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IEEE Journal of Quantum Electronics

Theoretical analysis of squeezed-light generation by second-harmonic generation

Toshiaki Suhara, M. Fujimura, Kenji Kintaka, Hiroshi Nishihara, Peter Kürz, T. Mukai

Published Apr 1, 1996• 20 citations
Publisher

Abstract

Theoretical analysis of squeezed light generation by phasematched SHG, applicable generally to various SHG configurations and appropriate for mutual comparison, is presented. The analysis is based on analytical solutions of the linearized differential equations in space coordinate and the input-output equations for the amplitude fluctuations, and calculations of squeezing spectra using the covariance matrixes. Formulations describing the squeezing characteristics in terms of the device parameters are derived. Typical numerical results are also given to illustrate the features of traveling-wave SHG, singly-resonant SHG, and doubly-resonant SHG configurations including cases where propagation losses are involved. The results, which are consistent with those in previous work, provide many insights for design and application of SHG devices for squeezed-light generation.

DOI
10.1109/3.488844

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Cascading of quadratic nonlinearity has been attracting great interests for its potential application to parametric devices, such as phase conjugators or effective Kerr media. In most configurations, the device consists of a single nonlinear element with uniform phase-mismatch. Cascading of several elements with different phase-mismatch has been theoretically investigated and predicted to improve performance of the device for classical applications. In this paper, amplitude squeezing in second-harmonic generation using cascaded quadratic nonlinear elements is numerically analyzed. The analyses are based on linearization of nonlinear coupling equations, where interacting fields are approximated as plane waves. Phase-mismatch of each element is varied independently and tolerance of squeezing performance to the fluctuation of the phase-mismatch is also investigated. It is predicted that the performance as a squeezing device can be also superior to that of a single element device, if a proper combination of the phase-mismatch of each element is chosen. For the fundamental wave, the tolerance to the fluctuation of the phase-mismatch will improve by nearly tenfold compared with the single element case. For the harmonic wave, squeezing beyond the limit of perfect phase-matched case (3dB) will be available, though the tolerance to the fluctuation of the phase-mismatch is quite small. These improvements can be attributed to the nonlinear phase rotation that keeps squeezed axis coincided with the amplitude phase in a stable manner.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 16, 2003•0 citations
Theoretical analysis of squeezed light generation by phasematched SHG, applicable generally to various SHG configurations and appropriate for mutual comparison, is presented. The analysis is based on analytical solutions of the linearized differential equations in space coordinate and the input-output equations for the amplitude fluctuations, and calculations of squeezing spectra using the covariance matrixes. Formulations describing the squeezing characteristics in terms of the device parameters are derived. Typical numerical results are also given to illustrate the features of traveling-wave SHG, singly-resonant SHG, and doubly-resonant SHG configurations including cases where propagation losses are involved. The results, which are consistent with those in previous work, provide many insights for design and application of SHG devices for squeezed-light generation.
A theoretical analysis based on the fluctuation propagation matrix method proposed by the authors has been performed for systematic study of the generation and conversion of squeezed light in various traveling-wave second-order nonlinear-optic devices. The important insights obtained are: (1) Second-harmonic generation (SHG) allows generation of a highly squeezed fundamental wave, and a highly amplitude squeezed harmonic wave can be obtained by pumping with amplitude-squeezed fundamental wave. (2) Degenerate optical parametric (de)amplification (DOPA and DOPDA) allow generation of squeezed vacuum states and substantial amplitude/phase squeezing of the signal wave. (3) Sum- and difference-frequency generation (SFG and DFG) using a strong pump wave allow wavelength conversion of squeezed light. The results are given in graphic form using normalized parameters which can readily be correlated to device parameters. © 1999 Scripta Technica, Electron Comm Jpn Pt 2, 82(12): 48–56, 1999
