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Wide band electro-optic intensity modulator frequency response measurement using optical heterodyne,… Lam, Alfred Kan Min 2005

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WIDE BAND ELECTRO-OPTIC INTENSITY MODULATOR FREQUENCY RESPONSE MEASUREMENT USING OPTICAL HETERODYNE, DOWN-CONVERSION TECHNIQUE by ALFRED K A N MIN L A M B. A . Sc., The University of British Columbia, 2002  A THESIS SUBMITTED IN P A R T I A L F U L F I L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF APPLIED SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES  ^  Electrical and Computer Engineering)  THE UNIVERSITY OF BRITISH C O L U M B I A March 2005 © Alfred Kan Min Lam, 2005  Abstract  In this thesis a novel system for measuring the frequency responses of electrooptic intensity modulators in the millimeter-wave regime is described. As the frequency responses of modulators increase, wide band, and cost effective methods to measure these responses need to be developed.  The system described in this thesis uses optical  heterodyning and a wide band photodiode to generate millimeter-waves to drive the device under test (DUT). The need for a wide band microwave sweeper can therefore be eliminated. Moreover, an inexpensive frequency shifter consisting of a Mach-Zehnder modulator and an optical bandpass filter is used to down-convert the output of the D U T to a low microwave frequency at which the output is easily measured. measures | S  21  The system  | in dBe.  The system can measure the frequency responses of different types of electrooptic  intensity  modulators,  modulators  electro-optic  such  as  polymer  Mach-Zehnder modulators, modulators,  and  should  mode-converter also  work  for  electroabsorption modulators. In this thesis, the frequency response measurement system is described, and mathematical expressions for the optical fields at the output of an electro-optic modulator are developed when the D U T is biased or operated at its maximum, quadrature, and minimum points. High frequency measurements on a 10 Gb/s LiNb0  3  Mach-Zehnder type modulator and a 40 Gb/s GaAs mode-converter type  modulator are made. The measurements show close agreement with | S | measurements 21  made using vector network analyzers and calibrated wide band photodiodes.  ii  In addition, the harmonic rejection feature of our system is described. Our system "rejects" higher order harmonics, due to the non-linearities, generated in the D U T with proper selection of the modulation and the shift frequencies. This feature means that our system can measure the linear frequency response of the D U T even i f it is operated, or biased, in a non-linear region.  iii  Table of Contents Abstract  ii  List of Figures  v  List of Tables  viii  Acknowledgements  ix  Co-authorship  x  Chapter 1. Introduction  1  1.1. Literature Review and Motivation 1.2. Thesis Overview 1.3. Supplementary Information on the Settings of the Measurement System References  1 4 5 7  Chapter 2. Electro-optic Intensity Modulator Frequency Response Measurement. 2.1. Introduction 2.2. Optical Heterodyne, Down-conversion Technique Theory 2.2.1. Modulator Optical Signal 2.2.2. Frequency Response Measurement System 2.3. Experimental Results 2.3.1. Wide Band Measurements 2.3.2. Harmonic Rejection 2.4. Conclusion References  9 9 11 11 16 23 23 31 33 34  Chapter 3. Summary, Conclusions and Recommendations for Future Work 3.1. Summary and Discussions 3.2. Recommendations for Future Work References  37 37 40 42  Appendices Appendix Appendix Appendix Appendix  43 43 46, 52  A. B. C. D.  Optical Heterodyning The Frequency Shifter Harmonic Rejection Requirements Electro-optic Intensity Modulator Frequency Response Measurement using Vector Network Analyzer Appendix E. Comparison of the System Dynamic Range of our System to that of a V N A References  55 59 63  iv  List of Figures Figure 2.1. Schematic diagram showing the measurement system used. PC: Polarization Controller, A T T N : Optical Attenuator, WPD: Wide Band Photodiode, L P D : Low Frequency Photodiode, BPT: Optical Bandpass Filter, MZI: Mach-Zenhder  17  Figure 2.2. Uncorrected frequency responses of the 10 Gb/s modulator measured using our system from 1 to 65 GHz and the V N A from 45 M H z to 50 GHz. The residual power signal of our system is shown as the dashed line  25  Figure 2.3. Corrected frequency responses of the 10 Gb/s modulator measured using our system from 1 to 50 GHz and the V N A from 45 M H z to 50 GHz  26  Figure 2.4. Three measurements showing the corrected frequency responses of the 10 Gb/s modulator using our system up to 60 GHz. The repeatability was +/- ~1 dB  27  Figure 2.5. Uncorrected frequency responses of the 40 Gb/s modulator measured using our system from 1 to 78 GHz and the V N A from 40 M H z to 65 GHz. The residual power signal of our system is shown as the dashed line  29  Figure 2.6. Corrected frequency responses of the 40 Gb/s modulator measured using our system from 1 GHz to 50 GHz and the V N A from 40 M H z to 50 GHz  30  v  Figure 2.7. Detected signals for /„, equals 10 GHz. The detected signals are at a) f = 2.4 GHz); b) f s  - f (=7.6 GHz); c) f s  m  (=12.4 GHz); e) 2f  m  - f  s  m  (=17.6 GHz); f) 2f  m  (=10 GHz); d) f  m  + f  (=20 GHz)  s  32  Figure A . l . A setup of an optical heterodyne system. PC: Polarization Controller, WPD: Wide band Photodiode  43  Figure B . l . Diagram showing the setup of the frequency shifter used in the measurement system  46  Figure B.2. The 3-dB pass-band of the filter was measured to be -1558.47 nm to-1558.66 nm  47  Figure B.3. Spectrum of the optical components from the frequency shifter and the DUT. a) The component from the frequency shifter, b) the high frequency sideband from the DUT, c) the low frequency sideband from the DUT, d) the optical carrier from the DUT. (Setting of the A N D O AQ6317B optical spectrum analyzer: R B W = 0.01 nm, Span = 1 nm)  49  Figure B.4. Diagram showing the ystem used to obtain the optical field shown in Figure B.3  50  Figure D . l . The V N A setup used to measure the frequency response of the DUTs in Chapter 2. WPD: Wide Band photodiode  55  Figure E. 1. Our system showing a higher system dynamic range than that ofthe50GHz V N A  60  vi  Figure E.2. The frequency response of the modulator when no laser source was supplied is shown as the dotted curve. It overshadowed the uncorrected frequency response of the 10 Gb/s modulator measured using the V N A , shown as the solid curve, starting at ~45 GHz. The uncorrected frequency responses of the 10 Gb/s modulator measured using our system, shown as the asterisks, shows continual roll-off beyond 50 GHz due to the virtually flat power output from the optical heterodyning and the constant residual power signal shown as the dashed line  vii  62  List of Tables Table 2.1. Optical and microwave frequencies as in Figure 2.1  17  Table C. 1. Table showing the frequencies of the electrical signals at the output of the low frequency photodiode due to the mixing of the signals at the output of the frequency shifter with the signals at the output of the DUT  53  vin  Acknowledgements My deepest appreciation goes to my parents for their love, trust, and support throughout my life including the course of this work. I would like to extend my sincere gratitude to my supervisor, Dr. N . A . F. Jaeger, for proposing this project and providing continual support during my research. His dedication and friendly guidance has been most invaluable to me in the course of this program. I would like to thank Sasa Ristic for his consistent encouragement during the course of this work, and his helpful comments and discussions regarding my research. I would also like to thank all the individuals in the electro-optics lab, department office, part ordering, and ... all others who have helped me. Finally, I would like to thank my family and friends for their encouragement, especifically my girlfriend, Joyce Chang, for her love and understanding.  ix  Co-authorship Alfred Kan M i n Lam conducted research, designed the measurement system, performed experiments, collected measurement data and analysed the data, and provided the first draft of the manuscript. Mair Fairburn measured the frequency response of the 40 Gb/s mode converter modulator using a 65 GHz V N A (Anritsu 37397C) shown in Figures 2.5 and 2.6. He also provided professional input and guidance regarding high speed measurement and feedback regarding the manuscript. Nicolas A . F . Jaeger provided input regarding the design of the measurement system and helped write the manuscript.  1  Chapter 1 Introduction  1.1 Literature Review and Motivation  Recent advances  in optoelectronic technology have resulted fiber optic  communications networks and systems with bandwidth in the tens-of-gigahertz.  The  realization of wide bandwidth systems has been achieved by the development of wide band optoelectronic devices, such as photodiodes or photoreceivers and electro-optic modulators.  