What is it about?

A numerical study of the effect of betatron oscillations on the second harmonic generation in free-electron lasers (FELs) is presented. Analytical expressions for the effective coupling strength factors are derived that clearly distinguish all contributions in subharmonics and each polarization of the radiation. A three-dimensional time-dependent numerical FEL code that takes into account the main FEL effects and the individual contribution of each electron to the second harmonic generation is presented. Also, the X- and Y-polarizations of the second harmonic are analyzed. The second harmonic was detected in experiments at the Advanced Photon Source (APS) Low Energy Undulator Test Line (LEUTL) and Linac Coherent Light Source (LCLS) in the soft X-ray regime. The approach presented in the article can be useful for a comprehensive study and diagnostics of XFELs. In the paper, the LCLS and Pohang Accelerator Laboratory X-ray Free-Electron Laser (PAL-XFEL) experiments are modeled. The simulation results are in a good agreement with the experimental data.

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Why is it important?

Second harmonic generation in crystals is the main nonlinear optical effect, therefore it is desirable to take into account the power of the FEL second harmonic.


Even harmonics are important when designing lasers with multiple radiation harmonics, higher-harmonic lasers can be used in two-photon spectroscopy. The presented formalism makes it possible to study more precisely the current and planned FEL experiments on the study of new materials, nanostructures and spectroscopy, and to evaluate the efficiency, spectrum and harmonic generation at existing and constructed FELs.

Aleksandr Kalitenko
Moskovskij gosudarstvennyj universitet imeni M V Lomonosova

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This page is a summary of: Numerical study of the second harmonic generation in FELs, Journal of Synchrotron Radiation, March 2021, International Union of Crystallography, DOI: 10.1107/s1600577521002538.
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