Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Letters

Squeezing in traveling-wave second-harmonic generation

Ruo-Ding Li, Prem Kumar

Published Nov 15, 1993• 30 citations
Publisher

Abstract

We have analyzed squeezing of the fundamental field by means of traveling-wave, type-II phase-matched, secondharmonic generation, taking into account depletion of the fundamental field and phase mismatch between the fundamental and the harmonic fields. For the phase-matched case we show that the generated squeezing is S = 1 - gamma, where gamma is the harmonic conversion efficiency. In the case of a large phase-mismatch we have identified a new mechanism that generates squeezing. It is the nonlinear phase shift of the fundamental field that is due to the cascaded chi((2)) nonlinearity.

DOI
10.1364/ol.18.001961

Related papers

Quantum-noise reduction in traveling-wave second-harmonic generation

Ruo-Ding Li, Prem Kumar

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.

Physical Review A•Mar 1, 1994•60 citations

Squeezing by nonlinear phase shifts from a cascaded second-order nonlinearity

Ruo-Ding Li, Prem Kumar

Squeezing can be generated by means of traveling-wave (TW) second-harmonic generation (S1 1C), even when there is a large phase mismatch between the fundamental and the harmonic fields. We show, in particular, that in the type-II geometry squeezed vacuum is created in the mode that is polarized orthogonal lo the fundamental beam. In the large phase-mismatch limit, where the fundamental field experiences little depletion and negligible second harmonic is generated, nonlinear phase shift of the fundamental wave introduced during the 5HG process is responsible for the creation of squeezing.

•May 8, 1994•0 citations

Squeezing in second-harmonic generation using cascaded nonlinear elements

Joji Maeda, Ichiro Matsuda

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

The effect of nonlinear media combination on amplitude squeezing in second-harmonic generation

Joji Maeda, Yutaka Fukuchi, Ichiro Matsuda

Combinations of quadratic nonlinear crystals with different phase mismatches are studied numerically in terms of amplitude squeezing in the second-harmonic generation. It is predicted that an appropriate choice of phase mismatches can lead to large amplitude squeezing in the fundamental field with much larger stability than in the phase-matched case. It is also predicted that another choice of phase mismatches can yield amplitude squeezing in the harmonic field beyond the theoretical limit of the phase-matched case.

Journal of Optics B Quantum and Semiclassical Optics•Jul 28, 2004•0 citations

Evolution of quantum noise in the traveling-wave second-order [χ^(2)] nonlinear process

Ruo-Ding Li, Prem Kumar

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.

Journal of the Optical Society of America B•Nov 1, 1995•15 citations

Amplitude squeezing by means of quasi-phase-matched second-harmonic generation in a lithium niobate waveguide

Darwin K. Serkland, Prem Kumar, Mark A. Arbore +1 more

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.

Optics Letters•Oct 1, 1997•48 citations
We have analyzed squeezing of the fundamental field by means of traveling-wave, type-II phase-matched, secondharmonic generation, taking into account depletion of the fundamental field and phase mismatch between the fundamental and the harmonic fields. For the phase-matched case we show that the generated squeezing is S = 1 - gamma, where gamma is the harmonic conversion efficiency. In the case of a large phase-mismatch we have identified a new mechanism that generates squeezing. It is the nonlinear phase shift of the fundamental field that is due to the cascaded chi((2)) nonlinearity.
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.
Squeezing can be generated by means of traveling-wave (TW) second-harmonic generation (S1 1C), even when there is a large phase mismatch between the fundamental and the harmonic fields. We show, in particular, that in the type-II geometry squeezed vacuum is created in the mode that is polarized orthogonal lo the fundamental beam. In the large phase-mismatch limit, where the fundamental field experiences little depletion and negligible second harmonic is generated, nonlinear phase shift of the fundamental wave introduced during the 5HG process is responsible for the creation of squeezing.
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.
Combinations of quadratic nonlinear crystals with different phase mismatches are studied numerically in terms of amplitude squeezing in the second-harmonic generation. It is predicted that an appropriate choice of phase mismatches can lead to large amplitude squeezing in the fundamental field with much larger stability than in the phase-matched case. It is also predicted that another choice of phase mismatches can yield amplitude squeezing in the harmonic field beyond the theoretical limit of the phase-matched case.
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 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.