Synthesis of electrooptic modulators for amplitude modulation of light

A technique is described for synthesizing electrooptic amplitude modulators having arbitrary modulation characteristics. The technique is an adaptation of the procedure of Ammann and Yarborough for synthesizing naturally birefringent networks. The desired amplitude-transmission versus applied-voltage function K(\upsilon) of the modulator is written as an exponential series containing a finite number of terms. The resulting modulator consists of a series of stages between an input and output polarizer, with each stage consisting of an electrooptic element and optical compensator. The induced birefringence of the electrooptic medium is assumed to be directly proportional to the applied modulating voltage υ. The question of how K(\upsilon) should be chosen is also investigated. Two cases are considered: 1) an amplitude modulator to be used with an envelope detector, and 2) an amplitude modulator to be used with a square-law detector. For each case, the ideal K(\upsilon) and several methods of approximating it are given. It is found that the manner in which K(\upsilon) is chosen is of great importance. Best results were obtained when the term coefficients (the C i ) of K(\upsilon) were chosen to directly optimize the modulator property (or properties) deemed most important. Modulator designs corresponding to several useful K(\upsilon) are given in tabular form.