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PIER PIER B PIER C PIER M PIER Letters
2009-07-06
A New Look at Numerical Analysis of Uniform Fiber Bragg Gratings Using Coupled Mode Theory
By
Jiun-Jie Liau,

    Dr. Jiun-Jie Liau

    Department of Electrical Engineering

    I-Shou University

    Taiwan, R.O.C

    Homepage

Nai-Hsiang Sun,

    Dr. Nai-Hsiang Sun

    Department of Electrical Engineering

    I-Shou University

    Taiwan

    Homepage

Shih-Chiang Lin,

    Dr. Shih-Chiang Lin

    Department of Communication Engineering

    I-Shou University

    Taiwan

    Homepage

Ru-Yen Ro,

    Prof. Ru-Yen Ro

    Department of Electrical Engineering

    I-Shou University

    Taiwan

    Homepage

Jung-Sheng Chiang,

    Dr. Jung-Sheng Chiang

    Department of Electrical Engineering

    I-Shou University

    Taiwan

    Homepage

Chung-Long Pan,

    Dr. Chung-Long Pan

    Department of Electrical Engineering

    I-Shou University

    Taiwan

    Homepage

Hung-Wen Chang

    Prof. Hung-Wen Chang

    Department of Photonics

    National Sun Yat-sen University

    Taiwan, ROC

    Homepage

Progress In Electromagnetics Research, Vol. 93, 385-401, 2009
doi:10.2528/PIER09031102
Abstract
The coupled mode theory (CMT) is used to analyze uniform Fiber Bragg gratings. The multi-mode CMT is expressed as the first-order vector ordinary differential equations (ODEs) with coefficients depending on the propagation distance. We show in this paper that by changing variables, the original couple mode equations (CMEs) can be re-casted as constant coefficient ODEs. The eigenvalue and eigenvector technique (EVVT), the analytic method for solving constant coefficient ODEs, is then applied to solve the coupled mode equations. Furthermore, we also investigate the application of Runge-Kutta method (RKM) to the calculation of the global transfer-function matrix for CMEs. We compare the transmission and the reflection spectra obtained by EVVT with those by RKM. Both results agree within machine accuracy. Numerical simulations conclude that solving constant coefficient ODEs improves the speed and accuracy of solutions to the original CMEs.
Citation
Jiun-Jie Liau, Nai-Hsiang Sun, Shih-Chiang Lin, Ru-Yen Ro, Jung-Sheng Chiang, Chung-Long Pan, and Hung-Wen Chang, "A New Look at Numerical Analysis of Uniform Fiber Bragg Gratings Using Coupled Mode Theory," Progress In Electromagnetics Research, Vol. 93, 385-401, 2009.
doi:10.2528/PIER09031102
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