1. Introduction

Optical rectification of near-infrared femtosecond laser pulses in lithium niobate (LiNbO$_3$) is an efficient method of generating intense pulsed terahertz radiation in the $\sim$0.1-2 THz frequency range on a tabletop scale. Intense electric and magnetic fields in this frequency range are in high demand for such new applications as terahertz-driven particle acceleration [1–3], molecular orientation and alignment [4–6], ultrafast spin control [7,8], and terahertz streaking [9,10]. To circumvent large velocity mismatch between terahertz waves and optical pump in LiNbO$_3$, pumping by laser pulses with tilted pulse front [11] is commonly used. The tilted-pulse-front technique requires mJ-level pumping laser pulse energy to provide both high optical intensity and a beam width much larger than the terahertz wavelength. The typical optical-to-terahertz conversion efficiency of this technique at room temperature is $\sim$0.1$\%$ [12,13]. The record efficiency of $\sim$1$\%$ has been achieved with 1.2-mJ pump pulses of optimized chirp and duration [14]. The record high terahertz pulse energy of 0.4 mJ was achieved with 60-mJ pump pulses [15].

Another way to circumvent optical-terahertz velocity mismatch in LiNbO$_3$ is Cherenkov scheme [16–18]. The Cherenkov scheme requires focusing of the pump laser beam to a size smaller than the terahertz wavelength in one (focusing to a line) or two (focusing to a spot) directions, to prevent destructive interference of terahertz waves emitted by different parts of the nonlinear source. Tight focusing allows one to achieve high optical intensity, required for efficient nonlinear optical rectification, with lower energy laser pulses than in the tilted-pulse-front configuration. In recent years, the Cherenkov scheme has been substantially elaborated [19–28]. At present, one of the most efficient Cherenkov-type terahertz emitters consists of a few tens of microns thick and $\sim$1$\times$1 cm$^2$ in size layer of LiNbO$_3$ attached to an output prism made of a high-resistivity Si [21,22,24–26]. The pump laser beam is focused by a cylindrical lens to a line on the entrance facet of the LiNbO$_3$ layer. The laser pulse propagates in the layer as a fundamental mode of an oversized dielectric slab waveguide and emits Cherenkov half-wedge of terahertz waves to free space through the Si prism. Using a thin LiNbO$_3$ layer not only prevents diffraction broadening of the pump laser beam but also reduces attenuation of terahertz waves in strongly absorbing LiNbO$_3$. (Structures with a thinner, a few microns thick, LiNbO$_3$ layer [23] or with a micron-size LiNbO$_3$ ridge waveguide [27,28] can provide a broader bandwidth but suffer from a very low coupling efficiency of the pump laser beam to the optical waveguide.) In the first experimental demonstration of the emitter [22], the efficiency 0.1$\%$ was achieved by converting 40-$\mu$J Ti:sapphire laser pulses in a 8-mm long structure with a 50-$\mu$m thick LiNbO$_3$ layer placed between a Si prism and a BK7-glass substrate. More recently, 15-20-$\mu$J pulses from a Ti:sapphire amplified laser system were converted into terahertz radiation with an efficiency as high as 0.25$\%$ in a 1-cm long structure with a 35-$\mu$m thick LiNbO$_3$ layer placed between a Si prism and a metal substrate [25]. Thus, the Cherenkov-type emitters demonstrate practically the same conversion efficiency as the tilted-pulse-front technique but at lower (tens of $\mu$J) pump pulse energies.

The efficiency of the Cherenkov-type emitters saturates with increasing the pump pulse energy [25]. This limits the maximum efficiency. The saturation has been mainly attributed to higher-order nonlinear effects, such as self-phase modulation, self-focusing, and multi-photon absorption of laser radiation [25]. Since these effects are less pronounced for longer optical wavelengths, one can expect that increasing the pump wavelength will increase the saturation pump pulse energy. It will allow to achieve a higher efficiency by increasing the pump pulse energy. The potential of long-wavelength pumping for efficient terahertz generation has been recently recognized [29–31] and experimentally demonstrated [32–34] for tilted-pulse-front excitation of semiconductors, where two-photon absorption of the pump and generation of free carriers absorbing terahertz radiation are the main limiting factors. Here, we experimentally examine the effect of long-wavelength pumping on the efficiency of Cherenkov-type emitters with a thin LiNbO$_3$ layer, for which free-carrier absorption of terahertz radiation is not so crucial.

