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.

Figure 1

(a) Schematic diagram of the theoretical setup. The right panel stands for the spatiotemporal change in $\left|\mathrm{\Delta }n\right|$. It shows the process of the spatiotemporal dynamic tuning on PhC. $a=702\mathrm{nm}$ is the lattice constant. (b) Band diagram of the third, fourth, and fifth TE bands. The self-collimation effect can occur at the normalized frequencies in the gray-shaded area. (c) Equifrequency contour (EFC) for the PhC structures of the fifth TE band.

Figure 2

(a,b) The transmission and reflection spectra of the setup shown in Fig. 1. (c) The electric field as a self-collimated beam propagating from left to right.

Figure 3

(a) Calculated signal spectra. Excitation is given around the wavelength centered at ${\lambda }_{\mathrm{in}}=1550\mathrm{nm}$, which corresponds to $k_x=0.87$ shown in Fig. 1. Here, $c$ is the velocity of light in vacuum and for simplicity we set $c=3\times {10}^8\mathrm{m}/\mathrm{s}$. The temporal full width at half maximum of the initial pulse is 1.6 ps. (b) The signal spectra of different $\mathrm{\Delta }n$ but the same velocity $v_m=0.06c$. (c) The signal spectra corresponding to different $\mathrm{\Delta }n$ but at the same velocity $v_m=0.09c$.

Figure 4

(a) The field intensity of the line alone the direction of the light. (b) Amplitude observed near the excitation source. (c) Wavelet transform of the signal in (b).