Transverse mode properties of beam-rotated unstable resonators for free electron lasers

Abstract

A novel class of ring unstable resonators (UR90) with 90-deg rotation of the beam on each round-trip has been proposed as a method of avoiding disadvantages of obscuration in the output beam. We herein consider exten- sion of this idea to include an internally focused beam, so that the portion of the beam near the focus can fit within the narrow gain region of a free electron laser. Modeling of transverse mode properties of empty cavities with or without an internal focus proceeds in the same general way. We have calculated the transverse mode in- tensity and phase distributions and the power retention fraction PR as a function of equivalent Fresnel number Feq over various ranges of F^. There is quasi-oscillatory behavior similar to that found in conventional unstable resonators, with poor mode loss separation occurring near an interger TV plus 7/8; hence, designs should avoid such values of Fpn. REE electron lasers (FEL's) operated as high-power oscillators present special problems regarding resonator design. The optical beam must be small in transverse extent in the (wiggler) gain region, but the optical flux on resonator mirrors must not be allowed to damage them. The flux can be reduced to acceptable levels in at least two ways. Very long paths from gain region to mirrors can be used to spread the beam by diffraction, but the great distances involved are undesirable. Alternatively, grazing incidence beam ex- panders/contractors can be used. With the latter, one has the choice of operation in either the stable or the unstable domain. Stable resonators can provide the advantage of an unobscured output beam if a practical means is available to separate out a fixed fraction of the total circulating beam for output, but this poses practical problems (materials damage, etc.) at high flux levels. Operation in the unstable regime avoids the latter dif- ficulty by using a scraper output mirror that outputs all of the outer portion of the beam, i.e., the scraper need not be a par- tially transmitting element. The special resonator problems of FEL's are, of course, related to the general question of choice of most favorable resonator design, e.g., stable or unstable; positive or negative branch; conventional or, perhaps, novel designs for special applications, etc. The excellent transverse mode separation properties of (both positive and negative branches) unstable resonators are well known and such resonators are very widely used. Because of the internal focus of the negative branch type and the possibility of breakdown in gaseous or solid gain media, the positive branch class is most widely used. For FEL's the breakdown problem is absent because gain takes place in a vacuum, and negative branch resonators are acceptable.