Analysis of Signal Propagation in Nonlinear Optical Fiber using SS-FEM with Sparse Matrix

희귀행렬 SS-FEM에 의한 비선형 광섬유의 전송신호 해석

  • 정백호 (호서대 정보통신공학부) ;
  • 이호준 (호서대 정보통신공학부)
  • Published : 2000.01.01

Abstract

Signal propagation in nonlinear optical fiber is analyzed numerically by using SS-FEM (Split-Step Finite Element Method). By adopting cubic element function in FEM, soliton equation of which exact solution was well known, has been solved. Also, accuracy of numerical results and computing times are compared with those of Fourier method, and we have found that solution obtained from using FEM was very relatively accurate. Especially, to reduce CPU time in matrix computation in each step, the matrix imposed by the boundary condition is approximated as a sparse matrix. As a result, computation time was shortened even with the same or better accuracy when compared to those of the conventional FEM and Fourier method.

Keywords

References

  1. G. P. Agrawal, Nonlinear Fiber Optics. Academic Press, pp. 50-55, 142-148, 1995
  2. L. Bergman, J. Morookian, and C. Yeh, 'An all-optical long-distance multi-Gbytes/s bit-parallel WDM single-fiber link,' J. Lightwave Technol., vol. 15, no. 9, 1577-1582, Sept. 1998 https://doi.org/10.1109/50.712239
  3. S. Shen, C. C. Chang, H. P. Sardesai, V. Binjrajka, and A. M. Weiner, 'Effects of self-phase modulation on sub-500 fs pulse transmission over dispersion compensated fiber links,' J. Lightwave Technol., vol. 17, no. 3, 452-461, March 1999 https://doi.org/10.1109/50.749385
  4. A. Carena, V. Curti, R. Gaudino, P. Poggiolini, and C. Benedetto, 'A time-domain optical transmission system simulation package accounting for nonlinear and polarization-related effects in fiber,' IEEE J. Select. Areas Commun., vol. 15, no. 4, pp. 751-765, May 1997 https://doi.org/10.1109/49.585785
  5. O. Lenzmann, I. Koltchanov, A. Lowery, D. Breuer, and A. Richter, 'Photonic multi-domain simulator,' in OFC '99, White Paper, 1998
  6. K. Hayata, A. Misawa, and M. Koshiba, 'Split-step finite-element method applied to nonlinear integrated optics,' J. Opt. Soc. Am. B, vol. 7, no. 9, 1772-1784, Sept. 1990
  7. M. Koshiba, Optical Waveguide Theory by the Finite Element Method. KTK, pp. 230-238, 1992
  8. 정백호, 이호준, '단계분할 유한 요소법에 의한 광섬유의 신호 전송 예측,' 1999년도 대한전기학회 하계학술대회 논문집, pp. 2441-2443, 1999. 7
  9. 홍순원, 이호준, '단계 분할 유한 요소법을 이용한 분산 보상 광 전송 시스템의 시뮬레이션,' 대한전자공학회 논문지, 36권, 8호, pp. 751-758, 1999. 8
  10. J. R. Taylor, Optical Solitons-Theory and Experiment. Cambridge Press, pp. 73-84, 1992
  11. J. Jin, The Finite Element Method in Electromagnetics, John Wiley & Sons, chapter 3, 1993