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

Qiang Jiang,Binming Liang,Jiabi Chen,Jinbing Hu,Yan Wang,Songlin Zhuang

doi:10.1038/srep24790

Abstract

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 np (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.

Highlights

Where c is the vacuum velocity of light, f0 is the original frequency of the light source and f1 is the Doppler frequency at the second interface of the PhC, was used to calculate the frequency shift, and was based on phenomenological theory
The radius of the silicon rods was estimated to be 0.226a from the equi-frequency surface (EFS), which is close to the design requirement[6]
In terms of the phase evolution, by using the electrical field data obtained from the static finite different time domain (FDTD) method, we calculated the frequency difference between the signal and the reference beams at detection point

Summary

Introduction

Where c is the vacuum velocity of light, f0 is the original frequency of the light source (for instance, CO2 laser in ref. 6) and f1 is the Doppler frequency at the second interface of the PhC, was used to calculate the frequency shift, and was based on phenomenological theory. We were inspired to elucidate the physical mechanism underlying the inverse Doppler Effect in PhC and determine the rationale for using equation (1) to obtain the inverse frequency shift[6]. Based on observations of Bloch harmonics and negative phase velocities in PhC waveguides resulting from the typical dispersion[17], we believe that some spatial harmonics in LH-PhC have vp·k < 0 in terms of the decomposition of Bloch waves, which leads to the inverse Doppler effect in moving PhC. By analyzing the phase evolution of the entire optical path using the static finite different time domain (FDTD) method, we obtain a Doppler shift that is in accordance with the experimental results. An improved dynamic FDTD method is proposed to reproduce the continuous motion of the PhC in the experiment[6] to the greatest extent, and the rationality of np, which was used in Eq (1)[6] is verified

Methods

Results

Conclusion