  We present a method to measure quadratic Terahertz optical nonlinearities in
Terahertz time-domain spectroscopy. We use a rotating linear polarizer (a
polarizing chopper) to modulate the amplitude of the incident THz pulse train.
We use a phase-sensitive lock-in detection at the fundamental and the second
harmonic of the modulation frequency to separate the materials' responses that
are linear and quadratic in Terahertz electric field. We demonstrate this
method by measuring the quadratic Terahertz Kerr effect in the presence of the
much stronger linear electro-optic effect in the (110) GaP crystal. We propose
that the method can be used to detect Terahertz second harmonic generation in
noncentrosymmetric media in time-domain spectroscopy, with broad potential
applications in nonlinear Terahertz photonics and related technology.
