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Calculation of optical-waveguide grating characteristics using Green's functions and Dyson's equation
Lars Rindorf1, Niels Asger Mortensen
1COM.DTU, Department of Communications, Optics and Materials, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
Summary
We developed a Green's function method to precisely calculate optical waveguide grating properties. This approach accurately models Bragg and long-period gratings with complex modulations, offering efficient O(N) scaling.
Area of Science:
- Photonics
- Waveguide Optics
- Computational Electromagnetics
Background:
- Optical waveguide gratings are crucial for various photonic applications.
- Accurate modeling of complex grating structures, including chirp and apodization, remains challenging.
- Existing methods may struggle with arbitrary dielectric modulations and imperfections.
Purpose of the Study:
- To present a novel, exact method for calculating optical waveguide grating characteristics.
- To address the limitations of current methods in modeling complex grating designs.
- To provide a computationally efficient tool for analyzing diverse grating types.
Main Methods:
- Utilizing Green's functions and Dyson's equation derived from the wave equation for transverse electric modes.
- Applying the method to analyze coupling of counterpropagating waves (Bragg gratings) and co-propagating waves (long-period gratings).
- Developing a numerical approach with O(N) computational complexity, where N is the number of discretization points.
Main Results:
- The method exactly solves for transmission spectra, dispersion, and time delay.
- It accurately models gratings with arbitrary dielectric modulation, including chirp, apodization, and imperfections.
- The approach is demonstrated for optical fiber gratings but is applicable to all 1D waveguide gratings.
Conclusions:
- The Green's function and Dyson's equation method offers an exact and efficient solution for analyzing optical waveguide gratings.
- This method provides a versatile tool for designing and understanding complex grating structures in photonics.
- The O(N) scaling makes it suitable for analyzing large and intricate photonic devices, including photonic crystals.
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