For instance, the bandwidths of commercially available photodiodes  currently exceed 50 GHz [1-3] and of electro-optic intensity modulators exceed 40 G H z [4-6]. At present, electro-optic intensity modulators with bandwidths in the 100 G H z range are under development [7-9].  The interest in ultrawide band electro-optic  modulators is due to the simplicity of A M photodetection in intensity modulation and is currently the most popular scheme, as compared to phase, frequency, and polarization modulation [10]. Most commonly, the frequency responses of electro-optic intensity modulators are measured using a vector network analyzer (VNA) with a calibrated photodiode, or a lightwave component analyzer, see for example [11-14]. These analyzers provide a means to easily measure the modulator's characteristics such as its amplitude and phase response. These analyzers are costly, especially for frequencies of 50 GHz and above.  2 Therefore, wide band, cost effective methods need to be developed to. measure the frequency responses of these modulators. Besides the analyzers described above, several techniques that are used to measure the frequency responses of electro-optic intensity modulators can be found in the literature, but the measurements are limited to frequencies of 50 GHz and below [15-17]. In 1978, Shingo Uehara proposed a swept frequency technique to measure the frequency response of an electro-optic intensity modulator from 0.1 to 2 GHz. In the technique, an amplitude modulated RF sweeper was used to drive the device under test (DUT), and a crystal (square law) detector and a lock-in amplifier were used to measure the responses [15]. In  1989, Tan et al. reported an optical modulator frequency  response  measurement using a N d : Y A G ring laser heterodyne technique [16]. In the technique, the DUT was stimulated with a small RF modulation signal and was supplied an optical source from a laser.  A second laser was mixed with the D U T to down-convert the  sideband of the DUT to a constant RF frequency using a photodiode. The power of the signal at the constant RF frequency was then easily measured using an electrical spectrum analyzer. The frequency range of the system was limited by the bandwidth of the microwave sweeper used. Another electro-optic intensity modulator frequency response  measurement  system was suggested by Watson et al. in 1993 [17]. In the system, a Mach-Zehnder modulator biased at its minimum transmission point was used as both a mixer and a frequency doubler. The output of this modulator was used as an optical input to the D U T that was operated at its linear region and was driven by an RF signal from a microwave  3 sweeper. The response of the modulator was then measured in a lightwave component analyzer.  Again, the frequency range of the suggested system was limited by the  bandwidth of the microwave sweeper used. The system described in this thesis does not need a costly wide bandwidth microwave sweeper; instead, it uses optical heterodyning and a wide band photodiode to generate a millimeter-wave to drive a DUT. Moreover, the system has the potential to increase its frequency range by using a wider band photodiode to meet the continuing increase in the bandwidth of electro-optic intensity modulators.  4 1.2 Thesis Overview  Chapter 2 is a manuscript that has been submitted to the "IEEE Transactions on Microwave Theory and Techniques". In the manuscript, a novel system for measuring the frequency responses of electro-optic intensity modulators at millimeter-wave frequencies is presented.  High frequency measurements on both a 10 Gb/s Mach-  Zehnder type modulator and a 40 Gb/s mode converter type modulator are made. The optical fields at the output of an electro-optic modulator when it is biased, or operated, at three different points on its transfer function are derived. In addition, the harmonic rejection feature of the system is described, which "rejects" higher order harmonics generated by non-linearities in the DUT. Chapter 3 gives a summary of the work conducted, conclusions and suggestions for improving the performance of the measurement system and for reducing the cost of the system. Chapter 4 contains five appendices. Appendix A describes the generation of millimeter-wave using optical heterodyning.  Appendix B describes the design of the  frequency shifter used in the measurement system.  Appendix C describes how the  system "rejects" the higher order harmonics and the requirements of achieving the rejection property.  Appendix D shows how a V N A and a calibrated wide band  photodiode are used to measure the frequency response of an electro-optic intensity modulator. Appendix E compares the system dynamic range of the measurement system to that of the Agilent 8150C V N A used.  5  1.3 Supplementary Information on the Settings of the Measurement System  The power of laser 1 (Agilent 81682A, with option 3 *) was set at 6.5 dBm, which was its maximum setting for the wavelength range covered in the experiments to measure the two DUTs, starting at 1558.4280 nm. The power of laser 2 (Agilent 81682A, without option 3) was maximized to 8.273 dBm, at 1558.4200 nm. The microwave power of a 1 GHz signal generated at the output of the 55 GHz photodiode (manufactured by Discovery Semiconductor Inc.) was estimated to be ~ -8 dBm using an electrical spectrum analyzer. The two DUTs and the Mach-Zehnder modulator in the frequency shifter were both operated, or biased, at their minimum points to maximize the sensitivity of the system, as will be described in Chapter 2. The Mach-Zehnder modulator in the frequency shifter was a 10 Gb/s L i N b 0 modulator (serial #: 277-171L) manufactured by JDS 3  Uniphase Ltd. Its D C input voltage was set at ~ 2.6 Volts in order to bias it at the minimum point. The power and frequency of the signal that stimulated the modulator in the frequency shifter were 18 dBm and 2.4 GHz, respectively. The D C input voltages to the two DUTs were - 2 . 6 Volts (the 10 Gb/s modulator) and -12 Volts (the 40 Gb/s modulator), respectively. The  low frequency  photodiode  used  was  manufactured  by Discovery  Semiconductor Inc. (model number: DSC-30H). The two DUTs were a 10 Gb/s MachZehnder modulator (serial #: 325-662H) manufactured by JDS Uniphase Ltd. and a 40  * Option 3 is a 60 dB built-in variable attenuator that reduces the maximum power by ~ 1.5 dB.  6 Gb/s mode converter modulator (serial #:0059-R03) manufactured by J G K B Photonics Inc. The two wide band photodiodes used in the measurement system are as follows: 1. PIN diode (DSC 10H) ; Manufacturer: Discovery Semiconductor Inc. 1  2. Waveguide-integrated  photodetector  (XPDV2020R) ; 2  Manufacturer:  U T 2  Photonics Inc. The span, resolution bandwidth, and the video bandwidth of the electrical spectrum analyzer (Agilent E4407B) were set at 500 kHz, 10 kHz and 100 Hz, respectively, when the response data were taken.  1  2  This photodiode was used in the system to measure the | S  21  | of the 10 Gb/s modulator.  This photodiode was used in the system to measure the | S  21  | of the 40 Gb/s modulator.  7  References [1] T. S. clement, D. F. Williams, P. D. Hale, and J. M . Morgan, "Calibrating photoreceiver response to 110 GHz," National Institute of Standards and  Technology.  [2] " D C to 65 GHz wide bandwidth InGaAs photodiodes and photoreceivers," Application Note, D I S C O V E R Y SEMICONDUCTORS, New Jersey, March 2000. [3] "50 GHz High Responsivity" Preliminary Data Sheet, U T PHOTONICS, Berlin, 2  Germany. [4] N . Dagli, "Wide-bandwidth lasers and modulators for RF photonics," IEEE Tran. On Microwave  [5]  F.  Theory and Techniques, vol. 47, No. 7, pp. 1151-1171, July 1999.  Rahmatian,  ultrahigh-speed  N.  A.  F.  AlGaAs-GaAs  Jaeger,  R.  polarization  James,  and  converter  E.  Berolo,  using  "An  slow-wave  coplanar electrodes," IEEE Photon. Technol. Lett, vol. 10, pp. 675-677, 1998.  [6]  M . M . Howerton, R. P. Moeller, A . S. Greenblatt, and R. Krahenbuhl, "Fully  packaged, broad-band L i N b 0  3  modulator with low drive voltage," IEEE  Photon.,  Technol. Lett., vol. 12, pp. 792-794, Jul. 2000. [7] K . Noguchi, O. Mitomi, and H . Miyazawa, "Millimeter-wave T i : L i N b 0 optical 3  modulators," J. of Lightwave Technology, vol. 16, No. 4, pp. 615-619, 1998. [8] D. Chen, H . Fetterman, A . Chen, W. H . Steier, L . R. Dalton, W. Wang, and Y . Shi, "Demonstration of 110 GHz electrooptic polymer modulators," Appl. Phys. Lett., vol. 70, no. 25, pp. 3335-3337, 1997. [9] K . W. Hui, B. Y . Wu, Y. M . Choi, J. H. Peng, and K . S. Chiang, "Design of modified phase reversal electrode in broad-band electrooptic modulators at 100 GHz," IEEE Tran. On Microwave Theory and Techniques, vol. 45, No. 1, pp. 142-145, Jan. 1997.  