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Journal of Experimental and Theoretical Physics Letters

Interaction of light waves in active nonlinear and periodically poled nonlinear crystals

Лаптев Георгий Дмитриевич, A. A. Novikov, A. S. Chirkin

Published Jul 1, 2003• 7 citations
Publisher

Abstract

The results of classical and quantum studies of the laser-radiation self-frequency conversion processes in periodically poled active nonlinear crystals are overviewed. The theoretical and experimental results of studying quasi-phase-matched self-frequency doubling and summation of the laser and pump frequencies in an active nonlinear periodically poled Nd:Mg:LiNbO 3 crystal are presented. The possibility of producing frequency-and polarization-entangled states and the sub-Poisson field statistics through a consecutive nonlinear optical frequency conversion in periodically poled nonlinear crystals is considered.

DOI
10.1134/1.1609574

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The results of classical and quantum studies of the laser-radiation self-frequency conversion processes in periodically poled active nonlinear crystals are overviewed. The theoretical and experimental results of studying quasi-phase-matched self-frequency doubling and summation of the laser and pump frequencies in an active nonlinear periodically poled Nd:Mg:LiNbO 3 crystal are presented. The possibility of producing frequency-and polarization-entangled states and the sub-Poisson field statistics through a consecutive nonlinear optical frequency conversion in periodically poled nonlinear crystals is considered.
We present a quantum theory of the parametric self-conversion of the laser radiation frequency in active nonlinear crystals with a regular domain structure. Such crystals feature simultaneous lasing and quasi-phase-matched parametric conversion of the laser radiation frequency. These processes are described using the Heisenberg-Langevin equations in two regimes of the subharmonic generation: super-and subthreshold. The spectral properties of the quadrature components of the laser frequency and its subharmonic and the photon statistics have been studied as dependent on the pump power, crystal length, and reflectance of the laser cavity output mirror. Using the obtained analytical expressions, these characteristics are calculated for a active nonlinear Nd:Mg:LiNbO 3 crystal with a regular domain structure. In the subthreshold regime, the maximum decrease in the spectral density of fluctuations in the subharmonic quadrature component relative to the standard quantum limit may reach 90%; in the above-threshold regime, these fluctuations are virtually not suppressed. A decrease in the spectral density of fluctuations of the laser frequency quadrature does not exceed 10%. In the subthreshold excitation regime, the subharmonic photons obey a super-Poisson statistics; in the above-threshold regime, the photon statistics is Poisson-like.
The results of quantum analysis of the light generated by consecutive and simultaneous quasi-phase-matched (QPM) wave interactions in periodically poled nonlinear crystals (PPNCs) are presented. In the case of the consecutive interactions of waves with multiple frequencies ω, 2ω and 3ω, the parametric amplification at low-frequency pumping is investigated. Generation of the quadrature-squeezed light at frequencies ω and 3ω in the 2ω frequency pumping field, the photon statistics and correlation as well as the entanglement properties for photons produced at different frequencies are studied. In the case of simultaneous QPM spontaneous parametric down-conversion processes in single PPNC, the main attention is paid to obtaining the polarization-entangled states at the collinear geometry of the wave interaction.
A quantum theory of self-convers of the lasing frequency in active nonlinear crystals placed in a cavity is developed. The generation of nonclassical (quadrature squeezed) light upon self-doubling of the laser radiation frequency is studied in detail, with no limitations on the relations between the relaxation times of the inverse population and the polarization of the medium and the lifetime of a photon in the cavity. The fluctuation spectra of the quadrature components of the fields of the laser radiation and its second harmonic are studied in dependence on the pumping parameters and the parameters of the cavity. Numerical calculations are performed for a Nd:Mg:LiNbO 3 crystal with a regular domain structure.
Theoretical calculations on transmission of quantum states such as Schrödinger cat (SC) states are considered in a periodically poled nonlinear crystal (PPNC). Combinations of various initial states (SC, coherent (C),and vacuum (V)) of light waves at frequencies ωeω_{e}ωe​ and 3ωe3ω_{e}3ωe​ at the input of a PPNC are studied. It is shown that the transmission and interference between superposition of macroscopically distinguishable states can be achieved by using a PPNC. Visualization and analyzes of transmission and interference processes are demonstrated with the help of reduced Wigner quasi-probability distribution functions of considered light waves.
The process of spontaneous parametric down-conversion (SPDC) in nonlinear crystals makes it fairly easy to generate entangled photon states. It has been known for some time that the conversion efficiency can be improved by employing quasi-phase-matching in periodically poled crystals. Using two single-photon detectors, we have analyzed the photon pairs generated by SPDC in a periodically poled lithium niobate crystal pumped by a femtosecond laser. Several parameters could be varied in our setup, allowing us to obtain data in close agreement with both thermal and Poissonian photon-pair distributions.