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IEEE Journal of Quantum Electronics

Enhancement of bright squeezing in the second harmonic by internally seeding the /spl chi//sup (2)/ interaction

Gregory S. Kanter, Prem Kumar

Published Aug 1, 2000• 5 citations
Publisher

Abstract

Second-harmonic generation (SHG) and parametric amplification result from the same physical configuration of the /spl chi//sup (2)/ process, but with different input conditions for the interacting fundamental and harmonic waves. In the former, the input harmonic field is usually in the vacuum state whereas, in the latter, the fundamental is in the vacuum state (or a small-amplitude coherent state). A different set of input conditions can lead to a nonlinear phase shift in both the fundamental and the harmonic waves, while not affecting their relative magnitudes. In conjunction with SHG, we show that this configuration can be used to generate a bright (high-intensity) amplitude-squeezed (sub-Poissonian) field at the harmonic frequency. Large amounts of squeezing are possible. An integrated device with the above characteristics can be fabricated by utilizing the recently developed quasi-phase-matching techniques.

DOI
10.1109/3.853542

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Second-harmonic generation (SHG) and parametric amplification result from the same physical configuration of the /spl chi//sup (2)/ process, but with different input conditions for the interacting fundamental and harmonic waves. In the former, the input harmonic field is usually in the vacuum state whereas, in the latter, the fundamental is in the vacuum state (or a small-amplitude coherent state). A different set of input conditions can lead to a nonlinear phase shift in both the fundamental and the harmonic waves, while not affecting their relative magnitudes. In conjunction with SHG, we show that this configuration can be used to generate a bright (high-intensity) amplitude-squeezed (sub-Poissonian) field at the harmonic frequency. Large amounts of squeezing are possible. An integrated device with the above characteristics can be fabricated by utilizing the recently developed quasi-phase-matching techniques.
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 experimental observation of bright amplitude squeezed light from a singly resonant second harmonic generator (SHG) based on a periodically poled potassium titanyl phosphate (KTP) crystal. Contrary to conventional SHG, the interacting waves in this device couple efficiently using quasi phase matching (QPM) and more importantly QPM allows access to higher valued elements of the nonlinear tensor than is possible under the constraint of birefringence phase matching. We observe a noise reduction of 13% below the shot noise limit in the generated second harmonic field. This noise reduction is greater than what could be expected using normal birefringence phase matched KTP with the same experimental parameters. Excellent agreement between experiment and theory is found.
We investigate, theoretically, the generation of bright and vacuum-squeezed light as well as entanglement in intracavity, type II, phase-matched second-harmonic generation. The cavity in which the crystal is embedded is resonant at the fundamental frequency but not at the second-harmonic frequency. A simple model for the process using semiclassical theory is derived, and quadrature-squeezing spectra of the involved fundamental fields are deduced. The analysis shows that vacuum squeezing reminiscent of subthreshold optical parametric oscillator squeezing is present and, in the ideal case, perfect. Under slight modifications of the operational conditions, the system is shown to produce efficient bright, squeezed light. Furthermore, we investigate the degree of polarization squeezing and find that three Stokes parameters can be squeezed simultaneously. Finally, we gauge the process for possible entanglement.
It is shown that coherent quantum simultons (simultaneous solitary waves at two different frequencies) can undergo quadrature-phase squeezing as they propagate through a dispersive ${\ensuremath{\chi}}^{(2)}$ waveguide. This requires a treatment of the coupled quantized fields including a quantized depleted pump field. A technique involving nonlinear stochastic parabolic partial differential equations using a nondiagonal coherent state representation in combination with an exact Wigner representation on a reduced phase space is outlined. We explicitly demonstrate that group-velocity matched ${\ensuremath{\chi}}^{(2)}$ waveguides which exhibit collinear propagation can produce quadrature-phase squeezed simultons. Quasi-phase-matched KTP waveguides, even with their large group-velocity mismatch between fundamental and second harmonic at 425 nm, can produce 3 dB squeezed bright pulses at 850 nm in the large phase-mismatch regime. This can be improved to more than 6 dB by using group-velocity matched waveguides.
Abstract We theoretically investigate the emergence of nonclassical features, two-mode squeezing, sub-Poissonian photon statistics, and bipartite entanglement, in the third harmonic generation (THG) process, employing a first-order interaction Hamiltonian within the short-time approximation. The study reveals that both first- and second-order squeezing exhibit strong dependence on the input field amplitudes, relative phase, and interaction strength. Asymmetric coherent inputs, where the harmonic mode carries greater intensity than the fundamental, enhance the degree of squeezing and lead to deeper nonclassical minima. The squeezing parameters display periodic phase-dependent oscillations, indicating phase-sensitive control of quantum correlations. Sub-Poissonian photon statistics in the fundamental mode further confirm the quantum nature of the generated light. Entanglement is analyzed through the Duan et al. inseparability criterion and the Hillery–Zubairy (HZ) criteria. While the Duan criterion fails to detect entanglement under purely coherent excitation in the short-time regime, both the HZ-1 and HZ-2 criteria confirm entanglement under specific phase conditions, with HZ-2 exhibiting greater sensitivity at elevated field strengths. These results underscore the potential of THG as a viable platform for the controllable generation of nonclassical light, with implications for continuous-variable quantum optics and integrated quantum photonics.
We have analyzed squeezing of the fundamental field by means of traveling-wave, type-II phase-matched, secondharmonic generation, taking into account depletion of the fundamental field and phase mismatch between the fundamental and the harmonic fields. For the phase-matched case we show that the generated squeezing is S = 1 - gamma, where gamma is the harmonic conversion efficiency. In the case of a large phase-mismatch we have identified a new mechanism that generates squeezing. It is the nonlinear phase shift of the fundamental field that is due to the cascaded chi((2)) nonlinearity.