This paper presents a unified, step-by-step development of laser amplification from the microscopic viewpoint of photon-atom interactions. Starting with the quantization of light (E = hν), introducing Einstein's three coefficients for absorption and emission, derive the coupled rate equations, use detailed balance to recover Planck's law, connect the rates to quantum-mechanical dipole matrix elements, and culminate in the concept of population inversion and the physical picture of laser build-up. The goal of this presentation about understanding the Stimulated emission towards Laser concepts, an level 1 understanding prior to journey of understanding quantum computing.
This paper presents a unified, step-by-step development of laser amplification from the microscopic viewpoint of photon-atom interactions. Starting with the quantization of light (E = hν), introducing Einstein's three coefficients for absorption and emission, derive the coupled rate equations, use detailed balance to recover Planck's law, connect the rates to quantum-mechanical dipole matrix elements, and culminate in the concept of population inversion and the physical picture of laser build-up. The goal of this presentation about understanding the Stimulated emission towards Laser concepts, an level 1 understanding prior to journey of understanding quantum computing.
This chapter begins with a heuristic derivation of atomic population rate equations which include changes to level populations due to stimulated transitions as well as level relaxations and pump. These equations are used to study the saturation of population inversion with increasing light intensity and its dependence on the type of gain medium (three-level gain media vs. four-level gain media), lineshape and nature of line broadening (homogeneous vs inhomogeneous broadening). How saturation affects lineshape and thus gain and absorption giving rise to phenomena like power broadening and spectral hole burning is also discussed. The chapter summarizes the equations of motion for atomic polarization, inversion and the cavity field describing their nonlinear dynamical coupling. These equations, known as the Maxwell-Bloch equations, provide a complete description of atom-field interaction in a laser. Approximations of these equations, including the rate equation approximation, to deal with different laser classes are briefly described. These will be used in the next few chapters to explore and understand the rich and varied behavior of lasers. The chapter ends with a summary of select gain media for different types of commonly used lasers.
In this book we treat the interaction of radiation with matter with special application to gain (amplifying) media typically existing in lasers. Tradition ally the interaction of radiation with matter is treated in terms of the index of refraction and the absorption of light, utilizing the model of electrons on springs. In Chap. 3 we show that this model is reasonable for some linear absorbing systems but is very awkward, if not outright unworkable, for a microscopic description of gain media. The essential failure of the electron-spring model is its difficulty in yielding net stimulated emission (and therefore gain) for an ensemble of systems.t In contrast, a more physically sound, quantum treatment of matter provides for the concept of population inversion and explains stimulated emission in a natural way. Hence from the very start we are compelled to base our understanding of the interaction of radiation with matter on a quantum-mechanical description of atoms. In Chaps. 1-13 a classical field interacts with quantum-mechanical atoms; in the remainder of the book, both field and atoms are treated quantum mechani cally.
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.
This textbook provides an accessible introduction to laser physics, exploring three key questions: What is special about laser light? What is the physics underlying its generation? And how can laser light be manipulated and used? The material is presented in a manner that helps the reader develop an understanding of the underlying physics principles and processes without getting bogged down in mathematical details, but there is enough mathematics for the understanding to be quantitative. The book begins by describing the special properties of laser light and focuses on the physics of light-matter interaction to understand how it acquires them. It builds upon Maxwells equations for light and the classical electron oscillator model for the atoms, augmented with a quantum mechanical picture of atomic energy levels, to provide an accurate physical understanding of light-matter interaction. This approach bypasses the need for a course in quantum theory. Derivations of key equations are included not only to help readers follow the development of the subject, but also to illustrate that to approximate, simplify, and get analytic results is integral to understanding any complex phenomenon. Subjects such as nonlinear pulse propagation and nonlinear optics are discussed, but only at a level that should help readers to get started in these fields. The choice of topics has been limited to atomic/molecular lasers to allow for their coverage in one semester-long course. Problems, references and illustrations are included throughout the book, making it an ideal textbook for advanced undergraduate and graduate physics and engineering students. Students do not require prior knowledge of physics much beyond an undergraduate-level introduction to electromagnetic theory, including Maxwell’s equations, polarization in atomic media and electromagnetic wave propagation. Key features: · Provides a qualitative and quantitative understanding of, and appreciation for, the special properties of laser light · Explores quantum statistics of laser light · Presents an analytical approach to pulse formation
The phenomena which are principally responsible for the interaction of radiation with matter in everyday life are absorption and spontaneous emis sion. Light falling on matter is absorbed, leaving atoms in excited states which spontaneously emit radiation with a spread of frequency inversely proportional to the decay time. The situation is modified when the atomic decay times are sufficiently long and the radiation sufficiently intense, for then radiation may fall on excited atoms, resulting in stimulated emission rather than absorption. We saw in Chap. 2 that this third process was required to obtain the Planck blackbody radiation law in Einstein’s derivation. It is stimulated emission which enables an atomic medium to amplify incident radiation, and therefore is an essential ingredient in light amplifiers and oscillators. In fact, the word LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.
Suppose that the gas is in equilibrium with a radiation field B(?, T). In a steady state, the number atoms leaving the lower state must equal the number leaving the upper state. Combining the last two equations, The probability that an atom will be in a state with energy Eu is exp{- Eu/kT) . This is proved in any book on statistical mechanics, but it is beyond the scope of this chapter. The relative populations of the two states is Using equation (33), Therefore, combining equations (37) and (38), Since the constants and depend only on the structure of the atom, and not on temperature or other aspects of the environment,25 Then So, using the Plank black-body law [equation (2)], These coefficients are called the Einstein coefficients; they depend only on the nature of the atom and not on the temperature, the ambient radiant intensity, or any other aspect of the atom’s environment. Therefore, equations (42) and (44) are true in general. In particular, note that this argument shows that stimulated emission must exist; i.e., . This proved the existence of stimulated emission long before it had been observed in the laboratory; today, of course, it is the basis of the laser (Light Amplification by Stimulated Emission of Radiation) industry. Stimulated emission is necessary, as I have already mentioned, to keep the Second Law of thermodynamics from being violated, because without it, atomic absorption and emission processes could not be in balance with emission from a black body. If there is an enclosure with perfectly black walls with temperature T, then the radiation field inside the enclosure must be equal to the Planck function B(?, T). But now introduce a gas into that enclosure. Without stimulated emission, there would be a continuous transfer of energy either to or from the gas. This, as we know, is impossible.