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Kluwer Academic Publishers eBooks

Quantum Noise Reduction in Singly Resonant Optical Devices

C. Cabrillo, J. L. Roldán, P. García-Fernández

Published Dec 19, 2005• 0 citations
Publisher

Abstract

Quantum noise in a model of a singly resonant frequency doubler including phase mismatch and a driving in the harmonic mode is analyzed. The squeezing spectra calculated inside the linear approximation are given. For squeezing in the fundamental mode, the optimum working point corresponds to turning points of dispersive bistability induced by cascading of the second order nonlinear response. In the case of the harmonic mode phase mismatch as well as a finite driving in the harmonic allows for surpass the 1/9 limit of the standard SHG scheme. The squeezing improvement when the driving is included is substantial for parameter values corresponding to reported experiments. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/0-306-47097-7_66

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Quantum noise reduction in singly resonant optical devices

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Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra calculated linearizing around such points are given. The use of a nonlinear normalization allows to disentangle in the spectra the dynamic response of the system from the contributions of the various noisy inputs. A general ``reference'' model for one-mode systems is developed in which the dynamic aspects of the problem are not contaminated by static contributions from the noisy inputs. The physical insight gained permits the elaboration of general criteria to optimize the noise suppression performance. With respect to the squeezing in the fundamental mode the optimum working point is located near the first turning point of the dispersive bistability induced by cascading of the second order nonlinear response. The nonlinearities induced by conventional crystals appear enough to reach it being the squeezing ultimately limited by the escape efficiency of the cavity. In the case of the harmonic mode both, finite phase mismatch and/or harmonic mode driving allow for an optimum dynamic response of the system something not possible in the standard phase matched Second Harmonic Generation. The squeezing is then limited by the losses in the harmonic mode, allowing for very high degrees of squeezing because of the non-resonant nature of the mode. This opens the possibility of very high performances using artificial materials with resonantly enhanced nonlinearities. It is also shown how it is possible to substantially increase the noise reduction and at the same time to more than double the output power for parameters corresponding to reported experiments.

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Quantum noise reduction in semiconductor lasers using dispersive optical feedback