8 [10] G. L . L i , and P. K . L . Y u , "Optical intensity modulators for digital and analog applications,"./ of Lightwave Technology, vol. 21, No. 9, pp. 2010-2030, Sep. 2003. [11] "MN4765A O/E Calibration module," Operation Manual, Anritsu, Morgan Hill, C A . [12] M . Matsumoto, "Fast electro-optical phase modulators completely measured in frequency and time domains," Electronics letters, vol. 25, No. 23, pp. 1569-1571, Nov. 1989. [13] "Agilent 8703B Lightwave Component Analyzer," Technical Specifications, Agilent Technologies, Palo Alto, C A . [14] "Agilent 8603 OA Lightwave Component Analyzer," Product Overview, Agilent Technologies, Palo Alto, C A . [15] S. Uehara, "Calibration of optical modulator frequency response with application to signal level control," Appl. Opt, vol. 17. pp. 68-71, 1978. [16] Tun S. Tan, Roger L . Jungerman, and Scott S. Elliott, "Optical receiver and modulator frequency response measurement with a N d : Y A G ring laser heterodyne technique," IEEE Tran. On Microwave Theory and Techniques, vol. 37, No. 8, pp. 1217-  1222, 1989. [17] C. D. Watson, D. A . Humphreys, and M . G. F. Wilson, "Calibration of optical modulators by optical down-conversion," IEEE Photonics Technology Letters, vol. 5, No. 9, pp. 1005-1007, Sep. 1993.  Chapter 2 Electro-optic Intensity Modulator Frequency Response Measurement  2.1.  Introduction  Ultrahigh speed electro-optic intensity modulators play an important role in wide band fiber optic communication systems. Modulators operating at speeds of 40 Gb/s are currently commercially available and modulators operating at speeds in the 100 GHz range are under development. These include modulators made in L i N b 0 [l]-[4], III-V 3  compound semiconductors [5]-[8], and electro-optic polymers [9]-[l 1]. As the frequency responses of optical modulators increase, cost effective methods by which to measure these responses need to be developed. Here we present a technique to measure the electro-optic | S | that uses optical heterodyning and a wide band 21  photodiode to make measurements at millimeter-wave frequencies. Optical heterodyning is used in the calibration of photodiodes and optical receivers as it offers the most accurate method for measuring their frequency responses [12]-[14]. In this method, a tunable laser is mixed with another laser at the photodiode to generate a beat frequency in the microwave regime. In our system, we heterodyne two lasers at a wide band photodiode to generate a millimeter-wave that drives the device under test (DUT). Clearly, two lasers that can be tuned to have a wavelength difference of ~1 nm have a difference frequency of -125 * A version of this chapter has been sumbitted to "IEEE Transcations on Microwave Theory and Techniques" for publication.  10 GHz at 1550 nm. Therefore, optical heterodyning can provide a cost effective method to do measurements at ultrahigh frequencies by eliminating the need for an ultrawide band microwave sweeper.  11  2.2. Optical Heterodyne, Down-conversion Technique Theory  Our system can measure the frequency responses of different types of electrooptic  intensity  modulators  such  as  Mach-Zehnder modulators,  mode-converter  modulators, electro-optic polymer modulators, and should be able to measure the frequency response of electroabsorption modulators. In what follows, we will develop mathematical expressions for the optical fields at the output of a Mach-Zehnder type modulator when it is biased or operated at its maximum, quadrature, and minimum points in a small-signal modulation analysis. Next, the system used to measure the frequency response of a D U T is presented, followed by a discussion of the harmonic rejection feature of our system.  2.2.1. Modulator Optical Signal  Here we assume a balanced electro-optic intensity modulator with the following transfer function, i.e., with zero intrinsic bias [15]  /„„,(,/) = /„ cos A 2  (1)  where I is the maximum output intensity, V is the half-wave voltage of the modulator, 0  and F i s the applied voltage given by  n  12  V = Vvc+y*F  (2)  or V = V +V w*&fJ). K  where V  is a D C voltage,  DC  (3)  m  is an RF voltage, F and / m  m  are the amplitude and the  frequency of the RF, or microwave, signal. Substituting equation (3) into (1), we find that the optical field at the output of the modulator can be written as  E  = 2 ^ l l ' J (V) = Iffl'l  cos(^ + ^ )  2  mt  •  c  J 1 e  *  (4)  where ju is the permeability of free space, e is the permittivity of the material, 0  KV  <I>DC  =  ^  7  7  ^  a  n  d  nV 0RF = ^  c  o  s  (  2  < « 0  o  r  nV i.e., M = —^,and  0RF =Mcos(2rfJ),  the frequency of the light. The term cos(<f> +^ ) DC  RF  can be expressed using Taylor  expansion and Bessel functions about the microwave frequency, f , m  see for example  [16]-[18],  cos(^ + ^ ) = c  cos^ {J (M) + 2£(-l)V „(M)cos[2«(2^ /)]} c  0  2  m  «=i  - sin </> {-2]T (-\yj _, (M) c o s h > - X)(2nf t)\} DC  2n  m  (5)  / is  13 where J is the Bessel function of the first kind of order n. n  For small-signal modulation (i.e., M«  1), we have  J (M)*l,  (6a)  0  J,(M)*M/2, J  (6b)  (M) » 0 for 1 < n < +oo,  (6c)  J _ , ( M ) « 0 for 2 < n < +oo .  (6d)  2n  and 2n  When the modulator is operated at its maximum point (i.e., <fi = 0, cos <j> -1, DC  DC  and sin <f> = 0), then equations (5) and (4) can be approximated, respectively, as DC  cos(0 +<p ) = \ DC  (7)  RF  and  E  out  =2 J ^ ' V V£  2  * =2 ^ I I ' \ £  2  cos(2#)  (8)  The optical signal at the output of the modulator consists of only one optical component at the frequency of the light source, f, and no first order sidebands are present.  14  When the modulator is operated at its quadrature point (i.e., <f>  DC  cos<j)  DC  = sin <p  =TT/4,  and  = 1 / V2), then equations (5) and (4) can be approximated, respectively,  DC  as cos(^  + <j) ) = - j = [1 - M c o s ( 2 ^ „ , 0 ] V2  DC  (9)  RF  and  E  \^LPJ <?  2  =^I [l-Mcos(2nfj)]e *' l ,2  oul  cos(2#)-  j2  n  V £  ^rj M{cos[2^f 2  + f )t]  + cos[2x(f-f )t]}  m  V 2f  A s can be seen in equation (10), the signal has an optical carrier at frequency / sidebands, one at / - f  m  and the other one at / + f . m  the amplitude o f the optical carrier, cos <j>  DC  the first sidebands,  sin^  D C  • J (M), 0  • J , ( M ) , increase.  (10)  m  A s <p  DC  and two  increases towards n 12,  decreases while the amplitudes o f  The amplitude increase i n the first  sidebands enhances the sensitivity o f our system, and the amplitude increases in other sidebands do not affect our measurement as they are "rejected", as w i l l be explained below. When  the  modulator  &DC = ^ / 2, cos fipc = 0, sin <p  DC  is  operated  at  its  minimum  point  (i.e.,  = 1), then equations (5) and (4) can be approximated,  respectively, as  cos(^  DC  +</> ) = -M cos(2nf t) RF  m  (11)  15 and E =-2^i: Mcos(2rfjy *' l2  2  oul  = -^I M{cos[2x(f  + f )t]  l n 0  m  + os[27r(f-f )t]} C  m  (12)  As shown in equation (12), the optical carrier is completely suppressed and the first sidebands are at the optical frequencies, / - f  m  and / + /„,.  Actually, the extinction  ratio of a particular modulator will place a limit on the amount to which the carrier can be suppressed. Nevertheless, the amplitudes of the first sidebands are the largest when the modulator is operated at this point. As can be seen in equations (8), (10), and (12), the amplitudes of the first sidebands are maximum and minimum when the D U T is operated at its minimum and maximum points, respectively.  Their amplitudes increase as the operating point is  changed from the maximum point to the minimum point in the transfer function. The increase in the amplitudes of the first sidebands enhances the sensitivity of our system as it measures the frequency response by shifting one of the first sidebands to a constant frequency in a low frequency photodiode and rejects higher order harmonics due to the non-linearities generated in the modulator. Thus, for an electro-optic intensity modulator with a transfer function such as that given in equation (1), our system gives the best or highest sensitivity when it is operated at its minimum point. Nevertheless, our system can easily measure electro-optic intensity modulators that are biased in their linear regime, with a small penalty as regards the sensitivity, for example, 3 dB at the quadrature point.  16  2.2.2. Frequency Response Measurement System  A schematic diagram of the system used to measure the frequency response of the modulator (DUT) is shown in Figure 2.1. Table 2.1 shows the optical and microwave frequencies present when the D U T is biased at any point other than its maximum point. The optical signals are labeled 1 to 5 and the microwave signals are labeled A to C, where the mixing of higher order harmonics is neglected.  (Note: In an improved,  dedicated system, all of the EDFAs and three of the polarization controllers could be eliminated.) Our system uses the outputs of the two lasers to generate a millimeter-wave signal to drive the DUT at the difference frequency  L = f  where f and f x  2  2  - f  (13)  are the frequencies of lasers 1 and 2, respectively. Appendix A shows  the details how a millimeter-wave signal can be generated by optical heterodyning. We also use a portion of the output of laser 1 as the optical input to the DUT, so that the output of the D U T has optical frequency components  f ,/j +f , x  m  and / , - / „ , .  Furthermore, we take a portion of the output from laser 2 as the optical input to the frequency shifter and shift its frequency by f  s  (the shift frequency) from f  2  to f - f . 