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Quantum Electronics

Interferometry of spontaneous parametric light scattering

Dmitry Korystov, S. P. Kulik, Alexander N. Penin

Published Oct 31, 2000• 9 citations
Publisher

Abstract

The interference of biphotonic light produced in the process of spontaneous parametric scattering (SPS) in two spatially separated non-centrally symmetric crystals is considered. A scheme of the nonlinear Mach—Zehnder interferometer is realised. It is shown that in this case, the frequency-angular intensity distribution in the far-field zone (the SPS spectrum) contains information not only on non-centrally symmetric crystals, where biphotonic fields are created, but also on the optical properties of the medium located between the scattering crystals. The algorithms for the determination of the dispersion law in this medium are developed.

DOI
10.1070/qe2000v030n10abeh001831

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The interference of biphotonic light produced in the process of spontaneous parametric scattering (SPS) in two spatially separated non-centrally symmetric crystals is considered. A scheme of the nonlinear Mach—Zehnder interferometer is realised. It is shown that in this case, the frequency-angular intensity distribution in the far-field zone (the SPS spectrum) contains information not only on non-centrally symmetric crystals, where biphotonic fields are created, but also on the optical properties of the medium located between the scattering crystals. The algorithms for the determination of the dispersion law in this medium are developed.
Two types of interference were observed using two-photon spontaneous parametric radiation from two nonlinear interaction regions. Two experimental setups analogous to the Young and Mach-Zehnder interferometers were used. An interesting feature of the two-photon Young interference is the opposite conditions for its observation by two different methods: by measuring intensity of light at a single frequency and by measuring correlation of intensities at two conjugated frequencies (method of coincidences). Two-photon Mach-Zehnder interference resembles the Ramsey method of separated fields, which is used in beam spectroscopy. A simple macroscopic quantum model agrees well with the experimental results and enables their interpretation in terms of ``biphotons'' carrying information about the pump phase.
A quantum theory is developed for the spontaneous optical parametric process in nonlinear, anisotropic, and dispersive media; the process is treated directly as a scattering problem rather than a problem involving equivalent coupled oscillators. Following the general procedure in quantum field theory, a general expression is obtained for the differential extinction coefficient, which contains all the information on the intensity of the spontaneous emission in the parametric scattering process. The tuning characteristics, beam divergence, and spectral properties of the spontaneous emission for colinear and noncolinear interactions are described in detail and illustrated with numerical examples on such standard nonlinear optical crystals as LiNbO3{\mathrm{O}}_{3}O3​, NH4{\mathrm{H}}_{4}H4​H2{\mathrm{H}}_{2}H2​PO4{\mathrm{O}}_{4}O4​, and KH2{\mathrm{H}}_{2}H2​PO4{\mathrm{O}}_{4}O4​ under various pumping conditions. Explicit formulas for the intensity of the spontaneous emission are also obtained. The spontaneous intensity calculated using the formulas given is shown to be in complete agreement with known experimental data on NH4{\mathrm{H}}_{4}H4​H2{\mathrm{H}}_{2}H2​PO4{\mathrm{O}}_{4}O4​ pumped at 3472 \AA{}.
We study both theoretically and experimentally the interference pattern in a nonlinear Mach–Zehnder interferometer formed by two aperiodically-poled crystals, where broadband squeezed light is generated by both crystals via parametric down-conversion with a common quasi-monochromatic pump. This configuration is important for measuring the squeezing produced by the first crystal and also for measuring a small phase shift introduced by a sample between the crystals. On the basis of the approximate quantum Rosenbluth formula for each crystal we develop an analytic model for the field evolution in the interferometer. We report an experimental observation of the interference fringes, caused by the dispersion of the generated PDC waves in both crystals forming the interferometer. We observe a displacement of the interference pattern caused by a sample between the crystals and infer the phase shift within a band of 20 nm. The experimental data are in a good agreement with the predictions of the developed model, up to imperfections of the samples.
The possibility to manage and control spectral and spatial properties of optical-terahertz nonclassical fields generated in strongly nondegenerate parametric down-conversion is demonstrated experimentally using Mach-Zehnder nonlinear interferometer and analyzed theoretically in terms of Schmidt modes. The interferometer can be used for measuring the dispersion properties of different materials in the terahertz frequency range. The key point is that the information about these properties is extracted from the measurements in the optical channel due to strong frequency-angular correlations between optical and terahertz photons. The developed theoretical approach is used to predict properties of the optical-terahertz fields and photon correlations in different regimes of nondegenerate parametric down-conversion. The considered interferometer is shown to be a promising source of terahertz fields with new features and frequency-filtered terahertz Schmidt modes.