Modes and states in quantum optics

This lecture by the instructor covers the fundamental concepts of modes and states in quantum optics, exploring the double linearity inherited by quantum optics from Maxwell equations and quantum mechanics. Topics include solutions of Maxwell's equations, basis change in the quantum electric field, paraxial and quasi-monochromatic approximation, optical frequency combs, continuous variables, homodyne detection, quantum resource like squeezed states, improved phase measurement, measuring quantum fluctuations, Wigner function representation, spectral and quantum frequency combs, synchronously pumped OPO, multimode phase space, eigenmodes, and multimode squeezing. The lecture delves into the practical applications of these concepts in metrology and quantum information.