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Physical Review A

Giant subthreshold amplification in synchronously pumped optical parametric oscillators

Giampaolo D’Alessandro, F. Papoff

Published Aug 7, 2009• 6 citations
Publisher

Abstract

Synchronously pumped parametric oscillators have been shown to have subthreshold giant amplification of such a magnitude that a macroscopic, entirely noise-driven, signal is present at output even when the device is below threshold. In this paper we quantify the magnitude of the amplification factor in terms of some key device parameters. We use non-normal operator theory to find the noise amplification factor (Kreiss constant) and show that the signal amplitude is proportional to it. We also determine that the noise sensitivity depends in a nontrivial way on the group velocity of the three fields.

DOI
10.1103/physreva.80.023804

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Synchronously pumped parametric oscillators have been shown to have subthreshold giant amplification of such a magnitude that a macroscopic, entirely noise-driven, signal is present at output even when the device is below threshold. In this paper we quantify the magnitude of the amplification factor in terms of some key device parameters. We use non-normal operator theory to find the noise amplification factor (Kreiss constant) and show that the signal amplitude is proportional to it. We also determine that the noise sensitivity depends in a nontrivial way on the group velocity of the three fields.
Noise plays a very important role in synchronously pumped optical parametric oscillators (SPOPOs). For example, these devices have been suggested as tunable source of short pulses. However, it was shown that in the pulse compression regime the signal pulses may suffer from considerable noise-induced jitter. In the context of quantum optics, optical parametric oscillators have been suggested as a tool to amplify and detect quantum fluctuations. However, this requires very large amplification factors.
Quantum fluctuations and squeezing of the signal field generated by a degenerate optical parametric oscillator are sensitive to the phase and amplitude fluctuations of the second-harmonic pump. The analysis reported here extends our previous calculations for a perfectly monochromatic noise-free pump to allow for finite pump amplitude and phase fluctuations. We treat the typically intense pump field with its fluctuations as a classical Gaussian stochastic process in two limits: first, when the pump has amplitude fluctuations but its phase is fixed and second, when its phase diffuses but its amplitude is fixed. Since pump amplitude noise affects the evolution of the signal field multiplicatively, it has a lesser impact on the quantum fluctuations of the signal than pump phase diffusion which compromises such fluctuations via the extreme phase sensitivity of the parametric amplification process. For the latter limit, our calculations extend the work of Gea-Banacloche and Zubairy [Phys. Rev. A 42, 1742 (1990)] to cavities with arbitrary transmission coefficients for the bounding mirrors.
Recently optical parametric amplifiers (OPAs) with vacuum inputs have been extensively studied and shown to generate a significant amount of squeezing, but little is known about the quantum noise behavior of an OPA with an injected signal field. We have performed a linearized quantum analysis of a nondegenerate OPA operated in the saturated gain regime showing that the amplified output intensity of a coherent-state input signal becomes squeezed when the classical small-signal gain falls below unity. In uses such as master-oscillator power amplifiers, for which the signal of interest is the mean output intensity, the output signal-to-noise ratio (SNR) can be higher than the input SNR over a broad operating range. For an OPA pumped at 90% of threshold, the SNR improvement is about a factor of 3, and with a 10-Db amplitude squeezed pump, the improvement increases to about a factor of 7. Such a tunable gain-saturated OPA with large-signal gain and improved SNR can be potentially useful in digital communication.
The redistribution of intrinsic quantum noise in the quadratures of the field generated in a sub-threshold degenerate optical parametric oscillator exhibits interesting dependences on the individual output mirror transmittances, when they are included exactly. We present a physical picture of this problem, based on mirror boundary conditions, which is valid for arbitrary transmittances. Hence, our picture applies uniformly to all values of the cavity Q factor representing, in the opposite extremes, both perfect oscillator and amplifier configurations. Beginning with a classical second-harmonic pump, we shall generalize our analysis to the finite amplitude and phase fluctuations of the pump.
The quantum analysis of radiation from a degenerate optical parametric oscillator synchronously pumped above its oscillation threshold is presented. It is shown that pulses of signal and pump fields at the output of the oscillator have the following properties: quantum fluctuations of the fields are independent in each individual pulse, but correlated in pulses of the pulse train with a temporal step multiple of the pulse period. The number of essentially correlated pulses is on the order of the oscillator cavity finesse. Cross-correlations between the pump and signal pulses are established above the oscillation threshold. These correlations lead to a significant quantum effect in the integral characteristics of the fields. A theoretical analysis revealed that the spectrum of field fluctuations measured using a balanced homodyne detection technique of phase quadratures of the fields with a pulsed local oscillator reveals quantum noise suppression in the vicinity of frequencies that are multiples of the pulse repetition rate.