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Journal of the Optical Society of America B

Photonic bandgap structures in planar nonlinear waveguides: application to squeezed-light generation

Daniela Tricca, C. Sibilia, S. Severini, M. Bertolotti, Michael Scalora, C. M. Bowden, Kazuaki Sakoda

Published Mar 1, 2004• 11 citations
Publisher

Abstract

Quadrature-amplitude and phase squeezing are theoretically investigated in a planar waveguide geometry where the use of a linear grating fabricated on top of the waveguide reproduces a photonic bandgap structure. The introduction of a nonlinear grating, obtained with a modulation of the nonlinear susceptibility χ(2), provides an additional degree of freedom that allows, together with the linear grating, tuning of the fundamental field in a selected resonance of the transmission spectrum and, at the same time, control of the phase-matching condition between the fundamental and second-harmonic fields. The results show that quadrature-amplitude squeezing is achieved for the fundamental field, increasing the second-harmonic input intensity. The second-harmonic field is tuned in the passband of the photonic bandgap. The low nonlinear conversion efficiency, given by a suitable selection of the mismatch, gives rise to the possibility of having a fundamental field of quite the same intensity, but less noisy than at the entry.

DOI
10.1364/josab.21.000671

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Quadrature-amplitude and phase squeezing are theoretically investigated in a planar waveguide geometry where the use of a linear grating fabricated on top of the waveguide reproduces a photonic bandgap structure. The introduction of a nonlinear grating, obtained with a modulation of the nonlinear susceptibility χ(2), provides an additional degree of freedom that allows, together with the linear grating, tuning of the fundamental field in a selected resonance of the transmission spectrum and, at the same time, control of the phase-matching condition between the fundamental and second-harmonic fields. The results show that quadrature-amplitude squeezing is achieved for the fundamental field, increasing the second-harmonic input intensity. The second-harmonic field is tuned in the passband of the photonic bandgap. The low nonlinear conversion efficiency, given by a suitable selection of the mismatch, gives rise to the possibility of having a fundamental field of quite the same intensity, but less noisy than at the entry.
Optical parametric process occurring in a nonlinear planar waveguide can serve as a source of light with nonclassical properties. Properties of the generated fields are substantially modified by scattering of the nonlinearly interacting fields in a photonic band-gap structure inside the waveguide. A quantum model of linear operator amplitude corrections to amplitude mean-values provides conditions for an efficient squeezed-light generation as well as generation of light with sub-Poissonian photon-number statistics. Destructive influence of phase mismatch of the nonlinear interaction can fully be compensated using a suitable photonic-band gap structure inside the waveguide. Also an increase of signal-to-noise ratio of an incident optical field can be reached in the waveguide.
Optical parametric process occurring in a nonlinear planar waveguide can serve as a source of light with nonclassical properties. The properties of the generated fields are substantially modified by scattering of the nonlinearly interacting fields in a photonic-band-gap structure inside the waveguide. A general quantum model of linear operator amplitude corrections to the amplitude mean values and its numerical analysis provide conditions for efficient squeezed-light generation as well as generation of light with sub-Poissonian photon-number statistics. The destructive influence of phase mismatch of the nonlinear interaction can fully be compensated using a suitable photonic-band-gap structure inside the waveguide. Also an increase of the signal-to-noise ratio of the incident optical field can be reached in the waveguide.
Two-mode nonlinear interaction (second-harmonic and second-subharmonic generation) in a planar waveguide with a small periodic corrugation at the surface is studied. Scattering of the interacting fields on the corrugation leads to constructive interference that enhances the nonlinear process provided that all the interactions are phase matched. Conditions for the overall phase matching are found. Compared with a perfectly quasi-phase-matched waveguide, better values of squeezing as well as higher intensities are reached under these conditions. Procedure for finding optimum values of parameters for squeezed-light generation is described.
Optical parametric process occurring in a photonic-band-gap planar waveguide is studied from the point of view of nonclassical-light generation. Nonlinearly interacting optical fields are described by the generalized superposition of coherent signals and noise using the method of quantum linear corrections to a classical strong mean-field' solution. Scattered back-propagating fields are taken into account. The possibility to generate squeezed light and light with sub-Poissonian statistics in dependence on the strength of scattering, strength of nonlinear interaction, linear and nonlinear phase mismatches as well as characteristics of the states of optical fields incident on the waveguide is discussed in detail.
Nonlinear optical phenomena associated with high-order soliton breakup in photonic crystal fibres and squeezed state generation in three dimensional photonic crystal microcavities are investigated. In both cases, the properties of periodically patterned, high-index contrast dielectric structures are engineered to control the dispersion and local field enhancements of the electromagnetic field. Ultra-short pulse propagation in a polarization-maintaining microstructured fibre (with 1 um core diameter and 1.1 m length) is investigated experimentally and theoretically. For an 80 MHz train of 130 fs pulses with average propagating powers in the fibre up to 13.8 mW, the output spectra consist of multiple discrete solitons that shift continuously to lower energies as they propagate in the lowest transverse mode of the fibre. The number of solitons and the amount that they shift both increase with the launched power. All of the data is quantitatively consistent with solutions of the nonlinear Schrodinger equation, but only when the Raman nonlinearity is treated without approximation, and self-steepening is included. The feasibility of using a parametric down-conversion process to generate squeezed electromagnetic states in 3D photonic crystal microcavity structures is investigated for the first time. The spectrum of the squeezed light is theoretically calculated by using an open cavity quantum mechanical formalism. The cavity communicates with two main channels, which model vertical radiation losses and coupling into a single-mode waveguide respectively. The amount of squeezing is determined by the correlation functions relating the field quadratures of light coupled into the waveguide. All of the relevant model parameters are realistically estimated using 3D finite-difference time-domain (FDTD) simulations. Squeezing up to ~20% below the shot noise level is predicted for reasonable optical excitation levels. To preserve the squeezed nature of the light generated in the microcavity, a unidirectional coupling geometry from the microcavity to a ridge waveguide in a slab photonic crystal structure is studied. The structure was successfully fabricated in a silicon membrane, and experimental measurements of the efficiency for the signal coupled out of the structure are in good agreement with the result of FDTD simulations. The coupling efficiency of the cavity mode to the output channel is ~60%.
Nonlinear optical waveguides hold promise as parametric amplifiers and as sources of quadrature-squeezed light. The confinement of the pump field drastically increases the efficiency of the nonlinear conversion. In addition, the control of the spatial mode profiles by the waveguide geometry should diminish the effect of gain-induced diffraction, which has been seen to limit the amount of attainable squeezing in bulk parametric crystals.1 Using subpicosecond laser pulses, we have observed parametric gain as well as quadrature squeezing in a quasi-phase matched KTP waveguide.