The efficiency of thin-film optical-waveguide modulators using electrooptic films or substrates

Abstract

This paper describes a new method for characterizing thin-film modulators which utilize TE <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\rightleftarrows</tex> TM wave conversion. The conversion is described in terms of a coupled wave model. The coupling constant <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> describes the strength of the coupling between the TE and TM waves. It is expressed in the form <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k = k_{pw}C</tex> where k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pw</inf> is the coupling constant of plane waves traveling through the relevant bulk medium. The coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> contains the parameters which characterize the guide. The model allows the comparison of structures utilizing electrooptic films and electrooptic substrates. Our results show that in general for single mode films (those approximately a half-wavelength thick), modulators of either type are about equally effective. It is tacitly assumed that k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pw</inf> is identical for each structure. For films which can support several modes (films a few wavelengths thick), the coefficient for devices utilizing electrooptic substrates approach zero. In contrast <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> approaches unity for similar thick-film devices which use electrooptic films.