The electro-optic effect for intense terahertz pulses

The χ(2) interaction between an intense terahertz (THz) pulse and a weak optical probe is addressed, and a general solution obtained for the situation of an undepleted THz wave. It is shown that the common description of a phase retardation proportional to the THz electric field strength breaks down in strong-field conditions, unless the THz field is suitably slowly varying. The solution is obtained from a consistent description of sum- and difference-frequency generation driven by the THz field, the input optical field, and all optical fields generated through the interaction itself. For an interaction between monochromatic THz and optical waves a minimum of four waves (three optical and one THz) need be considered in the weak-field limit; higher numbers of waves are needed at higher fields, with the extent of the required optical spectrum dependent on field strength, phase matching, and interaction length