Spatially partially coherent Fabry–Perot modes

Abstract

The recently developed coherence theory of stable laser resonators is applied to an ideal plane-parallel Fabry-Perot resonator. We make use of an explicit, integral-type, biorthogonal expansion of the exact, non- Hermitian, scalar propagation kernel. The resonator admits various spatially partially coherent modes because of the degeneracy of the conventional transverse modes. The spatial second-order modes of the Fabry-Perot resonator containing only homogeneous plane waves correspond to an eigenvalue of unity, and several types of such partially coherent modes are identified. These include the diagonal superpositions of the coherent Fox-Li modes and the general expressions for the cross-spectral densities associated with the propagation-invariant modes and the self-imaging modes. Some special cases are analyzed as illustrations.