级联AWGs色散补偿系统的传输理论分析
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摘要
随着阵列波导光栅(AWG)逐步进入实用化阶段，其发展的方向是在改善其性能的基础上扩大它的应用范围。本文分析的级联AWGs色散补偿系统正是AWG应用范围拓展的体现，此系统尤其适用于高码速、大容量的波分复用系统中。
首先，分析了级联AWGs系统色散补偿的理论基础，即时(?)空变换原理。其次，从两个角度(时域、空域)对级联AWGs系统进行了详细的分析：在时域，分析了色散补偿及脉冲平移的原理，分析推导出经过补散后的脉冲波形的解析表达式，并以一线性啁啾脉冲代入此表达式来作具体的分析；在空域，我们在实用化器件平坦光谱响应的设计要求前提下，将级联AWGs系统视为空间线性不变系统，富有新意的提出了用点扩展函数的方法来分析系统的传输特性，得出了较简洁的输出端焦场的解析表达式，并对系统的串扰特性进行了分析，在数学工具软件的辅助下，用计算机数值模拟分析了串扰与系统主要结构参数的重要关系，对系统的设计具有一定的指导意义。
With arrayed-waveguide grating (AWG) stepping into its utilization gradually, the orientation of development of it lies in expanding its application area on the basis of improving its capability. In this thesis, the cascade AWGs system that is used to compensate the dispersion is the very embodiment of expanding its application area and fits well the DWDM high-speed communicaion .
Firstly, In this thesis, the theorem foundation of cascade AWGs for dispersion compensation system, namely time-space fourier conversion is described. Secondly, we analyze the system from two perspectives : time domain and space domain. In time domain, we analyze the principle of dispersion compensation using cascade AWGs with space filter. Taking a linear chirp pulse for example, we obtain the expression of compensated pulse distribution. In space domain, a novel method in terms of point-spread function is used in the transmission theory of cascade AWGs which is looked on as a linear space invariant system , thus, a laconic expression of output field of the system is obtained. Furthermore, we give the dependences of the crosstalk vs the configuration parameters of the system, with the help of math auxiliary software.
首先，分析了级联AWGs系统色散补偿的理论基础，即时(?)空变换原理。其次，从两个角度(时域、空域)对级联AWGs系统进行了详细的分析：在时域，分析了色散补偿及脉冲平移的原理，分析推导出经过补散后的脉冲波形的解析表达式，并以一线性啁啾脉冲代入此表达式来作具体的分析；在空域，我们在实用化器件平坦光谱响应的设计要求前提下，将级联AWGs系统视为空间线性不变系统，富有新意的提出了用点扩展函数的方法来分析系统的传输特性，得出了较简洁的输出端焦场的解析表达式，并对系统的串扰特性进行了分析，在数学工具软件的辅助下，用计算机数值模拟分析了串扰与系统主要结构参数的重要关系，对系统的设计具有一定的指导意义。
With arrayed-waveguide grating (AWG) stepping into its utilization gradually, the orientation of development of it lies in expanding its application area on the basis of improving its capability. In this thesis, the cascade AWGs system that is used to compensate the dispersion is the very embodiment of expanding its application area and fits well the DWDM high-speed communicaion .
Firstly, In this thesis, the theorem foundation of cascade AWGs for dispersion compensation system, namely time-space fourier conversion is described. Secondly, we analyze the system from two perspectives : time domain and space domain. In time domain, we analyze the principle of dispersion compensation using cascade AWGs with space filter. Taking a linear chirp pulse for example, we obtain the expression of compensated pulse distribution. In space domain, a novel method in terms of point-spread function is used in the transmission theory of cascade AWGs which is looked on as a linear space invariant system , thus, a laconic expression of output field of the system is obtained. Furthermore, we give the dependences of the crosstalk vs the configuration parameters of the system, with the help of math auxiliary software.
