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Arbitrary-order interface conditions for slab structures and their applications in waveguide analysis
1Graduate Institute of Photonics and optoelectronics, National Taiwan University, Taipei 106-17, Taiwan.
Optics Express
|April 15, 2010
Summary
This study develops higher-order finite-difference methods for analyzing wave propagation in slab structures. These advanced techniques significantly improve accuracy and reduce computational resources for waveguide analysis.
Area of Science:
- Electromagnetics and Wave Propagation
- Computational Physics
- Materials Science
Background:
- Continuity relations are crucial for modeling electromagnetic wave behavior at interfaces.
- Existing finite-difference methods often struggle with accuracy and computational cost for complex waveguide structures.
- Higher-order approximations are needed to capture intricate wave phenomena in advanced optical devices.
Purpose of the Study:
- To extend continuity relations for field derivatives to arbitrary orders for transverse electric and magnetic waves.
- To develop a higher-order finite-difference formulation for analyzing guided modes in slab waveguides.
- To enhance computational efficiency and accuracy in electromagnetic wave simulations.
Main Methods:
- Systematic derivation of interface conditions for arbitrary order derivatives.
- Application of Taylor series expansion to develop higher-order finite-difference schemes.
- Incorporation of the Generalized Douglas scheme to improve error convergence by two orders.
- Numerical solution of guided modes in simple and multiple quantum well waveguides using the developed formulation.
Main Results:
- The developed finite-difference formulation achieves high-order truncation error (up to tenth order).
- Accurate results for guided modes were obtained in both simple and multiple quantum well waveguides.
- Significant reduction in sampled points, computation time, and memory usage was observed compared to lower-order methods.
- Validation of the higher-order schemes' effectiveness in complex waveguide scenarios.
Conclusions:
- The higher-order finite-difference formulation provides a computationally efficient and accurate method for analyzing guided modes in slab waveguides.
- The approach effectively handles abrupt interfaces and arbitrary order field derivatives.
- This work offers a valuable tool for the design and simulation of advanced optical and photonic devices.
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