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SPIE eBooks

Elements of Light-Matter Interaction

Yehoshua Y. Kalisky

Published Jul 31, 2014• 0 citations
Publisher

Abstract

This chapter briefly explains several concepts pertaining to the interaction between light and matter. Basic concepts such as Einstein coefficients, which describe the spontaneous emission and the stimulated absorption, as well as the classical and quantum mechanical description of absorption and emission processes are explained. More-detailed descriptions of various emission and absorption models can be found in several textbooks, such as those by Yariv, Siegman, and Miloni and Eberly.

DOI
10.1117/3.1002504.ch1

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This chapter briefly explains several concepts pertaining to the interaction between light and matter. Basic concepts such as Einstein coefficients, which describe the spontaneous emission and the stimulated absorption, as well as the classical and quantum mechanical description of absorption and emission processes are explained. More-detailed descriptions of various emission and absorption models can be found in several textbooks, such as those by Yariv, Siegman, and Miloni and Eberly.
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Abstract The quantum mechanical description of the interaction of light with atoms treats absorption, gain, and recombination as upward and downward induced transitions of electrons between two states by perturbation due to the optical electric field. This provides the basis for a quantitative theory of diode lasers. The chapter begins with Einstein’s description of absorption, stimulated emission, and spontaneous emission, setting the scene for calculation of the transition probability by solving the time-dependent Schrödinger equation for a coherent superposition of the wavefunctions of two states. The resulting absorption spectrum has a Lorentzian lineshape due to dephasing of these wavefunctions. Expressions for the optical absorption cross section and Einstein coefficients are derived in terms of the dipole matrix element, and the dipole is illustrated using a hypothetical one-dimensional atom. Fermi’s Golden Rule for transitions to a continuum of states (as in quantum wells) is introduced in terms of the momentum matrix element.
An impressively comprehensive textbook adopting a phenomenological approach to quantum physics. The chapters cover everything from basic definitions of key concepts to detailed discussions of the underlying theoretical framework, walking students step-by-step through the necessary mathematics and drawing clear connections between the theory and the most important modern research applications including quantum optics, fluids, nanophysics, entanglement, information, and relativity. With this book, students and researchers will have access to hundreds of real-world examples, exercises, and illustrations to support and expand their understanding. Instructors can tailor the content to suit the length and level of their course and will have access to an online solutions manual with fully worked solutions to all 300+ exercises in the book. Other online resources include Python simulations, additional exercises, and detailed appendices.
We treat the interaction between an electromagnetic radiation bath and a material system in the semi-classical picture: the radiation is treated according to the Maxwell equations, but the process of emission/absorption is described through the concept of a photon; on the other hand, the material system is modelled according to quantum mechanics, assuming a discrete two-level energy spectrum. This very simple model allows one to elaborate the elementary theory of the absorption/emission coefficients, both for the spontaneous and for the stimulated processes which will be described within the electric dipole approximation. Selection rules for allowed transitions are eventually obtained and the nature of high-order transition is briefly outlined. Finally, a qualitative description of the light amplification by stimulated emission of radiation is presented.
“Why is the sky blue?” or “why are clouds white?” are examples of basic questions that always intrigued the mind of young, and not-so-young, students before their exposure to the fundamentals of light–matter interaction, a phenomenon that occurs anytime and anywhere in our universe and constitutes the main thrust in this chapter. It starts by highlighting the basic aspects of absorption and spontaneous and stimulated emission, described (in terms of quantum mechanics) by using Einstein coefficients and transition moments ; further along, the (classical) macroscopic connection with the Beer–Lambert law is derived. The journey continues by visiting elastic scattering and its two modalities, Rayleigh and Mie scattering , depending on the scattering particle size. In the final step, inelastic Brillouin and Raman scattering are discussed, placing emphasis on the laser-spectroscopic techniques underlying these types of photon–matter interactions. The chapter ends with a brief description how prehistoric humans already knew how to prepare colors for paintings (as exemplified in the Altamira cave in Cantabria, Spain); and a short exposé into state-of-the-art single-molecule spectroscopy using a single photon. This thread of spanning an arc between (historical) breakthroughs and cutting-edge research will be common to all chapters of the book.