There are two un-expected features: a narrow diagonal peak and a vertical stripeextending from the exciton peak at 1570meV. . . . . . . . . . 55Figure 4.5 2D rephasing spectrum measured on an unencapsulated mono-layer MoSe2 sample at T = 20K. The narrow stripe along thediagonal has been eliminated by rotation of a lens near the Big-foot input. The verical stripe is still prominent, extending fromthe excition peak at 1630meV. . . . . . . . . . . . . . . . . . 56Figure 4.6 NPS3 Layer Structure. The red arrows represent the spin ofthe Ni atoms, showing a zig-zag antiferromagnetic ordering.Reproduced with permission from Springer Nature [4]. . . . . 59Figure 4.7 Temperature dependent absorption measurement of NiPS3 show-ing a narrow linewidth exciton (Peak I) and a two-magnonsideband (Peak II). Peaks Sα and Sβ are left unassigned. Re-produced with permission from Springer Nature [5]. . . . . . 61xvFigure 4.8 Reflection contrast spectra showing splitting of the WSe2 A ex-citon in a WSe2/WS2 heterostructure due to confinement of theMoire´ potential. Reproduced with permission from SpringerNature [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure A.1 A schematic showing the essential optical elements for gener-ating and manipulating the OPO pump beam. Of particular im-portance, the lens L1 is used to focus the FLINT beam into theLBO crystal for efficient frequency doubling. This frequencydoubled beam at ≈515nm is used to pump the OPO. . . . . . 71Figure A.2 A schematic showing the initial cavity alignment setup, utiliz-ing the undepleted fundamental coupled in through the outputcoupler. A telescope is used to roughly mode match and anoptical isolator protects the FLINT from the return beam. . . . 73Figure A.3 A schematic of the setup used to fine tune the cavity align-ment. A camera is utilized to view one of the beams trans-mitted through CM2. Utilizing the cavity end mirrors, OCand M3, one may overlap multiple cavity round trips on thecamera. When the cavity is length matched with the pump,one may also observe intensity modulation of the beam on thecamera. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74xviList of AbbreviationsAOM acousto-optic modulatorBBO beta barium borateDCM Dispersion compensating mirrorsDFG difference frequency generationFROG frequency resolved optical gatingFSR free spectral rangeFWHM full-width at half-maximumFWM four wave mixingGDD group delay dispersionLBO lithium triborateLO local oscillatorMDCS Multidimensional coherent spectroscopyOPO Optical Parametric OscillatorOR optical rectificationSBQMI Stewart Blusson Quantum Matter InstituteSFG sum frequency generationSHG second harmonic generationSPM self-phase modulationTMD Transition metal dichalcogenidesxviiAcknowledgmentsFirst, I would like to extend my gratitude to the professors and researchers thathave contributed to my time at UBC. To my supervisor, David Jones, thank youfor the opportunity to work in your group and continually providing support andencouragement. You were particularly generous with your time in assisting withthe extensive troubleshooting of the experimental system. To Arthur Mills andEvgeny Ostroumov, you were both instrumental in helping me to develop many ofthe hands-on skills and analysis techniques necessary to carry out this work. Andto Ziliang Ye, for generously sharing lab space, instrumentation, and ideas.To the friends I made along the way (Aaron, Aswin, Brad and many others),thank you for providing much needed community and support throughout grad-uate school.And to my partner, Zoe, thank you for reminding me of the little joys in the midstof growing-pains and stress.xviiiChapter 1IntroductionTwo dimensional materials provide a unique platform to study correlated electronphysics, and offer promising opportunities for electronic, optoelectronic and pho-tonic applications [1, 7]. The interesting properties of 2D materials are derivedprimarily from their reduced dimensionality. In a three dimensional conductor orsemiconductor electrons may rearrange such that the electric field produced by agiven electron is reduced, or screened, by the other electrons. For a given elec-tron in the material, this results in a potential which is reduced by a factor of ε (⃗q),the momentum dependent dielectric constant [8]. In two dimensions, the elec-trons are confined to a plane, and thus the screening is diminished. In this casethe interaction between two charges, separated by a distance ρ , is described bythe Rytova-Keldysh potential, which displays the behavior of the 3D unscreenedColoumb potential as ρ → ∞, but goes like ln(ρ) as ρ → 0 [9]. This leads toenhanced interactions among electrons and, along with unique 2D structural prop-erties, produces a variety of interesting quasiparticles such as excitons, phonons,and magnons. Excitons are of particular interest due to large binding energies andhigher-order interactions amongst themselves and other collective excitations.Following the mechanical exfoliation of graphene nearly two decades ago [10],numerous other van der Waals bonded materials have emerged which produce high-quality single crystal monolayers through mechanical exfoliation techniques. Oneparticular class, Transition metal dichalcogenides (TMD), have attracted significantattention as they possess a direct bandgap in the monolayer limit [11], allowing1for efficient light-matter coupling. In recent years there has also been a renewedinterest in transition metal phosphorous trichalcogenides as a system for exploring2D magnetism [12–14]. The unique properties of these 2D systems make thempromising platforms for information processing and storage through spin- or val-leytronics [15].As expected, these classes of materials host a variety of excitations and in-teractions, often leading to congested optical spectra with features concealed bybroadened lines. Common linear techniques such as photoluminescence and re-flection contrast provide ensemble averaged spectra, and thus intrinsic linewidthsare hidden by inhomogenous broadening which may be caused by poor samplepreparation or crystal defects. Multidimensional coherent spectroscopy (MDCS)is a nonlinear spectroscopy technique well suited to disentangle these complexspectra as it maps the correlation between the excitation and emission frequencies.This technique provides a direct measure of both the homogeneous and inhomoge-neous linewidths, and also reveals information about coupling between states anddynamics of the system.These capabilities can be leveraged to provide essentialinformation for applications requiring precise control and long-lived coherences.In order to study the interactions between multiple states through MDCS, onemust utilize a broadband source to simultaneously excite the states of interest.Ti:Sapph lasers are a common source with a tunable output spectrum in the vis-ible to NIR (680-1040nm or 1.19-1.82eV), but they typically require a high powerpump, resulting in large and expensive laser systems. Additionally, this spectralrange limits access to materials with larger band gaps. At the Stewart BlussonQuantum Matter Institute (SBQMI) we have developed a tunable, broadband Opti-cal Parametric Oscillator (OPO) based on the design by Coluccelli et al [16]. Asseen in Fig. 3.10 and Fig. 3.11, the OPO spectrum can be tuned from 650-900nm(1.38-1.91eV) with a simple adjustment of the cavity length, and additional tuningdown to 600nm (2.10eV) may be provided through use of another nonlinear crys-tal. These spectra provide access to exciton states (including trions and biexcitons)in the semiconducting TMDs MX2 (M = Mo, W; X = S, Se).As layed out by Geim and Grigorieva [17], there are numerous possibilities forstacking van der Waals materials. One interesting possibility is the study of TMDheterostructures where the constituent layers have differing chalcogen atoms. MS22and MSe2 (M = Mo, W) have bandgaps around 2eV (620nm) and 1.7eV (730nm),respectively, requiring a source with a bandwidth over 300meV (100nm) in order tosimultaneously probe excitons from both layers. These systems provide motivationfor even broader bandwidths to study interactions between excitations distant inenergy.This thesis presents our work to develop and characterize a broadband OPO. Wealso work to integrate this light source with a multidimensional coherent spectrom-eter, and present our initial verification of the full MDCS system. Basic theoreticalbackground as well as initial cavity design are discussed in Chapter 2, with char-acterization of the resulting OPO system presented in Chapter 3. Considerationsfor future developments of the OPO, potentially enabling broader bandwidths, arepresented in Section 3.3. Finally, a brief introduction to the MDCS technique andour initial measurements with the full system are presented in Chapter 4.3Chapter 2OPO Theoretical Backgroundand Cavity DesignIn order to study a wide variety of systems with MDCS, it is desirable to utilizea light source with a widely tunable spectrum. As shown in Table 2.1, two-dimensional TMDs have bandgaps in the visible and near infrared. Our ultrafastOPO is pumped by a compact ytterbium source and provides broad tunability overthe desired spectral region through the appropriate choice of nonlinear crystal andsimple cavity length adjustment. The design of the OPO cavity relies on an un-derstanding of Gaussian beam propagation, dispersion, and nonlinear optics. Theessential theory will be presented in this chapter.MoS2 MoSe2 WS2 WSe2Optical gap Eg(eV ) ∼ 2 ∼ 1.7 ∼ 2.1 ∼ 1.75Exciton binding energy (eV) ∼ 0.2 or 0.4 ∼ 0.6 ∼ 0.4 or 0.7 ∼ 0.4Table 2.1: Summary of relevant two-dimensional TMD electronic properties.In terms of optical excitation, these bandgaps are in the visible and nearinfrared, ranging from 590nm to 730nm. The exciton binding energiesrepresent experimentally measured values. Reproduced with permissionfrom Springer Nature [1].42.1 Gaussian Beam PropagationEffective operation of a cavity requires that both the longitudinal and transversemode of the circulating beam are periodic. Longitudinal peridiocity places a rel-atively straightforward restriction on the resonant frequencies. To understand thespatial periodicity in the transvers direction we follow the derivations of Nagourney[18]. Electromagnetic radiation obeys the wave equation,∇2 f = µ0ε0∂ 2 f∂ t2=1c2∂ 2 f∂ t2(2.1)in each spatial dimension. Assuming that the wavefront of the beam makes a smallangle with optical axis, z, allows us to consider a plane wave with additional smallspatial variation. The resulting paraxial wave equation is solved by a function ofthe formf (r,z) = exp[−i(φGouy(z)+ kz+k2q(z)(x2 + y2))](2.2)which exhibits Gaussian spatial dependence in the transverse direction. The termφGouy(z) accounts for a phase shift accumulated as the beam passes through a focus.For the purpose of this chapter we are concerned primarily with the complex beamparameter, q(z), which contains the essential parameters of the beam radius and thewavefront radius of curvature. Specifically,q(z) = q0 + z = inπω20λ+ z (2.3)where z is the distance from the beam waist, n is the index of refraction, ω0 is the1/e2 beam radius at the waist, and λ is the wavelength. The q parameter can alsobe expressed as1q(z)=1R(z)− i λnπω2(z)(2.4)where the function R(z) represents the radius of curvature and ω(z) is the 1/e2beam radius.Setting equation 2.4 equal to the inverse of equation 2.3, and separating out theimaginary and real parts, one can determine the beam radius and wavefront radiusas a function of z,5ω(z) = ω0(1+(λ znπω20)2)1/2(2.5)R(z) = z(1+(nπω20λ z)2)(2.6)Thus if we can measure the beam radius at the waist ω0, we can determinethe complex beam parameter and determine the beam radius at any point z alongthe optical axis. The results of this basic procedure are shown in Section 2.4,where we focus the pump beam using a lens and measure the beam profile aroundthe focus. From this measured data we can also determine the beam radius as afunction of z, allowing for a comparison with the ideal theoretical propagation ofEq. 2.5. Deviation from the ideal case is quantified through the M2 parameterwhich modifies Eq. 2.5, resulting in,ω(z) = ω0(1+M4(λ znπω20)2)1/2(2.7)M2 > 1 represents deviation from the ideal case, and M2 = 1 corresponds with adiffraction limited beam. The complex beam parameter also allows one to eas-ily model the propagation of a gaussian beam through the use of ABCD matriceswhich one may be familiar with from simple ray optics. Given a ray matrix repre-senting the transformation due to some optical element,(A BC D)the transforma-tion of the q parameter is given by,q′ =Aq+BCq+D(2.8)This transformation may, for example, represent free space propagation or alens. It is straightforward to show that one may also multiply together multipleABCD matrices to generate a composite transformation due to a series of opticalelements. The resultant matrix product also follows Eq. 2.8. This fact is particu-larly useful in the context of transverse cavity modes where one may represent thefull cavity round trip with a single matrix.6Assume that we have created an ABCD matrix for a cavity and can representthe complex beam parameter after one round trip with Eq. 2.8. In order to havea stable cavity we require that the transverse mode be periodic in one round trip,q′ = q. With a bit of foresight we recall Eq. 2.4, and solve for 1/q,1q=D−A2B±√(A−D)2 +4BC2B(2.9)Inspection of common ABCD matrices reveals that they have a determinant of oneand thus we can simplify the radicand,(A−D)2 +4BC = A2 +D2 +2AD−4(AD−BC)= (A+D)2−4(2.10)The elements of the ABCD matrix are real, while q is complex, and thus thetwo terms in Eq. 2.9 correspond directly to the two terms in Eq. 2.4. With thisinformation we can solve for the beam radius after traversal through the cavityrepresented by the ABCD matrix,ω2 =2Bλnπ√4− (A+D)2 (2.11)The beam radius must be real and thus we require that the radicand be positive, re-sulting in the stability condition, |A+D|< 2. This expression restricts the geome-try of the cavity, representing a necessary condition for a stable, periodic transversecavity mode.2.2 Dispersion and Dispersion CompensationDispersion plays an essential role in ultrafast optics where one deals with pulseshaving broad optical spectra. Material dispersion is a result of the light-matterinteraction between an incident electromagnetic wave and the resonant electronicstates of the propagation material. As the material resonances are generally wave-length dependent, this results in a wavelength dependent refractive index, n(ω). Toprovide a foundation for the cavity simulations described in Sec. 3.3.1, this sectionlays out some basic theory of dispersion following derivations which can be readily7found in textbooks on ultrafast and nonlinear optics [19, 20].It is convenient to represent the effects of dispersion through the propagationconstant, β (ω) = ωn(ω)c =2πn(λ0)λ0 , where λ0 represents the wavelength in vacuum.One may Taylor expand the propagation constant, resulting in,β (ω) = β (ω0)+∂β∂ω(ω−ω0)+ 12!