引文
1、 郑杰，鲁力，《光纤阵列—AWG—光纤阵列的自动调芯(耦合)系统》
2、 邱怡申，李雪梅，吕团孙，郭福源，阵列波导光栅复用／解复用器焦场的分析及光栅孔径对器件串扰影响的数值分析，中国激光，2002，29(9)：801～804
3、 雷红兵，欧海燕，胡雄伟，杨沁清，余金中，王启明，阵列波导光栅解复用器输入 输出波导结构串扰的数值分析，光子学报．Vol．28，No．7，630～633
4、 戴道锌，周勤存，敖献煜，何赛灵，AWG中阵列波导耦合系数的计算，光电子激光，Vol．13，No．7，675～678
5、 周勤存，吕俊，何建军，何赛灵，快速计算阵列波导光栅波导耦合系数的修正重叠积分方法，光子学报，Vol．31，No．8，975～978
6、 潘小龙，赵梓森，一种简化的基于BPM的AWG优化设计方法，半导体学报，Vol．23 No．1
7、 杨祥林，《光纤通信系统》，国防工业出版社，2000
8、 明海，张国平，谢建平，《光电子技术》，中国科学技术大学出版社，1998
9、 Massimo Artiglia,Comparison of dispersion-compensation techniques for lightwave systems.OFC'98 Technical Digest,Thv2,1998:364～365
10、 Y.k.Park.P.D.Yeates,J.-M.P.Delavaux et al. A field demonstration of 20Gb/s capacity transmission over 360Krn installed standard fiber. IEEE Photon. Technol. Lett. Vol.7, No.7,:816～818
11、 K.Kikuchi and C.Lorattanassane,Compensation for pulse waveform distortion in ultralong distance optical communication systems by using midway optical phase conjugator, IEEE Photon.Technol.Lett. Vol.6:104～105
12、 P Petruzzi,C Lowry, P Sivanesan,Dispersion compensation using only fiber Bragg gratings,IEEE Journal of Selected Topics in Quantum Electron, Vol,5, 1999
13、 Shikawa G.Sekiya M.Onaka H.,et al,10Gb/s repeaterless transmission
using standard single-mode fiber with prechirping and dispersion compensation techniques,IEICE Transactions on Electronics, E78-CISSI, pp 43～49, Jan.1995.
14、 U.Feiste,R.Ludwig,E.Dietrich, S.Diez,et al,40Gb/s transmission over 434 km standard fiber using polarization independent midspan spectral inversion, Electron.Lett.Vol.34,pp2044～2045,1998
15、 Mogilevtsev,Birks T A, Russell P St J.Group-velocity dispersion in photonic crystal fibers.Optics Letters, 1998,23:1662～1664
16、 Birks T A,Mogilevtsev D,Knight J C, et al, Dispersion compensation using single-material fibers.IEEE Photonics Technology Letters,1999, 11:674～676
17、 M.K.Smit, Electron.Lett., 24,385 (1988)
18、 Smit M.K,van Dam C.Phasar-based WDM-device:design and applications. IEEE Journal of Selected Topics in Quantum Electronics. 1996,2(2):236～250
19、 Takahashi H,Oda K,Toba H et al.Transmission characteristics of arrayed-waveguide N Ⅹ N wavelength multiplexer.J.of Light -wave Technol. 1995,13(3):447～455"
20、 Okamoto K.Recent progress of integrated optics planar lightwave circuits.[J].Opt.and Quant.Electron. 1999,31 (2): 107～129
21、 Muoz P, Pastor D,Capmany J.Modeling and design of arrayed waveguide gratings.J.ofLightwave Technol.2002,20(4):661～674
22、 Guo W B,Ma C S,Zhang D M et al.Parameter optimization and structural design of polymer arrayed waveguide grating multiplexer. Opt. Commun.2002,201 (13):45～53
23、 Ma C S,Guo W B,Zhang D M,et al.Analytical modeling of loss characteristics ofapolymer arrayed waveguide grating multiplexer. Opt.&Laser Teehnol.2002,34(8):621 ～ 630
24、 Daniel Fonseca,Ruben Luis,Adolfo V.T.Cartaxo,Design and Performance of AWG multiplexer/demultiplexer in WDM systems.
