A photoelastic modulator (PEM) has two parts (11, 13) of the same or dissimilar cross sections, joined together to form an abrupt junction (16). A transducer, for which the natural oscillation is at the half acoustic wavelength mode, excites a longitudinal standing wave of high purity in the PEM. A feedback system is used to achieve stable phase synchronisation of multiple PEMs working at the same oscillation frequency, where the outputs of an amplitude and phase sensor for one PEM is used to correct phase variations of other PEMs and to compensate optical retardation errors.