Resonant phase modulators are used to vary the phase of an optical laser beam. The induced sinusoidal phase variation f(t)=β*sin(Ω*t) at the modulation frequency Ω and peak phase change generates ­frequency sidebands at multiples of Ω about the central cw optical frequency, ω. The spectrum of a sinusoidally phase-modulated electric field after passing through the modulator is given by Bessel functions:

The amplitude in the m-th sideband at ω+m*Ω is proportional to Jm(β), where Jm is the m-th order Bessel function of the first kind. The amount of energy transferred from the fundamental J0(β) to the m-th sideband is proportional to the square of the electric field ­amplitude |Jm(β)|2. The modulation index β which describes how much energy is transferred from the carrier to the sidebands depends on many parameters such as the crystal material and its geometry, the laser wavelength as well as the applied RF power. The required value itself, which can be easily adjusted by tuning the RF level, varies a lot among the applications.