25、 Sangin Kim,Bidirectional Optical Cross Connects for Multiwavelength Ring Networks Using Single Arrayed Waveguide Grating Router, Journal of Lightwave Technology, Vol.20,No.2,February 2002.188～194
26、 Dragone C,Serasser T, Bogert GA et al.,Waveguide grating router with maximally fiat channel passband produced by spatical filtering. Electron. Lett.,1997,33(15): 1312～1314
27、 Okamoto K.Takiguchi K.Ohmori Y. 16-channel optical add/drop multiplexer using silica-based arrayed-waveguide gratings[J].Electron.Lett., 1995, 31: 723～724
28、 Takahashi H.Multiwavelength ring laser composed of EDFAs and an arrayed-waveguide wavelength multiplexer[J].Electron.Lett.,1993,,30(1): 44～45
29、 Miyazaki T, Edagawa N,Yamamoto S,A multiwavelength fiber ring-laser employing a pair of silica-based arrayed-waveguide-grating[J],IEEE Photon, Technol,Lett., 1997,9(7):910～912
30、 Kawanishi S,Takara H,Uchiyama K, Shake I,Kamatani O,and Takahashi H.,1.4Tb/s (200Gb/s×7ch)50km optical transimission experiment [J].Electron.Lett.,1997,33(20)
31、 Takada K,Yamada H,Okamoto K.Optieal spectrum analyzer using cascaded AWG's with different channel spacings[J].IEEE Photonics Technol. Lett., 1999,11 (7)
32、 M.Teshima,M.Koga and K.Sato,Performance ofmultiwavelength simul taneous monitoring circuit employing arrayed-waveguide gratings, J.Lightwave Technol, 1996,14,PP2277～2285
33、 Hirokazu Takenouchi Hiroyuki Tsuda and Takashi Kurokawa, Analysis of optical-signal processing using an arrayed-waveguide grating, Optics Express, Vol.6.No.6。
34、 D.Yelin,D.Meshulach,and Y.Silberberg.Adaptive femtosecond pulse compression.Optics Letters.Vol.22,No.23.1793～1795
35、 Andrew M.Weiner, Daniel E.Leaird,David H.Reitze,and Eung Gi Paek, Femtosecond Spectral Holography, IEEE Journal of Quantum Electroics Vol.28, No.10,October 1992.
36、 D.Meshulach,D.Yelin,and Y.Silberberg,Adaptive real-time femtosecond pulse shaping,J.Opt.Soc.Am.B,Vol.15,No.5,May 1998,1615～1619
37、 Ayman M.Kan'an and A.M.Weiner.Efficient time-to-space conversion of femtosecond optical pulses.J.Opt.Soe.Am.B Vol. 15,No.3 1242～1245
38、 Martin C.Nuss,Melissa Li,and T.H.Chiu.Time-to-space mapping of femtosecond pulses.Optics Letters.Vol. 19,No.9.664～666
39、 Daniel E.Leaird and Andrew M.Weiner.Fellow,IEEE.Femtosecond Direct Space-to-Time Pulse Shaping.IEEE Journal of Quantum Electronics. Vol.37, No.4 April 2001,494～504
40、 Dan M.Marom,Dmitriy Panasenko,Pang-Chen Sun,and Yeshaiahu Fainman. Spatial-temporal wave mixing for space-time conversion. Optics Letters. Vol.24, No.8.April 15,1999.563～565
41、 A.M.Weiner, Femtosecond optical pulse shaping and processing. Prog. Quant. Electron. 19,161～237 (1995)
42、 T.Kurokawa, H.Tsuda.K.Okamoto,K.Naganuma,H.Takenouchi,Y.Inoue and M.Ishii, Time-space-conversion optical signal processing using arrayed -waveguide grating, Electron.Lett. 33, 1890～1891 (1997),
43、 H.Takenouchi, H.Tsuda. K.Naganuma, T.Kurokawa, Y.Inoue and K. Okamoto, Differential processing of ultrashort optical pulses using arrayed -waveguide grating with phase-only filter, Electron.Lett. 34,1245～1246 (1998)
44、 H.Takenouchi, H.Tsuda,C.Amano,T.Goh,K.Okamoto and T.Kurokawa, An optical phase-shift keying direct detection receiver using a high-resolution arrayed-waveguide grating, in Technical Digest of Optical Fiber Conference (OFC)99, paper TuO4,
45、 H.Tsuda, H.Takenouchi, T. Ishii, K.Okamoto, T.Goh,K.Sato,A.Hirano, T.Kurokawa and C.Amano, Photonic spectral encoder/decoder using an arrayed-waveguide grating for coherent optical code division multiplexing, in Technical Digest of Optical Fiber Conference (OFC)99, paper PD32。
46、 Dan M.Marom, Dmitriy Panasenko, Pang-Chen Sun, and Yeshaiahu Fainman, Linear and nonlinear operation of a time-to-space processor, J.opt.Soc.Am. A/Vol. 18,No.2/February 2001.