2  s  When we combine this shifted optical signal with the signals at the output of the D U T using a 50/50-coupler, we obtain optical components at  f  2  - f ,f,f s  x  + /„,,  and  fi ~ fm • These optical signals are then mixed using a low frequency photodiode giving  17  Figure 2 . 1 . Schematic diagram showing the measurement system used. PC: Polarization Controller, A T T N : Optical Attenuator, WPD: Wide Band Photodiode, L P D : Low Frequency Photodiode, BPF: Optical Bandpass Filter, M Z : Mach-Zehnder TABLE I O P T I C A L A N D M I C R O W A V E FREQUENCIES A S IN FIG. 1  The optical frequencies in the fibers  The microwave frequencies in the cables A:/„  2:/  2  3 • f\ ~ fm>f\<f\ fm  fs'fm ~ fs' fm ^fm ~ fs 2-fm  *-fl-f.  fl ~ fs'f]  ~ fm'f]'f[  fm  18 down-converted components at f , f s  m  - f, f , s  2f  m  m  high frequency sideband of the D U T at / , + f - f  2  2  m  + f,  m  In particular, the  m  to give an electrical signal at (/, + f ) - (/  s  or rearranging, at (/, -f +f )  s  mixes with the constant optical field  m  from the frequency shifter at f  - f , and 2f .  s  or since (f  2  - f) = f , x  m  at f . s  -  2  f ), s  Therefore, we use  the term at the shift frequency, f , to measure the frequency response of the DUT. s  In the following, we show how the frequency response can be measured at the shift frequency.  The photocurrent resulting from heterodyning the signals from the  tunable lasers, when properly mixed at the wide band photodiode is given as  (14)  where P  ]m  and P  are the optical powers from the two lasers that reach the wide band  2m  photodiode, R  wpd  is the D C responsivity and p  wpd  is the frequency response of the wide  band photodiode. The D C term in equation (14) is constant and can be compensated for by adjusting the D C bias voltage. For small-signal modulation and neglecting the second and higher sidebands, the optical field at the output of the D U T , which is due to the heterodyne signal at f  can be written as  m  E  DUT  oc E  [cos0  oDUT  DC  J (M) - sin <j) J, ( M ) • cos(2^ 0]e 0  DC  m  and the optical field at the output of the frequency shifter can be written as  (15)  19  E  E  where  E  and  oDur  ofs  f  oc  j27t(f -f )l  E e  2  (16)  s  f  are the amplitudes o f the optical fields at the outputs o f the D U T  and the frequency shifter, respectively. Appendix B provides information on the design of the frequency shifter used. The following is a mathematical description o f the mixing o f the optical fields in the low frequency photodiode.  When the optical fields in equations (15) and (16) are  mixed i n the l o w frequency photodiode, the detected photocurrent is given as  hpd = lpdPlpd ( DUT R  where R  and p  lpd  lpd  + fs  E  E  • (E'DUT + fi ) E  )  (17)  are the D C responsivity and the frequency response o f the l o w  frequency photodiode, respectively.  Expanding equation (17) (and squaring i ), lpd  the  electrical power at the various frequencies is  Ipd •) = P Ipd Plpd 2  +  P  + P f ~f.  + P,  m  +P,2f,„-f,  (18)  <f> ]  (19a)  where  PDC *[Eo  +E  P  cc E  2  ODUR  E J (M)  2  L  J (M)cos  2  fi  2  oDUT  2  fi  <{>  2  0  sin + 2  x  +-E  J (M)sin  2  DC  cos(2^7)  2  ODUT  l  2  2  DC  20  sin 0  E  2  E  DC  fs  P .  ccE E J (M)cos 2  fm fi  2  our  2  E  fm  * ^^o(M)J * ^E  M  A  P  2  oDUT  o s j,* cos[2^r(/ 2  ra  fi  2 1  -f )t]  DC  c  oDur o  (19b)  cf> cos[2*(/„  2  fs  xE  P  cos(2^.0  2  ^ oDUT o M  K  s  (19c)  fjt]  (M)sin (2^ )cos(2# O 2  m  c  sin ( 2 ^ ) cos(2<t)  (19d)  2  c  =P 1fm-f,  Pi f„,  K  (19e)  fs  ODUT  E  sin (j) cos(4^ 0,  (19f)  4  "-^KDUTM*  m  DC  and the subscripts f , f s  - f, f  m  s  m  electrical signals P ,P _ ,P f  f  f  f  ,2 f  - f,  m  , P  2fi  s  _  and 2 f  m  are the frequencies of the detected  and P - , that are measured using the spectrum  f  2/  analyzer. The D C power, P , can be filtered out by a D C block. The term at f DC  A M signal. The terms at f  m  m  - f  s  and 2 f  m  - f  x  is the  are the down-converted components due  to the mixing of the output of the frequency shifter with the optical carrier at the output of the D U T and the mixing of the output of the frequency shifter with the lower frequency sideband at the output of the DUT, respectively. The term at 2 f  m  is due to the mixing of  the two sidebands. The term at the shift frequency, f , is due to the mixing of the output s  of the frequency shifter with the higher frequency sideband of the D U T and is proportional to M . M 2  2  gives the electrical frequency response of the D U T that we  21  want to measure, and | S the power at f  s  | is simply M  2  2]  properly scaled. A s shown in equation (19b),  is maximized when <j>  equals nil.  DC  This implies that the highest  sensitivity of our system can be obtained when the D U T is operated at the minimum point at which point the largest amplitude first sidebands are produced. obtained by normalizing the microwave power at f  s  21  2  with respect to that of the calibrated  electrical frequency response of the wide band photodiode. gives us the frequency response, | S  M c a n be  The normalized response  |, in dBe.  When the non-linear characteristics in the D U T are taken into account, the higher order harmonics are "rejected" by the optical field at the output of the frequency shifter. T o show how these harmonics are "rejected", the term cos(^ . +</> ) in equation (5) is /x  RF  expanded and substituted into equation (4), and the optical field at the output of the D U T is  {cos (j)  DC  - sin  [J ( M ) - 2 J ( M ) cos(47i/ 0  D C  m  2  0 + 2J  A  (M)  cos(8^  m  0-  ]  [2 J , (M) cos(2nf t) - 2 J ( M ) cos(67t/„ 0 n  + 2 J (M) cos(10<„0 5  3  }}e *' J2  (20)  When the optical signals in equations (16) and (20) are mixed in the low frequency photodiode, the electrical powers generated are given as  f,  p  x  4>DC cos(2^.0  EODUTEO/SJHM)*™  2  ^E  E M  2  2  ODUT  2  NFS  sin  2  (f)  DC  cos(2rf t) s  (21a)  22  p _ fm  KE; E;,JZ(M)CO  ft  DUT  <p c [ 2 ^ ( /  2 S  * oDUT o E  E  c  o  s  DC  P  -/,>]  m  cos[2^(/„ -./ .)r]  ^x-  2  fi  0S  (21b)  s  2/„,-A.  «:  (21c)  sin (2^ 2  £„ /r 4  X /  DC  + J (M)J (M) 2  ^y;„  s  i  n  3  M  + 2cos 0 J (M)J (M) 2  ^V„,  0 0  £ 0  V[  c  o  s  2  J+2  2  0DC ?/ ( ) J  M  2  + 2sin ^ . J ( M ) J 2  x  ]  + 2sin ^ J ( M ) J  / + 1  2  3  V»/„,  /, * lour l AiM) E  +  / + 3  E  f  2  (M)  M  ] -cosilmfj) • j (M)Jj(M)  +2sin (/> J {M)J,  2  3  y + 3  (M)  2  0  +2sin ^ J ( M ) J +2cos  (2 Id)  2  + 3  ( ) + 2cos ^  2  DC  x  0  +J (M)J, (M) +  L+2  ^ / r [  K  ) [ J ( M ) J , (M) + J (M)J  DC  (M) +  X  +1  ] • cos{2jgf t) (21e) 2  m  (/> J (M)J (M)  2  DC  ( M ) + 2cos  2  0  T  (f> J (M)J (M) DC  2  L+2  ] • cos{2jdf t)  (2If)  - c o s { 2 ^ P - l ) / +/,]}  (21g)  (M) +  2  m  m  and P, (  +1)/  „,_  « E  E Jl(M) 2  2  /s  ODUT  ofs  .cos{24(* + !)/„, - / J }  (21h)  where / = 1, 3 , 5, 7 , . . . , 7 = 2, 6, 10, 14, . . . , / = 4, 8, 12, 16, ... and  = 2, 3 , 4, 5 , ....  The D C power is not shown here as it can be filtered out by a DC block. Again, the term at the shift frequency, f,  in equation (21a) is the same as the term in equation (19b),  where the higher order harmonics are neglected. Nevertheless, they are both proportional to the electrical frequency response of the DUT, M . 2  The terms in equations (2Id),  (21e) and (2 If) are due to the mixing of the optical fields of the DUT itself. For example,  23  P „, « KomA  ( )? M  f  ()  J  M  Woe) cos(2# 0  s i n 2  m  sin ( 2 ^ ) c o s ( 2 r f j )  -KDUTM  2  (22)  2  /x  and «:^-[sin £*  (  ^ < / ( M ) +2cos ^ 2  2  /X  O C  J (M)J (M)] 0  2  2  DC  X  and [sin ^ 2  X  2  2  cos(4< 0 ;  cos(4^ r)  (23)  m  J ( M ) + 2cos ^ / ( M ) J ( M ) ] 2  D C  2  2  .[sin </> M / 4 +2cos ^ . J ( M ) ] 2  OU7  as J M)J (M) Q  2  2  / X  0  2  coefficients in equations (2Id) and (21e), respectively.  are the dominant  The higher order harmonics  generated in the DUT are shifted by the optical field at the output of the frequency shifter to frequencies of (k-\)f  m  +f , s  (21h). One can easily select f  m  is shifted to f . s  and (k + \)f  m  and f  s  -f ,  as shown in equations (21g) and  s  to ensure that none of the higher order harmonics  To do this, one must have f * s  —f, r m  where q and r are any integers  greater than zero. Appendix C shows how this requirement can be obtained in order to have none of the higher order harmonics shifted to f . s  This harmonic rejection means  that our system can measure the linear frequency response of the D U T even i f it is operated in a non-linear region.  