Abstract In this work, we study optical manipulation and conversion in the high-power regime, and thus the unavoidable intrinsic coupling between the pump light and the signal light, i.e. pump depletion, needs to be included. Compared with the transmission properties that are insensitive to the power of the signal light in the low-power regime with pump non-depletion, our results in the high-power regime with pump depletion show that the resonant transmission coefficients of the χ ( 2 ) nonlinearity can be manipulated from 0 to non-zero by adjusting the intensities of the signal light, and thus it behaves as an intensity-dependent all-optical switch. Although the resonant conversion efficiencies from four-wave mixing of the χ ( 3 ) nonlinearity are generally suppressed by power-dependent frequency shifts as a result of self-phase modulation (SPM) and cross-phase modulation (XPM) in the high-pump regime, the conversion efficiencies can be amplified by tuning the frequency detuning of the signal and pump lights. The optical transmission coefficients and conversion efficiencies can also be enhanced by utilizing the interplay between χ ( 2 ) and χ ( 3 ) nonlinearities in the high-pump regime. The mechanism of enhancing the conversion efficiencies to overcome the suppression from SPM and XPM provides a new way to convert frequency with high efficiencies.
All optical processing of data on an integrated photonic chip requires all-optical switches as a fundamental element to actively modulate the transmission of the signal light by the control light. Traditional all-optical switches as a function of the intensities of the input fields can be classified into three categories as the regular, the optical limiting and the bistable switches. In this work, a whispering gallery mode resonator coupled to a waveguide with third-order nonlinearity in the pump depletion regime is investigated. The transmission spectra of the signal light are able to be controlled by adjusting the power-dependent frequency shifts. We find that the frequency shifts of the cavity modes depend not only on the nonlinear processes of self- and cross-phase modulation but also on the coupling between the pump and the signal lights in the pump depletion regime. When the pump light is increased to milliwatts, the transmission coefficient of the nonresonant signal light has a critical point corresponding to the complete destructive interference from the combing effects of pump depletion, self- and cross-phase modulation. The results show that the output power of the signal light responds to the input power of the pump light with V-shaped curves. These input–output power curves can be utilized to construct a V-type all-optical switch for applications in automatic protection and monitoring the light intensity in optical communication network. Significantly, the V-type all-optical switch can also be constructed in system with both second- and third-order nonlinearities involved.
A theory for the nonlinear properties of optical-frequency conversion using nearly degenerate four-wave mixing in semiconductor lasers is presented for the first time. Because of pump depletion, the converted signal and the conversion efficiency depend on both the injected probe power and the frequency detuning. The relaxation resonance frequency and the damping rate are both related to the probe signal, especially for a high optical injection level. The theory is in good agreement with experiments.
We demonstrate theoretical conditions for highly efficient degenerate four-wave mixing in triply resonant nonlinear (Kerr) cavities. We employ a general and accurate temporal coupled-mode analysis in which the interaction of light in arbitrary microcavities is expressed in terms of a set of coupling coefficients that we rigorously derive from the full Maxwell equations. Using the coupled-mode theory, we show that light consisting of an input signal of frequency ${\ensuremath{\omega}}_{0}\ensuremath{-}\ensuremath{\Delta}\ensuremath{\omega}$ can, in the presence of pump light at ${\ensuremath{\omega}}_{0}$, be converted with quantum-limited efficiency into an output shifted signal of frequency ${\ensuremath{\omega}}_{0}+\ensuremath{\Delta}\ensuremath{\omega}$, and we derive expressions for the critical input powers at which this occurs. We find the critical powers in the order of 10 mW, assuming very conservative cavity parameters (modal volumes
10 cubic wavelengths and quality factors
1000). The standard Manley-Rowe efficiency limits are obtained from the solution of the classical coupled-mode equations, although we also derive them from simple photon-counting ``quantum'' arguments. Finally, using a linear stability analysis, we demonstrate that maximal conversion efficiency can be retained even in the presence of self- and cross-phase modulation effects that generally act to disrupt the resonance condition.