47、 Andrew M.Weiner, Senior Member.IEEE,Daniel E.Leaird.J.S.Patel.and John R. Wullert. Ⅱ ,Programmable Shaping of Femtosecond Optical Pulses by Use of 128-Element Liquid Crystal Phase Modulator. IEEE Journal of Quantum.Electronics.Vol.28,No.4 April 1992
48、 Parker M C,Walker S D. A fourier-fresnel integral-based transfer function model for a near-parabolic phase profile arrayed-waveguide grating. IEEE Photonics Technol Lett. 1999,11 (8): 1018
49、 Ou Haiyan, Lei Hongbing,Yang Qinqing,et al.Optimization of a 1 × 8 arrayed -waveguide grating multi/demultiplexer. Chinese Journal Of Semiconductors, 2000,21 (1): 12
50、 Dragone C.Efficiency of aperiod array with nearly ideal element pattern. IEEE Photonics Technol Lett. 1989,1(2):238
51、 Dragone C. Optimum design of a planar array of tapered waveguide. J Opt. Soc Am A,1990,7(11):2081
52、 Hiroyuki Tsuda,Katsunari Okamoto,Tetsuyoshi Ishii,Kazunori Naganuma, Yasuyuki Inoue, Hirokazu Takenouchi,and Takashi Kurokawa, Second and Third-Order Dispersion Compensator Using a High-Resolution Arrayed-Waveguide Grating,IEEE Photonies Technology Letters, Vol. 11, No.5,569～571
53、 A.M.Weiner, Femtosecond pulse shaping using spatial light modulators, Review of scientific instruments, vol.71 no.5, 2000:1929～1960
2、 邱怡申，李雪梅，吕团孙，郭福源，阵列波导光栅复用／解复用器焦场的分析及光栅孔径对器件串扰影响的数值分析，中国激光，2002，29(9)：801～804
3、 雷红兵，欧海燕，胡雄伟，杨沁清，余金中，王启明，阵列波导光栅解复用器输入 输出波导结构串扰的数值分析，光子学报．Vol．28，No．7，630～633
4、 戴道锌，周勤存，敖献煜，何赛灵，AWG中阵列波导耦合系数的计算，光电子激光，Vol．13，No．7，675～678
5、 周勤存，吕俊，何建军，何赛灵，快速计算阵列波导光栅波导耦合系数的修正重叠积分方法，光子学报，Vol．31，No．8，975～978
6、 潘小龙，赵梓森，一种简化的基于BPM的AWG优化设计方法，半导体学报，Vol．23 No．1
7、 杨祥林，《光纤通信系统》，国防工业出版社，2000
8、 明海，张国平，谢建平，《光电子技术》，中国科学技术大学出版社，1998
9、 Massimo Artiglia,Comparison of dispersion-compensation techniques for lightwave systems.OFC'98 Technical Digest,Thv2,1998:364～365
10、 Y.k.Park.P.D.Yeates,J.-M.P.Delavaux et al. A field demonstration of 20Gb/s capacity transmission over 360Krn installed standard fiber. IEEE Photon. Technol. Lett. Vol.7, No.7,:816～818
11、 K.Kikuchi and C.Lorattanassane,Compensation for pulse waveform distortion in ultralong distance optical communication systems by using midway optical phase conjugator, IEEE Photon.Technol.Lett. Vol.6:104～105
12、 P Petruzzi,C Lowry, P Sivanesan,Dispersion compensation using only fiber Bragg gratings,IEEE Journal of Selected Topics in Quantum Electron, Vol,5, 1999
13、 Shikawa G.Sekiya M.Onaka H.,et al,10Gb/s repeaterless transmission
using standard single-mode fiber with prechirping and dispersion compensation techniques,IEICE Transactions on Electronics, E78-CISSI, pp 43～49, Jan.1995.