∂ 2β∂ω2(ω−ω0)2 + 13!∂ 3β∂ω3(ω−ω0)3 + · · ·= β0 +β1(ω−ω0)+ β22 (ω−ω0)2 +β36(ω−ω0)3 + · · ·(2.12)with βn = ∂nβ∂ωn |ω=ω0 .To consider the effects of dispersion on an ultrafast pulse propagating througha length L of material, we add the spectral phase ψ(ω) = −β (ω)L to the double-sided input spectrum, E(ω), representing the Fourier transform of the real time-domain electric field. Neglecting spatial variation, one may take the inverse Fouriertransform to represent the electric field in the time domain,E(t) =12π∫E(ω)ei(ωt+ψ(ω))dω (2.13)Re-writing in terms of the single-sided spectrum A(ω) and separating out the car-rier frequency to give ω˜ = ω−ω0, we obtain,E(t) = Re[ei(ω0t−β0L)aout(t)]= Re[ei(ω0t−β0L)12π∫A(ω˜)ei(ω˜t−(β1ω˜+β22 ω˜2+...)L)dω˜] (2.14)where aout(t) is the temporal envelope after passing through the dispersive material.The effect of β1 on the resulting pulse is easily understood, via the Fourier shifttheorem, to produce a time delay of β1L. Looking more closely at β1 in terms ofthe index of refraction we obtain,β1 =1c(n(ω)+n′(ω)ω) =ngc=1vg(2.15)8where ng and vg are the group index and group velocity, respectively. This relationto the group velocity is clearly consistent with the previously derived time delay.For the purposes of an OPO, the pulses oscillating in the cavity must be overlappedin time with the pump pulses. By tuning the cavity length, the OPO spectrum willchange to satisfy vg/Lcavity = frep, where vg represents the group velocity of theoscillating signal pulses and frep is the pump repetition rate.Differentiating once more, the second order term is given by,β2 =1c(2n′(ω)+n′′(ω)ω) (2.16)and is referred to as group velocity dispersion. Multiplying by the length of thedispersive material produces the group delay dispersion (GDD). This term producesa linear delay as a function of frequency, or linear chirp, and will result in pulsebroadening. If we consider an unchirped Gaussian input pulse with a temporalenvelope given by ain(t) = e−t22τ2in , and thus a 1/e intensity half-width of τin, then wefindA(ω˜) =∫ ∞−∞ain(t)e−iω˜tdt= τin√2πe−(ω˜τin)2/2(2.17)We can calculate the output pulse envelope, aout , by plugging Eq. 2.17 into Eq.2.14. Looking solely at the effects of β2, we find that the output pulse is alsoGaussian, but temporally broadened with 1/e intensity half width given by τout =τin√1+( |β2|Lτ2in)2.In the context of the OPO, a linear chirp will serve as a spectral filter, limit-ing the output bandwidth, as any frequency which is delayed beyond the temporalextent of the pump pulses will not be amplified. Typical materials, including thenonlinear lithium triborate (LBO) crystal and fused silica substrates utilized in theOPO cavity optics, exhibit positive GDD. In order to counteract the pulse broad-ening effects, one may utilize dispersion compensation methods. Dielectric mirrorstacks may be designed to exhibit negative GDD, with longer wavelengths penetrat-ing deeper into the stack. Grating or prism compressors similarly produce negativedispersion by introducing additional free space path length for longer wavelengths.9Initial consideration of cavity dispersion are presented in Sec. 2.4.2, and detailedsimulations of the cavity dispersion and resulting cavity enhancement are presentedin Sec. 3.3.1.2.3 Nonlinear OpticsBoth the OPO and the MDCS technique rely on nonlinear optics. The OPO utilizesdifference frequency generation to produce two lower energy photons from a singlehigh energy pump photon. MDCS measures a third-order nonlinear response of thesample being studied, with the actual signal measured being the result of a four-wave mixing process resulting from the interaction of three optical pulses incidenton the sample. This section outlines the basic theory of nonlinear optics, highlight-ing the physics underpinning our experimental system and technique. This sectionfollows the derivations of Boyd [21].When considering the interaction of light with solid state material, we need tolook at the polarization of the material under an applied electric field. Recall fromelectrodynamics that the polarization in a linear dielectric material is given byP(t) = ε0χ(1)E(t) (2.18)where ε0 is the permittivity of free space and χ(1) is the electric susceptibility ofthe material. To describe nonlinear materials, one performs a Taylor expansion ofEq. 2.18, resulting in,P(t) = ε0(χ(1)E(t)+χ(2)E2(t)+χ(3)E3(t)+ . . .)(2.19)where in general χ(n) is represented by a tensor of rank n+1. For the purposes ofthe OPO, we consider the case in which electromagnetic waves at two frequenciespropagate through a nonlinear material. Ignoring spatial dependence, the total fieldcan be written as,E(t) = E1e−iω1t +E2e−iω2t + c.c. (2.20)We determine the second order polarization arising from this field by plugging it10into Eq. 2.19,P(2)(t) = ε0χ(2)[(E12e−i2ω1t +E22e−i2ω2t + c.c.)︸ ︷︷ ︸SHG+2(E1E2e−i(ω1+ω2)t + c.c.)︸ ︷︷ ︸SFG+2(E1E∗2e−i(ω1−ω2)t + c.c.)︸ ︷︷ ︸DFG+2(E1E∗1 +E2E∗2)︸ ︷︷ ︸OR](2.21)The four terms have been labelled with their associated nonlinear processes: sec-ond harmonic generation (SHG), sum frequency generation (SFG), difference fre-quency generation (DFG) and optical rectification (OR). DFG is also known as op-tical parametric amplification. In parametric amplification, one considers the caseof a strong pump beam at ω1 and a weak beam at ω2, commonly referred to as thesignal. The polarization of the nonlinear material acts a source term in the electro-magnetic wave equations, amplifying the signal beam and generating an idler beamat ω3 = ω1−ω2, satisfying energy conservation. Note that in an OPO, the signalbeam starts from zero-point fluctuations of the electromagnetic field. Assumingthat the pump is undepleted, both the signal and idler fields grow exponentially inthe limit of long nonlinear crystal lengths. However, adding in the spatial depen-dence of the fields, it is crucial to note that this growth is also dependent on phasemismatch, ∆k = k1 − k2 − k3. In practice, phasematching (∆k ≈ 0) is acheivedthrough the use of birefringent materials and careful choice of electric field polar-izations. The crystal angle and temperature also serve as degrees of freedom totune the optimally phasematched frequencies.The OPO developed in this work utilizes a biaxial nonlinear crystal, LBO, withType I phasematching (θ = 90◦,φ = 9.5◦). This means the signal and idler fieldshave the same polarization, and are orthogonal to the pump polarization. Thephasematching condition has a weak dependence on the crystal angle over thewavelength range of interest (650nm to 950nm), allowing for broad bandwidthoperation without angle tuning. An oven is used to control the crystal temperatureand allow tuning of the optimally phasematched wavelength.MDCS relies on the third-order nonlinearity of a sample, generating a four-wave mixing signal in response to three input fields. Leveraging momentum con-11servation, the signal can be isolated spatially in the case of a non-collinear geom-etry, with kFWM = k1 ± k2 ± k3. For a collinear geometry, the input fields musthave distinct carrier frequencies, allowing for spectral isolation of the signal atωFWM = ω1±ω2±ω3 [22].2.4 Broadband OPO Cavity DesignWorking from the concepts developed in Sec. 2.1 and 2.2, we will proceed todetermine and design the essential cavity parameters relating to cavity geometryand dispersion. Using details of the pump laser, we determine the required cavitylength. Subsequently, we simulate stable cavity configurations for the given cav-ity length and consider different focusing characteristics. These calculations wereutilized to inform the physical layout and alignment of the components, and pro-vided useful benchmarks for the characterization of the OPO system. Regardingdispersion, we highlight the optics selected for the cavity and discuss the trade-offbetween broad bandwidths and stability.Figure 2.1: A schematic of the OPO cavity layout. The curved mirrors, CM1and CM2, form a cavity focus centered in the LBO crystal. The greenarrow represents the pump beam coupled in through CM1. The yellowlines trace out the propagation of the signal beam inside the cavity.122.4.1 Cavity GeometryThere are a few basic cavity characteristics determined by the pump laser as wellas our desire for a Gaussian beam with minimal astigmatism. The synchronouscondition for OPO operation requires that the cavity round trip time of the signalpulse be matched with that of the pump laser. In our case, the FLINT Oscillator hasa repetition rate frep = 76.6MHz, corresponding to τrt ≈ 13.05ns. Using 800nmas an average for the signal wavelength, we can calculate the approximate cavitylength required,L =cng,air1frep≈ 3.913mwhere ng,air is the group index in air at 800nm. Accounting for the 1mm LBOcrystal (2mm round trip) reduces the required cavity length to 3.909m.The layout of our cavity optics is shown in Fig. 2.1. Similar to Colucelli etal [16], we chose to utilize focusing mirrors with a radius of curvature of 75mm.This provides a nice balance where we are able to achieve a tight cavity focus forefficient parametric generation while still maintaining a low angle of incidence onthe curved mirrors, and thus minimize astigmatism of the beam.Finally, we have also chosen a folded linear cavity design which results in asmaller cavity footprint, allowing the system to fit within limited available tablespace. Using a linear cavity also means the beam is retroreflected off of end mir-rors. This fact allows the cavity length to be easily tuned by placing the end mirrorson linear stages or piezo stacks, without significant change to the cavity alignment.With this information, we can simulate the stability conditions of our cavity.As discussed above, the overall cavity length is contrained by the pump repetitionrate. Choosing a symmetric cavity about the focus for simplicity, the remaining freeparameter is the curved mirror separation. Figure 2.2 shows the simulated cavityfocus (1/e2 waist radius) as a function of the curved mirror separation. Outsidethis range of stable separations, the transverse mode of the beam cannot be madeperiodic.As noted by Benko [23], there are number of considerations when choosing theseparation distance of the curved mirrors. Choosing a separation at either edge ofthe stability region will result in a tighter focus in the crystal, and a larger beamimpinging on the curved mirrors; however, it also results in larger astigmatism.13Figure 2.2: Plot of OPO Cavity Stability Region. The blue and orange linesrepresent the transverse vertical and horizontal axes, respectively. Out-side of these plotted curved mirror separations, the cavity is unstable.Choosing a separation on the long side of the separation range results in a strongersecondary cavity focus, which may result in higher powers on cavity optics. Forour purposes, we decided upon a separation at the center of the stability regionsuch that the astigmatism of the beam is minimized. This is important for ourapplication of collinear MDCS where the beam must be focused onto ≈ 10µmexfoliated flakes.With a chosen curved mirror separation of 76.5mm, we can proceed to simulatethe cavity mode over a full round trip. Starting from the cavity focus in the LBOcrystal, Fig. 2.3 shows the horizontal and vertical gaussian beam radius as a func-tion of z. Diverging from the focus of ≈ 