A modified tilted-pulse-front excitation scheme for efficient terahertz generation in LiNbO3

Pumping of LiNbO3 by femtosecond optical pulses with tilted intensity front (pulse front) allows one to obtain high efficiency of optical-to-terahertz conversion (up to 1% at room temperature [1]), large energy of generated terahertz pulses (up to sub-mJ level [2]), and high strength of terahertz fields (exceeding 1 MV/cm [3]). Strong terahertz pulses are in demand for various applications, including terahertz-driven particle acceleration [4], terahertz nonlinear spectroscopy [5], and terahertz streaking techniques [6]. Tilted-pulse-front optical pulses are conventionally obtained by diffraction of a laser pulse off an optical grating. A lens (or two-lens telescope) is used to relay-image such pulses into the LiNbO3 crystal [7,8]. In order to maximize the optical-to-terahertz conversion efficiency, the tilt angle  in the crystal should be close to a value defined by the equation

Pumping of LiNbO 3 by femtosecond optical pulses with tilted intensity front (pulse front) allows one to obtain high efficiency of optical-to-terahertz conversion (up to 1% at room temperature [1]), large energy of generated terahertz pulses (up to sub-mJ level [2]), and high strength of terahertz fields (exceeding 1 MV/cm [3]). Strong terahertz pulses are in demand for various applications, including terahertz-driven particle acceleration [4], terahertz nonlinear spectroscopy [5], and terahertz streaking techniques [6].
Tilted-pulse-front optical pulses are conventionally obtained by diffraction of a laser pulse off an optical grating. A lens (or two-lens telescope) is used to relay-image such pulses into the LiNbO 3 crystal [7,8]. In order to maximize the optical-to-terahertz conversion efficiency, the tilt angle  in the crystal should be close to a value defined by the equation , where n g is the optical group refractive index and n THz is the terahertz phase refractive index. Additionally, it is postulated that a good quality of the terahertz beam can be achieved if the image of the grating is parallel both to the pulse front and to the exit surface of the crystal [7,8].
Here, we extend the analysis of the tilted-pulsefront excitation scheme [7,8] to a more general geometry, namely, with the pulse front not parallel to the exit surface of the crystal (the grating image is still assumed to be parallel to the surface).
In our theory, the generated terahertz radiation is found analytically from the Maxwell equations with a nonlinear polarization included as a source [9,10]. The nonlinear polarization is found as a result of optical rectification of the tilted-pulse-front optical pulse, which experiences effects of both material and angular dispersion.
At first, we consider the conventional geometry of the tilted-pulse-front excitation scheme, i.e., with the pulse front parallel to the exit surface of the crystal, but for an arbitrary orientation of the grating im- . As a result, the energy of generated terahertz radiation does not decrease and even somewhat increases at a deviation of θ from the optimal value Fig. 1(b)]. In the case    , the terahertz energy [ Fig. 1 Now let us consider a more general geometry, depicted in Fig. 2, with the pulse front not parallel to the exit surface of the crystal (the grating image plane is assumed to be parallel to the exit surface). In this geometry, the generated terahertz radiation propagates normally to the pump pulse front and, therefore, impinges obliquely on the exit surface of the crystal. To prevent total internal reflection of the radiation and minimize Fresnel losses, a Si prism should be attached to the exit surface of the LiNbO 3 crystal (Fig.  2). Figure 3(c) shows the optical-to-terahertz conversion efficiency as a function of θ for different pump pulse durations. For a short pump pulse (50 fs), the efficiency is almost independent of θ in the interval from 30° to 75° and decreases rapidly for   75 .
With increase of the pump pulse duration, the maximum becomes more pronounced and shifts to larger θ. The maximal efficiency also increases (for a fixed energy of the pump pulse) and for pulse duration >100 fs exceeds the efficiency in the optimal case. For the pump pulse of a 400 fs duration, the maximum efficiency at   85 is about two times higher than in the optimal geometry, i.e., at     63.3.
To conclude, we have shown that a deviation of the grating image plane from the optimal orientation in the tilted-pulse-front excitation technique leads to a deterioration of the terahertz beam quality but does not affect significantly the terahertz energy (in the case    ). We have proposed a modified variant of the tilted-pulse-front excitation scheme with the pulse front not parallel to the exit surface of the crystal. We have shown that this geometry allows one to double the terahertz generation efficiency for long (>200 fs) laser pulses still preserving a high quality of the generated terahertz beam.