14、 U.Feiste,R.Ludwig,E.Dietrich, S.Diez,et al,40Gb/s transmission over 434 km standard fiber using polarization independent midspan spectral inversion, Electron.Lett.Vol.34,pp2044～2045,1998
15、 Mogilevtsev,Birks T A, Russell P St J.Group-velocity dispersion in photonic crystal fibers.Optics Letters, 1998,23:1662～1664
16、 Birks T A,Mogilevtsev D,Knight J C, et al, Dispersion compensation using single-material fibers.IEEE Photonics Technology Letters,1999, 11:674～676
17、 M.K.Smit, Electron.Lett., 24,385 (1988)
18、 Smit M.K,van Dam C.Phasar-based WDM-device:design and applications. IEEE Journal of Selected Topics in Quantum Electronics. 1996,2(2):236～250
19、 Takahashi H,Oda K,Toba H et al.Transmission characteristics of arrayed-waveguide N Ⅹ N wavelength multiplexer.J.of Light -wave Technol. 1995,13(3):447～455"
20、 Okamoto K.Recent progress of integrated optics planar lightwave circuits.[J].Opt.and Quant.Electron. 1999,31 (2): 107～129
21、 Muoz P, Pastor D,Capmany J.Modeling and design of arrayed waveguide gratings.J.ofLightwave Technol.2002,20(4):661～674
22、 Guo W B,Ma C S,Zhang D M et al.Parameter optimization and structural design of polymer arrayed waveguide grating multiplexer. Opt. Commun.2002,201 (13):45～53
23、 Ma C S,Guo W B,Zhang D M,et al.Analytical modeling of loss characteristics ofapolymer arrayed waveguide grating multiplexer. Opt.&Laser Teehnol.2002,34(8):621 ～ 630
24、 Daniel Fonseca,Ruben Luis,Adolfo V.T.Cartaxo,Design and Performance of AWG multiplexer/demultiplexer in WDM systems.
25、 Sangin Kim,Bidirectional Optical Cross Connects for Multiwavelength Ring Networks Using Single Arrayed Waveguide Grating Router, Journal of Lightwave Technology, Vol.20,No.2,February 2002.188～194
26、 Dragone C,Serasser T, Bogert GA et al.,Waveguide grating router with maximally fiat channel passband produced by spatical filtering. Electron. Lett.,1997,33(15): 1312～1314
27、 Okamoto K.Takiguchi K.Ohmori Y. 16-channel optical add/drop multiplexer using silica-based arrayed-waveguide gratings[J].Electron.Lett., 1995, 31: 723～724
28、 Takahashi H.Multiwavelength ring laser composed of EDFAs and an arrayed-waveguide wavelength multiplexer[J].Electron.Lett.,1993,,30(1): 44～45
29、 Miyazaki T, Edagawa N,Yamamoto S,A multiwavelength fiber ring-laser employing a pair of silica-based arrayed-waveguide-grating[J],IEEE Photon, Technol,Lett., 1997,9(7):910～912
30、 Kawanishi S,Takara H,Uchiyama K, Shake I,Kamatani O,and Takahashi H.,1.4Tb/s (200Gb/s×7ch)50km optical transimission experiment [J].Electron.Lett.,1997,33(20)
31、 Takada K,Yamada H,Okamoto K.Optieal spectrum analyzer using cascaded AWG's with different channel spacings[J].IEEE Photonics Technol. Lett., 1999,11 (7)
32、 M.Teshima,M.Koga and K.Sato,Performance ofmultiwavelength simul taneous monitoring circuit employing arrayed-waveguide gratings, J.Lightwave Technol, 1996,14,PP2277～2285
33、 Hirokazu Takenouchi Hiroyuki Tsuda and Takashi Kurokawa, Analysis of optical-signal processing using an arrayed-waveguide grating, Optics Express, Vol.6.No.6。
34、 D.Yelin,D.Meshulach,and Y.Silberberg.Adaptive femtosecond pulse compression.Optics Letters.Vol.22,No.23.1793～1795
35、 Andrew M.Weiner, Daniel E.Leaird,David H.Reitze,and Eung Gi Paek, Femtosecond Spectral Holography, IEEE Journal of Quantum Electroics Vol.28, No.10,October 1992.