13.9µm, the beam is roughly collimatedby a curved mirror and comes to a loose focus of ≈ 0.5mm at the end mirror. Afterretroreflecting from the end mirror, the beam passes back through the tight focus14Figure 2.3: Plot of OPO Cavity Mode over one full round trip. The orangetrace represents the transverse horizontal mode, while the blue repre-sents the transverse vertical mode. The mode passes through a tightcavity focus twice on each round trip, coming to a loose secondary fo-cus on each end mirror.between the curved mirror pair and is again roughly collimated. Finally the beamretroreflects off of the output coupler and completes a full round trip at the LBOcrystal. This cavity mode produces a tight focus in the LBO for efficient paramet-ric conversion of pump to signal photons, and also results in a roughly collimatedoutput beam.2.4.2 Cavity DispersionIn addition to spatial overlap, it is important that the oscillating signal pulse hasgood temporal overlap with the pump. While cavity length adjustments allow forthe signal and pump to share the same repetition rate, additional efforts are needed15to compensate for second order dispersion which, as discussed in Sec. 2.2, resultsin the signal pulse broadening in time. This is accomplished primarily throughDispersion compensating mirrors (DCM), consisting of a stack of dielectric materialwith layers of varying thickness. The layer structure can be arranged such that themirror exhibits negative GDD, allowing one to counteract positive GDD materials,such as the LBO crystal used for parametric generation.The optics chosen for the OPO cavity are shown in Table 2.2. Referencing thelabels from Fig. 2.1, CM1 and CM2 form the curved mirror pair while M1 and M2form the planar mirror pair. Finally, M3 corresponds to the metal end mirror andOC to the output coupler. The two dispersion compensating mirror pairs experiencetwo reflections each round trip, and the pulses also pass through the LBO twice eachtrip. This results in a net GDD of −200 f s2 when considering the air in the cavity.Cavity OpticsElement Reflectivity Average GDD Part NumberCurved Mirror Pair HR(0-10◦,670-970nm)>99.8%−50± 150 f s2(per mirror)Layertec 142349Planar Mirror Pair HR(0◦,570-1039nm)>99.8%−50 ± 20 f s2(per mirror)Layertec 102267Output Coupler PR(0◦,640-1100nm)=90%0 f s2 Layertec 106315Metal End Mirror R(450-2000nm)> 97.5%0 f s2 Thorlabs PF10-03-P01LBO Crystal AR(515nm,650-950nm)+50 f s2 Newlight; t=1mm,θ = 90◦,φ = 9.5◦Table 2.2: Summary of specifications for OPO cavity optics.When considering the design of the cavity dispersion, it is important to balancethe broad bandwidths provided by low dispersion with the stability provided bylarger dispersion. Considering the pulse in the time domain, non-zero GDD willproduce chirped pulses which are broadened in time. Similarly, in the frequencydomain, non-zero GDD produces a longitudinal mode spacing which varies as afunction of frequency, limiting the signal bandwidth which is synchronous withthe pump. However, recall that GDD is the derivative of the inverse group veloc-ity, and thus zero GDD corresponds to a frequency independent group velocity.16While a dispersionless cavity produces broad bandwidths, it also means that thesynchronous condition is met for a single cavity length. Thus, in order to producea stable output spectrum and avoid a strong sensitivity to cavity length fluctuations,it is desirable to operate with small but non-zero GDD. In order to partially com-pensate for the fused silica substrate of the output coupler, we decided to run thecavity with negative GDD.In order to further explore the dispersion dependence of the output signal spec-trum, we eventually incorporated a pair of fused silica wedges into the cavity de-sign. One of the wedges was placed on a linear stage to tune the amount of fusedsilica experienced by the oscillating signal pulses. This addition allowed for thecavity dispersion to be tuned from negative to positive, producing the expectedinstability near zero GDD. More details and results on dispersion tuning will bepresented in Sec. 3.3.17Chapter 3Characterization of OPO SystemFigure 3.1: CAD model of the pump beam path and OPO cavity. Coloredlines designate the beam paths with red representing the 1035nm pumplight, green the 517nm doubled pump light, and orange the tunable sig-nal output. These optics are mounted on a watercooled breadboardwhich helps to minimize the impact of environmental changes on theOPO operation.A CAD model of the OPO cavity can be seen in Fig. 3.1, and a full systemschematic is shown in Fig. 3.2. The OPO is pumped by femtosecond pulses witha center wavelength of ≈ 515nm, obtained from second harmonic generation of asolid-state Yb oscillator (Light Conversion FLINT Femtosecond Oscillator). To18obtain oscillation, this system relies on high peak intensity pump pulses for effi-cient parametric generation. Additionally, the pump beam should have a nearlyGaussian beam profile matched to the cavity mode such that down-converted pho-tons are contained within the cavity mode for further amplification. The followingsections highlight measurements of important system parameters related to theserequirements on the pump beam, and the resulting characteristics of the generatedsignal beam.Figure 3.2: Schematic of the full OPO setup. Colored lines designate thebeam paths with red representing the 1030nm FLINT beam, green the515nm pump light, and orange the tunable signal output. In additionto the pump laser and OPO cavity, a grating compressor is used at theoutput to compenesate linear chirp and generate high peak intensities atthe sample of interest.193.1 Pump Charcterization3.1.1 Transverse ModeAs an initial check, we measure the transverse profile of the beam from the FLINTFemtosecond Oscillator. This laser is specified to have an M2 < 1.3 and is col-limated. Measurements of the FLINT mode confirm it is well collimated on thescale of ≈ 1m, with a typical profile shown in Fig. 3.3. The beam radius is foundto be ≈ 0.75mm.Figure 3.3: Measurement of the transverse mode of the FLINT. Similar mea-surements at varying distances from the laser output show that the beamis well collimated.For the purposes of cavity mode matching, it is important to get detailed mea-surements of the transverse profile of the 515nm beam used to pump the OPO,which is obtained by frequency doubling the FLINT. To this end, we measuredthe pump mode by sending the beam through a weak lens and scanning a CCD20array through the focus to measure the transverse mode at various points along theoptical axis, z. By extracting the beam radius at each position, this measurementallowed us to compare the propagation with that of a theoretical gaussian beam andto extract the complex beam parameter, q(z). This measurement and the resultingfit is shown in Fig. 3.4. From the fit we find that the pump beam has M2x = 1.17and M2y = 1.14 along the x and y transverse directions.Figure 3.4: Measurements and fits of the 517nm transverse mode followinga weak focusing lens with f = 200mm. The solid lines show a fit of atheoretical Gaussian beam propagation to the measured data. In additionto the waist shown in the legend, this fit produces M2 ≈ 1.15.Utilizing q(z), one can easily simulate beam propagation through various opti-cal elements, and thus can design a system of lenses for mode matching with thecavity. After extracting the q parameter of the pump beam utilizing the techniquedescribed above, we were able to simulate the pump mode in the cavity for var-ious combinations of lenses. To do so, the q parameter was back-propagated to21the doubling crystal, then forward propagated through different potential lens sys-tems. Importantly, we also included the effect of the cavity input coupler, which iscurved and acts like a concave lens on the pump beam transmitted through it. Fig.3.5 shows the result of this simulation plotted over the cavity mode determined inSec. 2.4. This simulation utilized an f = 300mm lens to collimate the divergingpump light coming from the doubling crystal, and an f = 100mm focusing lens be-fore the input coupler to focus the pump at the LBO crystal inside the OPO cavity.Additionally, the measured pump radius is plotted to confirm the simulations.There are a few important points to note regarding the chosen lens system.First of all, the simulations utilized commonly available focal lengths which avoidsthe cost of custom optics. For this reason both the vertical and horizontal waists,ω0,V = 17.0µm and ω0,H = 21.6µm, are slightly larger than the cavity focus of13.9µm. The pump beam divergence also differs slightly from the cavity mode.However, the Rayleigh lengths for the pump beam are zR,V = 1.76mm and zR,H =2.84mm, while the cavity mode has zR = 0.76mm. If we assume that the LBOcrystal is centered in the cavity focus, and recall that the LBO is 1mm thick, thenthe pump and cavity modes should be approximately planar over the length of thecrystal. This would result in efficient coupling of the generated signal photons tothe cavity mode despite the imperfect matching of the pump mode further from thecavity focus.Additionally, one may note that the measured radii diverge more quickly thanthe simulations. This is due to the fact that M2 > 1 for both the horizontal and ver-tical pump mode, a fact which is not captured in the simulations. Measurementsof the output signal mode, which are representative of the cavity mode, produceM2 ≈ 1.2. Thus the actual cavity mode also diverges more quickly than the simu-lated cavity mode.3.1.2 Spectrum and Temporal CharacteristicsIn addition to confirming the transverse mode and comparing with the cavity mode,it is important to measure the spectra and autocorrelations of our pump beam. Tomeasure spectra we utilize a Thorlabs CCS175 Compact CCD Spectrometer. Al-though the device input is designed for a multimode fiber, we couple light into this22Figure 3.5: Overlap of pump and cavity mode. The dashed line shows thesimulated cavity mode near the LBO crystal. The solid colored linesshow the simulated propagation of the pump beam. The data pointsshow measured beam waists of the pump.port in free space to avoid spectral interference effects between transverse modesof the fiber. For the autocorrelation we utilize a Femtochrome FR-103MN IntensityAutocorrelator. To ensure efficient nonlinear conversion in both the frequency dou-bling and parametric generation stages of our setup, we desire to have optimallycompressed pulses with high peak intensity.The autocorrelator works by splitting the input pulses along two paths and scan-ning a relative time delay between the paths. The two paths are then overlappedspatially inside a doubling crystal, producing,E2ω(t,τ) ∝ (Eω(t)+Eω(t− τ))2 (3.1)where Eω(t) and Eω(t− τ) represent the electric field from the two time delayed23paths. By introducing an angle between the two paths, we can spatially isolatethe three terms on the right hand side of Eq. 3.1. Measuring only the second har-monic beam created by the cross term Eω(t)Eω(t−τ) results in the autocorrelationfunction,A(τ) =∫ ∞−∞I(t)I(t− τ)dt (3.2)With appropriate angle tuning of the SHG crystal inside the autocorrelator, pulsesin the visible to near infrared can be measured. Although the autocorrelation cannotproduce the temporal intensity profile for an arbitrary pulse shape, if we assumeshapes such as a Gaussian or Sech2 then we can obtain a pulse width from themeasured autocorrelation trace.Fig. 3.6 and Fig. 3.7 show a typical spectrum and autocorrelation of the FLINTlaser, with both showing reasonable agreement with a Gaussian pulse shape. As-suming a Gaussian pulse shape, these fits produce ∆λFWHM = 22.9nm and ∆tFWHM =88.2 f s, resulting in a time-bandwidth product ∆ν∆t = 0.57, larger than the trans-form limit of 0.44. The Fourier transform of the spectrum is also plotted alongsidethe autocorrelation, showing the transform limited pulse length of 64 f s.The spectrum of the pump beam, derived from the frequency doubled FLINTbeam, is shown in Fig. 3.9. With a group index mismatch of only ∆ng = ng,2ω −ng,ω = 0.015 there is minimal temporal walkoff in the LBO doubling crystal, or,equivalently, nearly all of the FLINT spectrum is doubled.Unfortunately, due to phasematching limitations of the crystal in the autocorre-lator, it was not possible to measure the autocorrelation of the pump beam. Even ifwe assume a transform limited Gausian pulse width of 95 f s, with only two lensesand an input coupler in the pump path, we expect minimal pulse broadening. Inany case, experimental implementation of the OPO designs demonstrated that thepump intensity was sufficient to reach threshold. In the future, one may explorethe effects of adding spectral phase to the pump pulse. Ultimately, for the use ofthe OPO system in spectroscopy studies, we care about the compression of the OPOsignal in order to generate a sufficient four-wave mixing signal through interactionwith the sample of interest. Measurements of the signal pulses are presented inSec. 