Analysis of a Tubular Gas Lens

If a cool gas is blown into a hot tube, it acts as a positive lens which will focus a light beam passing through the tube. Using a theory presented in Ref. 3, we give curves which show the temperature distribution in the tube as a function of the distance from the tube axis and also as a function of the distance along the axis. The focusing power of the lens is described by the difference in phase angle between a ray on the tube axis minus a ray at arbitrary distances from this axis and also as the second derivative of the phase angle on the axis of the tube. The phase curves, as a function of distance r from the tube axis, follow very closely an r 2 dependence. Expressions are given for the focal length of the lens. The power consumption of the lens is discussed, and a figure of merit is defined as focusing power per watt. The gas used for this lens should be selected such that (n − 1)/k is as large as possible (where n is the index of refraction, k the heat conductivity of the gas). Using CO 2 and a ¼-inch ID tube 5 inches long heated 20°C above the incoming gas, a focal length of 5 feet with a power consumption of 0.325 watt is calculated; the focal length is inversely proportional to power consumption within certain limits.