Abstract
We present a theoretical description of on- and off-resonance, 4¯-quasi-phasematched, second-harmonic generation (SHG) in microdisks made of GaAs or other materials possessing 4¯ symmetry, such as GaP or ZnSe. The theory describes the interplay between quasi-phasematching (QPM) and the cavity-resonance conditions. For optimal conversion, all waves should be resonant with the microdisk and should satisfy the 4¯-QPM condition. We explore χ(2) nonlinear mixing if one of the waves is not resonant with the microdisk cavity and calculate the second-harmonic conversion spectrum. We also describe perfectly destructive 4¯-QPM where both the fundamental and second-harmonic are on-resonance with the cavity but SHG is suppressed.
Highlights
GaAs and other zincblende-structured crystals such as GaP and ZnSe are attractive nonlinear optical materials because of their large nonlinear coefficients and broad transmission ranges
The 43m symmetry of zincblende semiconductors means that a 90° rotation about the axis is equivalent to a domain inversion
We explore the effects of varying microdisk radius and temperature on the SH conversion spectrum in Section 3, which is important for experimental realization of second-harmonic generation (SHG) in a GaAs microdisk
Summary
GaAs and other zincblende-structured crystals such as GaP and ZnSe are attractive nonlinear optical materials because of their large nonlinear coefficients and broad transmission ranges. 4 -QPM allows efficient χ(2) nonlinear optical mixing of the whisperinggallery modes of a GaAs microdisk without using external domain inversions. Waves propagating around a -normal GaAs microdisk effectively experience four 90° rotations and four domain inversions. We explore the interplay between cavity resonances and 4 -QPM in enhancing nonlinear-conversion efficiency in a GaAs microdisk. We describe perfectly destructive 4 -quasi-phasematching where both the fundamental and second-harmonic waves are on-resonance but SHG is suppressed. It is reasonable to ask what the effective propagation constant is at a wavelength that does not fall at a cavity resonance. We can extend the description of SHG in a microdisk to include cases where the fundamental and/or SH waves are not resonant with the cavity by replacing ∆m by ∆m′ in Eqs. C is the speed of light, λi is the wavelength, and δ fi,FSR is FSR in frequency units of wave i
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