Energy exchange between counter propagating light waves of equal frequency is possible in media with instantaneous and local nonlinear optical response which, however, provides a special form of nonlinearity tensor. The major requirement is that there has to be no Lagrangian describing the light-medium interaction. There is a limited region of the pump wave intensity where the signal wave amplification takes place. The thermal mechanisms of interaction between light waves and liquid crystals provide examples of "non-Lagrangian" nonlinearity.
Energy exchange between counter propagating light waves of equal frequency is possible in media with instantaneous and local nonlinear optical response which, however, provides a special form of nonlinearity tensor. The major requirement is that there has to be no Lagrangian describing the light-medium interaction. There is a limited region of the pump wave intensity where the signal wave amplification takes place. The thermal mechanisms of interaction between light waves and liquid crystals provide examples of "non-Lagrangian" nonlinearity.
Interaction of optical beams in media with diagonal-bipolar nonlinearity is theoretically investigated. It is shown that the nonlinearity is not Lagrangian and allows processes violating energy flux conservation law. Conditions for energy exchange to take place are found. Probe beam amplification in the field of counterpropagating pumps and wavefront conjugation are investigated to exhibit some remarkable features. Coherent interaction of waves of different frequencies through recording static gratings is shown to lead also to energy exchange processes owing to non-Lagrangian character of nonlinearity.
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.
In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.
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.
A review is given of the present state of theoretical and experimental work on the interaction of two coherent light beams of equal frequency in a nonlinear medium. It is shown that dynamic self-diffraction is substantially different for media with different types of response. Stationary energy transfer between interacting beams is possible in the case of nonlocal nonsymmetric response, whereas this type of transfer is forbidden in the case of local response. Different mechanisms for self-induced changes in the refractive index are examined together with the corresponding processes of energy transfer between the writing beams. The more important applications of dynamic self-diffraction are discussed.