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Journal of the Optical Society of America B

Quantum noise reduction in singly resonant optical devices

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

Published Mar 1, 2000• 1 citation
Publisher

Abstract

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.

DOI
10.1364/josab.17.000440

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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 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.
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 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.
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 present the analysis of a laser in which an intractivity χ (2) -nonlinear element couples the lasing mode to its second harmonic. The cavity is resonant for both modes. We investigate the potential for squeezing in this system by linearizing the quantum fluctuations around the steady states of the problem. In principle, more than 50% noise reduction below the vacuum level is possible in the second-harmonic field outside the cavity. The maximum squeezing, which is neither pure amplitude nor pure phase squeezing, occurs at a finite frequency-offset from the cavity resonance.
The mutual influence of second-harmonic generation and nondegenerate downconversion inside the same cavity is studied. The threshold behavior and the stability of a semiclassical solution with all four modes oscillating resonantly is investigated. It is shown that under certain conditions the self-pulsing instability that occurs in second-harmonic generation is absent in the combined system. The squeezing spectra for the quadrature-phase amplitudes in the second harmonic and the fundamental, as well as the photon statistics in the downconverted modes, are derived analytically. As one of the various nonclassical features of this system, the second harmonic is found to exhibit excellent noise suppression at very large frequencies, with the frequency component of best squeezing being tunable by the pump parameter. The intricate interaction of the two nonlinear processes can give rise to twin beams of correlated photons, with sub-Poissonian statistics in each beam. These results are contrasted with the results for each nonlinear process by itself.
Quantum squeezing-assisted noise suppression is a promising field with wide applications. However, the limit of noise suppression induced by squeezing is still unknown. This paper discusses this issue by studying weak signal detection in an optomechanical system. By solving the system dynamics in the frequency domain, we analyze the output spectrum of the optical signal. The results show that the intensity of the noise depends on many factors, including the degree or direction of squeezing and the choice of the detection scheme. To measure the effectiveness of squeezing and to obtain the optimal squeezing value for a given set of parameters, we define an optimization factor. With the help of this definition, we find the optimal noise suppression scheme, which can only be achieved when the detection direction exactly matches the squeezing direction. The latter is not easy to adjust as it is susceptible to changes in dynamic evolution and sensitive to parameters. In addition, we find that the additional noise reaches a minimum when the cavity (mechanical) dissipation κ(γ) satisfies the relation κ = Nγ, which can be understood as the restrictive relationship between the two dissipation channels induced by the uncertainty relation. Furthermore, by taking into account the noise source of our system, we can realize high-level noise suppression without reducing the input signal, which means that the signal-to-noise ratio can be further improved.