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Journal of the Optical Society of America B

Analysis of the generation of amplitude-squeezed light with Gaussian-beam degenerate optical parametric amplifiers

Kahraman G. Köprülü, Orhan Aytür

Published Jun 1, 2001• 14 citations
Publisher

Abstract

We investigate the generation of amplitude-squeezed states with degenerate optical parametric amplifiers that are pumped by focused Gaussian beams. We present a model that facilitates the calculation of the squeezing level for an experimentally realistic configuration in which there is a Gaussian input signal beam that has the same confocal parameter and waist location as the Gaussian pump beam, with no restriction on the interaction length-to-confocal parameter ratio. We show that the 3-dB squeezing limit that was thought to be imposed by the Gaussian pump profile can be exceeded in the (previously uninvestigated) tight-focusing regime. We find the maximum possible amplitude squeezing in this regime to be 4.65 dB. However, it is possible to increase the squeezing level further by spatially filtering the tails of the output signal beam, resulting in squeezing levels in excess of 10 dB.

DOI
10.1364/josab.18.000846

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We investigate the generation of amplitude-squeezed states with degenerate optical parametric amplifiers that are pumped by focused Gaussian beams. We present a model that facilitates the calculation of the squeezing level for an experimentally realistic configuration in which there is a Gaussian input signal beam that has the same confocal parameter and waist location as the Gaussian pump beam, with no restriction on the interaction length-to-confocal parameter ratio. We show that the 3-dB squeezing limit that was thought to be imposed by the Gaussian pump profile can be exceeded in the (previously uninvestigated) tight-focusing regime. We find the maximum possible amplitude squeezing in this regime to be 4.65 dB. However, it is possible to increase the squeezing level further by spatially filtering the tails of the output signal beam, resulting in squeezing levels in excess of 10 dB.
Summary form only given. The generation of quantum states of light, such as squeezed states, often relies on degenerate optical parametric amplification. The input signal in a degenerate optical parametric amplifier (DOPA) may be amplified or deamplified depending on the phase of the signal field relative to that of the pump field (/spl Delta//spl phi/=/spl phi//sub pump/-2/spl phi//sub signal/). We present the results of an accurate numerical DOPA model for the generation of amplitude-squeezed light with Gaussian pump and signal beams. We find that the widely accepted 3-dB limit imposed by the Gaussian beam profiles can actually be exceeded in the tight focusing regime.
This paper investigates the generation of quadrature-squeezed states of light using a degenerate optical parametric amplifier (DOPA) that is pumped by a focused Gaussian beam. The formulation that is presented facilitates the calculation of squeezing for an arbitrary local oscillator beam. This formulation also establishes a formal equivalence between the classical parametric gain and the measured level of squeezing. The maximum squeezing that can be achieved using a Gaussian-beam local oscillator is determined to be limited to 13.4 dB, as a consequence of gain-induced diffraction. The phase lag of the maximally squeezed quadrature is shown to be significantly different from the plane-wave theoretic value of $\ensuremath{\pi}/2,$ unless the focusing is very weak. The use of a second DOPA for generating a local oscillator beam that is matched to the squeezed field is also investigated. In this case, squeezing is limited only by the available pump power.
The generation of squeezed light in a single-pass parametric amplifier pumped by Gaussian beams is analyzed. Limits to the degree of squeezing that can be obtained are found that arise from spatial distortion of the signal beam that is significant for parametric gains greater than 3 dB. It is found that squeezing is limited to approximately 6 dB for typical experimental configurations. These limits severely constrain the design of quantum noise experiments unless high finesse cavities or waveguides are used.
This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.