An exact analysis of the temperature control of optical waveguides

In this paper we present an exact analysis of the variation with temperature of the effective index of an arbitrary optical waveguide. Our results allow the design of temperature compensated devices using only a single parameter calculated at one temperature avoiding the need to perform an analysis over a range of temperatures. We derive expressions for both weakly and strongly guiding waveguides. We derive a complete analytical solution for the design of micro channel fibers where the micro channels are filled with a temperature compensating material whose refractive index equals that of the fiber cladding at a specified reference temperature. We also analyse the more general case including the effects of thermal expansion. We illustrate our analysis with the application to athermal fiber Bragg gratings and arrayed waveguide grating filters.