Aspects of Nonlinear Optics and Many-Photon Effects

Guang S. He

This chapter describes the formation, development, and major subjects of nonlinear optics and photonics. The semiclassical theory treats the light as a classical electromagnetic field governed by Maxwell equations, while the optical medium is a molecular system governed by quantum mechanics; the key parameters for this theory are various-order nonlinear susceptibilities. The quantum theory of radiation treats light as an ensemble of photons and the medium as a molecular system, both of which are described by quantum mechanics, and the key aspect is the concept of the so-called intermediate state represented by a virtual energy state level. The semiclassical theory gives a concise quantitative description of various nonlinear multi-wave mixing effects as well as those nonlinear processes related to the induced refractive-index changes. In contrast, the quantum theory of radiation can provide a conceptual interpretation for almost all known nonlinear optical effects and phenomena.

Milivoj R. Belić

L. A. Lugiato, A. Gatti, G. Grynberg

Optical systems are macroscopic, but they are able to display relevant quantum effects, even at room temperatures. This feature makes optics special with respect to other disciplines (e.g. hydrodynamics and nonlinear chemical reactions), which are more traditional in the study of pattern formation phenomena. Recent years have witnessed an increasing interest in the analysis of spatial aspects of squeezing, and of quantum effects in nonlinear optical patterns.1-4

Optical Echo Holography, E. I. Shtyrkov

Ole Keller

Chahrour, Fouad, Ozdemir, Şahin K., Busch, Kurt +2 more

Thermalization of isolated quantum systems is an intriguing phenomenon at the forefront of contemporary physics. In this work, we demonstrate that nonlinear multimode optical platforms can be harnessed to induce effective quantum interactions between photons. Through numerical experiments where quantum beams propagate alongside classical light within multimode nonlinear optical systems, we reveal the thermalization of fundamental quantum light states--specifically single- and two-photon states. This thermalization is clearly manifested by the emergence of Rayleigh-Jeans and Boltzmann statistical distributions. Beyond providing a deeper understanding of how classical nonlinearities can be used to investigate quantum many-body dynamics, our findings will enable the exploration of a broader range of complex quantum phenomena, including aspects of quantum phase transitions, within readily accessible classical optical settings.