Techniques of non-collinear electro-optic sampling for efficient detection of pulsed terahertz radiation

Cherenkov radiation mechanism is an established technique to achieve phase matching between ultrashort optical pulses and terahertz (THz) waves having a large collinear velocity mismatch, in a nonlinear optical material such as LiNbO
₃
(LN). Phase matching is achieved with the optical and THz pulses propagating at angle with respect to each other. Recently, we have experimentally demonstrated that Cherenkov phase matching mechanism can also be used for efficient electro-optics (EO) sampling of broadband THz pulses [1]. In the detection case, the phase matching is achieved between an optical and THz pulse propagating non-collinearly at the Cherenkov phase-matching angle θ
_C
, satisfying the following equation: equation Here, n
_g
^LN
is the group index of the EO crystal at the sampling optical wavelength and n
_THz
^LN
is the refractive index of the EO crystal in the THz frequency region. An advantage of the non-collinear Cherenkov phase matching is that we can find a corresponding Cherenkov phase matching angle, θ
_C
, for any electro-optic crystal at a given optical sampling wavelength. When the EO crystal has a much larger refractive index in THz frequency region compared to that in optical region, a coupling prism is used as illustrated in Fig. 1. Moreover, using a low-loss coupling prism can also reduce absorption in the EO crystal. Silicon is an ideal coupling prism material owing to low absorption losses and is non-dispersive in the THz frequency region. From Snell's law, the incident angle α of THz wave with respect to the prism- EO crystal interface is given as follows: equation Equation (2) leads to the relation,
_sin
β =
_cos
θ
_C
. Therefore, Eq. (1) reduces to the following equation for the apex angle of the coupling prism (α) at the Cherenkov phase-matching condition given by the ratio of the group index of the EO crystal at the sampling optical wavelength n
_g
^LN
, and the refractive index of Si, n
_THz
^Si
, in the THz frequency region: equation.