3.2.24Figure 3.6: Typical optical spectrum of the Light Conversion FLINT Fem-tosecond Laser. The spectral widths listed in the figure are extractedfrom fits of Gausian and Sech2 pulse shapes, and represent the full-width at half-maximum of the fitted curve. From the fits we can alsoextract a center wavelength of 1030.9nm.3.1.3 SHG Conversion EfficiencyThe FLINT beam profile measurement was used to select an appropriate focusinglens for the second harmonic generation stage. The LBO doubling crystal, suppliedby Newlight Photonics, has a specified damage threshold of 19GW/cm2. Utilizingan f = 75mm lens, the FLINT beam is focused to ω0 ≈ 30µm. With a maximumaverage power of 6.5W, the resulting power density in the LBO crystal is 6.5Wπ(30µm)2 =2.3×10−4GW/cm2, well below the damage threshold.Neglecting pump depletion the generated second harmonic field follows E2ω ∝E2ω , meaning the power of the second harmonic will follow a quadratic relation-ship with the power of the fundamental. This relationship can be observed at low25Figure 3.7: Typical intensity autocorrelation of the Light Conversion FLINTFemtosecond Laser. The temporal widths listed in the figure are ex-tracted from fits of Gausian and Sech2 pulse shapes, and represent thefull-width at half-maximum pulse width, not the fitted autocorrelationwidth. The transform limited (TL) pulse is obtained by Fourier trans-forming the spectrum.pump powers where the conversion efficiency is small and thus it is reasonable toassume an undepleted pump. However, we see this relationship become linear aspower is transferred from the pump to the second harmonic. For the case of perfectphasematching with pump depletion, the power of the second harmonic is given by[19, 21],P2ω(L) = Pω(0)tanh2(ωde f f LEω(0)cn)(3.3)with L being the length of the crystal, de f f the effective nonlinear coefficient, andPω(0) and Eω(0) being the power and field amplitude of the fundamental beforethe crystal. This relation is consistent with quadratic trend seen at low power and26Figure 3.8: Typical optical spectrum of the second harmonic generated fromthe Light Conversion FLINT Femtosecond Laser utilizing a LBO crystal.The spectral widths listed in the figure are extracted from fits of Gausianand Sech2 pulse shapes, and represent the full-width at half-maximumof the fitted curve. From the fits we can also extract a center wavelengthof 514.9nm.linear trend at higher powers; however, the assumption of perfect phasematchingmeans that the saturation at lower conversion efficiencies is not well captured. Forhigh pump powers above 5W we see a conversion efficiency above 50%, providingover 3W of pump power for the OPO.27Figure 3.9: Measurement of the second harmonic power and conversion effi-ciency for the frequency doubled FLINT beam. The second harmonicpower grows quadratically at low pump powers before becoming ap-proximately linear as the pump power is significantly depleted.3.2 Signal Characterization3.2.1 Transverse ModeThe output signal mode should be representative of the OPO cavity mode. As aquick check of the signal transverse mode we conduct the same measurement thatwas presented in Sec. 3.1.1. The fit to a theoretical Gaussian beam propagationproduces M2 ≈ 1.2 for both the vertical and horizontal transverse directions, andshows the astigmatism due to the angled curved mirrors, producing a shift of ≈6mm in the focus position for the vertical and horizontal directions following thef = 200mm lens used for the measurement.283.2.2 Spectral and Temporal CharacterizationThe spectrum of the OPO is determined by both the gain curve of the parametriccrystal and the dispersion of the cavity. The effect of the gain profile is straight-forward, while the dispersion essentially dictates which frequencies have temporaloverlap with the pump and thus undergo parametric amplification. The situationis complicated by the dispersion compensating mirror pairs which, due to theirbroadband reflectivity, have oscillations in the GDD as a function of wavelength.Further exploration of the cavity GDD is presented in Sec. 3.3.At a single crystal temperature and angle, it is possible to tune the center wave-length around 150nm by simply adjusting the cavity length. This observation sug-gests that there is sufficient phasematching over this tuning range, and thus limitedbandwidth can be attributed solely to cavity dispersion. Initial measurements ofthe OPO output spectra showed typical full-width half-maximum bandwidths ofless than 20nm, far less than reported for similar OPO systems [16]. Utilizing apair of fused silica wedges arranged at Brewster’s angle, we were able to tune theaverage cavity dispersion. By slowly inserting more fused silica into the cavitymode, we observed the spectra broaden. Around zero average GDD, the OPO out-put spectrum becomes very unstable as the range of OPO cavity lengths matchedto the pump repetition rate becomes narrower. We also observe discontinuous andnon-monotonic tuning in this regime, as reported by Stankevicˇiu¯te˙ et al. [24] andattributed to DCM oscillations. As expected, when we continue tuning into thepositive dispersion regime, the tuning direction of the center wavelength changes.In the case of negative dispersion, the synchronous wavelength decreases with in-creasing cavity length. For positive dispersion, the synchronous wavelength in-creases with increasing cavity length. We chose to operate with slightly negativedispersion, producing stable broadband spectra as shown in Fig. 3.10. The multi-peak structure of the spectra appears to be correlated with the cavity dispersionstructure.In addition to the fused silica wedge pair, we also experimented with cavity dis-persion by removing the planar pair of dispesion compensating mirrors. Removingthe fused silica wedges and replacing the DCM pair with silver mirrors (EdmundOptics, Ultrafast Enhanced Silver) resulted in a slightly positive average GDD with29reduced GDD oscillations at longer wavelengths. The resulting spectra are shownin Fig. 3.11. The reduced GDD oscillations resulted in more uniform spectra acrossthe full tuning range. Having power distributed evenly across the pulse bandwidthwas also advantageous for MDCS studies, providing uniform power across the ex-citations of interest.Measurements were also taken utilizing a BBO crystal for parametric amplifi-cation in the OPO, producing similar bandwidths which again appeared to be lim-ited by the cavity dispersion. Ultimately we decided to utilize the LBO crystalwhich exhibits much smaller spatial walkoff, approximately 7 mrad compared with55 mrad for BBO [25]. This fact resulted in simplified cavity alignment, reducedpump threshold power, and increased output signal power. However, it should benoted that the phasematching window of beta barium borate (BBO) extends downto ≈600nm and may thus be useful for studies of materials with larger band gaps.The temporal characterization of the OPO pulses proved challenging due to thebroad bandwidth. For narrower ≈ 20nm bandwidth spectra, obtained by tuning thecavity dispersion further from zero, we were able measure near tranform limitedpulse lengths of ≈ 60− 65 f s, depending on the center wavelength. However, forthe desired broad bandwidth spectra we were unable to utilize the FemtochromeAutocorrelator as the doubling bandwidth of the nonlinear crystal inside the auto-correlator could not support the full pulse bandwidth. For narrower bandwidths,the autocorrelation trace will change in intensity as the crystal angle is changed,indicating tuning about the optimal phasematching angle. However, for the broad-band OPO pulses we observed that the structure of the autocorrelation trace wouldchange as the crystal angle was tuned. This observation is consistent with a chirpedpulse in which only part of the spectrum is doubled at any given crystal angle. Asthe angle was tuned, intensity would transfer from a central peak into two sidepeaks. Eventually the side peaks overtake the central peak and merge together intoa single peak.To confirm that the evolution of the autocorrelation structure was due to lim-ited phasematching bandwidth, we utilized a thin BBO doubling crystal and lever-aged the delay stages inside the MONSTR Sense Technologies Bigfoot UltrafastSpectrometer to construct a FROG measurement system. Even with the thin BBOcrystal, we observe some narrowing of the doubled spectrum due to limited SHG30Figure 3.10: OPO Signal Spectra obtained at varying cavity length and crys-tal temperature with two pairs of DCM. The temperatures listed repre-sent the setpoint of the crystal oven. Additionally, a pair of fused silicawedges were used inside the cavity to tune closer towards zero GDD.bandwidth. To compare with the autocorrelation measurements, we binned thewavelength axis of the uncompressed FROG trace into≈ 10nm bins to simulate theautocorrelation traces that would result for the limited phase matching bandwidthexpected in the Femtochrome Autocorrelator. The structure of the resulting wave-length binned traces qualitatively matches the evolution of the three-peak structureseen with the Femtochrome. This suggests a substantial improvement of the dou-bling bandwidth for the FROG measurements compared with the Femtochrome, andprovides a clearer signal to optimize the grating compressor.FROG traces can be seen in Fig. 3.12, showing uncompressed and optimallycompressed pulses for a spectrum centered about 810nm. Even the optimally com-pressed pulse shows residual chirp, resulting in significant intensity in the wings of31Figure 3.11: OPO signal spectra obtained at varying cavity length and crystaltemperature with a single pair of DCM.The temperatures listed repre-sent the setpoint of the crystal oven. The single DCM pair resultedin slightly negative GDD, with reduced residual GDD oscillations atlonger wavelengths.the pulse. This is a clear limitation of the grating compressor used to compensatethe pulse dispersion as this approach adds higher-order dispersion in addition to theintended second-order dispersion. We also note that the spectrum obtained for thecompressed pulse is narrower than that of the uncompressed pulse. This is likelydue to a difference in the doubling crystal angle alignment for measurements ofthe uncompressed and compressed pulses. For initial testing of the Bigfoot Spec-trometer we typically utilized narrower bandwidth pulses which produced betterautocorrelation traces with minimal intensity in the wings.Looking forward to MDCS measurements, we were primarily interested incharacterizing the pulse lengths after propagation through the Bigfoot Spectrome-ter and the objective lens utilized to focus the pulses onto 2D material samples. In32Figure 3.12: (a) and (b) show SHG frequency resolved optical gating (FROG)traces of the OPO spectrum measured after the Bigfoot spectrome-ter for two grating compressor settings, with (a) showing a stronglychirped pulse. (c) and (d) show the autocorrelation and spectra ob-tained by integrating over the wavelength and delay axes, respectively.The OPO spectrum and transform limited temporal pulse envelope arealso shown. Limited SHG bandwidth results in some narrowing of theFROG spectra.33order to achieve this, we further leveraged the inherent capabilities of the Bigfootto create a collinear autocorrelator. The Bigfoot outputs a train of four pulses (A,B, C and D) with variable time delay, each with a unique frequency modulation in-troduced by an acousto-optic modulator (ωA, ωB, ωC and ωD). These output pulseswere aligned through the objective lens and focused in a BBO crystal. A high passfilter was used to isolate the second harmonic light generated in the BBO, and thislight was loosely focused onto the Bigfoot photodectector.Figure 3.13: Characterization of the OPO Signal pulse after passing throughthe Bigfoot spectrometer and objective lens. The autocorrelation tracemeasured utilizing the Bigfoot lock-in detection is shown on the right,along with the transform limited pulse shape produced by assuming aflat spectral phase and Fourier transforming the spectrum.In order to measure the intensity autocorrelation, we set the delay τ betweenpulses A and B to zero. Similarly, we set the delay t between pulses C and D tozero. Thus we effectively have two pulses, which we label AB and CD, and wecan scan the delay T between them. Second harmonic photons will be generatedat many different frequencies. For example, from pulse A we generate a secondharmonic pulse with frequency 2(ωL +ωA), where ωL is the center frequency ofthe OPO signal pulse. Similarly, from the temporally overlapped A and B pulseswe will generate photons with frequency 2ωL +ωA +ωB. For an intensity auto-correlation we are only interested in measuring the second harmonic photons gen-34erated by the interaction of pulse AB with pulse CD. To isolate these photons weutilize the lock-in detection capabilities of the Bigfoot. Photons with frequencies2ωL +ωA +ωD and 2ωL +ωB +ωC are generated by the overlap of pulses AB andCD and will optically interfere to generate a beatnote at,ωAC = (2ωL +ωB +ωC)− (2ωL +ωA +ωD)= (ωC−ωD)− (ωA−ωB)(3.4)This is the same lock-in frequency utilized to detect the four-wave mixing signalgenerated in an MDCS scan. Thus by scanning T and observing the resulting defaultlock-in signal we can obtain an autocorrelation that is representative of the pulseseen by the sample. An