Nonlinear Čerenkov Radiation in Nonlinear Photonic Crystal Waveguides

We study nonlinear Čerenkov radiation generated from a nonlinear photonic crystal waveguide where the nonlinear susceptibility tensor is modulated by the ferroelectric domain. Nonlinear polarization driven by an incident light field may emit coherently harmonic waves at new frequencies along the direction of Čerenkov angles. Multiple radiation spots with different azimuth angles are simultaneously exhibited from such a hexagonally poled waveguide. A scattering involved nonlinear Čerenkov arc is also observed for the first time. Čerenkov radiation associated with quasi-phase matching leads to these novel nonlinear phenomena.

Figure 1

A collection of dipoles ($P_{\mathrm{non}}$) driven by incident light emits coherent radiation. In nonlinear photonic crystal $P_{\mathrm{non}}$ will change its phase $+\pi$ (dashed) or $-\pi$ (solid) as ${\chi }^{(2)}$ alters its sign compared with that in homogenous material (dotted), which leads to an effective change in the phase velocity of $P_{\mathrm{non}}$ as well as Čerenkov angle.

Figure 2

Phase-matching process for NCR in nonlinear photonic crystal waveguide. Dashed lines represent polarization and curves are radiation waves. The insets are (a) domain structure and (b) reciprocal lattice of hexagonally poled ${\mathrm{LiTaO}}_3$.

Figure 3

The pattern of NCR from fundamental waves of $1.064$ and $1.319\mu \mathrm{m}$ projected on the screen behind the sample: (a) measured and (b) calculated.

Figure 4

Phase-matching processes for Čerenkov arcs of direct NCR (a) and QPM-NCR involving ${\overrightarrow{G}}_{-1,1}$ and ${\overrightarrow{G}}_{1,0}$ (b) with scattered ${\overrightarrow{\beta }}^{\prime }({\omega }_2)$.

Figure 5

Dependence of SH power on input power of fundamental $1.064\mu \mathrm{m}$. (a) Direct Čerenkov SHG and (b) QPM Čerenkov SHG with ${\overrightarrow{G}}_{1,-1}$. Dots are measured data which are well fitted to be quadratic (line).