Modes in helical gas lenses

Helical gas lenses incorporate four coaxial helices at temperatures +T, -T, +T, and -T, respectively. Because of the resulting change in refractive index of the gas filling the space inside the helices, optical beams can be guided by this system over long distances. A general expression for the modes of propagation is given; it involves Hermite polynomials in two complex variables. For small temperature differences the mode fields reduce to Laguerre-Gauss functions. Calculated irradiance patterns are shown for various mode numbers and various values of T.