The characteristics of squeezed light generated by both passive (occurring in a cavity external to a laser) and active (occurring within a laser cavity) second-harmonic generation (SHG) are investigated and contrasted. Squeezing of both the fundamental and the second harmonic is discussed, and the issue of doubly versus singly resonant behavior is addressed. We examine passive squeezing by explicitly modeling the intrinsically noisy output of the pump laser and coupling it to a passive, multiport, lossy SHG cavity. Low-frequency degradation of the squeezing caused by the laser pump noise is predicted and provides a probable explanation for previous discrepancies between theory and experiment. Active squeezing is quantitatively modeled by a three-level laser model that retains all laser dynamics. Previously disparate predictions are reconciled. For one parameter set two regimes of squeezing are predicted: 50% squeezing at frequencies lower than the laser relaxation oscillation, and near-perfect squeezing at frequencies above. A particular problem of active squeezing is highlighted: The fast dephasing of the laser coherence introduces considerable excess noise likely to mask squeezing in experimental situations. We conclude that, although passive SHG is a practical source of squeezing, active SHG is unlikely to be so in the foreseeable future.
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.
With the help of second-order nonlinear interactions and hence Hamiltonian, we construct the equations of motion corresponding to pump and signal (second harmonic) fields in a second harmonic generation. The corresponding coupled differential equations involving the non-commuting field operators are not solvable in closed analytical forms. With the help of a perturbation method, we obtain analytical solutions of these field operators up to cubic orders in the interaction constant. In an appropriate limit (truncating the solution up to the second order in the interaction constant), these solutions lead to the existing solutions under the short-time approximation. The present analytical solutions are exploited to investigate the squeezing and the antibunching of photons of the input coherent light coupled to the said second-order nonlinear medium. We report the squeezing and antibunching effects of the pump field even for solutions up to the second order and hence the present results are consistent with earlier results. However, for the second harmonic mode, we report the squeezing involving the leading cubic term in the interaction constant.
We consider the process of second-harmonic generation (SHG) in a cavity that is resonant for both the fundamental- and second-harmonic modes. It has been previously shown that such a system displays a phase instability leading to self-pulsing and that one gets important intensity squeezing on both the fundamental- and second-harmonic mode for pump intensities close to but below, this instability threshold. Such a squeezing has been recently observed. We have analytically calculated the intensity-noise spectrum of the frequency-doubled field above such an instability threshold, using a semiclassical input-output technique for the treatment of quantum fluctuations.1 Such a method, introduced to deal with fluctuations around a stable solution, has been generalized to the self-pulsing domain. As expected, the instability brings excess noise to the output beams, especially around the zero-frequency, the self-oscillation frequency, and its harmonics. Remarkably, some regions exist in which where the noise increase is small; squeezing still occurs in this frequency range far in the instability domain.
Cascading of quadratic nonlinearity has been attracting great interests for its potential application to parametric devices, such as phase conjugators or effective Kerr media. In most configurations, the device consists of a single nonlinear element with uniform phase-mismatch. Cascading of several elements with different phase-mismatch has been theoretically investigated and predicted to improve performance of the device for classical applications. In this paper, amplitude squeezing in second-harmonic generation using cascaded quadratic nonlinear elements is numerically analyzed. The analyses are based on linearization of nonlinear coupling equations, where interacting fields are approximated as plane waves. Phase-mismatch of each element is varied independently and tolerance of squeezing performance to the fluctuation of the phase-mismatch is also investigated. It is predicted that the performance as a squeezing device can be also superior to that of a single element device, if a proper combination of the phase-mismatch of each element is chosen. For the fundamental wave, the tolerance to the fluctuation of the phase-mismatch will improve by nearly tenfold compared with the single element case. For the harmonic wave, squeezing beyond the limit of perfect phase-matched case (3dB) will be available, though the tolerance to the fluctuation of the phase-mismatch is quite small. These improvements can be attributed to the nonlinear phase rotation that keeps squeezed axis coincided with the amplitude phase in a stable manner.