A Quadratic Conduction Gas Lens

Abstract

A lens system for a periodic light-beam waveguide is proposed and analyzed in which gas is enclosed in a circular cylinder heated with a cos 2φ temperature distribution. We show that this temperature distribution may be produced by cutting a cylindrical hole in the center of a square block which has two opposite sides of equal temperature above the ambient temperature, and two sides of a lower temperature. Heat conduction across the gas produces an index of refraction variation which, in two orthogonal azimuthal planes, increases or decreases as the radius squared. The effect of thermal convection is analyzed by solving the governing equations as an expansion in powers of the Rayleigh number; the solution reveals that convection effects can be made negligible over a practical range of lens parameters. The major attributes of the lens system are that only temperature controls are required and the aberrations associated with thermal convection can be readily minimized.