Abstract

Mode propagation through first-order systems with loss or gain is derived based on a canonical transform theory developed recently. In analogy to quantum theory, creation and annihilation operators are defined for the construction of high-order modes. The evolution of these mode-generation operators through an optical system is shown to describe the propagation of the actual fields that are parameterized by two raylike labels—two guiding rays. The mode-generating operators create a set of generalized modes that may be reduced to the ordinary Her-mite–Gaussian modes only in a lossless system. Many characteristics of these generalized modes are evaluated by operator algebraic manipulations without the need for the explicit form of the actual modes that are shown also to be Hermite–Gaussian but involve complex scaling parameters.

© 1982 Optical Society of America

First-order optics: operator representation for systems with loss or gain

Moshe Nazarathy and Joseph Shamir
J. Opt. Soc. Am. 72(10) 1398-1408 (1982)

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 theory of conventional and phase-conjugate resonators

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

Propagation law for the generating function of Hermite-Gaussian-type modes in first-order optical systems

Martin J. Bastiaans and Tatiana Alieva
Opt. Express 13(4) 1107-1112 (2005)

Mode Coupling in First-Order Optics

J. A. Arnaud
J. Opt. Soc. Am. 61(6) 751-758 (1971)