Doppler shift generated by a moving diffraction grating under incidence by polychromatic diffuse light

TL;DR

This paper explores how moving diffraction gratings affect the spectral response of broad angular incident light, revealing unique features like flat bands and spectral compression due to Doppler shifts, with implications for devices and natural phenomena.

Contribution

It introduces the spectral response of moving gratings under polychromatic diffuse light, highlighting unique dispersion features and potential for spectral compression and intensity enhancement.

Findings

Flat band in dispersion relation near Wood anomalies

Spectral compression due to Doppler shifts from multiple incident angles

Potential for increased diffracted light intensity using moving gratings

Abstract

We consider the spectral response of moving diffraction gratings, in which the incident light extends over a broad angular range and where the diffracted light is observed from a specific angle. We show that the dispersion relation between the frequency perceived by an observer who is looking at a moving grating and the incident frequency can exhibit some unique features, such as a flat band (i.e., a local minimum). An observer can see the light diffracted into a non-specular diffraction order from a multitude of incident light rays and the angle of incidence of each ray is frequency-dependent, as a consequence, when the grating is moving, each incident ray experiences a Doppler shift in frequency that depends on its angle of incidence. We find that remarkable features appear near a Wood anomaly where the angle of incidence, for a given diffraction angle, can change very quickly with frequency. This means that light of multiple frequencies and incident from multiple angles can be mixed by the motion of the grating into the same diffracted ray and their frequencies can be compressed into a narrower range. The existence of a flat band means that a moving grating can be used as a device to increase the intensity of the perceived diffracted light due to spectral compression. The properties of a grating in motion in sunlight can also be relevant to the study of naturally occurring gratings which are typically in oscillatory motion.