Abstract
Bargmann space techniques in quantum mechanics [1, 2, 3, 4] consist in performing a transformation upon the modes of an harmonic oscillator that renders the modes and the creation and annihilation operators particularly simple. In this paper the Bargmann space techniques are extended to the optical propagation of gaussian beams in a lenslike medium with possible loss or gain [5] yielding a considerably simplified derivation of the algebra of modes and mode generating operators.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V. Bargmann, “On a Hilbert space of analytic functions and an associated integral transform, Part I,” Comm. Pure Appl. Math. 14 pp. 187–214 (1961).
V. Bargmann, “On a Hilbert space of analytic functions and an associated integral transform, Part II: A family of related function spaces and applications to distribution theory,” Comm. Pure Appl. Math, 20 pp. 1–101 (1961).
P. Kramer, M. Moshinski, and T.H. Seligman, “Complex extensions of canonical transformations in quantum mechanics,” in Group theory and its applications, ed. E.M. Loebl,Academic Press, New York (1975).
K.B. Wolf, Integral Transforms in Science and Engineering, Plenum Press, New York (1979).
M. Nazarathy, A. Hardy, and J. Shamir, “Generalized mode propagation in first-order optical systems with loss or gain,” J. Opt, Soc. Am. 72 pp. 1409–1420 (1982).
M. Nazarathy and J. Shamir, “First order optics–a canonical operator representation: lossless systems,” J. Opt. Soc. Am 72 pp. 356–364 (1982).
M. Nazarathy and J. Shamir, “First-order optics: operator representation for systems with loss or gain,” J. Opt. Soc. Am. 72 pp. 1398–1408 (1982).
J.A. Arnaud, Beam and Fiber Optics, Academic Press, New York (1976).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer Science+Business Media New York
About this paper
Cite this paper
Nazarathy, M. (1984). Bargmann Space Methods in First-Order Optics. In: Mandel, L., Wolf, E. (eds) Coherence and Quantum Optics V. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0605-5_62
Download citation
DOI: https://doi.org/10.1007/978-1-4757-0605-5_62
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-0607-9
Online ISBN: 978-1-4757-0605-5
eBook Packages: Springer Book Archive