Quantum Optics and Lasers

Abstract

These lecture notes present a comprehensive treatment of quantum optics and laser physics, integrating the quantum theory of light with the classical and semiclassical description of laser systems. The course begins with the quantization of the electromagnetic field in free space, formulated through Maxwell’s equations in covariant form and the Lagrangian–Hamiltonian formalism. The development proceeds to mode expansion, creation and annihilation operators, and the construction of quantum states of light, including Fock, coherent, and squeezed states. Photon statistics, density operators, polarization, and multi-mode systems are systematically analyzed, with particular emphasis on nonclassical light, squeezing, antibunching, and phase-space representations such as the Wigner function. The manipulation of quantum states using linear optical elements—phase shifters and beam splitters—is treated within a fully quantum framework, highlighting input–output relations and state transformations. The second part of the course addresses laser physics from both microscopic and macroscopic perspectives. Fundamental laser properties are derived from Einstein coefficients and Planck’s radiation law, followed by discussions of line broadening, optical amplification, pumping mechanisms, and phenomenological laser models. Solutions of the wave equation, including Gaussian beams and Hermite–Gauss modes, are developed to describe laser beam propagation. Finally, optical resonators are analyzed in detail, including planar and spherical cavities, stability criteria, and the ABCD matrix formalism. Overall, the lectures establish a unified theoretical framework connecting quantum field quantization, nonclassical states of light, and laser dynamics, equipping students with the conceptual and mathematical tools required for advanced studies in modern quantum optics and photonics.