2. Experimental

The experimental scheme is shown in Fig. 1. An amplified Ti:sapphire laser with 800-nm wavelength and 50-fs pulse duration pumps an optical parametric amplifier (OPA), which has output with tunable wavelength ranging from 1300 to 2100 nm. The pulse duration of the OPA output radiation remains almost the same as that of the 800-nm exciting laser (we take it equal to 60 fs in the intensity estimations below). The beam from OPA or directly from the Ti:sapphire laser is focused by a cylindrical lens (with the focal length of 40 mm for the OPA beam or 100 mm for the laser beam) to a line on the entrance facet of a 40-$\mu$m thick, 1-cm wide, and 9-mm long LiNbO$_3$ layer attached to a rectangular Si prism with the apex angle of 41$^\circ$. (To fabricate the structure, a mm-thick slab of LiNbO$_3$ was glued to the Si prism, ground down to 40 $\mu$m, and then its facets were polished.) An iris diaphragm is used to adjust the optimal focal beam width ($\approx$20 $\mu$m) for efficiently exciting the fundamental mode of the LiNbO$_3$ slab waveguide [21]. The optical ([001]) axis of the LiNbO$_3$ crystal is in the layer plane and orthogonal to the laser propagation direction. The polarization of the pump optical beam is aligned parallel to the axis in order to maximize the optical rectification coefficient [21]. The apex angle of the prism is complimentary to the Cherenkov emission angle in Si $\theta _c\approx 49^\circ$. The emission angle is defined by formula $\cos \theta _c=n_g/n_\textrm {THz}$, where $n_g\approx 2.22$ [35] is the extraordinary optical group refractive index of LiNbO$_3$ ($n_g$ varies insignificantly over the used wavelength range) and $n_\textrm {THz}\approx 3.418$ is the terahertz phase refractive index of Si [36].

 

Fig. 1. Schematics of the experimental setup.

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The energy of the terahertz radiation emitted from the output prism was detected by a Golay cell, which was screened from stray optical radiation by a Si wafer and a low pass filter (LPF). To measure the energy spectrum of the terahertz radiation, terahertz band-pass filters were placed in front of the Golay cell. The optical beam profile and the optical power at the exit facet of the LiNbO$_3$ layer were monitored by means of a CCD camera and a power meter.

3. Results and discussion

Figure 2 shows the conversion efficiency as a function of the pump pulse energy for different pump wavelengths. Since the radius of the incident optical beam was different for 800 nm and longer wavelengths, we normalized the optical pulse energy to a unit length of the focal line, for a correct comparison of the dependences. The upper scale in Fig. 2 shows the corresponding values of the incident pump intensity, which were substantially lower than the damage threshold for LiNbO$_3$ [37,38]. In general, all curves in Fig. 2 exhibit a linear increase in the low-energy region followed by a saturation at higher energies. The slope of the initial linear segment of the curves is slightly lower for longer wavelengths. It can be explained by a decreasing wavelength dependence of the nonlinear coefficient $|d_{33}|$ of LiNbO$_3$ [39–41].

 

Fig. 2. Conversion efficiency as a function of the pump pulse energy (per unit length of the focal line) for different pump wavelengths. The star points show the efficiency when using a metal substrate. The upper scale shows the incident pump intensity.

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For 800 nm, the efficiency saturates at $\sim$0.4% and $\sim$50-$\mu$J/cm pump pulse energy per unit length (or $\sim$20 $\mu$J of total pulse energy), in agreement with previous findings [25]. For longer wavelengths, the efficiency saturates at larger pump energies per unit length and reaches higher maximum values, according to our expectations. In particular, the efficiency as high as 1.2% is achieved at $\sim$300-$\mu$J/cm (or $\sim$30-$\mu$J) pulse energy of 2100-nm pump. Interestingly, placing a metal plate on the surface of the LiNbO$_3$ layer, which was opposite to the Si prism, allowed us to enhance the efficiency by about 10% (two star points in Fig. 2). For 800-nm pump, a similar metal substrate-induced enhancement of the efficiency was observed in [25].

