  In recent years, electro-optic sampling, which is based on Pockel's effect
between an electromagnetic mode and a copropagating, phase-matched ultrashort
probe, has been largely used for the investigation of broadband quantum states
of light, especially in the mid-infrared and terahertz frequency range. The use
of two mutually delayed femtosecond pulses at near-infrared frequencies allows
the measurement of quantum electromagnetic radiation in different space-time
points. Their correlation allows therefore direct access to the spectral
content of a broadband quantum state at terahertz frequencies after Fourier
transformation. In this work, we will prove experimentally and theoretically
that when using strongly focused coherent ultrashort probes, the electro-optic
sampling technique can be affected by the presence of a third-order nonlinear
mixing of the probes' electric field at near-infrared frequencies. Moreover, we
will show that these third-order nonlinear phenomena can also influence
correlation measurements of the quantum electromagnetic radiation. We will
prove that the four-wave mixing of the coherent probes' electric field with
their own electromagnetic vacuum at near-infrared frequencies results in the
generation of a higher-order nonlinear correlation term. The latter will be
characterized experimentally, proving its local nature requiring the physical
overlap of the two probes. The parameters regime where higher order nonlinear
correlation results predominant with respect to electro-optic correlation of
terahertz radiation is provided.
