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Physical Review A

Competing nonlinearities

Monika A. M. Marte

Published May 1, 1994• 33 citations
Publisher

Abstract

The interaction between two cavity resonant nonlinear processes in an intracavity ${\mathrm{\ensuremath{\chi}}}^{(2)}$ medium is studied, namely frequency doubling of a pump field of frequency ${\mathrm{\ensuremath{\omega}}}_{1}$ and subsequent down-conversion of the second harmonic to a pair of photons of frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}\ensuremath{\Delta}. A closed set of semiclassical equations of motion for appropriately chosen quantities of the full system is derived and an explicit stationary solution is given. Its features and stability are discussed, the most striking being a stable plateau in the second harmonic, i.e., the field of frequency ${\mathrm{\ensuremath{\omega}}}_{2}$=2${\mathrm{\ensuremath{\omega}}}_{1}$ becomes independent of the pump field ${\mathit{scrE}}_{1}$, provided ${\mathit{scrE}}_{1}$ is larger than a certain threshold value. It is demonstrated that undamped self-pulsing can only prevail, if the ratio of the rates of second harmonic generation over and parametric down-conversion exceeds a value which depends solely on the relative damping rates of the second harmonic and fundamental, which yields a tentative theoretical explanation of the experimentally observed quenching of the self-pulsing.

DOI
10.1103/physreva.49.r3166

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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.
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We consider second-harmonic generation by a non-linear crystal placed in an empty resonant cavity and pumped by an external coherent field. It was recently predicted that the stationary state loses its stability through a Hopf bifurcation when the input intensity reaches a critical value. A new amplitude self-modulated state then arises. We construct explicitly this new time-periodic solution and prove its stability in the vicinity of the transition point. As the input intensity is further increased, numerical investigations indicate a new transition to another time-periodic solution; this transition involves an hysteresis cycle. The two periodic solutions differ by the number of maxima in one period: at low input intensity, there is one maximum per period, whereas at high input intensity there are two.
We have generated squeezed states of light by the process of second harmonic conversion within an optical cavity resonant at both fundamental and harmonic frequencies. The experiment consists of a standing-wave cavity containing a crystal of lithium niobate doped with magnesium oxide and driven by the field from a frequency-stabilized Nd:YAG laser (incident power, ~10 mW). The total field reflected from the cavity illuminates a pair of high quantum efficiency photodiodes, whose individual photocurrents are summed. Observations of squeezing are made by analyzing the spectral density of fluctuations for this sum photo-current while the cavity detuning is scanned through resonance. An intensity regulator holds the reflected light intensity constant during the scan by control of the incident light level. Reductions in photocurrent fluctuations of 12% relative to the vacuum-state or shot-noise level are achieved for frequency offsets near 4 MHz. Since significantly higher degrees of squeezing are predicted by our theoretical analysis, we discuss those processes that currently limit the observed noise reduction, including phase noise produced by the intracavity crystal in the absence of nonlinear conversion.