Master equation approach to the second harmonic and subharmonic generation

Federico Bosia, Nicola Maria Pugno, Alberto Carpinteri

Michael Dörfle, R. Graham

Second harmonic generation and subharmonic generation in a cavity are described by the usual master equation (1) for the statistical operator of the system of two modes (fundamental and second harmonic). The master equation is equivalent to a partial differential equation for the Wigner function which is a generalized Fokker-Planck equation involving partial derivatives of the first, second and third order (2). In the semi-classical limit the third order derivatives are negligible and the Wigner distribution satisfies the Fokker-Planck equation equivalent to the Langevin equation with the formally classical Gaussian white noise ξ1, ξ2 with the only non-vanishing correlation coefficients β1, β2 are the mode amplitudes (normalized to photon numbers), g is the coupling constant, Δ1, 2 the frequency mismatch, x is the damping rate, Fp the amplitude of the pump field.

Nicolas Pettiaux, Ruo-Ding Li, Paul Mandel

P. L. Chu, Boris A. Malomed, Gang‐Ding Peng

Zehui Zhai, Yongming Li, Jiangrui Gao

Quantum fluctuation and quantum entanglement of the pump fields reflected from an optical cavity for type-II second-harmonic generation are theoretically analyzed. The correlation spectra of quadrature components between the reflected subharmonic fields are interpreted in terms of pump parameter, intracavity losses, and normalized frequency. High correlation of both amplitude and phase quadratures can be accessed in a triple resonant cavity before the pitchfork bifurcation occurs. The two reflected subharmonic fields are in an entangled state with quantum correlation of phase quadratures and anticorrelation of amplitude quadratures. The proposed system can be exploited as a source for generating entangled states of continuous variables.

Z. Y. Ou

It is known1 that in type-I second-harmonic generation in a doubly resonant cavity where a subharmonic mode is coupled to a harmonio mode through a χ(2) process, self-pulsing may occur for high input fundamental power. Squeezing2 and QND measurements3 are possible near the self-pulsing threshold. For type-II harmonic generation, however, there are two sub-harmonic modes coupled to the harmonic mode through the same χ(2) process but with different arrangements of polarizations. The extra subharmonic mode will make the dynamics of the system totally different.