Abstract

Accurate eigenvalue equations for planar waveguides with arbitrarily graded-index profile are derived and expressed in closed forms. A combination of the modified Airy functions and the Wenzel-Kramers-Brillouin (WKB) solutions are employed as field solutions, which turn out to represent almost exact field profiles. The use of new trial solutions enables us to calculate phase shifts at turning points very precisely, allowing us almost exact eigenvalues. It is demonstrated that the results obtained by the proposed method are in excellent agreement with those by the finite element method,achieving significant improvement over the conventional WKB method.

[IEEE ]

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  1. F. Xiang and G. L. Yip, "A modified WKB method for the improved phase shift at a turning point", J. Lightwave Technol., vol. 12, pp. 443-452, Mar. 1994.
  2. I. C. Goyal, R. Jindal and A. K. Ghatak, "Planar optical waveguides with arbitrary index profile: An accurate method of analysis", J. Lightwave Technol., vol. 15, pp. 2179-2182, Nov. 1997.
  3. M. S. Chung and C. M. Kim, "Analysis of optical fibers with graded-index profile by a combination of modified Airy functions and WKB solutions", J. Lightwave Technol., vol. 17, pp. 2534-2541, Dec. 1999 .

J. Lightwave Technol. (3)

F. Xiang and G. L. Yip, "A modified WKB method for the improved phase shift at a turning point", J. Lightwave Technol., vol. 12, pp. 443-452, Mar. 1994.

I. C. Goyal, R. Jindal and A. K. Ghatak, "Planar optical waveguides with arbitrary index profile: An accurate method of analysis", J. Lightwave Technol., vol. 15, pp. 2179-2182, Nov. 1997.

M. S. Chung and C. M. Kim, "Analysis of optical fibers with graded-index profile by a combination of modified Airy functions and WKB solutions", J. Lightwave Technol., vol. 17, pp. 2534-2541, Dec. 1999 .

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