Inhomogeneous spatial distribution of residual amplitude modulation in optical phase modulation using a bulk...

Residual amplitude modulation is one of the major sources of instability in many precision measurements using frequency modulation techniques. Although a transverse and inhomogeneous distribution of residual amplitude modulation has long been observed, the underlying mechanism is not well understood. We perform measurement and analysis of this spatial inhomogeneity using several electro-optic crystals of different types. Two distinct components are identified in the spatial distributions, and their detailed properties, some of which are previously unnoticed, are mapped out and analyzed, showing that the spatial inhomogeneity can be explained by acousto-optic interaction inside the crystal. Moreover, this spatial inhomogeneity can be further suppressed, improving the 1000-s stability of residual amplitude modulation to 3×10^-7 (8×10^-8) at modulation frequency of 11 MHz (120 kHz), corresponding to a frequency instability of 1×10^-17 (3×10^-18), estimated for a cavity-stabilized laser using a Pound-Drever-Hall discrimination slope of 1×10^-4 V/Hz.