example of the resulting autocorrelation trace can be seenin Fig. 3.13. As expected from the FROG measurements, higher order dispersionprevents compression to the tranform limit.3.2.3 Output PowerWe characterize the output power of the OPO as a function of central wavelengthand LBO crystal oven temperature. Adjusting the crystal temperature alters theoptimally phasematched wavelength, shifting towards longer wavelengths with in-creasing temperature. This trend is reflected Fig. 3.14, showing a typical maximumaverage power of 0.4W . The maximum pump threshold is found to be around1.75W , well below the maximum pump power of 3.4W . The pump threshold dropsas low as 0.75W , depending on the crystal temperature and center wavelength.To measure pump depletion, we took a reference measurement by blockingthe cavity mode to prevent signal oscillation and measured the power of the pumpbeam transmitted through the curved mirror pair. We then measure the transmittedpump power with a signal beam oscillating in the cavity. We found the maximumpump depletion to be ≈ 65%.3.2.4 Spectral StabilityGiven that dense, finely sampled multidimensional spectra require measurementson the scale of tens of minutes to hours, it was important for the OPO to producea stable output spectrum. To this end, we implemented multiple passive stabiliza-35Figure 3.14: Measurements of the OPO output power as a function of cen-ter wavelength for varying LBO crystal temperatures. One can see thepeak parametric gain shifts to longer wavelengths as the crystal tem-perature is increased.tion efforts. High quality Thorlabs Polaris kinematic mounts were utilized for allreflective optics, and all optics were mounted onto fixed height one inch posts.These optomechanical components provided long term alignment stability, withthe pump and cavity optics maintaining sufficient alignment over the course of aweek to obtain above threshold parametric generation utilizing only cavity lengthtuning. In addition, we designed and installed an enclosure surrounding the cavity,and built the cavity on a water-cooled optical breadboard. These efforts served toisolate the cavity from air currents and temperature fluctuations in the lab, whilealso providing dust protection for the cavity optics.Even with these passive measures, both short and long term instabilities werefound in the OPO spectrum and output power. As shown in Fig. 3.16, the short term36Figure 3.15: Spectral Stabilization Scheme. A reflection off of the first com-pressor grating is used to monitor the OPO output spectrum. A reflec-tion grating is used to spatially disperse the spectrum. An adjustableslit is used to isolate one edge of the spectrum to be measured by aphotodiode. This photodiode signal is then used as feedback to adjustthe cavity length.instability is dominated by a 30Hz oscillation, which was attributed to a buildingresonance observed in other experiments in the building. Long term drift appearsto be correlated with environmental conditions such as temperature and humiditywhich would change the effective cavity length.Our initial implementation of a spectral locking scheme utilized a piezo actu-ator (Thorlabs DRV517) attached to a linear stage under the output coupler. Theactuator was controlled via a software PID loop written in Python. The softwarewould read in the latest spectrum, calculate the spectral center-of-mass, and sub-ract the target wavelength to produce an error signal for the PID loop. The updatedfeedback value from the PID loop was then applied to the piezo actuated stage.This scheme functioned well for long term drifts; however, the bandwidth was lim-ited to≈ 10Hz due to the polling time of the piezo actuator controller, and the loadof the stage and optomechanics would have likely also placed a significant limit onthe PID bandwidth.In order to compensate both the short term instabilities and long term spectraldrift, we implemented the active spectral locking scheme illustrated in Fig. 3.15.37Leakage from one of the cavity mirrors is used to sample the OPO spectrum. Thislight is directed onto a reflection grating before going through an adjustable slit.The light transmitted through the slit is focused onto a photodiode. By adjustingone edge of the spectrum to pass through the edge of the slit, we obtain a photodi-ode signal which, for small deviation in center frequency, varies proportionally tothe change in frequency. This signal is then sent through a differential amplifier,where a reference voltage is subtracted, producing our error signal.Figure 3.16: Long term OPO stability. The spectrum is actively stabilized,exhibiting a slow drift due to the decreasing output power. We see asimilar drift in the output pointing, suggesting that the power drift isdue to changing cavity alignment as the cavity length is adjusted tocompensate environmental changes.38The OPO cavity utilizes two piezo stacks to allow active feedback on the cavitylength. One cavity end mirror, M3 in Fig. 3.2, is epoxied onto a piezo stack with3µm range. A 7mm diameter silver mirror (Thorlabs PF03-03-P01) is used to min-imize the load on the piezo stack and allow for high frequency operation in order tocompensate the 30Hz mechancial vibrations. As mentioned previously, the outputcoupler is mounted onto a linear stage utilizing an actuator with an in-line piezostack. This piezo actuator provides 30µm of range, allowing for compensation oflong term drifts due to temperature and humidity.The piezo mounted mirror assembly will tend to sag under the force of gravityas the DC voltage offset is increased. For this reason, as well as the limited range,we apply only an AC feedback signal to this piezo mirror. In order to accomplishthis, the error signal from the differential amplifier is sent into the ’fast’ loop filter.The feedback signal from this loop filter is split and sent to both the piezo mirrorand a second (’slow’) loop filter. The feedback signal from the slow loop filteris sent to the piezo actuated stage. In this way, any DC offset accumulated onthe piezo mirror is removed by adjustment of the piezo actuated stage. Fig. 3.16shows the frequency spectrum of the center wavelength instability for both the free-running and locked states, demonstrating suppression of the 30Hz noise peak byover one order of magnitude.This locking scheme exhibits the same issue as the commonly encounteredside-of-fringe locking technique - the error signal depends on the laser intensity aswell as the center frequency. Thus this locking scheme will produce spectral shiftsin response to fluctuations or drifts in the laser intensity. Unfortunately we findthat the output power of the OPO tends to drop over the course of a day. This inten-sity drift was initially presumed to be caused by pointing drift of the pump laser,resulting in reduced coupling of the signal into the cavity mode. However, after im-plementation of active pointing stabilization, this intensity drift was still observed.Having eliminated pointing drifts, the most likely cause is a misalignment of thecavity mode as the piezo actuated stage under the output coupler accumulates alarge DC offset due primarily to humidity changes in the lab. Fig. 3.17 showssimultaneous measurements of the OPO signal pointing, power, and spectrum inaddition to cavity temperature and humidity. With stable pump power and point-ing, this data suggests that the signal pointing, and thus the cavity alignment, drifts39in time as the cavity length is adjusted to compensate changes in humidity. Driftingcavity alignment results in reduced output power and, consequently, spectral drift.Future stabilization efforts should be focused on lab environment stability or animproved enclosure for environmental isolation.3.3 Towards Broader BandwidthsSubstantial effort has gone into increasing the bandwidth of the OPO at SBQMI,with particular focus paid to the impact of cavity GDD. DCM pairs are used tocounter the dispersive effects of material inside the cavity. Ideally the DCMs wouldallow bandwidths limited only by the phasematching condition in the parametricgain medium. Unfortunately, as discussed in the following sections, broadbandmirror coatings result in oscillations of the GDD. Because the circulating signallight in the OPO must have temporal overlap with the pump to undergo parametricamplification, these GDD oscillations restrict the achievable bandwidth. At theend of this chapter, we also present potential future developments to overcome thecurrent bandwidth limitations.3.3.1 Passive Cavity SimulationsIn order to better understand the bandwidth limitations of the OPO, we decided tosimulate the cavity enhancement over the full range of phasematched wavelengths.As noted previously, the OPO bandwidth appears to be limited by intra-cavity dis-persion. For this reason, our simulations do not incorporate the parametric processor frequency dependent reflectivity of the mirrors. Instead, we determine the dis-persion of the cavity mirrors, nonlinear crystal, fused silica and air. The resultingsimulations capture the effect of the passive cavity on a frequency comb with arepetition rate matched to that of the OPO pump laser.The calculations start with basic cavity optics. For a given frequency to beresonant in the cavity, the optical path length, L, for one round trip must be equalto an integer multiple of the wavelength: 2πm = ωc L. This expression neglectsdispersion, resulting in an evenly spaced set of resonant cavity modes. In thissimplified case, assuming the cavity length is such that the OPO signal repetitionrate is matched to that of the pump, the OPO bandwidth will be unlimited (of course,40Figure 3.17: Short term spectral stability with the OPO free-running andlocked.The OPO spectrum is measured with the Thorlabs CCS175Spectrometer with a scan rate of 100Hz, resulting in a Nyquist fre-quency of 50Hz. Each spectrum is fit to a Gaussian curve to determinethe center wavelength. A prominent 30Hz peak is observed when theOPO is free-running. When locked, the power spectrum drops by a fac-tor of 10 across the FFT bandwidth.41the phase matching conditions of the parametric process will set a bandwidth limit).As we add in dispersion due to the elements inside the cavity, the cavity resonancestructure changes. Including dispersion from the various elements inside the cavity,the resonance condition becomes,2πm =ωcnair(ω)Lair +ωcnLBO(ω)LLBO +ωcnFS(ω)LFS +φmirror(ω)= β airm Lair +βLBOm LLBO +βFSm LFS +φmirrorm(3.5)where Lair/LBO/FS is the round trip length of air, LBO, and fused silica, nair/LBO/FSare the indices of refraction, and φmirror is the phase introduced by the cavity mir-rors.We can derive the free spectral range (FSR) for this case by looking at twoneighboring modes, m and m+1. In terms of β = ωc n we have,2π(m+1) = β airm+1Lair +βLBOm+1LLBO +βFSm+1LFS +φmirrorm+1= β airm Lair +βLBOm LLBO +βFSm LFS +φmirrorm +2π= (β airm +∂β air∂ν|m∆ν)Lair +(β LBOm +∂β LBO∂ν|m∆ν)LLBO+(βFSm +∂βFS∂ν|m∆ν)LFS +(φmirrorm +∂φmirror∂ν|m∆ν)(3.6)Subtracting Eq. 3.5 from Eq. 3.6 and solving for ∆ν yields the FSR,|∆νFSR|= 2π∣∣∣∣∣(∂β air∂ν|mLair + ∂βLBO∂ν|mLLBO + ∂βFS∂ν|mLFS + ∂φmirror∂ν|m)−1∣∣∣∣∣(3.7)Clearly, dispersion causes a frequency dependent FSR. The synchronous pump-ing condition requires the signal beam to have the same repetition rate as the pump(ie the frequency modes of the signal have a set spacing), and therefore there willbe a limited range over which the signal modes can be near resonance with thecavity modes.42Mirror PhaseThe mirrors in the OPO cavity are produced by Layertec. A data sheet is providedwith each mirror, providing measurements of reflectivity, transmission, and GDDas functions of wavelength. For the purposes of the simulation, we were concernedprimarily with the dispersion properties of the mirrors. GDD, or second order dis-persion, is simply given by GDD = ∂2φ∂ω2 . Thus through direct integration we canretrieve the phase introduced by the cavity mirrors. Of course, the original con-stant phase offset and linear phase component (ie group velocity offset) cannot beobtained through the integration. Fortunately, the constant offset is inconsequen-tial and the group velocity offset changes only the absolute cavity length at whichsynchronous pumping occurs, but the structure of the resonance map is preserved.Round Trip PhaseThe cavity enhancement for a field injected into a cavity can be written as [26]B =(ti1− rircav)2 11+(2Fπ )2sin2(φ(ω)2 )(3.8)where ti,ri and rcav are field transmission/reflection coefficients for the input cou-pler and remaining cavity mirrors, respectively. For the case of the OPO, the signalis generated within the cavity so we can set ti = 1 as no intensity is lost couplinginto the cavity. The cavity finesse F is given by,F =π√rircav1− rircav (3.9)Finally, φ(ω) is the frequency-dependent phase accumulated in one round trip ofthe cavity. For a straightforward calculation of the enhancement, we simply calcu-late the accumulated phase for each mode of a frequency comb,φ =ωcnair(ω)Lair +ωcnLBO(ω)LLBO +ωcnFS(ω)LFS +φmirror(ω) (3.10)and plug that phase into Eq. 3.8.One additional complication is that the OPO signal beam has a varying carrier-43envelope offset frequency, which is what allows for the continuous tuning of thesignal. To calculate the necessary offset to apply to our frequency grid, we first findthe frequency at which the synchronous pumping condition is met, ∆νFSR = frep.It is this central synchronous mode, fsync, which we need to shift onto resonancewith the cavity. We can easily find the detuning from the next resonant mode:φdet = 2π−mod(φ ,2π). This is the phase that must be introduced by fCEO.