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Laser Physics Letters

General formula for the natural width of optical parametric oscillator spectral lines

A. S. Chirkin

Published Oct 1, 2020• 1 citation
Publisher

Abstract

Abstract A new approach to the quantum analysis of the spectral linewidths of optical parametric oscillators (OPOs) is proposed. The approach is based on introducing a Hermitian frequency deviation operator. The spectral linewidths in the triply resonant OPO above-threshold regime have been calculated. It has been found that the width of the generated spectral line depends on the loss at all interacting frequencies, the photon number of frequency under study, and the threshold photon number of pump. The formula obtained for the spectral width is general; in particular cases, it yields the well-known results. The developed simple approach can be applied to the quantum analysis of the spectra of various oscillatory systems, for example, the multifrequency parametric and non-linear optomechanical interactions and lasers.

DOI
10.1088/1612-202x/abb6e6

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Abstract A new approach to the quantum analysis of the spectral linewidths of optical parametric oscillators (OPOs) is proposed. The approach is based on introducing a Hermitian frequency deviation operator. The spectral linewidths in the triply resonant OPO above-threshold regime have been calculated. It has been found that the width of the generated spectral line depends on the loss at all interacting frequencies, the photon number of frequency under study, and the threshold photon number of pump. The formula obtained for the spectral width is general; in particular cases, it yields the well-known results. The developed simple approach can be applied to the quantum analysis of the spectra of various oscillatory systems, for example, the multifrequency parametric and non-linear optomechanical interactions and lasers.
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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.
Coherence properties of light beams generated by optical parametric oscillators (OPOs) are discussed in the region of threshold. Analytic expressions, that are valid throughout the threshold region, for experimentally measurable quantities such as the mean and variance of photon number fluctuations, squeezing of field quadratures, and photon counting distributions are derived. These expressions describe non-Gaussian fluctuations of light in the region of threshold and reproduce Gaussian fluctuations below and above threshold, thus providing a bridge between below and above threshold regimes of operation. They are used to study the transformation of fluctuation properties of light as the OPOs make a transition from below to above threshold. The results for the OPOs are compared to those for the single-mode and two-mode lasers and their similarities and differences are discussed.
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.
A full quantum treatment about the process of parametric down-conversion with frequency degenerate but polarization non-degenerate in an optical parametric oscillator (OPO) cavity is presented. Using the linearized Langevin equations and spectral matrix, we calculated the squeezing spectra of the coupled mode in the output field. The squeezing as a function of driving field and detection frequency is obtained. The results obtained, which are compared with those found semiclassically by Reynaud et al. , indicate that it is possible to generate a two-mode coherent squeezed state with large amplitude. The quantum correlation between the signal and the idler modes is also discussed. It is shown that there is an inseparable relationship between the two-mode squeezing and the intermode quantum correlation.
We present in this paper a general model for determining the quantum properties of the light generated by a synchronously pumped optical parametric oscillator (SPOPO) operating below threshold. This model considers time and frequency on an equal footing, which allows us to find new quantum properties, related for example to the carrier envelope offset (CEO) phase, and to consider situations that are close to real experiments. We show that, in addition to multimode squeezing in the so-called ‘supermodes’, the system exhibits quadrature entanglement between frequency combs of opposite CEO phases. We have also determined the quantum properties of the individual pulses and their quantum correlations with the neighboring pulses. Finally, we determine the quantum Cramer–Rao limit for an ultra-short time delay measurement using a given number of pulses generated by the SPOPO.