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•Jan 1, 1995•1 citation
Quantum noise in a model of a singly resonant frequency doubler including phase mismatch and a driving in the harmonic mode is analyzed. The squeezing spectra calculated inside the linear approximation are given. For squeezing in the fundamental mode, the optimum working point corresponds to turning points of dispersive bistability induced by cascading of the second order nonlinear response. In the case of the harmonic mode phase mismatch as well as a finite driving in the harmonic allows for surpass the 1/9 limit of the standard SHG scheme. The squeezing improvement when the driving is included is substantial for parameter values corresponding to reported experiments. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra calculated linearizing around such points are given. The use of a nonlinear normalization allows to disentangle in the spectra the dynamic response of the system from the contributions of the various noisy inputs. A general ``reference'' model for one-mode systems is developed in which the dynamic aspects of the problem are not contaminated by static contributions from the noisy inputs. The physical insight gained permits the elaboration of general criteria to optimize the noise suppression performance. With respect to the squeezing in the fundamental mode the optimum working point is located near the first turning point of the dispersive bistability induced by cascading of the second order nonlinear response. The nonlinearities induced by conventional crystals appear enough to reach it being the squeezing ultimately limited by the escape efficiency of the cavity. In the case of the harmonic mode both, finite phase mismatch and/or harmonic mode driving allow for an optimum dynamic response of the system something not possible in the standard phase matched Second Harmonic Generation. The squeezing is then limited by the losses in the harmonic mode, allowing for very high degrees of squeezing because of the non-resonant nature of the mode. This opens the possibility of very high performances using artificial materials with resonantly enhanced nonlinearities. It is also shown how it is possible to substantially increase the noise reduction and at the same time to more than double the output power for parameters corresponding to reported experiments.
Quantum noise in a model of singly resonant frequency doubling, including phase mismatch and driving in the harmonic mode, is analyzed. The use of a nonlinear normalization allows us to disentangle in the spectra the squeezing induced by the system dynamics from the deleterious effect of the noise coming from the various inputs. The physical insight gained permits the elaboration of general criteria to optimize noise-suppression performance. The subsequent application to the specific system here addressed reveals excellent squeezing behavior. In particular, unlimited degrees of squeezing in the harmonic mode are possible by means of an adequate phase mismatch or driving in the harmonic mode. This is in contrast with the standard phase-matched second-harmonic generation in which the squeezing is limited to 1/9. The applicability of the model, as well as possible experimental implementations, is extensively discussed.
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 introduce a model of squeezing and noise reduction in the Kerr effect that accounts for noise in all quadratures of the driving field. Consequently we show that Kerr squeezing is much more sensitive to driving noise than squeezing produced by second harmonic generation (SHG). We experimentally demonstrate this sensitivity using a nonlinear system that tunes between strong classical SHG and Kerr behaviours. Whilst the system experiences strong squeezing in the SHG limit, it experiences no squeezing in the Kerr limit, although it does experience strong classical noise reduction, or `classical squeezing'.
We present a semiclassical and quantum analysis of a nonlinear optical interaction in a cavity in which an externally driven fundamental mode at frequency \ensuremath{\omega} transforms into the second-harmonic mode 2\ensuremath{\omega} and then into the fourth-harmonic mode 4\ensuremath{\omega} via cascaded frequency-doubling processes $\ensuremath{\omega}+\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}2\ensuremath{\omega}$ and $2\ensuremath{\omega}+2\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}4\ensuremath{\omega}.$ In the adiabatic limit of the strongly damped fourth-harmonic mode the nonlinear system is equivalent to the process of intracavity second-harmonic generation combined with nonlinear two-photon absorption from the second-harmonic mode. Semiclassical steady states and linear stability analysis show that possible operation regimes are substantially different from those for the pure second-harmonic-generation process. It is shown in particular that the system is characterized by two critical points: Starting from a certain critical value of the driving field intensity, one observes self-pulsing instability; however, at higher intensities, beyond a second critical point, the system turns back to the stable generation regime. Moreover, under appropriate values of the control parameters, one may arrive at a complete quenching of self-pulsing behavior and at stabilization of the steady states in the entire domain of the driving field intensity. These stabilization properties become important when turning to the analysis of the quantum fluctuations and quadrature squeezing effect in the fundamental and second-harmonic modes within the ranges of linearized treatment of fluctuations. Due to the emergence of stability in the behavior of the system at high level of coherent excitation, the system becomes capable of generation of bright light with enhanced squeezing properties.
This thesis describes the phase and amplitude noise properties of semiconductor lasers subjected to weak, dispersive optical feedback. In the first half, experiments demonstrating reductions in the laser frequency noise power spectrum and spectral linewidth by several orders of magnitude are presented. Weak optical feedback is applied to the laser by an external cavity containing an atomic vapor. The presence of the vapor adds to the dispersion of the cavity and simultaneously locks the laser to a fixed frequency reference. The role of 1/f frequency noise in limiting the effectiveness of this linewidth reduction technique is investigated and 1/f noise is found to be the dominant contribution to the linewidth under strong optical feedback conditions. An electronic feedback scheme utilizing FM sideband locking is then implemented alongside the optical feedback, and an additional reduction in the low frequency 1/f frequency noise power spectrum by over two orders of magnitude is obtained. With both systems operating simultaneously, the spectral linewidth is narrowed from its free-running value of about 20 MHz to 1.4 kHz. Excellent absolute frequency stability is also achieved. In the second half, the effects of optical feedback on the quantum mechanical amplitude noise properties of the laser are examined. A fully quantum mechanical theory of amplitude and phase noise for a semiconductor laser with weak optical feedback is developed, and the nature and limits of the noise reduction using this technique are established. Particular attention is given to the feedback-induced enhancement of the amplitude squeezing which can be obtained in a pump-suppressed semiconductor laser: an improvement in the squeezing by 3 dB is predicted under moderate pumping. Somewhat larger noise reductions are expected when the laser is operating closer to threshold. Measurements performed on a laser biased close to threshold are then described and a reduction in the low frequency amplitude noise power spectrum by 7 dB is obtained. An experimental investigation of the effects of optical feedback on the amplitude squeezing in a semiconductor laser is then discussed. The low frequency squeezing in a room temperature device is increased from 3% below the standard quantum limit (SQL) under free-running conditions to 19% below the SQL with optimal feedback. The experimental results are found to agree poorly with the single-mode model and a multi-mode model including the effects of asymmetrical cross-mode non-linear gain is developed to explain the discrepancy. Finally, further experimental investigation into the generation of amplitude squeezed light is presented using a commercial laser with no intentional external modifications. Squeezing as large as 29% below the SQL is measured using a balanced homodyne detector with the laser operating near room temperature, corresponding to 41% below the SQL at the output facet of the laser.