φdet =2π fCEOcnair(ω)Lair+2π fCEOcnLBO(ω)LLBO+2π fCEOcnFS(ω)LFS+∂φmirror∂ω(3.11)Thus we can solve for the offset frequency, and add it to our frequency grid beforecalculating the enhancement.2D Resonance MapsThe enhancement is calculated as a function of frequency and cavity length, Lair,producing a 2D map, such as those shown for two different cavity configurationsin Fig. 3.18 and Fig. 3.19. These maps correspond with the measured spectra pre-sented in Fig. 3.10 and Fig. 3.11, respectively. The step-like features of the centraltuning curve are a result of the residual GDD oscillations of the dispersion com-pensating mirror pairs, and produce ≈ 50nm full-width at half-maximum (FWHM)spectra at points across the tuning range. These bandwidths are comparable tothose observed in the lab, and the central wavelength of the step features corre-sponds with the central wavelength of the observed broad spectra. We note onepeculiarity in the positive GDD tuning curve, Fig. 3.19. The step feature centeredaround 725nm is particularly sensitive to cavity length, and would thus be unsta-ble. We believe this is the reason that only narrower ≈ 20nm bandwidths are seenbelow 750nm in this configuration.Due to the GDD oscillations of the DCM, this simulation does not function prop-erly near zero average GDD. Fig. 3.20 helps to illustrate the problem. For largeraverage GDD, the function fsync(Lair) is single-valued. However, as the averageGDD approaches zero, the function becomes multivalued. In order to simulate thissituation, one would need to consider other parameters which may influence thecenter frequency of the signal spectrum, such as the parametric gain profile or the44Figure 3.18: Simulated cavity enhancement as a function of relative cavitylength and wavelength. The simulation includes dispersion due to twoDCM pairs, the LBO crystal, fused silica wedges, and air. The fusedsilica wedges are used to bring the average cavity GDD closer to zero.This map can be compared with measured spectra obtained utilizingthe same cavity configuration, shown in Fig. 3.10.spectral tuning history. This ambiguity in synchronous frequency, coupled withstrong sensitivity to cavity length, produces the unstable and discontinuous tuningof the OPO spectrum observed near zero average GDD.3.3.2 Alternative Dispersion Compensation and Single PassBroadeningIn order to obtain spectral bandwidths beyond the ≈ 50nm bandwidths attainablewith our DCM pairs, we first considered the possibility of utilizing of an intracav-ity prism compressor instead of the DCM pairs for dispersion management. Thisapproach has a few obvious drawbacks. To compensate the dispersion of the air45Figure 3.19: Simulated cavity enhancement as a function of relative cavitylength and wavelength. The simulation includes dispersion due to oneDCM pair, the LBO crystal, fused silica wedges, and air. The fusedsilica wedges are used to raise the average cavity GDD to avoid unstableoperation. This map can be compared with measured spectra obtainedutilizing the same cavity configuration, shown in Fig. 3.11.and LBO would require approximately 25cm prism separation. The compressorwould need to be inserted before either the end mirror, M3, or output coupler. In-corporating this compressor into the cavity would require a substantial redesign. Inaddition, the prism separation would need to be tuned to obtain the optimal band-width at different center wavelengths. This would result in transverse movementof the beam on the mirror, such that the mirror would need to be translated in boththe tranverse and longitudinal directions in order to tune the spectrum over the fullphase-matched range of the LBO crystal.Beyond the design considerations, the prism compressor has substantial third-order dispersion which cannot be tuned separately from the GDD. Thus, there46Figure 3.20: Plot of the OPO FSR as a function of wavelength with averagezero GDD cavity configuration. The resonance map simulations rely onthe single-valued determination of the synchronous wavelength, thewavelength for which the cavity FSR is equal to the pump repetitionrate. Near zero GDD there exist multiple synchronous wavelengths.is only a single region around 850nm where one could expect to see bandwidthsbeyond those achievable with the DCM pairs.A more promising approach may take inspiration from Yb fiber laser systemswhere spectra beyond the gain bandwidth have been demonstrated, using a nonlin-ear medium to broaden the spectrum before the output coupler, and a spectral filteris to produce a stable, periodic evolution in the cavity [27, 28]. Recently a similarapproach has been applied to NIR OPOs, where spectra are achieved beyond theparametric-gain bandwidth by introducing a second crystal into the cavity whichproduces self-phase modulation (SPM) [29, 30]. In the case of these OPO systems,the non-zero cavity dispersion is essential in producing a spectral filter, where theedges of the strongly chirped signal pulses fall outside the duration of the pump47pulse and thus experience no gain. These systems display the significance of con-sidering discrete cavity elements in modelling pulse dynamics and ultimately theoutput spectra.In order to improve the OPO bandwidth, one could leverage similar nonlinearbroadening techniques to those mentioned above. Intracavity self-phase modula-tion would allow the single-pass generation of broader spectra, reducing the signif-icance of GDD oscillations, and allowing for the cavity to be run in a stable normaldispersion regime. To this end, future work could explore the addition of a sec-ond cavity focus through which a crystal with a high χ(3) nonlinearity (eg Ta2O5or ZnSe) can be translated through the focus to control broadening. This configu-ration would not only produce broad bandwidths, but provides greater bandwidthtunability, ideal for selective excitation of a given state in MDCS.48Chapter 4Multidimensional CoherentSpectroscopy: Towards Studies ofExcitonic SystemsFigure 4.1: A schematic of the MDCS system constructed at SBQMI. Pulsesfrom the OPO are split and delayed in the spectrometer before being fo-cused onto the sample of interest. The four wave mixing (FWM) signalreflected from the sample is then measured on a photodetector and iso-lated using lock-in detection.49MDCS is a nonlinear optical spectroscopy with the capability to distinguish be-tween homogeneous and inhomogeneous broadening, identify couplings betweenstates, and observe ultrafast dynamics with high energy resolution [31, 32]. Thetechnique is an optical extension of 2D NMR and has found broad use in atomicand molecular systems. In recent years MDCS has also been applied to semicon-ductor systems such as quantum dots, quantum wells, and TMDs [22, 33, 34].A schematic of the MDCS setup at SBQMI can be seen in Fig. 4.1. The 80MHzOPO pulse train is aligned into the Bigfoot Spectrometer, which splits each pulseto generate the various pulse sequences used to produce 2D spectra. As shownin Fig. 4.1, MDCS consists of exciting a sample with three pulses and varyingeither τ , the coherence time, or T, the population time. This generates a third-orderpolarization in the material, which will radiate a four wave mixing (FWM) signala time t after the third pulse. The emitted field is spectrally resolved, and the resultis a map of FWM intensity as a function of emitted frequency and the varied timedelay, typically τ . By Fourier transforming with respect to τ , one obtains a 2Dspectrum, correlating the excitation frequencies with the emitted field. The abilityto spectrally resolve the excitation axis allows one to separate the homogeneousand inhomogeneous linewidths of a given excitation, and readily identify coherentcoupling between states.4.1 MonstrSense Bigfoot Spectrometer - CollinearMDCSThe MDCS system at SBQMI, a Bigfoot Ultrafast Spectrometer from MONSTRSense Technologies, provides a versatile solution for studying 2D systems withbroadband optics spanning the visible/NIR and resolutions as high as 10µeV . Itutilizes a collinear geometry, which allows for high spatial resolution as the exci-tation pulses may be focused through an objective lens.The Bigfoot Spectrometer consists of nested Michelson interferometers, gen-erating four output pulses - three excitation pulses (A, B and C) and a local os-cillator (LO) pulse. These output pulses are either reflected from or transmittedthrough a sample of interest, and then aligned onto a photoreceiver. Delay stagesin three of the interferometer arms allows control of the relative delays between50the pulses. A CW reference laser is used to track these delays with high resolutionand determine accurate time axes for the 2D scans. Each arm of the interferom-eter also contains an acousto-optic modulator (AOM) used to frequency shift eachpulse. Utilizing lock-in detection, it is possible to distinguish signals measured bythe photoreceiver at various linear combinations of the AOM frequencies. In prac-tice, a particular linear combination, fC− fLO− ( fA− fB) = 30kHz is detected andthe AOM frequencies are changed to measure different types of 2D spectra (e.g.rephasing, non-rephasing, etc.).The three excitation pulses are used to produce a FWM signal via the sample’sthird order polarization, as introduced in Sec. 2.3. The LO pulse is then scanned int over the signal, producing an interferogram which can be Fourier transformed toretrieve the emission spectrum. In the simplest configuration, the LO pulse is com-bined with the excitation pulses at the output of the spectrometer and reflects off ofthe sample. This configuration also allows for the straightforward implementationof the autocorrelation measurement described in Sec. 3.2.2 by replacing the sam-ple with a nonlinear crystal and utilizing a spectral filter to isolate the frequencydoubled autocorrelation signal.The alignment process of the spectrometer is well documented in the accompa-nying manual. Essentially one utilizes two apertures and a beam profiler to producespatial overlap of the excitation pulses. In order to calibrate the delay stage zeropositions, one can observe optical beating between two pulses either on the beamprofiler or using the photoreceiver and lock-in detection. With the spectrometeraligned, the output pulses are directed through a microscope setup and focusedonto the sample of interest. The output pulses and FWM signal generated in thesample are then reflected from the sample substrate back through the microscopesetup and directed onto the photoreceiver. At this point, one should be careful toobserve the raw photoreceiver signal without lock-in detection, adjusting the gainas necessary to ensure that the signal is not saturating. The raw signal can be ob-served utilizing the ’Real-time Scope’ feature of the MONSTR Sense software,and selecting ’Signal Scope.’ Alternatively one can connect the photoreceiver out-put directly to an oscilloscope. Finally, as an additional check with the MONSTRSense software, one can monitor the four-wave mixing spectrum on the ’1D Spec-trometer’ tab. The amplitude of this signal should vary linearly with the detector51gain.Featured in a variety of published MDCS studies, monolayer MoSe2 serves asa good reference material with which to verify the functionality of the Bigfootspectrometer. With a sufficiently broad excitation spectrum, one can study the in-teraction of the trion and exciton states in MoSe2. Hao et al. [35] present 2Drephasing spectra highlighting coherent coupling between intravalley trions andexcitons, mediated by Coloumb interactions. This coherent coupling is clearlyidentified through the appearance of off-diagonal peaks both above and below thediagonal. Measurements taken as a function of the population time, T, reveal thedephasing of this coherent interaction after≈250fs. On picosecond timescales theyobserve transfer of spectral amplitude from the diagonal to the off-diagonal peaks,indicating incoherent population transfer which is attributed to phonon-mediatedup- and down-conversion. Further studies from the same group [2] leverage thevalley-selective optical excitation in monolayer MoSe2 to highlight intervalley in-teractions. Through the use of alternating excitation pulse polarization, excitonsand trions are alternately excited in the K and K’ valleys. The resulting 2D spec-trum is shown in Fig. 4.2. Exciton and trion peaks appear on the diagonal, withhigher-order neutral and charged biexcitons appearing as off-diagonal peaks with≈20meV and≈5meV binding energies, respectively. Accompanying co-circularlypolarized measurements confirm that these biexciton peaks arise from intervalleyinteractions.Other MDCS studies of MoSe2 focus on sample quality through measurementsof the exciton homogeneous and inhomogeneous linewidths. Martin et al. [36] re-port reduced homogeneous exciton linewidths for hexagonal boron nitride (hBN)encapsulated monolayer samples, suggesting a reduction in defects due to encapsu-lation. They additionally find encapsulated samples to exhibit minimal degradationafter exposure to high optical powers and temperature cycling. Purz et al. [3] ex-tend this analysis of sample quality by performing hyperspectral MDCS to observevariations in the homogeneous and inhomogeneous linewidth across the surface ofan encapsulated MoSe2 sample. The resulting maps are shown in Fig. 4.3. Micro-scope images of the sample reveal Region A, marked in green in Fig. 4.3a, to havea bubble or crack. Resulting hyperspectral imaging reveals this location to havehigher anti-correlation between the homogeneous and inhomogeneous linewidths.52Figure 4.2: Rephasing 2D spectrum of MoSe2 generated with pulses hav-ing alternating σ+ and σ− polarization. The diagonal peaks representthe exciton (X) and trion (T). The off-diagonal peaks are identified asbound charged (XT b,T Xb) and neutral (XX) biexcitons. Due to valley-selective optical excitation, the alternating polarizations generate exci-tons in both the K and K’ valleys, highlighting these intervalley interac-tions. Reproduced with permission from Springer Nature [2].This variety of published data on MoSe2 provided multiple options for bench-marking, including straightforward measurements of exciton linewdiths and cou-pling with trions and higher-order excitons. For comparison with these studies,we took measurements at room temperature and 20K. An initial room temperaturemeasurement can be seen in Fig. 4.4. The expected A exciton peak is seen onthe diagonal around 1.57eV, consistent with published data on room temperatureunencapsulated samples. In addition, we observed two artifacts in our referencemeasurements: a narrow stripe along the diagonal of the map and a vertical stripeextending from exciton or trion peaks. This particular map was measured at roomtemperature on an unencapsulated MoSe2 monolayer.The diagonal stripe suggests that the sample is producing a photon echo atdelay t = τ . However, initial troubleshooting of the feature confirmed that it wasnot related to the sample, as it still appeared when the beam was moved off the53Figure 4.3: Hyperspectral MDCS measurements obtained on an hBN encap-sulated monolayer MoSe2 sample. (a) and (b) show spatial maps of thehomogeneous (γ) and inhomogeneous (σ ) exciton linewidths, with (c)highlighting correlations between γ and σ for different regions of thesample. (d) shows the exciton resonance energy measured at differentpoints across the sample. Reprinted from [3] with the permission of AIPPublishing.sample onto the silica substrate, or simply reflected off of a silver mirror. Thedesign of the spectrometer is such that each of the four pulses, after passing throughthe respective AOMs, is retroreflected back out the input towards the OPO. It wasdetermined that if these retroreflected pulses were coupled back into the Bigfootspectrometer, then they would undergo a second frequency shift. The resultingpulses at frequencies fA + fD and fB + fC would be overlapped in time at t = τand linearly interfere at the detector, producing a signal at the lock-in frequency.By setting t = τ = 5ps, we isolate the signal generating the diagonal feature, and54Figure 4.4: 2D rephasing spectrum obtained from an unencapsulated mono-layer MoSe2 sample at room temperature. There are two unexpectedfeatures: a narrow diagonal peak and a vertical stripe extending fromthe exciton peak at 1570meV.observed the FWM lock-in signal intensity while adjusting the beam pointing intothe spectrometer. The sensitivity of this signal to the beam pointing was consistentwith the retroreflection thoery, and we soon determined that the flat surface of a lensnear the input of the spectrometer was producing this effect. Adjusting the angleof the lens eliminated the diagonal stripe from the 2D spectra. Figure 4.5 shows a2D spectrum obtained after determining the source of the diagonal feature. It wasmeasured on an unencapsulated MoSe2 monolayer on a silica substrate at T=20K,and shows biexciton features consistent with the measurements reported by Hao et.al. [2]. A linear polarization was used for the excitation beam, such that each pulsecouples to both the K and K’ valleys. The vertical stripe feature is still prominent55at 1630meV, extending from the exciton peak on the diagonal.Figure 4.5: 2D rephasing spectrum measured on an unencapsulated mono-layer MoSe2 sample at T = 20K. The narrow stripe along the diago-nal has been eliminated by rotation of a lens near the Bigfoot input.The verical stripe is still prominent, extending from the excition peak at1630meV.Troubleshooting the vertical artifact proved to be more difficult. This featurewould appear on measured spectra at the same emission energy as the dominantdiagonal peak, typically the MoSe2 A exciton in our testing. Notably, the featurealso extended beyond the spectrum of the excitation laser. This vertical feature isnot observed in published 2D spectra of MoSe2, but appeared consistently in ourmeasurements across various samples. We tested multiple MoSe2 samples, bothencapsulated and unencapsulated, at room temperature and in the liquid heliumcryostat. The consistent appearance of the feature suggests that it was caused by56the spectrometer, OPO or cryostat system, rather than being a real effect from thesample.In order to obtain a typical 2D spectrum, the τ delay is stepped slowly be-tween measurements of the emitted FWM spectrum. This means that the τ delay ismost susceptible to noise in the system, such as drift in laser alignment, or fluctua-tions and drift of the sample position. In order to minimize these potential effects,we attempted to window the data along the τ scan axis before taking the Fouriertransform. This would help to minimize abrupt changes in the time domain signal,which would correspond to the broad vertical stripe in the frequency domain. Un-fortunately this windowing did not appear to have a significant effect on the verticalfeature.We also made initial attempts to limit possible causes of laser intensity fluctu-ations at the sample. One method we used was to increase the stage settling timefor the delay stages inside the Bigfoot by hundreds of milliseconds. This wouldensure that any perturbation to optics caused by the stage movement would havesufficient time to dissipate. We also lowered the lock-in time constant and reliedmore heavily on averaging in order to speed up individual scans and minimize theeffect of potential laser alignment or intensity drifts. Unfortunately these tests didalso did not have any significant effect on the vertical stripe feature.Testing conducted by MONSTR Sense on another Bigfoot Spectrometer sys-tem suggested that there was an assymmetry in measured noise caused by the factthat the τ axis starts at zero, while t is scanned through negative values. By includ-ing negative τ delays they observed suppresion of the vertical feature. Negativeτ delays correspond to a change in pulse ordering, such that the resulting spectrais the sum of a rephasing and non-rephasing spectrum. As of October 2022, theBigfoot software has been updated to incorporate this scan type. This new featurewill need to be tested at SBQMI to determine if it effectively eliminates the verticalfeature we observe.Other troubleshooting of the vertical feature would benefit from further min-imization of any potential alignment or intensity drifts. To this end, it would bebeneficial to run the OPO in a higher dispersion regime which is less sensitiveto cavity length fluctuations. With the current spectral stabilization setup, reduc-ing this cavity length sensitivity will minimize adjustment of piezo actuators, thus57also minimizing drifts in power and output pointing. The higher dispersion willalso result in narrower bandwidths. While reduced bandwidths may limit potentialmeasurements, it also allows for reduced scan times. Scan times may be furtherminimized through appropriate reductions in the lock-in time constant and delaystage scan lengths. In cases where the FWM has not fully decayed over the short-ened delay scan length, a window function may be used in post-processing to bringthe signal smoothly to zero. Additional efforts could also be made to stabilize thehelium cryostat used to cool the samples, thus minimizing fluctuations in relativealignment of the sample and excitation beam.4.2 Future Studies: MDCS for Ultrafast Studies of 2DMaterialsExcitons in semiconducting systems consist of an electron in the conduction bandand a hole in the valence band, bound by the Coloumb interaction. As stated previ-ously, excitons play a significant role in 2D materials where reduced screening canlead to stronger Coloumb interactions, even producing higher-order excitons suchas trions and biexcitons. Strong coupling with optical excitation, varied interac-tions with other quasiparticles, and the possibilities to engineer charge and energytransfer processes through excitons makes these systems exciting for fundamentaland applied studies.4.2.1 NiPS3The transition metal phosphorous trichalcogenides were studied in the bulk formin the 1980s and 1990s, revealing a layered material with magnetic ordering belowa critical temperature [37–39]. In recent years they have resurfaced as a systemexhibiting magnetic order even in the monolayer or bilayer limit [12–14]. Thezig-zag antiferromagnetic ordering in NiPS3 can be seen in Fig. 4.6, with the redarrows showing the spin of the Ni atoms.These materials are especially interesting as there are recent predictions of cou-pling between electronic and magnetic degrees of freedom, allowing control of themagnetic ordering by electrical or optical means, such as modification of the carrierdensity [40]. NiPS3 has received particular attention as various optical measure-58Figure 4.6: NPS3 Layer Structure. The red arrows represent the spin of theNi atoms, showing a zig-zag antiferromagnetic ordering. Reproducedwith permission from Springer Nature [4].ments have highlighted this coupling. Kim et al. [14] report a strong shift in theoptical spectral weight of NiPS3 as the sample temperature rises above the Ne´eltemperature (ie the critical temperature for AFM ordering), suggesting a strongcorrelation between the magnetic ordering and the electronic structure. Variousother reports have demonstrated a coupling between excitons and magnetic orderin NiPS3 through pump-probe [41] and photoluminescence [42]. These observa-tions point towards the possibilities of optical control of magnetic order.Recently, Kang et al. [5] presented absorption spectra (Fig. 4.7) showingan ultra-narrow exciton peak (0.4meV) and an exciton-magnon peak, where anexciton-magnon is a quasiparticle consisting of an exciton and magnon bound to-gether by an interionic exchange [43]. The narrow linewidth of the exciton peakis presented as evidence of an exciton condensate with interactions mediated bythe AFM ordering. Hwangbo et al. [42] dispute the exciton condensate claimthrough time dependent photoluminescence measurements which suggest an in-trinsic linewidth of only 30µeV .MDCS is the ideal technique to directly probe the exciton lifetime and identifypossible inhomogeneous broadening. MDCS can be used to take high resolutionspectra of the exciton peak in NiPS3 to reveal whether the peak is inhomogeneouslybroadened, and thus whether an exciton condensate is a viable explanation for thenarrow linewdiths observed. Future MDCS studies at SBQMI may also observethe linewidth as a function of temperature and exciton density to look for anoma-59lous behaviour near critical points for exciton condensation. These high resolu-tion scans will additionally show coupling to peaks Sα and Sβ shown in Fig. 4.7.Looking at time dynamics of this coupling may also reveal additional informationabout the physical origin of the peaks. MDCS also provides direct measures ofcoupling between excitons and magnons. Lower resolution scans may provide ad-ditional information about coupling between excitons and the magnetic order, andin particular may provide details about the role of excitons in the coherent magnonexcitation reported by Belvin et al. [41]. An alternate pulse ordering producinga zero quantum spectra would also likely shed light on interactions among exci-tons, potentially answering questions about the cause of exciton dissociation [41].These measurements would provide important information for fundamental studiesof strongly correlated systems, as well as for potential spintronic applications.4.2.2 Transition Metal DichalcogenidesTMDs and TMD heterostructures provide an exciting platform to study two di-mensional systems as a wide variety of exciton states have been demonstrated inthese systems. MDCS studies in particular have clearly shown intervalley couplingbetween excitons in the K and K’ valleys of momentum space [35], formation oftrions and biexcitons [2], and interlayer excitons formed in heterostructures [44].Van der Waals heterostructures provide a means to engineer new materials withinteresting physics