Quantum theory of the free-electron laser: Large gain, saturation, and photon statistics

Journal Article · Fri Mar 01 00:00:00 EST 1985 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.31.1607· OSTI ID:5892451

Gea-Banacloche, J

Starting from the general QED Hamiltonian for the free-electron laser (FEL), a quantum-mechanical, many-particle theory of the FEL in the laboratory frame is presented. When suitable variables are introduced, the Hamiltonian is seen to a good approximation to be formally identical to the nonrelativistic Hamiltonian in the resonant (Bambini-Renieri) frame used in other treatments. The derivation is given for a general multimode laser field, although only the simpler case of single-mode operation is discussed in detail. It is shown how the large-gain evolution equations for the field, in the small-signal regime, may be obtained from the quantum theory. Then, from fourth-order perturbation theory, the change in the first two moments of the photon-number distribution in a single pass through the FEL is computed. Large-gain and saturation terms are obtained, for arbitrary values of the quantum recoil (i.e., both the classical and quantum-mechanical regimes are included). The evolution of the photon statistics over many cavity round trips is discussed. In the small-signal regime, the variance of the photon-number distribution is shown to correspond, to a good approximation, to that of thermal, or ''chaotic,'' radiation. At saturation, a significant reduction of the fluctuations is expected, but no conclusions can be drawn from the perturbation-theory approach. A numerical calculation of the buildup of the field from vacuum (through spontaneous emission) is presented. For simplicity, a uniform, circularly polarized, static wiggler is assumed in the text; however, the theory may be generalized (along lines shown) to deal with nonuniform, linearly polarized and/or traveling electromagnetic-wave wigglers.

• Research Organization: Institute for Modern Optics, The University of New Mexico, Albuquerque, New Mexico 87131
• OSTI ID: 5892451
• Journal Information: Phys. Rev. A; (United States), Vol. 31:3
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
FREE ELECTRON LASERS
GAIN
PHOTON EMISSION
SATURATION
ELECTROMAGNETIC FIELDS
FLUCTUATIONS
HAMILTONIANS
QUANTUM ELECTRODYNAMICS
STATISTICS
AMPLIFICATION
ELECTRODYNAMICS
EMISSION
FIELD THEORIES
LASERS
MATHEMATICAL OPERATORS
MATHEMATICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
VARIATIONS
420300* - Engineering- Lasers- (-1989)