24  2.3. Experimental Results 2.3.1. Wide Band Measurements  Frequency response measurements on both a 10 Gb/s L i N b 0 Mach-Zehnder 3  type modulator and a 40 Gb/s GaAs mode converter type modulator have been made. Laser 1 was swept from 1558.4280 nm and laser 2 was fixed at 1558.4200 nm, i.e., starting at a nominal 1 GHz difference. Both modulators were operated at their minimum points to obtain large amplitudes of the first sidebands. The shift frequency, f , was set s  at 2.4 GHz. The Mach-Zehnder modulator in the frequency shifter was operated at its minimum point to suppress the optical carrier and an optical bandpass filter was used to further suppress the carrier and to filter out the higher frequency sidebands. While not optimal, this frequency shifter was inexpensive to implement and was readily available. Nevertheless, an extremely small residual carrier remains. The response signals of the 10 Gb/s and the 40 Gb/s modulators at 1 GHz were about 32 dB and 37 dB above the residual power signal at f , respectively. s  For comparison purposes, Figure 2.2 shows the "uncorrected" frequency response of the 10 Gb/s modulator measured using our system from 1 to 65 GHz as asterisks, the "uncorrected" frequency response of the modulator measured using an Agilent 8510C vector network analyzer (VNA) from 45 M H z to 50 G H z as the solid curve, and the residual power signal as the dashed line.  By "uncorrected", we mean that the  measurement is not corrected by the frequency response of the wide band photodiode used.  Appendix D shows how the frequency response of an electro-optic intensity  modulator can be measured by a V N A . As can be seen, the two uncorrected responses  25 are in good agreement, but our system continues to give values above 50 GHz. Figure 2.3 shows the "corrected" frequency responses, M a n d | S 2  21  |, of the modulator up to 50  GHz. Figure 2.4 shows three measurements of the corrected frequency responses,  M, 2  of the 10 Gb/s modulator up to 60 GHz (the maximum frequency for which this wide band photodiode was calibrated). The repeatability was +/- ~1 dB.  3  1 i  •  i  —  -3  +  -6  I i  I i  measured using our system measured using the V N A residual power signal  —  -9 m T3  w  o m  -12 -15 -1B i  -21  1  -24  4- .  +  K .%  -27 -3D -33 -36 0  10  20  30  40  5D  6D  70  Frequency (GHz)  Fig. 2.2. Uncorrected frequency responses of the 10 Gb/s modulator measured using our system from 1 to 65 G H z and the V N A from 45 M H z to 50 GHz. The residual power signal of our system is shown as the dashed line.  26  3  i  I  0  i  i  i  —  measured using our s y s t e m measured using the V N A  1 1 1 1  i  -3 i i  -B -9  m •D  i \»  -12  "Ark  CM  cn -15 o  —  r  ±  1  L  1  -18  1  -21 -24  1 If  J  -27 -3D  •  10  15  20  25  3D  35  40  45  50  Frequency (GHz)  Fig. 2.3. Corrected frequency responses of the 10 Gb/s modulator measured using our system from 1 to 50 GHz and the V N A from 45 M H z to 50 GHz.  27  28 Next, the frequency response of the 40 Gb/s modulator was measured using our system with a different wide band photodiode; this was the photodiode that was used by the modulator manufacturer to measure | S | using a 65 G H z V N A (Anritsu 37397C). 21  Figure 2.5 shows the uncorrected response of the 40 Gb/s modulator measured using our system from 1 GHz to 78 GHz as asterisks, the uncorrected frequency response measured using the 65 GHz V N A as the solid curve, and the residual power signal as the dashed line.  Again, the two measurements are in good agreement.  The response of the  modulator measured using our system continues to roll off up to 78 GHz, at which frequency the response power was ~2 dB above the residual power signal. Figure 2.6 shows the corrected frequency responses, M  2  and | S |, of the modulator up to 50 GHz 21  (the maximum frequency for which this wide band photodiode was calibrated). Both responses show the 3-dB electrical point at -45 GHz.  29  3 D -3 -6 -9 -12 -15  S -1B -a — -21 §  -24  £  -27 -3D -33 -36 -39  +  measured using our system measured using the VNA residual power signal  -42 -45 -40 D  10  20  30 40 50 Frequency (GHz)  60  70  BO  Figure 2.5. Uncorrected frequency responses of the 40 Gb/s modulator measured using our system from 1 to 78 G H z and the V N A from 40 M H z to 65 GHz. The residual power signal of our system is shown as the dashed line.  30  1  Wig  .  •a  1  "  1  i  measured using the V N A 1 1 1 l l l  h f \J \ *  m  I  measured using our system  1 I  1  •*-  3  fflWte  \  O  LU  -B  -12  0  15  20  25  30  Frequency  (GHz)  35  40  45  50  Figure 2.6. Corrected frequency responses of the 40 Gb/s modulator measured using c system from 1 GHz to 50 GHz and the V N A from 40 M H z to 50 GHz.  31 2.3.2. Harmonic Rejection  As discussed previously, one important feature of our system is that it rejects higher order harmonics generated in the DUT. When the D U T is modulated by a signal with the difference frequency, f , m  higher harmonics are shifted to frequencies of (k -1) f  +f  m  s  and (k + Y)f - f m  s  the  where k  = 2, 3, 4, 5, ... and is the order of the harmonic as shown in equations (21g) and (21h). As an example, Figure 2.7 shows the spectrum of the detected electrical signals using a 25 GHz photodiode as the "low frequency" photodiode, a wide band electrical spectrum analyzer and a DC block when f  m  equals 10 GHz. The DUT is biased in its linear region  to obtain higher amplitudes of the rejected signals. As can be seen, the signals labeled (a) and (e) are the frequency response of the D U T at frequencies f  s  equations (21a) and (21c)). Signal (b), at f  m  - f, s  and 2 f  m  - f  s  (see  is due to the mixing of the carrier at  the output of the D U T and the optical field at the output of the frequency shifter, see equation (21b). (c) is the A M signal of the D U T at f , m  shifted second harmonic signal at f  m  (f), at 2 f , m  +f  s  see equation (22). (d) is the  (see equation (21g) when k = 2), and signal  is mainly due to the mixing of the carrier and the second sidebands of the  DUT and the mixing of the two first sidebands of the DUT (see equation (23)). Signal (f) is large as a result of a large second harmonic generated by the wide band photodiode used.  32  -20  1  i  i  1  •  (c)  -30 E in T3  OJ CO  -40  o  Q-  ^  (f)  (b)  03 OJ  -50  i  ----  -—  OJ  o CL  |  -60  (e)  ;  (a)  cu  QL  (d)  -70  -80  i  i  i  i  i  8  Figure 2.7. Detected signals for f  m  (=2.4 GHz); b) f  m  10 12 14 Frequency (GHz)  (=17.6 GHz); f) 2 / (=20 GHz). m  1  16  18  20  equals 10 GHz. The detected signals are at a) f  s  -/ (=7.6 GHz); c) /„,(=10 GHz); d) f v  1  m  +/,(=12.4 GHz); e) 2/„,  33 2.4 Conclusion In this paper we have presented a novel system for measuring the frequency responses of electro-optic intensity modulators at millimeter-wave frequencies.  High  frequency measurements on both a 10 Gb/s Mach-Zehnder type modulator and a 40 Gb/s mode converter type modulator have been made. We have also derived the optical fields at the output of an electro-optic modulator when it is biased or operated in three different points in its transfer function. We showed that the sensitivity of our system is the highest when the D U T is operated at its minimum point. The electrical frequency responses measured using our system were in good agreement with | S 1 measurements using vector 21  network analyzers with calibrated wide band photodiodes.  In addition, the harmonic  rejection feature of the system was described. With proper selection of f  m  and f , x  our  system rejects higher order harmonics due to the non-linearities generated in the DUT. Our system's frequency response is primarily limited by two factors.  One is the  frequency response of the wide band photodiode used and the frequency to which it is calibrated. The second is the system's dynamic range. Nonetheless, an improved design should be capable of increasing the signal strength and reducing the residual power at the output of the frequency shifter, enhancing the system's dynamic range.  34  References [1] Kazuto Noguchi, Osamu Mitomi, and Hiroshi Miyazawa, "Millimeter-wave Ti : L i N b 0  3  optical modulators," J. of Lightwave Technology, vol. 16, No. 4, pp. 615-  619, 1998. [2] M . M . Howerton, R. P. Moeller, A . S. Greenblatt, and R. Krahenbuhl, "Fully packaged, broad-band L i N b 0  3  modulator with low drive voltage," IEEE  Photon.,  Technol. Lett., vol. 12, pp. 792-794, Jul. 2000. [3] K . Noguchi, O. Mitomi, H . Miyazawa, and S. Seki, " A broadband T i : L i N b 0  3  optical modulator with a ridge structure," Journal of Lightwave Tech., vol. 13, pp. 11641168, Jun. 1995. [4] W. K . Burns, M . M . Howerton, R. P. Moeller, A . S. Greenblatt, and R. W. McElhanon, "Broad-band reflection travelling-wave L i N b 0  3  modulator," IEEE Photon.  Technol. Lett., vol. 10, pp. 805-806, Jun. 1998.  [5]  F.  Rahmatian,  ultrahigh-speed  N . A . F.  AlGaAs-GaAs  Jaeger,  R.  polarization  James,  and  converter  E.  Berolo, " A n  using  slow-wave  coplanar electrodes," IEEE Photon. Technol. Lett, vol. 10, pp. 675-677, 1998.  [6] R. Spickermann, S. R. Sakamoto, M . G. Peters, and N . Dagli, "GaAs/AlGaAs traveling wave electrooptic modulator with electrical bandwidth greater than 40 GHz," Electron. Lett., vol. 32, pp. 1095-1096, Jun. 1996.  [7] T. Ido, S. Tanaka, M . Suzuki, M . Koizumi, H . Sano, and H. Inoue, "Ultra high-speed multiple quantum well electroabsorption optical modulators with integrated waveguides," J. Lightwave Tech., vol. 14, pp. 2026-2034, Sept. 1996  35 [8] K . K . Loi, X . B . Mei, J. H . Hodiak, C. W. Tu, and W. S. C. Chang, "38 G H z bandwidth 1.3 U m M Q W electroabsorption modulators for RF photonic links," Electron. Lett., vol. 34, pp. 1018-1019, May 1998. [9] D. Chen, H . Fetterman, A . Chen, W. H . Steier, L . R. Dalton, W. Wang, and Y . Shi, "Demonstration of 110 GHz electrooptic polymer modulators," Appl. Phys. Lett., vol. 70, no. 25, pp. 3335-3337, 1997. [10] D. Chen, D. Bhattacharya, A . Udupa, B. Tsap, H . R. Fetterman, A . Chen, S. Lee, J. Chen, W. H . Steier, and L. Dalton, "High-frequency polymer modulators woth integrated finline transitions and low V p i , " IEEE Phot. Tech. Lett., vol. 11, Jan. 1999.  [11] W. Wang, D. Chen, H . R. Fetterman, Y . Shi, W. H . Steier, and L . R. Dalton, "60 GHz polymer electro-optic phase modulators," in Proc. 1995 Dig. LEOS Summer Topical Meet., RF Optoelectronics, WC2, pp. 5-6, Aug. 1995. [12] Tun S. Tan, Roger L . Jungerman, and Scott S. Elliott, "Optical receiver and modulator frequency response measurement with a N d : Y A G ring laser heterodyne technique," IEEE Tran. On Microwave Theory and Techniques, vol. 37, No. 8, pp. 1217-  1222, 1989. [13] R. Thomas Hawkins II, Michael D. Jones, Steven H . Pepper, and Jeffery H . Goll, "Comparison of fast photodetector response measurements by optical heterodyne and pulse response techniques," J. of Lightwave Technology, vol. 9, No. 10, pp. 1289-1294, 1991. [14] P. D. Hale, T. S. Clement, and D. F. Williams, "Frequency response metrology for high-speed optical receivers," NIST, OFC, Mar. 2001.  36 [15] Osamu Mitomi, Kazuto Noguchi, and Hiroshi Miyazawa, "Estimation of frequency response for high-speed L i N b 0  3  optical modulators," IEE Proc. -Optoelectron.,  vol.  146, No. 2, pp. 99-104, April 1999. [16] Frank Bowman, "Introduction to Bessel functions," Dover, N Y , 1958. [17] George B. Arfken, and Hans J. Weber, "Mathematical  methods for physics ts,"  Harcourt, San Diego, 2001. [18] C. J. Tranter, "Bessel functions  Universities Press LTD., London, 1968.  with some physical  applications"  The English  37  Chapter 3 Summary, Conclusions, and Recommendations for Future Work  3.1. Summary and Conclusions  A wide band, cost effective system for measuring the frequency responses of electro-optic intensity modulators in the millimeter-wave regime has been described. The theory on which the system is based has also been described, and measurements on two high-speed electro-optic intensity modulators, including a 10 Gb/s L i N b 0  3  Mach-  Zehnder type and a 40 Gb/s GaAs mode-converter type modulator, have been made up to 65 and 78 GHz, respectively. The optical field expressions at the output of the modulator when it was operated at three different points on its transfer function have been presented. It was shown that the highest sensitivity of the system could be obtained by operating, or biasing, the DUTs at their minimum points.  In addition, the harmonic  rejection feature of the system and the requirements for achieving the harmonic rejection have been described. The technique for measuring the frequency response of an electrooptic intensity modulator using a vector network analyzer has also been presented. The cost effective aspect of this measurement system has been achieved by using the method of optical heterodyning. Instead of using a costly wide bandwidth microwave sweeper to drive the D U T at millimeter-wave frequencies, the method of generating a millimeter-wave by mixing two tunable lasers in a wide band photodiode has been used.  38 The frequency response of the system is limited by the frequency response of the wide band photodiode used in the optical heterodyning and the frequency to which it is calibrated. Moreover, a wide band microwave amplifier is not required to increase the power of the millimeter-wave signals generated in order to make the wide band measurements, which is a costly component. Finally, all of the EDFAs and three of the polarization controllers could be eliminated in an improved and dedicated system, as will be explained in section 3.2. Moreover, the need of an electrical spectrum analyzer could also be eliminated. Eliminating these components would further reduce the overall cost of the system. The system has shown the ability to make wide band measurements on both a Mach-Zehnder and a mode converter modulator. The experimental results showed the frequency responses of a 10 Gb/s and a 40 Gb/s modulator up to 65 GHz and 78 GHz, respectively. These frequency ranges are wider than those measured using the V N A s . To further increase the frequency range of the system as the speed of the modulators continuous to increase, the system needs only to use a photodiode with a wider bandwidth.  Photodiodes with bandwidth of 75 GHz are currently commercially  available. Such photodiodes should allow measurements approaching, i f not exceeding, 100 GHz. In addition, the frequency responses measured by the system have been in close agreement with the responses measured using the two V N A s .  Furthermore, the  system has a higher dynamic range than that of the V N A s , as is described in Appendix E. In conclusion, the experiments indicate that the system can measure the frequency responses of electro-optic intensity modulators in the millimeter-wave regime.  The  system provides a wide band, cost effective method to measure accurately the frequency  39 responses of the modulators. It also has the potential to increase its frequency range by using wider band photodiodes.  40  3.2. Recommendations for Future Work  There are three main recommendations for improving the performance and for reducing the cost of the measurement system. They are, designing a better frequency shifter, using polarization maintaining (PM) 50/50 optical couplers, and eliminating the electrical spectrum analyzer. The first recommendation is to design a better frequency shifter so that it can output optical fields with both higher power and higher signal-to-noise ratio (SNR). The increase in both power and SNR of the optical field at the output of the frequency shifter can strengthen the frequency response signal and, in turn, increase the frequency range of the system. Possible frequency or wavelength shifters can be found in the literature, see for example [1-2]. The second recommendation is to use three polarization maintaining optical couplers to replace the two single mode 50/50 optical couplers connected to the lasers and the one used for the optical heterodyning. This would eliminate the need for three of the polarization controllers used in the system and preserve more optical power for heterodyning. Moreover, the sensitivity of the system would be enhanced since more microwave power would be generated by the wide band photodiode. The last recommendation is to develop an electrical signal measurement system to replace the electrical spectrum analyzer used in the system.  A possible design is to  down-convert the response signal at the shift frequency to an IF frequency signal using an RF mixer. A n electrical amplifier is needed to boost up the power of the IF signal and the signal at the IF frequency can be easily measured using a voltmeter.  The other  41  suggestion is to measure the response signal at the shifter frequency using a square law detector and a voltmeter. Moreover, developing an automated GPIB/HPIB data acquisition system using LabView would reduce the time to collect the response data. Using a local oscillator that outputs a signal at the shift frequency to replace the R F source used in the system would further reduce the cost of the system. For further research in this field, the development of a system to measure the phase response of the electro-optic intensity modulators is recommended [3]. would be able to fully measure an electro-optic intensity modulator's S develop a phase response measurement system.  21  Users  if we could  It is believed that the design of this  system would provide strategy or clues to the design of the phase response measurement system.  42  References [1] S. T. Winnall, A . C. Lindsay, and G. A. Knight, " A wide-band microwave photonic phase and frequency shifter," IEEE Tran. On Microwave  Theory and Techniques, vol. 45,  No. 6, pp. 1003-1006, Jun. 1997. [2] F. Agullo-Lopez, J. M . Cabrera, and F. Agullo-Rueda, Electrooptics Phenomena. Materials and Applications, Academic Press, Inc., London, Great Britain, 1994, pp.198 [3] Private discussion with Dr. Nicolas A. F. Jaeger.  43  Appendices  Appendix A: Optical Heterodyning  A n optical heterodyning system uses a pair of tunable lasers, a polarization controller, a 50/50 optical coupler and a wide band photodiode.  Figure A . l shows an  optical heterodyning system. The polarization controller is used to adjust the orientation of the polarization angle in one fiber so that it aligns with the polarization angle in the other fiber.  Laser  1 Microwave  Laser  ^^^^M  2  : Optical  Fiber  : Cable/Microwave  Cable  Figure A . l . A setup of an optical heterodyne system. PC: Polarization Controller, WPD: Wide band Photodiode.  44 The following mathematical description shows how a microwave or a millimeterwave can be generated in the system shown in Figure A . 