Nonlinear harmonic generation of coherent amplification and self-amplified spontaneous emission. Page: 1 of 15
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Nonlinear Harmonic Generation of Coherent
Amplification and Self-Amplified Spontaneous
Zhirong Huang 1, Kwang-Je Kim
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA /
Nonlinear harmonic generation in a uniform planar undulator is analyzed using
the three-dimensional Maxwell-Klimontovich equations that include both even and
odd harmonic emissions. After a certain stage of exponential growth, the dominant
nonlinear harmonic interaction is caused by strong bunching at the fundamental. As
a result, gain length, transverse profile, and temporal structure of these harmonic
radiations are eventually determined by those of the fundamental. Transversely
coherent third-harmonic radiation power is found to approach one percent of the
fundamental power level for current high-gain FEL projects, while the power of the
second-harmonic radiation is less but still significant for relatively low-energy FEL
Key words: Nonlinear Harmonic generation; Coherent Amplification;
Self-amplified spontaneous emission
PA CS: 41.60.Cr; 42.55.Vc; 42.65.Ky
The submitted manuscript has been create
by the University of Chicago as Operator of
Argonne National Laboratory ("Argonne")
under Contract No. W-31-109-ENG-38 with
the U.S. Department of Energy. The U.S.
Government retains for itself, and others act-
ing on its behalf, a paid-up, nonexclusive,
irrevocable worldwide license in said article
to reproduce, prepare derivative works, dis-
tribute copies to the public, and perform pub-
licly and display publicly, by or on behalf of
In a high-gain free-electron laser (FEL) employing a planar undulator, a one-
dimensional (1-D) model  and a three-dimensional (3-D) simulation  in-
dicate that strong bunching at the fundamental wavelength can drive substan-
tial harmonic bunching and sizable power levels at the harmonic frequencies.
1 Corresponding author. Tel: (630)252-6023; Fax: (630)252-5703; Email:
Preprint submitted to Elsevier Preprint
11 August 2000
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Huang, Z. & Kim, K.-J. Nonlinear harmonic generation of coherent amplification and self-amplified spontaneous emission., article, August 22, 2000; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc722622/m1/1/: accessed July 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.