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 show that nonclassical intensity correlations and quadrature entanglement can be generated by frequency doubling in a resonator with two output ports. We predict twin-beam intensity correlations
6dB below the coherent-state limit, and that the product of the inference variances of the quadrature fluctuations gives an Einstein-Podolsky-Rosen correlation coefficient of
VEPR=0.64<1, using the criterion of Reid [Phys. Rev. A 40, 913 (1989)]. Comparison with an entanglement source based on combining two frequency doublers with a beam splitter shows that the dual-ported resonator provides stronger entanglement at lower levels of individual beam squeezing. Calculations are performed using a self-consistent propagation method that does not invoke a mean-field approximation. Results are given for physically realistic parameters that account for the Gaussian shape of the intracavity beams, as well as intracavity losses.