The phase-conjugation operator is investigated in the context of the canonical operator theory of first-order optics, which was introduced in a previous series of articles. The matrix representation of this operator and its action on the generalized modes are derived, elucidating the relation between forward and reversed propagation in this new context. The resulting formalism makes possible the derivation of the eigenmodes of conventional and phase-conjugated resonators with loss or gain. Various resonator properties—confinement, stability, mode biorthogonality, and real or complex character of the spot-size parameter—simply follow from the guiding-ray-label representation.
© 1983 Optical Society of America
Moshe Nazarathy, Amos Hardy, and Joseph Shamir, "Generalized mode theory of conventional and phase-conjugate resonators," J. Opt. Soc. Am. 73, 576-586 (1983)