Efficient procedures for the optimization of defects in photonic crystal structures.

Area of Science:

• Photonics
• Computational Physics
• Materials Science

Background:

• Photonic crystals offer unique light manipulation properties.
• Designing defect locations in photonic crystals is crucial for device functionality.
• Optimization algorithms are needed to efficiently explore complex design spaces.

Purpose of the Study:

• To develop and compare stochastic and quasi-deterministic binary optimizers for photonic crystal defect design.
• To assess the performance of these algorithms in finding optimal defect locations for high transmission.
• To introduce an algorithm for estimating bit-fitness values to enhance optimization.

Main Methods:

• Development and application of seven stochastic binary optimizers (genetic algorithms, evolutionary strategies) and one quasi-deterministic optimizer (hill-climbing inspired).
• Testing on photonic crystal structures, including waveguide bends and power dividers.
• Extensive statistical analysis and comparison of optimizer performance, including fitness table estimation.

Main Results:

• All eight optimizers outperformed standard codes in finding global optima with high probability.
• Many photonic crystal structures with high transmission can be found for any operating frequency.
• An extended microgenetic algorithm, two mutation-based algorithms, and the hill-climbing inspired algorithm were identified as the four best performers.

Conclusions:

• The developed optimizers are effective for optimizing defects in photonic crystals.
• The proposed bit-fitness estimation algorithm improves optimizer performance.
• The four best algorithms are valuable for photonic crystal optimization and similar binary optimization problems.