36、 D.Meshulach,D.Yelin,and Y.Silberberg,Adaptive real-time femtosecond pulse shaping,J.Opt.Soc.Am.B,Vol.15,No.5,May 1998,1615～1619
37、 Ayman M.Kan'an and A.M.Weiner.Efficient time-to-space conversion of femtosecond optical pulses.J.Opt.Soe.Am.B Vol. 15,No.3 1242～1245
38、 Martin C.Nuss,Melissa Li,and T.H.Chiu.Time-to-space mapping of femtosecond pulses.Optics Letters.Vol. 19,No.9.664～666
39、 Daniel E.Leaird and Andrew M.Weiner.Fellow,IEEE.Femtosecond Direct Space-to-Time Pulse Shaping.IEEE Journal of Quantum Electronics. Vol.37, No.4 April 2001,494～504
40、 Dan M.Marom,Dmitriy Panasenko,Pang-Chen Sun,and Yeshaiahu Fainman. Spatial-temporal wave mixing for space-time conversion. Optics Letters. Vol.24, No.8.April 15,1999.563～565
41、 A.M.Weiner, Femtosecond optical pulse shaping and processing. Prog. Quant. Electron. 19,161～237 (1995)
42、 T.Kurokawa, H.Tsuda.K.Okamoto,K.Naganuma,H.Takenouchi,Y.Inoue and M.Ishii, Time-space-conversion optical signal processing using arrayed -waveguide grating, Electron.Lett. 33, 1890～1891 (1997),
43、 H.Takenouchi, H.Tsuda. K.Naganuma, T.Kurokawa, Y.Inoue and K. Okamoto, Differential processing of ultrashort optical pulses using arrayed -waveguide grating with phase-only filter, Electron.Lett. 34,1245～1246 (1998)
44、 H.Takenouchi, H.Tsuda,C.Amano,T.Goh,K.Okamoto and T.Kurokawa, An optical phase-shift keying direct detection receiver using a high-resolution arrayed-waveguide grating, in Technical Digest of Optical Fiber Conference (OFC)99, paper TuO4,
45、 H.Tsuda, H.Takenouchi, T. Ishii, K.Okamoto, T.Goh,K.Sato,A.Hirano, T.Kurokawa and C.Amano, Photonic spectral encoder/decoder using an arrayed-waveguide grating for coherent optical code division multiplexing, in Technical Digest of Optical Fiber Conference (OFC)99, paper PD32。
46、 Dan M.Marom, Dmitriy Panasenko, Pang-Chen Sun, and Yeshaiahu Fainman, Linear and nonlinear operation of a time-to-space processor, J.opt.Soc.Am. A/Vol. 18,No.2/February 2001.
47、 Andrew M.Weiner, Senior Member.IEEE,Daniel E.Leaird.J.S.Patel.and John R. Wullert. Ⅱ ,Programmable Shaping of Femtosecond Optical Pulses by Use of 128-Element Liquid Crystal Phase Modulator. IEEE Journal of Quantum.Electronics.Vol.28,No.4 April 1992
48、 Parker M C,Walker S D. A fourier-fresnel integral-based transfer function model for a near-parabolic phase profile arrayed-waveguide grating. IEEE Photonics Technol Lett. 1999,11 (8): 1018
49、 Ou Haiyan, Lei Hongbing,Yang Qinqing,et al.Optimization of a 1 × 8 arrayed -waveguide grating multi/demultiplexer. Chinese Journal Of Semiconductors, 2000,21 (1): 12
50、 Dragone C.Efficiency of aperiod array with nearly ideal element pattern. IEEE Photonics Technol Lett. 1989,1(2):238
51、 Dragone C. Optimum design of a planar array of tapered waveguide. J Opt. Soc Am A,1990,7(11):2081
52、 Hiroyuki Tsuda,Katsunari Okamoto,Tetsuyoshi Ishii,Kazunori Naganuma, Yasuyuki Inoue, Hirokazu Takenouchi,and Takashi Kurokawa, Second and Third-Order Dispersion Compensator Using a High-Resolution Arrayed-Waveguide Grating,IEEE Photonies Technology Letters, Vol. 11, No.5,569～571
53、 A.M.Weiner, Femtosecond pulse shaping using spatial light modulators, Review of scientific instruments, vol.71 no.5, 2000:1929～1960