We demonstrate for the first time natural phase matching for optical frequency doubling in a high-Q whispering-gallery-mode resonator made of lithium niobate. A conversion efficiency of 9% is achieved at 30 microW in-coupled continuous wave pump power. The observed saturation pump power of 3.2 mW is almost 2 orders of magnitude lower than the state-of-the-art value. This suggests an application of our frequency doubler as a source of nonclassical light requiring only a low-power pump, which easily can be quantum noise limited. Our theoretical analysis of the three-wave mixing in a whispering-gallery-mode resonator provides the relative conversion efficiencies for frequency doubling in various modes.
We manipulated the simulation and apparatus to generate the entangled quantum photons by the enhanced higher quality factor in waveguide of whispering gallery mode resonator in silica microsphere. As the several nonlinear optics effects have been validated in micro-disk (lithium niobate materials based), others micro-cavity (microfiber and micro ring on the chip) and second harmonic generation (SHG) on the surface of silica microsphere because of the characterization of enhanced higher quality factor Q and smaller volume mode in these resonator. However until now for the second third nonlinearity of spontaneous parametric down conversion (SPDC), third order nonlinearity of spontaneous parametric down conversion (TOSPDC) and spontaneous four wave mixing (SFWM) in whispering gallery mode (WGM) resonator of silica microsphere rarely have not been fully investigated and verified to generate the triple and pair entangled photons where are widely applied on the applications of biosensor, quantum communications and spectroscopy, respectively. Specially, the features of silica microsphere have attracted many applications due to the simple fabrication, simplified materials melted by silica fiber. The work we demonstrated in this paper based on the breaking of the dispersion rules to make perfect phase matching in normal dispersion in silica microsphere depending on the blue laser spectrum in visible spectrum, then manipulated the modified size of microsphere to detune the pump laser of free spectral range (FSR) and both shift the geometrical dispersion are characterized in the variation of FSR given by (see PDF for equation), where n is refractive index, R is the microspheres radius and m is mode numbers in resonator, to compensate the materials dispersion given by (see PDF for equation), where c is the speed of light and λ is pump laser wavelength to fulfill the perfect phase matching in parametric down conversion regimes and the modeling fabrication coupling results also will be presented.
We investigate quantum pump depletion and non-Gaussian state generation in doubly pumped Kerr microresonators operating in the intraresonance regime. The pump modes are treated quantum mechanically rather than as undepleted classical amplitudes, allowing pump depletion, back-action, entanglement generation, quadrature fluctuations, and Wigner-function negativity to emerge from the same multimode dynamics. Starting from the Kerr four-wave-mixing selection rule, we distinguish an effective resonant photon-conversion model from the full Kerr Hamiltonian containing self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM). The reduced model isolates the photon-conversion network responsible for the discrete
Zn+1 phase structure, whereas the full model retains operator-valued nonlinear Kerr phases. For the
n=2 intraresonance branch, the four-mode reduced initial-value problem with fixed coherent pump phases has a residual
Z3 symmetry and generates cat-like Wigner structures near the interaction length at which the generated-mode population
⟨n1⟩ is maximal and the pump population
⟨n0⟩ is strongly depleted. The resulting states are not the canonical even or odd coherent states of Dodonov, Malkin, and Man'ko, but multicomponent Schrödinger-cat-like states characterized by Wigner negativity, non-Poissonian statistics, pump-mode quadrature squeezing, and large single-mode Schmidt numbers. Comparison of the reduced and full Kerr dynamics shows that uncompensated SPM/XPM-induced phase shearing suppresses the interference fringes and Wigner negativity responsible for the clearest cat-like signatures. These results identify quantum-depleted intraresonance Kerr dynamics as a route to symmetry-organized non-Gaussian states in Kerr resonators.