Multiple-wavelength conversion based on the anomalous Doppler effect induced by dynamic tuning in a self-collimation photonic crystal

The Doppler effect of relative motion-induced frequency shift as an interesting fundamental wave phenomenon draws significant research interest in many applied aspects of physics and engineering. Photonic settings represent an important class of platforms to observe and manipulate this effect. Here, an anomalous Doppler effect via dynamic index tuning in a photonic crystal (PhC) is proposed and investigated theoretically by considering the guided reflection of light from a moving front at near the speed of light. A virtual waveguide constructed in a square lattice PhC slab utilizing the self-collimation effect is proposed, and the moving equivalent reflector is realized by photonic band shift induced by a pump light for changing the refractive index dynamically. The anomalous Doppler shift occurs at multiple wavelengths, which depends on the Bloch nature of this photonic crystal and its band structure. Moreover, another kind of small spectral shift caused by adiabatic wavelength conversion is also observed. This nonstationary procedure is studied combining the full-wave numerical simulation and wavelet transform analysis. This work sheds light on the emergence of anomalous Doppler effect and wavelength conversion via dynamic index tuning in photonic crystals and can be important for manipulating such effects in practical photonic devices.