Abstract
In this study, we used differential geometry to develop an effective field theory to study the behavior of light propagation in distorted photonic crystals (DPCs) of averagely homogeneous refractive index media. To study the light-ray trajectories in DPCs, we derived a geodesic equation based on the principle of least action by defining the metric tensor in terms of the lattice-position distortion. The geodesic equation implies that the lattice-position distortion can curve the trajectory. We present multiple exact solutions for the trajectory for simple distortion under the condition of having the same values of the lattice point filling factor at each unit cell. These solutions explicitly demonstrate that the light is only bent through the introduction of lattice distortion, and that these results are consistent with the finite-difference time-domain simulation results.
- Received 30 November 2020
- Revised 25 May 2021
- Accepted 25 May 2021
DOI:https://doi.org/10.1103/PhysRevA.103.063506
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