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Physical Review A

Squeezing in an optical parametric oscillator with arbitrary output mirror coupling: Extension to double cavities

Bartram S. Abbott

Published Mar 1, 1995• 0 citations
Publisher

Abstract

Quantum noise and squeezing of the field produced by a degenerate optical parametric oscillator operating below threshold are considered. This analysis extends previously reported calculations for single cavities to double cavities whose mirror transmission coefficients are arbitrary. The double-cavity configuration improves the overall squeezing of the system for both the intracavity field as well as the output field. The double-cavity configuration may be conducive to experimental verification of this and previous work.

DOI
10.1103/physreva.51.2346

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Annual Meeting Optical Society of America•Jan 1, 1993•0 citations
Quantum noise and squeezing of the field produced by a degenerate optical parametric oscillator operating below threshold are considered. This analysis extends previously reported calculations for single cavities to double cavities whose mirror transmission coefficients are arbitrary. The double-cavity configuration improves the overall squeezing of the system for both the intracavity field as well as the output field. The double-cavity configuration may be conducive to experimental verification of this and previous work.
In a recent work,1 the influence of arbitrary values of output-mirror transmission on the quantum noise and squeezing in a degenerate optical parametric oscillator (DOPO) with a single output mirror was studied. The work being presented here is a theoretical extension of that research to the case of a DOPO in a double-sided cavity with arbitrary transmission coefficients for the two output mirrors. Additionally, the pump field will be allowed to have amplitude and phase noise. Both intracavity and extracavity fields will be treated for a variety of squeezing characteristics of the input fields entering the DOPO cavity. The dependence of squeezing of the output and intracavity fields on the spatial phase, which determines the locations of the nodes and antinodes, of the average pump field will also be analyzed. As in Ref. 1, the generalization of the good-cavity results to arbitrary quality cavities is highly nontrivial.
We consider here the problem of quantum noise in light produced by an optical parametric oscillator operating below threshold inside a singlesided cavity. By employing the correct boundary conditions on quantum fields at the output mirror, a procedure that is valid for arbitrary mirror transmission, we derive exact expressions for quantum noise reduction for arbitrary pump phase and mirror out-coupling. We find that for a given out-coupling, squeezing of quantum noise in the intracavity field increases to a final value of 50%, as the pump intensity is increased and the oscillation threshold is approached. The output field on the other hand exhibits perfect squeezing of noise in one quadrature of its central Fourier component at threshold regardless of the mirror out-coupling. The present approach, which is based on boundary conditions, is quite general and applicable to any matter-field interaction problem inside a cavity. In fact, we have previously employed this approach in the calculation of the intrinsic linewidth of a laser with arbitrary out-coupling.1
We consider here the problem of quantum noise in light produced by an optical parametric oscillator operating below threshold inside a single-sided cavity. By employing the correct boundary conditions on quantum fields at the output mirror, a procedure that is valid for arbitrary mirror transmission, we derive exact expressions for quantum-noise reduction for arbitrary pump phase and output-mirror coupling. We find that for a given output-mirror power reflectance R, squeezing of quantum noise in the intracavity field increases to a final fractional value equal to R/(1+R) as the pump intensity is increased and the oscillation threshold is approached. The output field, on the other hand, exhibits perfect squeezing of noise in one quadrature of its central Fourier component at threshold regardless of the output-mirror coupling. The present approach, which is based on boundary conditions, is quite general and applicable to any matter-field interaction problem inside a cavity.
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.
High-Q cavities play a central role in quantum optics for the generation and study of novel quantum mechanical states of light like squeezed states. It is however not widely recognized that even low-Q cavities can produce such states. For example, a degenerate optical parametric oscillator (DOPO) with one nearly perfect mirror can produce perfectly squeezed output light regardless of the second mirror transmission, provided the DOPO is at oscillation threshold. Moreover, the squeezing bandwidth increases with increasing transmission of the second mirror.