1. The operating wavelengths and the corresponding frequencies of lasers 1 and 2 can be related by the following expressions,  and  where / j and f  2  are the optical frequencies, A\ and A are the operating wavelengths of 2  lasers 1 and 2, respectively, and c is the speed of light. The optical fields at the output of lasers 1 and 2, E and E , can be expressed as x  2  E (t) = A e  J  x  x  and E (t) = A e 2  2  respectively, where A and A are the amplitudes of the lasers. At the output of the wide x  2  band photodiode, the photocurrent can be expressed as,  i = R cP( \ E  D  +E )-(El 2  +E* ). 2  45 Substituting the expressions of the optical fields, E and E , into the equation above, the x  2  photocurrent, i, at the output of the wide band photodiode can then be expressed as  i = R {A DC  + A] + 2pA A [cosC2nfj)  2 X  1  + cos(2u/»]},  2  or  / = R [P P +2-pDC  ]+  where P = Af and P = x  A  2  Jp\P • cos(2^„,0]  2  2  [1] are the optical powers that reach the wide band  photodiode from lasers 1 and 2, R  DC  and p are the D C responsivity and the calibrated  frequency response of the wide band photodiode, respectively, f  m  frequency, i.e., f  = f ~f ,  m  frequencies, i.e., f  }  s  or f  2  m  = /, +/ .  = f ~f\, 2  and f  s  is the difference  is the sum of the two optical  Since the frequency response of the wide band  2  photodiode, p , approaches zero as the frequency is in the terahertz range, 2pA A x  2  cos(2nfJ),  frequency, f , m  (f  x  is zero.  the term,  In the system described in Chapter 2, the difference  is achieved by keeping A constant (f 2  is decreased). Therefore, f , m  is expressed as  fm  =  fi ~ f\ •  2  is constant) and increasing X\  46 Appendix B: The Frequency Shifter  The frequency shifter used consists of a Mach-Zehnder modulator and an optical bandpass filter made up by cascading two Bragg grating fdters. The shifter generates an optical signal to down-convert the higher frequency first sideband of the D U T to a constant microwave frequency, at which the response signal is measured. Moreover, it "rejects" higher order harmonics generated by the DUT. The frequency shifter used in the system was inexpensive to implement and readily available in our laboratory. Figure B.1 shows a diagram of the setup of the frequency shifter used in the measurement system.  RF  Source  — — O p t i c a l  Fiber  : Cable/Microwave Cable Figure B.1. Diagram showing the setup of the frequency shifter used in the measurement system.  1: optical frequency ( / ) , 2: shifted optical frequency ( / 2  frequency (f ), s  M Z : Mach-Zehnder, BPF: Optical Bandpass filter.  2  - f ), s  A : the shift  47 The Mach-Zehnder used in the frequency shifter was a 10 Gb/s L i N b 0  3  modulator. It was driven by a 18 dBm, 2.4 GHz signal. The modulator was operated, or biased, at its minimum point to maximize the amplitudes of the first sidebands and to suppress the carrier. The center wavelength of the cascaded Bragg grating filters was measured to be at -1558.58 nm and the 3-dB pass-band of the filters was measured to be -1558.47 nm to -1558.66 nm, see Figure B.2.  Figure B.2. The 3-dB pass-band of the filter was measured to be -1558.47 nm to -1558.66 nm.  48 The pass-band of the filter was used to determine the setting of the operating wavelength of the laser (laser 2) that supplied an optical source to the frequency shifter. The operating wavelength of laser 2 was set so that the lower frequency first sideband optical field of the Mach-Zehnder was passed while its carrier and its higher frequency first sideband were filtered out. The use of two cascaded Bragg gratings provided better filtering of the carrier so that the power due to the mixing of the residual carrier and the lower frequency first sideband was minimized at the shift frequency, f . s  Nevertheless,  the lower frequency first sideband, the residual carrier and the other higher order sidebands that were passed mixed with the optical fields at the output of the DUT. One can easily select f  s  and f  m  to ensure that none of higher order harmonics that are due to  the mixing of these sidebands with the optical field at the output of the D U T is shifted to f , as will be explained in Appendix C below. s  Figure B.3 shows the spectrum of the optical components from the frequency shifter and the D U T (the 10 Gb/s modulator) for a difference frequency of ~30 GHz. Figure B.4 shows the system that is used to obtain the optical fields shown in Figure B.3.  49  0 -5 fi"  -10 -15 m T3  -20 (b)  CD  AmpI  "a -25 (a) -3D -35 -4D  /  I  -45 -50 1558.2  1558.3 155B.4 155B.5 1558.B 1558.7  155B.8 1558.9  1559  1559.1  Wavelength (nm)  Figure B.3.  Spectrum of the optical components from the frequency shifter and the D U T .  a) The component from the frequency shifter, b) the high frequency sideband from the D U T , c) the low frequency sideband from the D U T , d) the optical carrier from the D U T . (Setting of the A N D O A Q 6 3 1 7 B optical spectrum analyzer: R B W = 0.01 nm, Span = 1 nm)  50  Figure B.4. Diagram showing the system used to obtain the optical field shown in Figure B.3.  51 The optical spectrum shown in Figure B.4 was obtained using an A N D O AQ6317B optical spectrum analyzer. The wavelength of laser 2 was set at -1558.42 nm. As can be seen, the optical field at the output of the frequency shifter can be found at -1558.45 nm, that is approximately equal to the wavelength of the lower frequency first sideband of the frequency shifter, i.e., the sum of 1558.42 nm and the shift frequency (2.4 GHz = 0.02 nm). The wavelength offset of about 0.01 nm is due to the offset of the laser and the optical spectrum analyzer. The optical carrier and the two first sidebands of the D U T can be found at -1558.66 nm, and -1558.90 nm and -1558.42 nm.  The  difference frequency can be confirmed using this equation,  where A, is the wavelength of the optical carrier of the D U T (or the operating wavelength of laser 1), and A is the wavelength of one of its first sidebands. s  The  coefficient, 1.25/0.01, denotes the conversion ratio of the electrical frequency in gigahertz to the wavelength in nanometer for X\ « 1550 nm.  52 Appendix C : Harmonic Rejection Requirements  As stated in Chapter 2, the measurement system can "reject" higher order harmonics, due to the non-linearities, generated in the DUT. This appendix describes how the higher order harmonics are rejected and lists the requirements for achieving the rejection property. When the D U T is driven by an RF, or microwave, signal with the difference frequency, f , m  and the optical input to the D U T is supplied by a light source with the  optical frequency, f , x  the optical frequencies of the sidebands and the carrier at the  output of the D U T are / , - 2 / „ , /,-3/„, /,-4/  fi+4f ,  /, +3/„„  m  f f l  (see equation (20) in Chapter 2).  , or f ±nf , x  / , +2f , m  /, + / „ , / „  /j - / „ ,  where n = 0, ± 1 , ± 2 , ± 3 , ± 4  m  At the output of the frequency shifter, the lower  frequency first sideband at optical frequency, f - f , 2  s  and other sidebands at f - kf , 2  s  where k is any positive integers, are produced. Table C l shows the frequencies of the electrical signals at the output of the low frequency photodiode generated due to the mixing of the optical fields at the output of the frequency shifter with the optical fields at the output of the DUT. Note that the optical fields at f  2  - kf are negligibly small and s  are not shown for k > 4. The optical fields with frequencies greater than f +2f x  optical fields with frequencies less than f -2f x  since they are also negligibly small.  m  m  and  at the output of the DUT are not shown  53  \  Frequencies of \ the signal \ at the \ output of \ the \ DUT fi+2f  m  fx  +L  f  f  f  2f  f -f  2f -f,  fm  f~2fm  Frequencies \ of the signal \ at the output of\ the frequency \ shifter \ fi  -f  DC  fl-fs  - f -f  f  Jm Js  m  3/.  m  fi-2f  -L-^f  2f  2fm-2f  2f.-2f,  fi-lf  -f -2f  If  *f -3f,  2fm-Vs  fi-*f,  -f -*f,  4/,  2fm~4f  2fm~4f  m  m  m  Table C . l . Table showing the frequencies of the electrical signals at the output of the low frequency photodiode generated due to the mixing of the optical fields at the output of the frequency shifter with the optical fields at the output of the DUT.  54 According to Table C l , all of the electrical signals in the second column will not be at f if f * f . The frequencies of electrical signals in the third column will not be s  s  m  at the shift frequency, except the one that measures the frequency response of the DUT. In the fourth column, the frequencies of the electrical signals generated can be expressed as f - kf , where k is any positive integers greater than or equal to zero. Here, the m  s  electrical signals will not be at the shift frequency, f , if f *—f . Therefore, to reject s  s  m  k  1  2  these signals, one must select f *—f . Similarly, one must select f * — f s  k  m  s  3  fifth column. For the last column, one must select f * — f x  m  k  m  for the  to reject the higher order  k  harmonics. Therefore, in general, one must select f *—f , where q and r are any s  m  r  integers greater than zero, to ensure that none of the higher order harmonics is shifted to  55 Appendix D: Electro-optic Intensity Modulator Frequency Response Measurement using Vector Network Analyzer  A V N A can measure the magnitude and phase characteristics of networks and of components such as filters, attenuators and antennas.  