Abstract
The physical effects of optical mode dispersion in the electron beam of a free-electron laser are investigated for modes that carry orbital angular momentum. The analysis is performed using a derived equivalence between two different formulations that describe the radiation fields in the linear regime.
Highlights
The coherent electromagnetic (EM) signal field generated in a free-electron laser (FEL) is optically guided within the source electron beam (e-beam) during exponential gain [1,2,3]
Through the type of virtual waveguide geometry chosen, flexibility in the form of the expansion mode basis so that particular modes of interest may be examined in detail or so that a specific basis set can be chosen to optimally suit a given FEL geometry
The eigenmodes of a quadratic index fiber, for example, are useful as a virtual dielectric waveguide model because they are composed of composite Gaussian functions
Summary
The coherent electromagnetic (EM) signal field generated in a free-electron laser (FEL) is optically guided within the source electron beam (e-beam) during exponential gain [1,2,3]. Is reexpressed through an expansion of the field as a sum over dielectric waveguide eigenmodes This provides: (a) a unified description that shows the equivalence between the formalisms in the linear gain regime, and (b) a compact set of mode coupled equations used to study the amplification and coupling to OAM modes in the FEL with the effects of energy spread included. The latter is a useful extension to results presented in Ref. The resulting equations are used to explore the unique effects of longitudinal dispersion of OAM modes in the FEL, which arise due to the helical transverse phase dependence and mode-dependent coupling characteristics
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