Coupled micro-resonators for second-order integrated nonlinear optics

Abstract

We investigate second-order nonlinear processes in a system of two coupled identical optical micro-resonators. The double resonance and phase-matching conditions are simultaneously obtained thanks to the frequency splitting induced by the resonator coupling. The analysis made in the framework of the coupled mode theory is applied to the second harmonic generation process in two whispering gallery mode microdisks made in III-V materials.

Figures (5)

• Figure 1: System of coupled ring or disk resonators of perimeter $2L$. $A_i$ and $B_i$ are the F and SH mode amplitudes within the structure. $k_i$ are the coupling between the access bus waveguides and the structure. $\kappa_i$ are the coupling coefficient between the two resonators. $A_{in}$ is the input F mode amplitude. $A_T$ and $B_T$ are the F and SH output mode amplitude on the trough port. $A_D$ and $B_D$ are the output mode amplitude on the drop port.
• Figure 2: Description of the structure numerically studied consisting of two GaP WGM microdisks embedded in air. a) side view and b) top view. $g$ is the air gap separating the two disks, $H$ and $R$ are their thickness and radius.
• Figure 3: Transmission spectra calculated on the drop port and azimutal quantum number mismatch. a) for a single resonator the double resonance $\nu_{F0}=\nu_{SH0}/2$ and the condition $|\Delta m-2|<1/2$ can not be fulfilled due to the dispersion. b) By coupling the two disks it is possible to reach both conditions simultaneously.
• Figure 4: a) Nonlinear detuning $\delta(g)$ calculated using a combinations of FDTD simulations and EIM. b) Coupling coefficients $\kappa_1$ and $\kappa_2$ deduced from FDTD simulations. The vertical dashed line gives the air gap value $g_0$ fulfilling the double resonance condition.
• Figure 5: Conversion efficiency $\eta(\nu_F)$ calculated for $\delta(g_0)=0$.