Generalization of Second-Order Quasi-Phase Matching in Whispering Gallery Mode Resonators Using Berry Phase

Abstract

Second-order nonlinearities in whispering gallery mode resonators are highly investigated for their many applications such as wavelength converters, entangled photon sources, and generation of frequency combs. In such systems, depending on the material under scrutiny, the derivation of quasi-phase matching equations can lead to the appearance of additional quanta in the selection rule on the azimuthal confinement order. Here, we demonstrate that these additional quanta show up due to the Berry phase experienced by the transverse spin angular momentum components of the whispering gallery modes during their circulation within the resonator. We first detail the case of Zinc-blende materials and then generalize this theory to other crystal symmetries relevant for integrated photonics

Nonlinear optics in gallium phosphide cavities: simultaneous second and third harmonic generation

“…In the case of a cavity with cylindrical symmetry, the phase matching conditions of a nonlinear process can be expressed in terms of the azimuthal indices m [33]. Additional angular momentum quanta are accumulated due to the Berry phase of the WGM orbiting the cavity [34], whose amount depends on the symmetry of the cavity material's crystal lattice [35]. GaP possesses 43m symmetry, with the crystal axis inverting with a π/2 rotation.…”

Nonlinear optics in gallium phosphide cavities: simultaneous second and third harmonic generation

“…In the case of a cavity with cylindrical symmetry, the phase matching conditions of a nonlinear process can be expressed in terms of the azimuthal indices m [20]. Additional angular momentum quanta are accumulated due to the Berry phase of the WGM orbiting the cavity [53], whose amount depends on the symmetry of the cavity material's crystal lattice [29]. GaP possesses 43m symmetry, with the crystal axis inverting with a π/2 rotation.…”

Broadband highly efficient nonlinear optical processes in on-chip integrated lithium niobate microdisk resonators of Q-factor above 108

“…The versatility of broadband NQPM for a wide range of nonlinear optical processes, including SHG, THG, FHG, and OPO, realized on the same microdisk resonator is quite appealing for further investigations. Previous works have unveiled the indispensable role of the natural 'poling' of the effective nonlinearity in X-cut LN microdisk on mitigating the wave-vector mismatch (Δk) which is also oscillating due to the anisotropic refractive indices along the periphery of the microdisk [44,49]. Specifically, the oscillation of Δk relaxes the stringent requirement by QPM at unique poling period.…”