Optical EngineeringExtraction of electro-optic coefficient in thin-film linear electro-optic Mach-Zehnder interferometers with nonperiodic intensity-voltage output characteristics
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The intensity-voltage output characteristics of thin-film linear electro-optic Mach-Zehnder interferometer modulators can be nonperiodic for configurations where the optic axis is perpendicular to the applied electric field. As a result, the electro-optic coefficient for the material can not be determined assuming a periodic half-wave voltage. From the Jones matrix calculation, an analytic expression of the output intensity is derived in terms of the phase retardation. A method of determining the linear electro-optic coefficient is proposed based on the determination of the first intensity minimum in intensity-voltage characteristics. This method provides a simple expression for determining the electro-optic coefficient given values for the ordinary and extraordinary refractive indices, the modulator geometry, and the first half-period voltage. The first half-period voltage is found to be approximately inversely proportional to the square root of the electrode length. The method shows close agreement to the exact Jones matrix method for the case where the sum of the principal refractive indices in one arm of Mach-Zehnder interferometer is close to that of the other arm under an electric field.