Adiabatic whisper-gallery mirrors for EUV and soft X-ray laser cavities

The use of whisper-gallery mirrors in laser cavities for the extreme ultraviolet and soft X-ray regimes has been studied. Vinogradov proposed a cavity scheme that would use a cylindrical whisper-gallery mirror and a pair of laser amplifiers. When compared with the latter, the low-order modes of such a cavity are small, making single-mode operation difficult to achieve. A strategy for increasing the size of the cavity modes by using mirrors of an elongated shape was examined. A particular family of curves was proposed as a candidate for the form of the elongated mirrors, based upon an analysis relating the mode structure of a mirror of arbitrary shape to that of a round mirror. When the condition of adiabaticity is not met, the analysis of the eigenmodes of such a mirror must be refined to include the effects of mode coupling. The choice of the mirror shape so as to minimize the net mode coupling will result in a special family of mirror shapes.