For all the wavelengths, the efficiency saturation (and subsequent decline seen in Fig. 2) can be attributed to the nonlinear distortion and absorption of the pump pulse in LiNbO$_3$. This is confirmed by Fig. 3. Firstly, Fig. 3(a) illustrates a correlation between the saturation of the conversion efficiency and a knee in the curve of the transmitted optical energy. Both the saturation and the knee occur at $\sim$100 $\mu$J/cm. This correlation indicates that multi-photon absorption (namely, 5-photon absorption at 1500 nm in Fig. 3 [34]) and possibly other losses, such as related to the nonlinear distortion of the optical beam in the LiNbO$_3$ layer, indeed play a role in the efficiency saturation. Secondly, Figs. 3(b)–3(e) illustrate that the optical beam indeed experiences strong nonlinear distortion in the LiNbO$_3$ layer at high pump energies. In particular, the transverse profile of the optical beam changes drastically with increasing the pump energy. At low pump energies [Figs. 3(b) and 3(c)], the beam is $\sim$20 $\mu$m thick and, accordingly, fills only a part of the LiNbO$_3$ layer thickness. This indicates that the beam propagates in the central part of the layer as a fundamental mode of a dielectric slab waveguide. The light intensity distribution is uniform along the width of the optical beam [vertical direction in Figs. 3(b)–3(e)]. At high pump energies [Figs. 3(d) and 3(e)], the optical beam thickens and fills the whole output aperture of the LiNbO$_3$ layer. This indicates excitation of the higher order modes of the dielectric slab waveguide. The presence of hot spots in the beam profile is a result of nonlinear beam distortion due to high order nonlinear effects, such as self-focusing and self-phase modulation.

 

Fig. 3. (a) Conversion efficiency and transmitted optical pulse energy as functions of the pump pulse energy (per unit length of the focal line) for 1500 nm. (b)–(e) Images of the transmitted laser beam profile at different pump pulse energies.

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Figure 4(a) shows the terahertz energy spectra measured with pumping at different wavelengths. The pump energy was taken near the saturation value: 30 $\mu$J/cm for 800 nm, 90 $\mu$J/cm for 1300 nm, 220 $\mu$J/cm for 1500 nm, and 200 $\mu$J/cm for 2000 nm. For all wavelengths, the spectra extend from $\sim$0.2 to $\sim$3 THz. The two-peak shape of the spectra agrees, in general, with the spectrum measured by the standard electro-optic sampling for 800-nm pump [25]. The ratio of the spectral peaks is, however, different for 800 nm and longer (1300-2000 nm) wavelengths. For 800 nm, the main peak is at $\sim$2 THz. For longer wavelengths, the main peaks are at $\sim$0.5 THz; there are also peaks at $\sim$2 THz but they are less pronounced.

 

Fig. 4. (a) Terahertz energy spectra (normalized to unity) for different pump wavelengths at the saturation pump energies. (b) Terahertz energy spectra for 1500-nm, 200 $\mu$J/cm pump with and without metal substrate. (c) Terahertz energy spectra for 1300-nm pump at low and high pump energies.

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Figure 4(b) confirms, in general, the theoretical prediction of [24] (see also [25]) that placing a metal substrate should accentuate the lower frequencies in the generated spectrum.

Figure 4(c) shows that pumping at high energies generates lower-frequency spectrum than pumping at low energies. This can be explained by an increase in the optical beam thickness due to its nonlinear distortion at high pump energies [see Figs. 3(d) and 3(e)]. Indeed, the optical beam transverse size enters the effective optical pulse duration that defines the generated spectrum [42].

4. Conclusion

We have achieved about three-fold enhancement (up to 1.3%) in the optical-to-terahertz conversion efficiency of a LiNbO$_3$-based Cherenkov-type emitter by increasing the optical pump wavelength from 800 to 2100 nm. The enhancement has been obtained due to suppression of the efficiency saturation by long-wavelength pumping. The efficiency of 1.3% achieved with 30-$\mu$J pump pulses is record high for sub-mJ-level of optical pumping.

In comparison to optical rectification in organic crystals and tilted-pulse-front technique, the Cherenkov-type emitters provide a unique combination of high ($\sim$1%) conversion efficiency at room temperature with a wide interval of possible pump wavelengths and sub-mJ-level of optical pumping, which can be provided by high (MHz) repetition rate laser amplifiers. Such emitters hold promise for generating mW-level average terahertz power.