Photonic Quasicrystals for Nonlinear Optical Frequency Conversion

We present a general method for the design of 2-dimensional nonlinear photonic quasicrystals that can be utilized for the simultaneous phase matching of arbitrary optical frequency-conversion processes. The proposed scheme—based on the generalized dual-grid method that is used for constructing tiling models of quasicrystals—gives complete design flexibility, removing any constraints imposed by previous approaches. As an example we demonstrate the design of a color fan—a nonlinear photonic quasicrystal whose input is a single wave at frequency $\omega$ and whose output consists of the second, third, and fourth harmonics of $\omega$, each in a different spatial direction.

Figure 1

The color fan.

Figure 2

Structure of the photonic quasicrystal, produced with the parameters of Table . Scale is in $\mu \mathrm{m}$, drawn with an aspect ratio of approximately $1:20$. Red arrows indicate the three tiling vectors ${\mathbf{a}}^{(i)}$.

Figure 3

Numerical Fourier transform of the crystal in Fig. 2 showing Bragg peaks at the positions of the required mismatch vectors, as indicated by arrows. Scale is in $(\mu \mathrm{m}{)}^{-1}$; intensity is in arbitrary units.