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International Journal of Modern Physics B

DIFFRACTION AND SQUEEZED LIGHT

Robert R. Tucci

Published Nov 30, 1993• 2 citations
Publisher

Abstract

We discuss the effect of diffraction on squeezed light propagation. All electric fields concerned are approximated to be monochromatic and paraxial. We consider: (1)(propagation without gain) a squeezed signal propagating in free space, and (2)(propagation with gain) a squeezed signal propagating in a non-linear crystal which amplifies the signal by a process of frequency halving (degenerate parametric amplification). The pump beam required for this process is assumed to have a Gaussian amplitude profile. For propagation without gain, our expression for the final signal is exact, but for propagation with gain, it is given as a perturbative expansion. The lowest order term in the expansion neglects diffraction of the signal and assumes flat pump wavefronts. Higher order terms include these factors and thus improve the accuracy with which the signal’s transverse behavior is described. We present graphs showing the dependence of squeezing on pump and signal beam parameters. We also find and discuss approximate formulas that characterize these graphs in various regimes.

DOI
10.1142/s0217979293003735

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We discuss the effect of diffraction on squeezed light propagation. All electric fields concerned are approximated to be monochromatic and paraxial. We consider: (1)(propagation without gain) a squeezed signal propagating in free space, and (2)(propagation with gain) a squeezed signal propagating in a non-linear crystal which amplifies the signal by a process of frequency halving (degenerate parametric amplification). The pump beam required for this process is assumed to have a Gaussian amplitude profile. For propagation without gain, our expression for the final signal is exact, but for propagation with gain, it is given as a perturbative expansion. The lowest order term in the expansion neglects diffraction of the signal and assumes flat pump wavefronts. Higher order terms include these factors and thus improve the accuracy with which the signal’s transverse behavior is described. We present graphs showing the dependence of squeezing on pump and signal beam parameters. We also find and discuss approximate formulas that characterize these graphs in various regimes.
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.
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.
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.
Squeezed light, in which the quantum noise in one amplitude component is reduced below the vacuum level, has been generated using parametric processes. The starting point described here is the nonlinear Schrodinger equation which models light propagating through optical fibers. When such a dispersive nonlinear medium with a third-order susceptibility is pumped with an optical beam, squeezing can result. It is found that the degree of squeezing oscillates as a function of fiber length in the normal dispersion regime, whereas in the anomalous dispersion regime, it grows exponentially with fiber length. Examination of squeezing near the fiber’s zero dispersion wavelength shows that odd-order dispersive terms have no effect on squeezing. However, small values of higher-order even terms have significant effects on squeezing. In practice, high-frequency components of the squeezing spectrum are difficult to obtain. However, it is shown that a cross-correlation technique may be used to explore the frequency dependence of the squeezing spectrum.
We study the effect of non-coherent-state pumps on the behavior of the degenerate parametric amplifier. This is done both by developing some exact results and by extending the parametric approximation. Relations are found between the number fluctuations in the pump and those in the signal. The effect of initial phase uncertainty in the pump on the squeezing in the signal is also determined. In addition, we find that rotational symmetry in phase space of the signal-mode state is twice that of the pump-mode state. This implies, for example, that a pump in the squeezed vacuum state will produce a signal-mode state with a four-pronged structure. The effect of a squeezed pump with nonzero amplitude is studied by using a more general form of the parametric approximation. It is shown that in the time interval during which the parametric approximation is valid the effect of this pump is the same as one which is an incoherent superposition of coherent states. We find that while the squeezing of the pump degrades the squeezing of the signal it enhances its amplitude-squared squeezing.