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Optics Letters

Observation of sub-Poissonian light in traveling-wave second-harmonic generation

Sun-Hyun Youn, Sang-Kyung Choi, Prem Kumar, Ruo-Ding Li

Published Oct 1, 1996• 22 citations
Publisher

Abstract

We report the generation of sub-Poissonian pulses of light by means of traveling-wave second-harmonic generation (SHG) in a type II phase-matched nonlinear crystal. On direct detection, the quantum noise on the output light, which is polarized orthogonally to the input fundamental field, is measured to be below the shotnoise limit by as much as 0.3 +/- 0.2 dB (6 +/- 4%). We show that the input fundamental-power dependence of the measured Fano factor, direct-detection noise as a fraction of the shot-noise limit, is in qualitative agreement with the quantum theory of SHG.

DOI
10.1364/ol.21.001597

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Optics Letters•Jul 15, 1999•65 citations
We report the generation of sub-Poissonian pulses of light by means of traveling-wave second-harmonic generation (SHG) in a type II phase-matched nonlinear crystal. On direct detection, the quantum noise on the output light, which is polarized orthogonally to the input fundamental field, is measured to be below the shotnoise limit by as much as 0.3 +/- 0.2 dB (6 +/- 4%). We show that the input fundamental-power dependence of the measured Fano factor, direct-detection noise as a fraction of the shot-noise limit, is in qualitative agreement with the quantum theory of SHG.
Sub-Poissonian pulses of light are generated by means of traveling-wave optical parametric deamplification. Upon direct detection the quantum noise on the deamplified pulses is measured to be below the shot-noise limit by as much as 0.5\ifmmode\pm\else\textpm\fi{}0.2 dB (11\ifmmode\pm\else\textpm\fi{}4 %). The parametric-gain dependence of the measured Fano factor---direct-detection noise as a fraction of the shot-noise limit---agrees with the quantum theory of the amplifier when diffraction effects are taken into account.
We analyze the evolution of quantum noise in both the fundamental and the harmonic fields that are undergoing traveling-wave interaction in a second-order [χ(2)] nonlinear medium. Assuming perfect phase matching between the fundamental and the harmonic fields and arbitrary input boundary conditions, the behavior of quantum noise in the propagating fields is studied by linearization of the nonlinear-operator equations around the mean-field values. We first consider the degenerate case that is applicable to type-I phase-matching geometries, obtaining expressions for squeezing in both the fundamental and the harmonic fields. We then analyze the polarization-nondegenerate case that applies to type-II phase-matching geometries. In the special case, when the two orthogonally polarized fundamental inputs are of equal amplitude, we obtain analytical results and show that the type-II phase-matched second-harmonic-generation process can be configured to generate sub-Poissonian light in both polarization components of the fundamental field. Finally, we numerically solve the linearized quadrature-operator equations along with the nonlinear mean-field equations for the general case of type-II phase matching. For both type-I and type-II processes, we find that whenever the fundamental field experiences deamplification it is associated with amplitude squeezing and phase desqueezing. If, in contrast, the fundamental field experiences amplification, then it is accompanied by amplitude desqueezing, but with squeezing in the phase quadrature. The harmonic field is amplitude squeezed if the input boundary condition leads to harmonic conversion and is phase squeezed if the input boundary condition leads to parametric amplification.
We analyze squeezing of both the fundamental and harmonic fields undergoing traveling-wave, second-harmonic generation (SHG) in second-order (${\mathrm{\ensuremath{\chi}}}^{(2)}$) nonlinear media. We take into account depletion of the fundamental field as well as the phase mismatch between the fundamental and harmonic fields. The behavior of the quantum noises on the propagating fields is studied by linearizing the nonlinear operator equations around the mean-field values. We first consider the degenerate case that is applicable to type-I phase-matching geometries, obtaining expressions for squeezing in both the fundamental and harmonic fields under the conditions of perfect phase matching and large phase mismatch. We show that in the case of a large phase mismatch, the intensity-dependent self-phase shift of the fundamental field, arising due to cascading of the ${\mathrm{\ensuremath{\chi}}}^{(2)}$ nonlinearity, is responsible for the squeezing generation. We also numerically solve the linearized quadrature-operator equations together with the nonlinear mean-field equations. We find that in the case of a finite phase mismatch the harmonic field can be highly squeezed. This is in contrast to the perfectly phase-matched case where the maximum squeezing is limited to 50%. Finally, we analyze the nondegenerate case that applies to type-II phase-matching geometries. Here we show that the commonly used type-II phase-matched SHG process with the input harmonic field in the vacuum state is equivalent to a type-I SHG process in parallel with a degenerate optical-parametric process. The latter causes squeezing in the mode that is polarized orthogonal to the fundamental beam. In the perfect phase-matching case, the squeezing in the orthogonally polarized mode follows the simple expression S=1-\ensuremath{\gamma}, where \ensuremath{\gamma} is the harmonic conversion frequency.
We demonstrate that traveling-wave second-harmonic generation produces amplitude-squeezed light at both the fundamental and the harmonic frequencies. Quasi-phase-matched second-harmonic conversion efficiencies approaching 60% were obtained in a 26-mm-long single-mode LiNbO(3) waveguide with pulses from a mode-locked laser at 1.53 microm. The amplitude noise of the transmitted fundamental field was measured to be 0.8 dB below the shot-noise level, and the generated 0.765-microm harmonic light was measured to be amplitude squeezed by 0.35 dB. The conversion-efficiency dependence of the observed squeezing at both wavelengths agrees with theoretical predictions. Waveguide losses appear to degrade the squeezing, but the maximum observed squeezing is currently limited only by the available input power.
Recently, we have observed as much as 7 dB of quantum-noise reduction in the direct difference detection of twin-beam signal and idler outputs from a traveling-wave optical parametric amplifier (OPA).1 The OPA, which consists of a type-II phase-matched KTiOPO4 crystal, is pumped by the second harmonic of a mode-locked and Q-switched Nd:YAG laser. Here we describe an experiment in which we used these twin-beam pulses to improve on the optimal (shot-noise-limited) direct-detection signal-to-noise ratio (SNR) that can be achieved with coherent-state pulses of light of the same peak power.
We experimentally demonstrate generation of bright sub-Poissonian light by means of parametric deamplification in a phase-sensitive fiber amplifier that is based on a balanced nonlinear Sagnac interferometer. On direct detection, the photocurrent noise falls below the shot-noise limit by (0.6 +/- 0.2) dB (1.4 dB when corrected for detection losses). To observe the noise reduction we employed a scheme that used two orthogonally polarized pulses to cancel the noise that arises from the predominantly polarized guided-acoustic-wave Brillouin scattering in the fiber. We also present a simplified semiclassical theory of quantum-noise suppression by this amplifier, which is found to be in good agreement with the experimental results.