Abstract

The canonical operator theory introduced recently for the description of lossless first-order optics is extended here to first-order systems with loss or gain, elucidating the relation between canonical operator and complex ray methods. The spread functions in the space, frequency, and hybrid domains are derived in terms of the ABCD ray-transfer matrix as well as in terms of four other new matrix descriptions of geometrical optics. The fourfold correspondence among these matrices, the Hamilton characteristics, and the spread functions in the space, frequency, and hybrid domains leads to the derivation of four fundamental explicit canonical representations of the transfer operator and to their parameterization in terms of characteristic matrix elements. The relation between adjoint operators and bidirectional propagation is derived within canonical operator theory of first-order optics as well as within a more-general setting for all reciprocal (but not necessarily lossless) optical systems.

© 1982 Optical Society of America

First-order optics—a canonical operator representation: lossless systems

Moshe Nazarathy and Joseph Shamir
J. Opt. Soc. Am. 72(3) 356-364 (1982)

Generalized mode propagation in first-order optical systems with loss or gain

Moshe Nazarathy, Amos Hardy, and Joseph Shamirt
J. Opt. Soc. Am. 72(10) 1409-1420 (1982)

Misaligned first-order optics: canonical operator theory

Moshe Nazarathy, Amos Hardy, and Joseph Shamir
J. Opt. Soc. Am. A 3(9) 1360-1369 (1986)

Generalized mode theory of conventional and phase-conjugate resonators

Moshe Nazarathy, Amos Hardy, and Joseph Shamir
J. Opt. Soc. Am. 73(5) 576-586 (1983)

Nonideal phase-conjugate resonators—a canonical operator analysis

Moshe Nazarathy, Joseph Shamir, and Amos Hardy
J. Opt. Soc. Am. 73(5) 587-593 (1983)