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Journal of Experimental and Theoretical Physics

Parametric frequency conversion in layered nonlinear media

G. Kh. Kitaeva, Alexander N. Penin

Published Feb 1, 2004• 24 citations
Publisher

Abstract

Frequency-angular distributions of signal wave intensity are calculated for spontaneous parametric down-conversion and parametric frequency conversion in spatially nonuniform nonlinear media. Wave reflection from interfaces is taken into account, and both regular and irregular nonuniform distributions of second-order nonlinear susceptibility are considered. A unified approach using a scattering matrix and a generalized Kirchhoff law is applied in calculations of spontaneous and stimulated processes in dissipative nonlinear media. Interference of electromagnetic zero-point fluctuations of the vacuum, nonlinear interference, and nonlinear diffraction are examined for media with various absorptive properties. Theoretical foundations are developed for diagnostics of nonuniform distributions of the second-order susceptibility, based on measurement of the line profiles of nonlinear signals.

DOI
10.1134/1.1675895

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Frequency-angular distributions of signal wave intensity are calculated for spontaneous parametric down-conversion and parametric frequency conversion in spatially nonuniform nonlinear media. Wave reflection from interfaces is taken into account, and both regular and irregular nonuniform distributions of second-order nonlinear susceptibility are considered. A unified approach using a scattering matrix and a generalized Kirchhoff law is applied in calculations of spontaneous and stimulated processes in dissipative nonlinear media. Interference of electromagnetic zero-point fluctuations of the vacuum, nonlinear interference, and nonlinear diffraction are examined for media with various absorptive properties. Theoretical foundations are developed for diagnostics of nonuniform distributions of the second-order susceptibility, based on measurement of the line profiles of nonlinear signals.
The influence of disordering of one-dimensional quasi-phase matched structures in nonlinear optical crystals on spectral characteristics of parametric processes is studied. Two different correlation functions are introduced for describing the random change of the sign of the second-order nonlinear susceptibility. The optimal conditions for quasi-phase matching of the interacting waves are found. The second aim of the paper is the investigation of important features of spontaneous parametric down-conversion (SPDC) in a homogeneous nonlinear slabs with emphasis of spatial inhomogeneity of interacting waves (in paraxial approximation). We estimate the absolute values of the emission rate of photon pairs produced by SPDC when all fields are in single Gaussian modes.
The generation of photon pairs inside metallo-dielectric layered media by spontaneous parametric down conversion is highly efficient. A theoretical model of spontaneous parametric down conversion based on vectorial quantum-mechanial approach is used to obtain spatial, frequency and temporal photon-pair characteristics. As an example, a structure consisting of eleven alternating Galium-Nitride and silver layers is analyzed. Strong constructive interference of the sub-frequency fields results in narrow spatial and frequency distributions of photon-pairs emitted at high generation rates. Photon pairs are mainly created in Galium-Nitride layers, the silver layers serve as a linear reflector.
Nonlinear optics is the study of the response of dielectric media to strong optical fields. The fields are sufficiently strong that the response of the medium is, as its name implies, nonlinear. That is, the polarization, which is the dipole moment per unit volume in the medium, is not a linear function of the applied electric field. In the equation for the polarization, there is a linear term, but, in addition, there are terms containing higher powers of the electric field. This leads to significant new types of behavior, one of the most notable being that frequencies different from that of the incident electromagnetic wave, such as harmonics or subharmonics, can be generated. Linear media do not change the frequency of light incident upon them. The first observation of a nonlinear optical effect was, in fact, second-harmonic generation – a laser beam entering a nonlinear medium produced a second beam at twice the frequency of the original. Another type of behavior that becomes possible in nonlinear media is that the index of refraction, rather than being a constant, is a function of the intensity of the light. For a light beam with a nonuniform intensity profile, this can lead to self-focusing of the beam. Most nonlinear optical effects can be described using classical electromagnetic fields, and, in fact, the initial theory of nonlinear optics was formulated assuming the fields were classical. When the fields are quantized, however, a number of new effects emerge. Quantized fields are necessary if we want to describe fields that originate from spontaneous emission. For example, in a process known as spontaneous parametric down-conversion, a beam of light at one frequency, the pump, produces a beam at half the original frequency, the signal. This second beam is a result of spontaneous emission.
On the interface between two isotropic linear media the re°ection and transmission of separate monochro- matic waves occur in a normal incidence, which are described by Fresnel's formulas. On the interface between two nonlinear media, namely one of the media may be linear in a limit, the re°ection and the transmission are complicated by a wave mixing of di®erent frequencies. A maximum generality of improved Fresnel formulas is impossible. By using the rotating-wave approximation and the parametric approximation, a model of the parametric down-conversion has been derived in the nonlinear and quantum optics. We present a classical ex- pression of the e®ect of the wave mixing on the interface and treat even the possibility of quantum input{output relations.
We study conditions for the generation of strongly correlated photons of two extremely different frequency ranges, optical and terahertz, via the spontaneous parametric down-conversion effect in a nonlinear medium. Analytical expressions for the correlation function are derived using equations of the generalized Kirchhoff law for the second-order field moments with account of both classical thermal and quantum vacuum field fluctuations, possible inherent absorption of the medium at terahertz frequencies, and angular divergences of signal and idler radiation caused by a transverse limited spatial profile of the Gaussian pump beam. Associated with the current absence of terahertz photon counting detectors and coincidence schemes, the possible experimental limitations in measuring the second-order optical-terahertz field correlations are studied. Numerical calculations of noncollinear eee-geometry parametric down-conversion in a Mg:LiNbO3\mathrm{Mg}:\mathrm{LiNb}{\mathrm{O}}_{3}Mg:LiNbO3​ crystal demonstrate angular characteristics, particular features of the temperature and spectral behavior of the second-order quantum correlation function of optical-terahertz biphotons.