Mechanism Analysis of the Inverse Doppler Effect in Two-Dimensional Photonic Crystal based on Phase Evolution

Although the inverse Doppler effect has been observed experimentally at optical frequencies in photonic crystal with negative effective refractive index, its explanation is based on phenomenological theory rather than a strict theory. Elucidating the physical mechanism underlying the inverse Doppler shift is necessary. In this article, the primary electrical field component in the photonic crystal that leads to negative refraction was extracted, and the phase evolution of the entire process when light travels through a moving photonic crystal was investigated using static and dynamic finite different time domain methods. The analysis demonstrates the validity of the use of n(p) (the effective refractive index of the photonic crystal in the light path) in these calculations, and reveals the origin of the inverse Doppler effect in photonic crystals.