This spectrum of a phase-modulated electric field is given by Bessel functions. The optical intensity of each sideband is proportional to the square of the electric field amplitude. The amplitude of the kth sideband is proportional to Jk(m), where Jk is the Bessel function of order k. The fraction of optical power transferred into each of the first-order sidebands is [J₁(m)]², and the fraction of optical power that remains in the carrier is [J₀(m)]².

Our multi-axis stages are designed for applications where precise positioning and high stability are required. Shown here is a typical application of aligning an optical modulator to a laser beam with our four-axis kinematic device alignment stage.

A Model 4001/3 or 4061/3 resonant phase modulator is the ideal component to use in a Pound-Drever-Hall laser frequency stabilization system. This optical FM frequency discriminator technique* is used to lock the optical frequency of a laser to a stable Fabry-Perot reference cavity. The system consists of a single-frequency laser beam that is sinusoidally phase modulated and coupled into an axial mode of the Fabry-Perot resonator cavity. The stabilization signal is fed back to a high-voltage amplifier that drives a piezoelectric transducer (PZT). The frequency-stabilized light transmitted by the cavity is clean spatially as well as spectrally. *R.W.P. Drever, et al. “Laser Phase and Frequency Stabilization Using an Optical Resonator,” Appl. Phys. B31, pp. 97–105 (1983).