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Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory
L C Botten1, T P White, A A Asatryan
1Centre for Ultrahigh-Bandwidth Devices for Optical Systems (CUDOS) and Department of Mathematical Sciences, University of Technology, Sydney, Broadway New South Wales 2007, Australia. Lindsay.Botten@uts.edu.au
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
Summary
We developed a Bloch mode scattering matrix method to model 2D photonic crystals. This approach accurately predicts how light propagates, reflects, and transmits through these complex optical structures.
Area of Science:
- Photonics
- Condensed Matter Physics
- Computational Electromagnetics
Background:
- Photonic crystals offer unique light manipulation properties.
- Accurate modeling of light propagation in photonic crystals is crucial for device design.
- Existing methods may face challenges with complex or inhomogeneous structures.
Purpose of the Study:
- To introduce a rigorous Bloch mode scattering matrix method for 2D photonic crystals.
- To establish the formal properties and theoretical underpinnings of the method.
- To enable accurate simulation of light interaction with photonic crystal interfaces.
Main Methods:
- Developed a scattering matrix formalism based on Bloch modes.
- Incorporated reciprocity and energy conservation principles.
- Derived modal orthogonality and normalization relations for inhomogeneous media.
Main Results:
- Established a rigorous method for modeling 2D photonic crystal structures.
- Derived key relations for Bloch mode propagation, reflection, and transmission.
- Demonstrated the applicability of the method to interfaces between photonic crystals.
Conclusions:
- The Bloch mode scattering matrix method provides a robust framework for photonic crystal analysis.
- The method facilitates the study of light propagation and interface phenomena.
- This formulation is essential for the design and optimization of photonic devices.