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 LiNb${\mathrm{O}}_{3}$, N${\mathrm{H}}_{4}$${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$, and K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ under various pumping conditions. Explicit formulas for the intensity of the spontaneous emission are also obtained. The spontaneous intensity calculated using the formulas given is shown to be in complete agreement with known experimental data on N${\mathrm{H}}_{4}$${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ pumped at 3472 \AA{}.
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, N{\mathrm{H}}_{4}$${\mathrm{H}}_{2}PO4, and KH2PO4 under various pumping conditions. Explicit formulas for the intensity of the spontaneous emission are also obtained. The spontaneous intensity calculated using the formulas given is shown to be in complete agreement with known experimental data on N{\mathrm{H}}_{4}$${\mathrm{H}}_{2}PO4 pumped at 3472 \AA{}.
This chapter outlines the noise source on the basis of a quantum theory. A quantum theory is, however, needed for a rigorous analysis of the spontaneous parametric scattering process and a clear understanding of the spontaneous parametric process is important for a number of reasons. First, since the frequency and phase-matching conditions for the spontaneous emission are the same as those for the corresponding stimulated parametric process, the tuning characteristics of optical parametric oscillators and amplifiers can be determined from the spontaneous parametric emission prior to the construction of an actual oscillator or amplifier. It is, however, far from clear whether such an amplifier can be made practical, although there are interesting fundamental issues related to squeezing in optical parametric processes that have attracted a great deal of attention. For optical parametric processes, one is usually interested in the transparent region of the optical media.
The quantum theory of three-wave optical parametric interactions in a crystal such as LiNbO3 is formulated in a symmetrical manner with respect to interaction time and distance. The formalism leads to a unique treatment of parametric interactions of both cavity type and propagation type, in that the resemblance between time in the cavity type and distance in the propagation type of interaction in the classical description is preserved. Three-wave effects of harmonic generation, parametric amplification (including spontaneous emission), and frequency conversion are treated in a unique and symmetric manner. Using Feynman's operator techniques, quantum states resulting from parametric interactions, previously unavailable, are derived, from which characteristics of the processes are deduced.
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.
The emission properties of atoms lie at the foundations of both quantum theory and light-matter interactions. In the context of macroscopic media, exact knowledge thereof is important both in current quantum technologies and in fundamental studies. While for isotropic media, this is a very well-studied problem, there are still big gaps in the theory of anisotropic media. In particular, to the best of our knowledge, an explicit expression for the spontaneous emission rate in general anisotropic media has not been presented. In this work, we first derive the quantized electromagnetic field operators to calculate the emission rate in uniaxial media. For the more general case of biaxial media we propose an approximate expression based on interpolation between the limiting cases of uniaxial media. We support our model with numerical simulations which are in strong agreement for typical media configurations and, furthermore, show how local field effects can be taken into account in the model.
A review is given of experimental and theoretical achievements in studies of multiphoton spontaneous scattering processes in atomic and molecular media. An analysis is made of integral multiphoton scattering, particularly of scattering in statistically inhomogeneous media with short-range quasiorder. A study of the intensity of the noncoherent multiphoton scattering component provides direct information on the nonlinear polarizability of atoms and molecules whilst the coherent component is associated with various atomic and molecular correlation mechanisms. An analysis of the spectra of elastic and inelastic multiphoton scattering processes yields information on the translational and rotational motion of the molecules. In particular, it is possible to measure the higher-order rotational relaxation times and to verify the adequacy of the various stochastic models of molecular motion. Observations of the spectral lines of three- or more-photon scattering, which obeys new selection rules, yield detail on the fine structure of the molecules and their linear and nonlinear vibrations. Examples are given of the most interesting spectra of three- or more-photon scattering in gases, liquids, and crystals obtained in singleand multichannel systems. The stochastic theory of multiphoton scattering in liquids is discussed, using the spherical tensor concept. The derived general expression reduces to known results for certain cases.
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.