A Scalar Resonator Theory for Optical Frequencies

Publisher Website
Google Scholar
Abstract
A scalar resonator theory for optical or near-optical frequencies is developed. For an arbitrary resonator system a general integral equation is derived which represents a solution of Helmholtz's equation between the reflectors and satisfies Maxwell's equations along the surface of the reflectors. To meet the consequences of the boundary conditions an eigenmode is defined as an energy distribution which when launched from an arbitrary mathematical surface between the reflectors reproduces itself within an amplitude factor after a number of bounces given by the periodicity of the system under consideration. The eigenvalues of the integral equation determine the diffraction losses and the resonance spectrum. The mode patterns between the reflectors can be deduced from the corresponding eigenfunction. The general theory is discussed in connection with resonator systems with spherical reflectors. This reveals a physical picture of the low-loss and high-loss regions as the reflector spacing is varied. With the example of the Fabry-Perot interferometer it is demonstrated that the present resonator theory agrees with geometrical optics as the Fresnel number becomes very large. The scalar formulation to be presented accounts for the phenomenon of diffraction and is consistent with the microwave and the antenna theories. The general theory when applied to a periodic sequence of thin lenses suggests that it may equally well be the basis of a theory for beam waveguides.

This publication has 28 references indexed in Scilit: