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Journal of Optics B Quantum and Semiclassical Optics

Spectral properties of the single beams generated by an optical parametric oscillator

A. Porzio, C. Altucci, Paolo Aniello, A. Chiummo, Corrado de Lisio, S. Solimeno

Published Aug 1, 2002• 4 citations
Publisher

Abstract

The quantum nature of the parametric interaction affects the spectral properties of the single output beams in a way which depends critically on the damping coefficients of the signal, idler and pump modes. When they are of the same order relaxation oscillations appear in the single-beam spectra. The single outputs are described in the frequency domain by analytic transfer functions, representing the system response to white noise sources. We report numerical simulations of the single-beam spectra referring to different optical parametric oscillator working conditions. In particular we study how these spectra depend on detuning, pumping level and cavity dampings to better clarify the conditions for which relaxation oscillations appear.

DOI
10.1088/1464-4266/4/4/313

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The quantum nature of the parametric interaction affects the spectral properties of the single output beams in a way which depends critically on the damping coefficients of the signal, idler and pump modes. When they are of the same order relaxation oscillations appear in the single-beam spectra. The single outputs are described in the frequency domain by analytic transfer functions, representing the system response to white noise sources. We report numerical simulations of the single-beam spectra referring to different optical parametric oscillator working conditions. In particular we study how these spectra depend on detuning, pumping level and cavity dampings to better clarify the conditions for which relaxation oscillations appear.
The dependence of quantum correlations of twin beams on the pump finesse of an optical parametric oscillator is studied via a semi-classical analysis. It is found that the phase-sum correlation of the output signal and idler beams from an optical parametric oscillator operating above threshold depends on the finesse of the pump field when the spurious pump phase noise generated inside the optical cavity and the excess noise of the input pump field are involved in the Langevin equations. The theoretical calculations can explain the previously experimental results quantitatively.
We investigated the intensity noise spectra of a single beam of a pump-enhanced continuous-wave optical parametric oscillator (OPO), which was used to generate quantum-correlated twin beams, as a function of the pump power. With a triply (pump-, signal-, and idler-) resonant cavity, the oscillation threshold of our OPO was 8.5±1.3 mW and the measured slope conversion efficiency was 0.72±0.02. Twin beams with a power of 240 mW were generated at a pump power of 350 mW. The relaxation oscillation frequencies, which depend on the pump power, were observed when the pump power of the OPO was 12.5–28 mW. The experimental results confirm the predicted increase in OPO relaxation frequency with pump power. We experimentally inferred squeezing of the single-beam intensity, for the first time to our knowledge, by exploiting the nature of quantum noise that is dependent on loss.
We investigated the intensity noise spectra of the single beam of a pump-enhanced continuous-wave (cw) optical parametric oscillator (OPO), which was used to generate quantum correlated twin beams, as a function of the pump power. With a triply (pump-, signal-, and idler-) resonant cavity, the oscillation threshold of our OPO was about 8.5+/-1.3 mW and the measured slope conversion efficiency was 0.72+/-0.02. A twin beams with power of 240 mW were generated at pump power of 350 mW. The relaxation oscillation frequencies, which depend on the pump power, were observed when the pump power of OPO was from 12.5 mW to 28 mW. The experimental results confirm the predicted increase in OPO relaxation frequency with pump power. Squeezing of the single beam intensity was for the first time inferred experimentally by exploiting nature of quantum noise dependent on loss.
Optical parametric amplifiers (OPA's) and optical parametric oscillators (OPO's) can exhibit squeezed amplification when an injected signal beam is used to elicit small-signal gain saturation. This paper extends previous work on OPA/OPO noise behavior under signal injection. Doubly resonant and triply resonant, single-ended cavities are considered in the good-cavity limit. Owing to the nonlinear coupling between the signal and idler beams within the cavity, both are sensitive to the detuning of each beam from its respective resonance. Signal and idler output noise spectra are found by linearizing the quantum coupled-mode equations about the classical mean-field solutions. Cavity detunings lead to frequency dependent phase shifts between the low-noise and high-noise quadratures of both the signal and idler beams. Moreover, the phase of the low-noise quadrature need not coincide with that of the corresponding mean field. The resulting large-signal, signal-to-noise ratio improvement afforded by squeezed amplification is therefore sensitive to the cavity detunings. The effects of classical excess noise on the pump beam and the injected signal beam are also considered.
SUMMARY Parametric processes in the interaction of electromagnetic field with a medium in an optical cavity are well known to produce states of light with nonclassical properties. The quantum correlations between these states can be employed for a realization of an EinsteinPodolsky-Rosen (EPR) paradox [l], in the original formulation using continuous variables, as proposed [2] and experimentally demonstrated [3] in the case of Nondegenerate Parametric Amplification below threshold. In this paper we study EPR-like behaviour between the signal and idler fields emitted by a degenerate optical parametric oscillator (OPO) above threshold; these fields, generated by conversion of a pump photon of frequency 2w0 in two photons of frequency w. , are spatially separated in the far field, showing non-local quantum correlations. The system is described by the full Hamiltonian for the operators associated with the pump and signal fields; the optical cavity introduces proper damping constants and corresponding vacuum field operators [4,5]. Above the threshold for the generation of the signal field, we consider the fluctuations in the intensity difference and in the phase sum of the signal beams, which are related to their degree of mutual correlation. By linearizing around the stationary state, we calculate the spectral variances of these quantities (i.e. the Fourier transform of the two time correlation functions). The Heisenberg uncertainty principle sets a lower limit to the product of the spectral variances for the fluctuations in the intensity and in the phase of each individual signal field; by using the idler beam to infer results of measurements on the correlated signal beam, we have an EPR paradox if the product of the spectral variances for the fluctuations in the intensity difference and phase sum of the fields, is below the uncertainty limit. This feature is apparent for a wide interval around zero frequency in the far field of the active OPO system, depending on the parameter space; in particular there is maximum correlation between signal beams, and therefore maximum breaking of the uncertainty limit, if the damping constant of the signal field is larger than that of the pump field.