Also, it is commonly used to  measure S  To do that, the V N A is first  21  of an electro-optic intensity modulator.  calibrated to remove unwanted effects of the cables and other components in the measurement path. Once the calibration is performed, a measurement setup, shown in Figure D . l , is used to measure the frequency response of a DUT.  WPD • p"tical  Fiber  Cable/Microwave  Cable  Figure D . l . The measurement setup used to measure the frequency responses of the DUTs in chapter 2. WPD: Wide Band Photodiode.  56 The following shows a mathematical description of how the frequency response of a DUT is measured using a V N A . Here we assume a balanced electro-optic intensity modulator with the following transfer function, i.e., with zero intrinsic bias [2]  nV / ,(F) = / c o s ( — )  (1)  2  ou  0  where I is the maximum output intensity, V is the half-wave voltage of the modulator, a  n  and F i s the applied voltage given by  V =V  DC  where V  is a D C voltage, V  DC  RF  +V  RF  =V  DC  + V cos(2<0  (2)  m  is an RF voltage, V and f m  m  are the amplitude and the  frequency of the RF, or microwave, signal. Substituting equation (2) into (1), the optical field at the output of the modulator can be expressed as  E  oul  where ju  0  =2]^l)!J(V)  = l]^Ll)!  2  cos(^ . x  +  0 )-e^  (3)  RF  is the permeability of free space, s is the permittivity of the material,  nV <I>DC =^f~  and ^  nV = - i c o s ( 2 ^ 0 or <f> =Mcos(2rfJ), m  RF  TTV  i.e., M = ^  ,  and /  57 is the frequency of the light. The term cos(c# + <p ) can be expressed using Taylor DC  RF  expansion and Bessel functions about the microwave frequency, f , see for example [3m  5],  cos(^  DC  + <V) = cos <f> {J (M) + 2]T (-1)" J DC  0  2n  (M) cos[2«(2^ r)]} ra  n=\ +00  - sin ^  { - 2 ^ (-1)"J _ (M) cos[f> -1)(2^„,0]} 2n  x  (4)  where J is the Bessel function of the first kind of order n. n  From equations (3) and (4), the optical field at the output of the modulator can be expressed as  E  =2^/: {cos^[J (M)-2J (M)cos(4<,0 / 2  DUT  0  2  +2J (M)cos(8<,,0-  - sin fa [2J (M) cos(2<0 - 2J (M) cos(6^„,0 + 2 J (M) cos(l Oxfj) X  3  5  ]  4  ]} •  (5)  The photocurrent at the output of the wide band photodiode, due to the optical field in equation (5), is  ipd  and the voltage is  nd Ppd ( DUT  =R  E  • DUT E  )  ( ) 6  58  V  - Y^T  ?°  =  *- *-  (VLX  ^pdPpd  + V  + V  + V  ^  }  ( 7 )  b  where  V  Vm  = s i n ( 2 ^ ) [ J ( M ) J , (M) + J, (M)J x  0  ( M ) + J (M)J  M  2  + J (M) J 3  V  jfm  = [sin^ .J /x  2 y  /2  F  2  = [cos0 J (M) DC  c  k/2  DC  + 2cost J (M)J (M) DC  2  3  + 2cos0 J (M)J (M)  2  %  +2sin^ J (M)^  J+2  m  DC  + 3  +  k  (M) +  DC  jf , m  and kf  m  i  (8)  J+]  ]• cos(2^/ 0  (9)  ra  2sm0 J,(M)J (M) DC  + 2sm</> J (M)J (M)  k+2  and the subscripts, DC, if ,  o  ] • cos(2mfj)  2sin(j) J,(M)J (M)  0  + 2cos<p J (M)J (M) oc  (M) +  i+3  (M) + 2cos^ . • J ( M ) J . ( M ) + x  (M)  l+2  +  k+i  k+]  ]• cos(2nkf t),  (10)  m  are the frequencies of the voltages, i = 1,3,  5, 7 , . . . , / = 2, 6, 10, 14, ....and* = 4, 8, 12, 16, .... The V N A measures 4 — I V 0  f  (/  8  = 1) at its receiving port and the voltage to the D U T , V , at its output port. jn  The  V relationship, 20 • l o g — - , gives | S | in dBe. To obtain the highest signal strength, the f  21  ^in  DUT is best operated at its quadrature point (i.e.,c# = TT 14) on its transfer function such /x  that the term, sin(2t^ ), is maximized in equation (8). /x  59  Appendix E: Comparison of the System Dynamic Range of our System to that of a VNA  Here we compare the system dynamic range (SDR) of our measurement system and that of the 50 GHz Agilent 8510C V N A (microwave section: 85107B) that was used to measure the | S  21  | of the 10 Gb/s modulator in Chapter 2. (Note that both our system  and the V N A used the wide band photodiode manufactured by Discovery Semiconductor Inc.) The SDR is the amount of attenuation that can be measured from a 0 dB reference [6]. For the V N A and our system, it is the difference of the power at the output point, P , and the minimum power that can be measured above the noise floor at the receiving ref  point, P  mjn  , i.e., SDR = P  ref  -P  m i n  measured at the output port and P and P  min  in dB [6]. For the 50 G H z V N A , P min  ref  is the power  is the noise floor of the V N A ; for our system, P  ref  are the power generated in optical heterodyning and the residual signal power,  respectively. The SDR of our system is -82 to -79 dB for modulation frequencies below 55 GHz (this is the 3-dB frequency of the wide band photodiode and the maximum frequency for which the wide band photodiode was calibrated). On the other hand, the SDR of the 50 G H z V N A is between 60 dB and 89 dB depending on the modulation frequency [6]. Figure E . l shows the SDR of our system as the asterisks and that of the V N A as the solid curve. As can be seen, the SDR of our system decreases by only 3 dB over the frequency range and is higher than that of the V N A for frequencies above -20 GHz. The SDR of the V N A decreases by 29 dB over its 50 GHz span, and the decrease is due to the decrease of P . This decrease in P , and thus is the SDR, degrades the ref  ref  60 V N A ' s performance over the frequency. The SDR of the Agilent new 110 GHz model N5250A performance network analyzer (PNA) is also shown as the dashdotted curve in Figure E . l , which has a high SDR over the 110 GHz span. Our system could have the similar SDR as that of the 110 GHz P N A i f a wider band photodiode was used for the optical heterodyning.  120  1  •*• \  100  \  m T3 CD d CB CE  CB  - --  N  8D  60  our system the V N A the P N A  \  Q  B  40  20 V-  20  40  60  B0  100  120  Frequency (GHz)  Figure E . l Our system showing a higher system dynamic range than that of the 50 GHz V N A . The system dynamic range of the 110 GHz P N A is also shown.  61  Figure E.2 shows how the decrease of P , and thus the SDR, affects the ref  frequency range of the measurement using the 50 GHz V N A . When the laser shown in Figure D . l , in Appendix D, is turned off, the measured | S in Figure E.2. Since P  ref  2]  | is shown as the dotted curve  decreases by 29 dB, while the power at the receiving port is  nearly constant (this power is due to the dark current at the output of the wide band photodiode), the measured | S figure.  21  | for which the laser is off increases as shown in the  The dotted curve increases as frequency increases and it meets the frequency  response of the D U T shown as the solid curve at ~ 45 GHz. Therefore, the measured, uncorrected frequency response of the D U T beyond ~ 45 GHz is overshadowed by the dotted curve. In contrast, the frequency response of the D U T measured using our system shows continual roll-off beyond 50 GHz as a result of the virtually constant power output from the wide band photodiode.  62  10  -10 h -20 rCD  I  S . -30 CO  o  if. * ii 1 >ll.'  1  -40  * I '! ' 1  'iii .*  i ' i i!  1  LU  -50  1 1 i  I S< IJ-KJ  i  i&l  : >i ; • ;;<: tf'fUntf  -BO If«4'*J«.^a,t - i 1  » i  -70 "  Y»"rt  fi. V » ' l S  '  !! : : '  -80  JI  1  'ii  1  J r S 'i • *! ' "iff :  l_ - »*_*{ * r  i  +  J -,-.„_ j_ _ 1  , i •  :i i i 10  -  20  i  ;1  1  i i i i i  .  measured using our system measured using the VNA measured using the VNA when no laser source was supplied residual power signal  30 40 Frequency (GHz)  50  60  70  Figure E.2. The frequency response of the modulator when no laser source was supplied is shown as the dotted curve. It overshadowed the uncorrected frequency response of the 10 Gb/s modulator measured using the V N A , shown as the solid curve, starting at -45 GHz. The uncorrected frequency responses of the 10 Gb/s modulator measured using our system, shown as the asterisks, shows continual roll-off beyond 50 GHz due to the virtually constant power output from the optical heterodyning and the constant residual power signal shown as the dashed line.  63  References [1] G. L . L i , and P. K . L. Y u , "Optical intensity modulators for digital and analog applications,"./ of Lightwave Technology, vol. 21, No. 9, pp. 2010-2030, Sep. 2003. [2] Osamu Mitomi, Kazuto Noguchi, and Hiroshi Miyazawa, "Estimation of frequency response for high-speed LiNbO^  optical modulators," IEE Proc. -Optoelectron.,  vol.  146, No. 2, pp. 99-104, April 1999. [3] Frank Bowman, "Introduction to Bessel functions," Dover, N Y , 1958. [4] George B. Arfken, and Hans J. Weber, "Mathematical  methods for  physicists,"  Harcourt, San Diego, 2001. [5] C. J. Tranter, "Bessel functions  with some physical  applications"  The English  Universities Press LTD., London, 1968. [6] "Agilent 8510C network analyzer," Data Sheet, Agilent Technologies, Palo Alto, C A .  

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