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Quantum statistics of a novel frequency doubler

Andrew G. White, Hans‐A. Bachor, David E. McClelland

Published May 8, 1994• 0 citations

Abstract

Monolithic cavities are used in experiments requiring compactness, reduced optical losses, and high mechanical, temperature, and frequency stability. The evanescently coupled monolith, or MOTIRR (MOnolithic Total Internal Reflection Resonator) is of particular interest because it allows very high finesse, the limit to the losses being set solely by the intrinsic absorption of the monolith material and the surface quality of the monolith and coupler. Singly and doubly resonant frequency doubling systems are predicted to exhibit squeezing in both the fundamental and the second harmonic modes. This has been observed in dielectric-coated monolithic systems, which have produced the most intense bright squeezing yet observed. However, because these systems use dielectric coatings, they are wavelength dependent, reducing the utility of the beam for applications of bright squeezing, such as spectroscopy. Evanescently coupled systems have no particular wavelength dependence and are thus suitable as broadband doublers. Indeed, they have recently been used to generate bright squeezed light. However, current designs impose a fixed phase relationship between the fundamental and the second harmonic. If this relationship is not at an optimum, which is normally the case, the effective nonlinear coupling constant can be degraded significantly, which, in turn, may degrade the squeezing. We present a novel design for a MOTIRR that allows the phase between the fundamental and second harmonic to be tuned experimentally. Further, it uses polarization-sensitive coupling to allow independent control of the amplitudes of the fundamental and second-harmonic modes. Preliminary results on conversion efficiencies and quantum-noise behavior of the fundamental and second-harmonic modes are given.

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Monolithic cavities are used in experiments requiring compactness, reduced optical losses, and high mechanical, temperature, and frequency stability. The evanescently coupled monolith, or MOTIRR (MOnolithic Total Internal Reflection Resonator) is of particular interest because it allows very high finesse, the limit to the losses being set solely by the intrinsic absorption of the monolith material and the surface quality of the monolith and coupler. Singly and doubly resonant frequency doubling systems are predicted to exhibit squeezing in both the fundamental and the second harmonic modes. This has been observed in dielectric-coated monolithic systems, which have produced the most intense bright squeezing yet observed. However, because these systems use dielectric coatings, they are wavelength dependent, reducing the utility of the beam for applications of bright squeezing, such as spectroscopy. Evanescently coupled systems have no particular wavelength dependence and are thus suitable as broadband doublers. Indeed, they have recently been used to generate bright squeezed light. However, current designs impose a fixed phase relationship between the fundamental and the second harmonic. If this relationship is not at an optimum, which is normally the case, the effective nonlinear coupling constant can be degraded significantly, which, in turn, may degrade the squeezing. We present a novel design for a MOTIRR that allows the phase between the fundamental and second harmonic to be tuned experimentally. Further, it uses polarization-sensitive coupling to allow independent control of the amplitudes of the fundamental and second-harmonic modes. Preliminary results on conversion efficiencies and quantum-noise behavior of the fundamental and second-harmonic modes are given.

We present a new technique for the efficient and simple production of amplitude-squeezed light with high coherent excitation, using a frequency doubler, in which only the fundamental wave is resonantly enhanced. Our theory predicts up to nearly 90% squeezing in the second-harmonic wave under ideal conditions. In our first experiment we measured up to 30% squeezing [having taken into account the limited quantum efficiency (63%) of our detection system] in a stable 50 mW beam. Compared to doubly resonant frequency doubling our new approach has considerable technical advantages.

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.

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.

We discuss different approaches to the generation of bright amplitude-squeezed light using second-order nonlinear effects in optical cavities. A 0.2 mW beam at 1064 nm exhibiting 4 dB squeezing has been generated using a phase-sensitive type-I parametric amplifier pumped by a frequency-doubled Nd:YAG laser. In applying frequency-doubling processes to the generation of amplitude-squeezed light, the appearance of parasitic parametric oscillation must be considered. This effect has been observed in a singly-resonant frequency doubler. We also describe recent developments in optical cavity design for doubly-resonant frequency-doubling. Finally, we show theoretically that phase-mismatched second-harmonic generation in an optical cavity can be employed to generate a strong effective Kerr nonlinearity. This system appears promising for achieving optical bistability and for generating squeezed light of high power. Keywords: Non-classical light, squeezed light, amplitude squeezing, nonlinear op...

The most efficient sources of squeezed light have employed χ(2) processes in parametric downconversion or upconversion. In second harmonic generation both the fundamental and second harmonic modes are in an amplitude squeezed state. The upconverted mode is the squeezed state with the shortest wavelength involved in the process; therefore, frequency doubling is a promising scheme with which squeezing can be pushed toward the blue end of the spectrum. We measured the amplitude and phase noise properties of the second harmonic light generated in a frequency doubling monolithic cavity.