Non-sinusoidal Terahertz Pulses with Spectral Phase up to Second Order

A time-domain expression for a class of pulses is derived analytically and compared with measurements of ultrabroadband terahertz pulses. A terahertz spectrum is developed based on the optical rectification of infrared pulses with a Gaussian envelope, including spectral phase up to second order. The time-domain representation of this spectrum is identified with derivatives of the Faddeeva function, which can be calculated via recursion relation. The familiar relationship between second order spectral phase and chirp is identified and compared with measurements of terahertz pulses acquired via electro-optic sampling.