arising from the interlayer interactions. One interesting sys-tem recently reported is a MoSe2/WSe2 heterostructure which may host an excitoncondensate [45]. MDCS may be used as an indirect probe of the coherence of theelectrically generated interlayer excitons forming the condensate. There is alsothe possibility of combining TMDs with other classes of materials to combine thecharacteristics of the individual layers. As an example, Kezilebieke et al. [46] pre-sented evidence for topological superconductivity in a heterostructure combiningsuperconducting NbSe2 with the 2D ferromagnet CrBr3.Additonal possibilities arise by introducing some relative twist angle betweenthe layers of a heterostructure, creating a Moire´ potential which has a lower period-icity than the underlying lattice. This potential can trap excitons, creating a ladderof interlayer exciton states [47]. Essentially creating a tunable lattice of trapped60Figure 4.7: Temperature dependent absorption measurement of NiPS3 show-ing a narrow linewidth exciton (Peak I) and a two-magnon sideband(Peak II). Peaks Sα and Sβ are left unassigned. Reproduced with per-mission from Springer Nature [5].excitons, this provides an interesting platform for information processing.While the interlayer excitons are difficult to probe directly due to a reduced os-cillator strength, the Moire´ potential can also affect intralayer excitons through thespatially dependent potential energy and enhanced coupling between the layers. Jinet al [6] report on the observation of Moire´ excitons in a WSe2/WS2 heterostruc-ture. As seen in Fig. 4.8, the A exciton peak of the WSe2 layers splits into threepeaks for small twist angle. A theoretical model allowed the authors to show dif-61ferent spatial distributions for each of the three states. Future MDCS studies atSBQMI could investigate these Moire´ excitons, specifically contributing importantmeasurements of the coherence time of these excitons, which is particularly im-portant for their potential applications. Along these lines, one may also be able touncover interactions limiting the exciton coherence time, thus suggesting potentialimprovements in fabrication and design. MDCS could also help to measure po-tential coherent interactions among excitons localized in different regions of thesample. These measurements would prove crucial for potential applications in in-formation storage and processing where interactions between excitons in differentregions may corrupt information.Clearly there are numerous exciting opportunities in 2D heterostructures andMDCS can inform our understanding of coherent coupling between heterostructurelayers, and aid in the study of charge and energy transfer processes.Figure 4.8: Reflection contrast spectra showing splitting of the WSe2 A ex-citon in a WSe2/WS2 heterostructure due to confinement of the Moire´potential. Reproduced with permission from Springer Nature [6].62Chapter 5ConclusionIn this thesis we have presented the details of the commissioning and operationof the MDCS system we constructed at SBQMI. The OPO system constructed wasshown to produce bandwidths over 50nm across the visible and near IR, providingaccess to a variety of 2D material systems for study with MDCS. The long termspectral drift is highlighted as a potential issue for future studies requiring highspectral resolution or long averaging, with improved environmental isolation rep-resenting a clear path forward towards improved stability. We have also presenteddetails of our cavity enhancement simulations, highlighting the effect of cavity dis-persion on the resulting output spectra and providing a way to predictably tune thebandwidth at a particular center wavelength by leveraging cavity dispersion tuning.The potential for enhanced bandwidths through single-pass SPM is also discussed.In addition to increased bandwidth, this approach would likely result in more stableoutput spectra due to the larger positive dispersion required.We have also presented initial measurements and troubleshooting conductedwith the MONSTR Sense Technologies Bigfoot Spectrometer. Pulse characteriza-tion techniques leveraging the pulse delay and lock-in detection capabilities of thespectrometer allow for straightforward optimization of pulse compression at thesample position. Two prominent artefacts appeared in our measured 2D spectra. Anarrow diagonal peak which we determined to be caused by a retroreflection, andan elongated vertical feature which we were unable to eliminate. Further testing byMONSTR Sense Technologies suggests this feature may be caused by noise asym-63metry when the t delay is scanned over negative times, but τ is not. Since the workin this thesis was completed, a software update was provided to include scanningover negative τ delays. Finally, we have presented initial thoughts on interestingmaterial systems which would benefit from MDCS studies.64Bibliography[1] K. Mak and J. Shan, “Photonics and optoelectronics of 2d semiconductortransition metal dichalcogenides,” Nature Photonics, vol. 10, pp. 216–226,2016.[2] K. Hao, J. Specht, P. 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In order to minimize astigma-tism of the output beam, the angle of incidence on the curved mirrors is minimizedto be roughly 4◦, limited by the radius of the mirrors and the mirror separation re-quired to obtain a stable cavity mode. The cavity alignment is further constrainedby the inclusion of a crystal oven, which is used to optimize the phasematching ofthe LBO crystal via temperature tuning. This introduces apertures near the cavityfocus which place an upper bound on the angle of incidence on the curved mirrors.Finally, the alignment procedure is complicated by the fact that the cavity mirrorsare designed to transmit the 517nm pump light, and thus the pump cannot be usedfor alignment. For this reason we use residual 1035nm light from the initial dou-bling process to align the cavity and find an appropriate cavity length, then proceedto overlap the 517nm beam with the cavity mode defined by the 1035nm light. Thereader is encouraged to refer back to Fig. 3.1 and Fig. 3.2 to familiarize themselveswith the system scale and full layout.A.1 Initial Optics Placement1. Utilize two irises and the first pair of mirrors to align the 1035nm beamfrom the FLINT oscillator along a line of mounting holes on the watercooledbreadboard, as sketched in Fig. A.1. The half wave plate and polarizing70Figure A.1: A schematic showing the essential optical elements for generat-ing and manipulating the OPO pump beam. Of particular importance,the lens L1 is used to focus the FLINT beam into the LBO crystal forefficient frequency doubling. This frequency doubled beam at≈515nmis used to pump the OPO.beam splitter at the output of the FLINT may be utilized to minimize theoutput power during alignment.2. Insert the half wave plate and adjust to obtain horizontally polarized light(parallel with the plane of the breadboard). Once the doubling crystal isinstalled, this will generate vertically polarized 517nm light as the LBO iscut for Type I SHG.3. Insert the focusing lens, L1, used to increase peak intensity in the LBO dou-bling crystal. Overlap the reflection off the front surface of the lens with theincoming beam to ensure the lens is perpendicular to the beam. Adjust thetransverse position until the beam is centered on the irises used in step 1.This ensures that the beam is centered on the lens.4. Place the LBO doubling crystal near the focus of the beam on a linear stageand center the beam by eye.5. Align the collimating lens, L2, using the same procedure as in step 2. Tooptimize the z-position, check the beam radius a few meters from the lens toensure it is well collimated.6. Insert the two dichroic mirrors used to isolate the 517nm light from the resid-ual 1035nm light. These will be used to align the 517nm pump into the OPOcavity.717. Measure the power of the 517nm beam after the dichroics and maximize thispower by adjusting the LBO crystal degrees of freedom (z,θ ,φ ).8. Now, starting with a collimated 517nm beam, use the two dichroic mirrorsto align the beam along a line parallel to the 1035nm beam path from Step 1.9. Place the curved mirrors such that they are approximately 76.5cm apart, andthe 517nm beam is centered on both mirrors.10. Insert and align the focusing lens for 517nm.11. Place the rest of the cavity mirrors in their approximate location, utilizingFig. 3.1 as a guide. Adjust the four planar mirrors symmetrically such thatthe total cavity length is ∼3.91m.A.2 IR Cavity Alignment1. Now referring to Fig. A.2, block the 517nm beam after the dichroics.2. Couple the undepleted fundamental (1035nm), transmitted through the firstdichroic, into the cavity through the output coupler (OC)(a) A telescope will be needed to roughly match the IR mode with thecavity mode at the output coupler (∼0.5mm). Based on the ∼1.75mmIR beam waist, a 350mm and -100mm lens provides a sufficient match.(b) It is also important to place an isolator in this path to block the returningbeam and prevent damage to the FLINT.3. Use the two mirrors outside the cavity to center the IR beam on the OC andM24. Starting with M2, adjust each optic so that the beam is centered on the fol-lowing optic (i.e. center the beam on CM1 using M2, on CM2 using CM1,etc.). Note that the clearance should be tight on the curved mirrors to mini-mize astigmatism of the cavity mode.72(a) Once the beam has been aligned up to M3, the CM separation can beoptimized. Observing the beam impinging on M3, adjust the separationuntil the ellipticity of the IR mode is minimized and the beam is looselyfocused.5. Adjust M3 to overlap the retroreflection with the incoming beamFigure A.2: A schematic showing the initial cavity alignment setup, utilizingthe undepleted fundamental coupled in through the output coupler. Atelescope is used to roughly mode match and an optical isolator protectsthe FLINT from the return beam.6. When alignment of IR is close, one should be able to look at one of theoutputs from CM2 and see multiple round trips of the IR spatially separated.As shown in Fig A.3, place a camera (such as the Point Grey Flea3) at theoutput and utilize both end mirrors (OC and M3) to optimize the alignment.7. Once spatial overlap is optimized, scan the cavity length using the linearstage under the OC and look for modulation of the IR beam on the camera.If the spatial alignment is good and the length is correct, the output beamshould be TEM00 and the contrast of the modulation should be high.(a) If you cannot see modulation at the output, but you were able to seeand overlap the multiple round trips spatially, you may need to adjustthe position of the OC or M3. Carefully measure the cavity length andadjust accordingly.73Figure A.3: A schematic of the setup used to fine tune the cavity alignment.A camera is utilized to view one of the beams transmitted through CM2.Utilizing the cavity end mirrors, OC and M3, one may overlap multiplecavity round trips on the camera. When the cavity is length matchedwith the pump, one may also observe intensity modulation of the beamon the camera.8. Insert the LBO crystal into the cavity. Adjust the oven rotation mount so theIR beam is roughly perpendicular to the crystal surface. Re-optimize spatialand temporal overlap. Also ensure that the IR beam is not clipping on theoven faces.A.3 Overlap Pump with Cavity Mode1. After aligning the cavity with the IR, unblock the 517nm beam and overlapit with the IR inside the cavity. It is easiest to use the first dichroic to overlapthe beams on M1, and the second dichroic for overlap on M3.(a) Ensure the 517nm beam remains centered on the focusing lens. Youwill likely have to adjust the horizontal position of the focusing lens.If this is the case, iterate between roughly overlapping the green andIR, and adjusting the lens position. Though it may take a number ofiterations, this process should converge and their will be good overlapbetween the green and IR.742. Block the green beam again and double check the alignment of the cavitybased on the modulation of the IR output at M1. Optimize the alignmentif it has changed slightly due to the adjustment of the dichroics. As neces-sary, iterate between getting overlap of green and IR, and optimizing cavityalignment.3. Now block the IR beam and place a white card at the output of the OC.Maximize the power of the 517nm beam.4. Scan the cavity length (SLOWLY!) on the short side of the optimal IR cavitylength determined previously. This can be done with the micrometer or amotorized actuator, though it is easiest to start with the motorized actuator. Ifyou are scanning slowly enough and the correct length is within the scanningrange, you should see a bright red flash at the output - this is the signal beam!(a) The oven temperature should be set at≈ 70◦C to optimize phasematch-ing at 700nm5. If alignment is lost, return to the IR Cavity Alignment (but don’t removeoven).75
Thesis/Dissertation
eng
Physics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Jones, David John, 1969-
Design and operation of a multi-dimensional coherent spectroscopy system
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