대한전자공학회논문지SD (Journal of the Institute of Electronics Engineers of Korea SD)

대한전자공학회 (The Institute of Electronics and Information Engineers)
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Airy 함수와 WKB 해를 이용한 언덕형 굴절율 분포를 갖는 광섬유 해석

Analysis of Optical Fibers with Graded-Index Profile By a Combination of Modified Airy Functions and WKB Solutions

  • 정민섭 (서울시립대학교 전자전기공학부) ;
  • 김영문 (서울시립대학교 전자전기공학부) ;
  • 김창민 (서울시립대학교 전자전기공학부)
  • Jeong, Min-Seop (Dept.of Electronics Electric Engineering, University of Seoul) ;
  • Kim, Yeong-Mun (Dept.of Electronics Electric Engineering, University of Seoul) ;
  • Kim, Chang-Min (Dept.of Electronics Electric Engineering, University of Seoul)
  • 발행 : 2000.02.01
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초록

수정된 Airy 함수들과 WKB 시도해를 조합하여 언덕형 굴절율 분포를 가지는 광섬유에 대한 매우 정확한 고유방정식을 수학적으로 유도하였다. 적절한 경계조건을 적용하여 일반적인 WKB 방법이 가지는 고유한 오차 문제를 개선하도록 위상 천이 보정항 δ를 이끌어냈다. 모의 전산을 통하여, 유도된 고유방정식의 결과가 유한차분법에 의한 결과와 잘 일치함을 보였다.

An almost exact eigenvalue equation for optical fibers with graded-index profile Is derived mathematically based on a combination of the modified Airy functions and the WKB trial solution. By applying proper boundary conditions, a phase shift correction term $\delta$ is found out which improves the inherent error problems of the conventional WKB method. It is shown through computer simulations that results of the derived eigenvalue equation are in excellent agreement with those of the finite-element method.

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참고문헌

  1. M. J. Adams, An introduction to optical waveguides, John Wiley & Sons, Ch. 8, 1981
  2. R. Srivastava, C. K. Kao, and R. V. Ramaswamy, 'WKB analysis of planar surface waveguides with truncated index profiles', J. Lightwave Technol., Vol. LT-5, No. 11 pp. 1605-1609, November 1987
  3. C. M. Kim and R. V. Ramaswamy, 'WKB analysis of asymmetric directional couplers and its application to optical switches', J. Lightwave Technol., Vol. LT-6, No.6, pp. 1109-1118, June 1988 https://doi.org/10.1109/50.4103
  4. F. Xiang and G. L. Yip, 'A modified WKB method for the improved phase shift at a turning point', J. Lightwave Technol., Vol. LT-6, No.3, pp. 443-452, March 1994 https://doi.org/10.1109/50.285327
  5. S. Roy, A. K. Ghatak, I. C. Goyal, and R. L. Gallawa, 'Modified Airy function method for the analysis of tunneling problems in optical waveguides and qunatum-well structures', IEEE J. Quantum Electron., Vol. QE-29, No.2, pp.340-345, February 1993 https://doi.org/10.1109/3.199287
  6. C. M. Kim and M. S. Chung, 'Eigenvalue equeations of N-parallel graded-index waveguides: WKB analysis', IEEE J. Quantum Electron., Vol. QE-33, No.9, pp.1608-1613, September 1997 https://doi.org/10.1109/3.622643