An Efficient Split-Step Time-Domain Dynamic Modeling of DFB/DBR Laser Diodes

연산자 분리 방법을 통한 DFB/DBR 레이저 다이오드의 효율적인 시영역 동적 모델링

  • 김병성 (韓國電子通信硏究院 交換傳送技術硏究所) ;
  • 정영철 (光云大學校 電子工學部/電子通信工學科)
  • Published : 2000.07.01

Abstract

A novel and efficient approach for the numerical solution of time-dependent coupled-wave equations, which are frequently used for the modeling of DFB(Distributed Feedback), DBR(Distributed Bragg Reflector), and FP(Fabry Perot) laser diodes, is proposed. In this approach, the coupled wave equations are split into two sets of equations. One of two sets of equations contains only the phase factors and the other contains only the coupling terms. The separate equations are solved exactly in their split form successively. This new numerical scheme, which we call the SS-TDM(Split-Step Time Domain Model), is found to require an order of magnitude smaller number of subsections to get accurate results than the previous methods while the computation time for each time step is comparable to the previous methods.

DFB(Distributed Feedback) 및 DBR(Distributed Bragg Reflector) 레이저 다이오드의 모델링에 많이 사용되는 시간 변수가 있는 결합 파동 방정식의 수치해를 효율적으로 구할 수 있는 새로운 방법을 제안 하였다. 이 방법에서는 결합 파동 방정식을 두 세트의 방정식으로 분리하여 해석한다. 한 세트의 방정식들에는 위상 인자 및 이득 인자만 포함되고, 다른 한 세트의 방정식에는 결합항만이 포함된다. 본 논문에서 SS-TDM(Split-Step Time Domain Model)이라고 명명한 새로운 수치해석법은 기존의 방법에 비하여 매시간 스텝당 계산 시간은 비슷한 반면에 분할 구간의 수가 10배 이상 적게 하여도 정확한 결과를 얻을 수 있음을 확인하였다.

