Effect of Fresnel Diffraction on Wigner Distributions of Optical Fields and how to Use It in Optical Resonator Theory
Résumé
According to a scalar theory, diffraction affects the electric field amplitude as well as its angular spectrum, providing a natural space–frequency phase space on which the Wigner distribution can be defined. The phase space is equipped with an Euclidean structure, so that the effect of diffraction is a rotation of the Wigner distribution associated with the optical field. The rotation is shown to split into two specific rotations. Wigner distributions associated with transverse modes of a resonator are invariant in such rotations, and a complete theory of optical resonators is developed on the basis of this property, including waist existence and related formulae, and naturally introducing the Gouÿ phase.