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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Surface effect on spontaneous parametric down-conversion

A. Lukš, Vlasta Peřinová, J. Křepelka

Published Dec 18, 2012• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.2012005

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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.
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.
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.
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.
Introduction One of the most impressive accomplishments of wave optics is its success in providing a coherent and succinct description of the interactions between electromagnetic waves and matter (gases, solids, etc.). Maxwell's equations, which describe the propagation of light, and the Laplace–Lorentz equations, which describe the source terms of light, allow one to take into account the phenomena of refraction, diffusion, and diffraction of light by dense media. It is amazing – to say the least – that such a theory can account for the complex interactions of an electromagnetic wave with an immense ensemble of atoms (each approximated in terms of individual harmonic oscillators), by means of a simple optical index n op . Such an achievement is reminiscent and, indeed, on par with the level of concision achieved by the concept of effective mass in representing the interaction of a conduction electron with a crystalline lattice. In the description of all these effects, an electromagnetic wave with (angular) frequency ω forces free carriers into oscillatory motion at the same frequency, leading to radiative re-emission at this same frequency. This behaviour is a natural by-product of the linear equations we have employed up until now. In this chapter, we will see that non-linear media (i.e. materials whose response to external excitations contains non-linear terms), may by used to perform frequency conversion as evidenced, for example, by second harmonic light generation or optical parametric oscillations.