Keywords

References

  1. L. A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits, John Wiley & Sons, Inc, 1995
  2. P. E. Green, Fiber Optic Networks, Prentice Hall, Englewood Cliffs, NJ, 1993
  3. G. P Agrawal and N. K. Dutta, Semiconductor lasers, 2nd ed., Van Nostrand Reinhold, 1993
  4. P. Vankwikelberge, G. Morthier, and R. Baets, 'CLADISS-A longitudinal multimode model for the analysis of the static, dynamic, and stochastic behavior of diode lasers with distributed feedback,' IEEE J. Quantum Electron, vol. 26, no. 10, pp. 1728-1741, 1990 https://doi.org/10.1109/3.60897
  5. A. J. Lowery, 'New dynamic semiconductor laser model based on the transmission-line modelling method,' IEE Proc.-Optoelectron., vol. 134, no. 5, pp. 281-289, 1987
  6. A. J. Lowery, A. Keating, and C. N. Murtonen, 'Modeling the static and dynamic behavior of quarter-wave-shifted DFB lasers,' IEEE J. Quantum Electron., vol. 28, pp. 1874-1883. 1992 https://doi.org/10.1109/3.144479
  7. E. A. Avrutin, J. M. Arnold, and J. H. Marsh, 'Analysis of dynamics of monolithic passively mode-locked laser diodes under external periodic excitation,' IEE Proc.-Optoelectron., vol. 143, no. 1, pp. 81-88, 1996 https://doi.org/10.1049/ip-opt:19960175
  8. L. M. Zhang and J. E. Carroll, 'Large-signal dynamic model of the DFB laser,' IEEE J. Quantum Electron., vol. 28, no. 3, pp. 604-611, 1992 https://doi.org/10.1109/3.124984
  9. L. M. Zhang, J. E. Carroll, and C. Tsang, 'Dynamic response of the gain-coupled DFB laser,' IEEE J. Quantum Electron., vol. 29, pp. 1722-1727, 1993 https://doi.org/10.1109/3.234427
  10. L. M. Zhang and J. E. Carroll, 'Semiconductor 1.55 mm laser source with gigabit/second integrated electroabsorptive modulator,' IEEE J. Quantum Electron., vol. 30, no. 11, pp. 2573-2577, 1994 https://doi.org/10.1109/3.333709
  11. D. J. Jones, l. M. Zhang, J. E. Carroll, and D. D. Marcenac, 'Dynamics of monolithic passively mode-locked semiconductor lasers,' IEEE J. Quantum Electron, vol. 31, no. 6, pp. 1051-1058, 1995 https://doi.org/10.1109/3.387042
  12. C. K. Gardiner, R. G. S. Plumb, P. J. Williams, and T. J. Reid, 'Three-section sampled-grating DBR lasers: modelling and measurements,' IEE Proc.-Optoelectron., vol. 143, no. 1, pp. 24-30, 1996
  13. 김병성, 정영철, 김선호, '전계흡수변조기가 집적된 광대역 파장가변 SGDBR/SSGDBR 레이저 다이오드의 동적 특성,' 대한전자공학회논문지 제35권 D편, pp. 53-61, 1998
  14. B. S. Kim, Y. Chung, and S. H. Kim, 'Dynamic analysis of widely tunable laser diodes integrated with sampled- and chirped-grating distributed Bragg reflectors and an electroabsorption modulator,' IEICE Trans. on Electronics, vol. E81-C, no. 8, pp. 1342-1349, 1998
  15. B. S. Kim, Y. Chung, K. H. Park, and S. H. Kim, 'Optical mm-wave signal generation using a multi-section distributed feedback laser diode,' Microwave & Optical Tech. Lett., vol. 20, no. 1, pp. 64-66, 1999 https://doi.org/10.1002/(SICI)1098-2760(19990105)20:1<64::AID-MOP17>3.0.CO;2-B
  16. S. K. C. Liew, 'Above-threshold analysis of three-section DFB/DBR lasers with second-order gratings,' IEEE J. Selected Topics in Quantum Electron., vol. 1, no. 2, pp. 363-370, 1995 https://doi.org/10.1109/2944.401216
  17. D. D. Marcenac, Fundamenatals of laser modelling, Ph. D. dissertation, Cambridge University, 1993
  18. C. F. Tsang, D. D. Marcenac, J. E. Carroll, and L. M. Zhang, 'Comparison between 'power matrix model' and 'time domain model' in modelling large signal response of DFB lasers,' IEE Proc.-Optoelectron., vol. 141, no. 2, pp. 89-96, 1994 https://doi.org/10.1049/ip-opt:19949916
  19. M. G. Davis and R. F. O'Dowd, 'A transfer matrix rrethod based large-signal dynamic model for multielectrode DFB lasers,' IEEE J. Quantum Electron., vol. 30, no. 11, pp. 2458-2466, 1994 https://doi.org/10.1109/3.333696
  20. T. Makino, 'Effective-index matrix analysis of distributed feedback semiconductor lasers,' IEEE J. Quantum Electron., vol. 28, pp. 434-440, 1992 https://doi.org/10.1109/3.123270
  21. B. S. Kim and Y. Chung, 'Novel numerical solution of time-dependent coupled wave equations', Electron. Lett., vol. 35, no. 1, pp. 84-85, 1999 https://doi.org/10.1049/el:19990010
  22. K. Petermann, 'Calculated spontaneous emission factor for double heterostructure injection lasers with gain induced mode guiding,' IEEE J. Quantum Electron., vol. QE-15, pp. 556-570, 1979
  23. H. F. Liu, S. Arahira, T. Kunii, and Y. Ogawa, 'Generation of wavelength-tunable transform-limited pulses from a monolithic passively mode-locked distributed Bragg reflector semiconductor laser,' IEEE Photon. Tech. Lett., vol. 7, no. 10, pp. 1139-1141, 1995 https://doi.org/10.1109/68.466570
  24. L. Olofsson and T. G. Brown, 'The influence of resonator structure on the linewidth enhancement factor of semiconductor lasers,' IEEE J. Quantum Electron., vol. 28, no. 6, pp. 1450-1458, 1992 https://doi.org/10.1109/3.135297
  25. A. Yariv, Optical electronics, 4th ed., Saunders College Publishing, Chap. 13, 1991
  26. M. Okai, M. Suzuki, and A. Aoki, 'Complex-coupled 1/4-shifted DFB lasers with a flat FM response,' IEEE J. Selected Topics in Quantum Electron., vol. 1, no. 2, pp. 461-465, 1995 https://doi.org/10.1109/2944.401229
  27. K. David, G. Morthier, P. Vankwikelberge, R. G. Baets, T. Wolf, and B. Borchert, 'Gain-coupled DFB lasers versus index-coupled and phase-shifted DFB lasers: a comparison based on spatial hole burning corrected yield,' IEEE J. Quantum Electron., vol. 27, no. 6, pp. 1714-1723, 1991 https://doi.org/10.1109/3.89938
  28. B. S. Kim, Y. Chung, and S. H. Kim, 'Dynamic analysis of mode-locked sampled-grating distributed-Bragg-reflector laser diodes,' IEEE Jr. of Quantum Electron., Submitted, 1999 https://doi.org/10.1109/3.798085
  29. S. S. Orlov, A. Yariv, and S. V. Essen, 'Coupled-mode analysis of fiber-optic add-drop filters for dense wavelength-division multiplexing', Opt. Lett., vol. 22, no. 10, pp. 888-890, 1997
  30. B. S. Kim and Y. Chung, 'Split-step time domain modeling of add-drop filters including a grating-written directional coupler,' CLEO/Pacific Rim '99, Seoul, Korea, 1999 https://doi.org/10.1109/CLEOPR.1999.814706
  31. L. Dong, P. Hua,T. A. Birks, L, Reekie, and P. St. J. Rusel, 'Novel Add/Drop Filters for Wavelength-Division-Multiplexing Optical Fiber Systems Using a Bragg Grating Assisted Mismatched Coupler,' IEEE Photon. Technol. Lett., Vol. 8, No. 12, pp. 1656-1657, 1996 https://doi.org/10.1109/68.544709