Abstract
The dual Doppler effect, in the simultaneous occurrence of both normal and inverse Doppler effect in one moving two-dimensional wedge-type photonic crystal, is proposed. An improved finite-different time-domain algorithm is used to verify this phenomenon. The spatial Fourier Transformation has been applied to complex electrical field data to reveal the mechanism. The harmonics with negative spatial frequencies show a lagging phase evolution, while those with positive spatial frequencies show a front phase evolution. Different wedge-type photonic crystals are designed to filter out the required harmonics based on the systematic study of spatial Fourier Transformation and wave vector diagram. Our work paves a new way for Doppler cooling of atomic gases, radar deception, invisibility cloaks, microstructure dual frequency interferometer and so on.
Highlights
The Doppler effect can be observed in every walk of life
The negative refractive index (NRI) feature can be observed in some photonic crystals (PhC) whose equi-frequency contour (EFC) is shrinking towards center
Seddon’s experiment[2,14,15], we have revealed that the inverse Doppler shift in the PhC is caused by some spatial harmonics in the PhC which have vg ⋅ k < 0 in terms of the decomposition of Bloch waves, where vg is the group velocity
Summary
Applications of the effect has been widely established, including radar, laser vibrometry, blood flow measurement, and the search for new astronomical objects It can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in the frequency for observers towards which the source is approaching. Seddon with an experimental magnetic, nonlinear transmission line in 20032 After that, this anomalous effect was observed in more than one kind of special dispersive media, like left-handed material (LHM) whose effective permittivity ε and permittivity μ are both negative, and photonic crystals (PhC) using shock discontinuities[3]. It is significant to investigate the Doppler effect phenomenon in the PhC if both backward waves and forward waves couple to the vacuum by appropriate design of the wedge type of the photonic crystal. It is firstly observed that the dual Doppler shift is governed by the forward wave and backward wave in the PhC, and the shifts can be calculated with the effective indexes of the PhC corresponding to each harmonic
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