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Journal of Modern Optics

Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave pump

Michael Vasilyev, Nikolai M. Stelmakh, Prem Kumar

Published Aug 14, 2009• 23 citations

Abstract

We analyze the spatial-frequency dependence of the gain of phase-insensitive and phase-sensitive optical parametric amplifiers with plane-wave pumping. We discuss the dependence of their spatial bandwidths on pump power and crystal length, L, and observe that the well-known (k s/L)1/2 approximation of spatial bandwidth is not very accurate (here k s is the signal beam's wavevector magnitude). We derive an alternative approximation that is highly accurate at large gains and moderately accurate at low gains. The differences between the phase-insensitive and phase-sensitive amplifier bandwidths are shown to be insignificant for gains above several dB. Maximum phase-sensitive gain and bandwidth are realized by imposing an optimum phase profile onto the input signal's spatial spectrum, which has nearly parabolic shape with added series of π/2 phase discontinuities at spatial frequencies outside the main bandwidth of the amplifier. We show that, apart from the discontinuities, such a profile can be closely approximated by placing the image plane into the middle of the nonlinear crystal (converging input beam). The phase discontinuities contribute an additional narrow component to the point-spread function of the phase-sensitive amplifier.

DOI: 10.1080/09500340903156814

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We experimentally investigate the gain response of a frequency-degenerate but polarization-nondegenerate traveling-wave optical parametric amplifier that consists of a type II phase-matched potassium titanyl phosphate crystal pumped by a frequency-doubled Q-switched mode-locked Nd:YAG laser. Both the optical phase-sensitive and phase-insensitive configurations of the parametric amplifier are studied. Experimental results are in excellent agreement with the theory of an optical parametric amplifier when the Gaussian-beam nature of the various fields is taken into account. In the phase-sensitive configuration a gain of >100 (20 dB) could be easily obtained in the amplified quadrature, which is limited only by the available pump power. Because of gain-induced diffraction and phase fluctuations, however, maximum deamplification in the orthogonal quadrature is limited to <0.5(-3 dB).

We experimentally demonstrate a single-pumped, non-degenerate phase-sensitive parametric amplifier with a precise control of phase and amplitude of the in-going waves and investigate in detail its gain, attenuation and saturation properties in comparison with operation in phase insensitive amplifier (PIA) mode. We experimentally observe the variation of the gain and attenuation as a function of the relative phase, pump power and the signal-idler power ratio. The phase sensitive gain spectrum is studied over a 24 nm symmetrical bandwidth and we achieve a maximum phase sensitive amplification (PSA) gain of 33 dB. A departure from the theoretical maximum attenuation as the gain increases is observed and explained.

We used a spatially broadband optical parametric amplifier for image amplification. In the phase-sensitive configuration of the amplifier, we observed noiseless amplification of input images. For a gain of $\ensuremath{\simeq}2.5$, we measured noise-figure values of ( $0.2\ifmmode\pm\else\textpm\fi{}0.6$) and ( $0.4\ifmmode\pm\else\textpm\fi{}0.5$) dB, respectively, for two amplifiers of different lengths. These experimental values agree with theory (for an ideal noiseless amplifier the noise figure is 0 dB) and are almost 2 dB lower than the quantum limit of an ideal phase-insensitive amplifier.

Dual-pump fiber optical parametric amplifiers offer wide, flat gain spectra across arbitrary wavelengths, often outperforming the use of single-pump designs. However, gain flatness depends on the pump frequencies’ center of gravity relative to the nonlinear fiber’s zero-dispersion wavelength. This study experimentally investigated the gain, gain flatness, and noise figure of degenerate dual-pump fiber-optic phase-sensitive amplification at various separations between these points. We demonstrated 38 dB gain with 1.5 dB gain flatness variation over a 30 nm bandwidth as well as a noise figure below the conventional 3 dB quantum limit for a degenerate signal.

We compute the eigenmodes of a spatially-broadband optical parametric amplifier with elliptical Gaussian pump and show that the well-amplified eigenmodes can be compactly represented by a low-dimensional subspace of the first few Laguerre- or Hermite-Gaussian (LG or HG, respectively) modes of an appropriate waist size. We also show that the first few eigenmodes are well matched to single LG or HG modes. For sufficiently large pump waists, the optimum waist size of the compact basis is in the vicinity of the geometric average of the pump waist size and the inverse spatial bandwidth of the nonlinear crystal in the parametric amplifier. The use of such compact representation can greatly simplify numerical computation of the spatial eigenmodes of the amplifier and thus lead to improving the experiments on traveling-wave image amplification and spatially-broadband vacuum squeezing.