We demonstrate the use of a transient polarization grating induced by two femtosecond laser pulses propagating in a LiNbO3 crystal for the generation of frequency tunable, narrow-band, picosecond THz pulses. Employing pump pulses with 150 fs duration and 2 μJ energy, the generated THz pulse has an energy up to 1.8 pJ, a pulse duration of 3 – 5 ps and a bandwidth of 0.1 THz. The central frequency can be tuned in the range from 0.5 to 3 THz. The generation efficiency of the transient grating method in comparison to other techniques is discussed. The possibility of shaping the temporal waveform of the THz pulses by simply shaping the spatial intensity distribution of the pump pulses is demonstrated.
©2004 Optical Society of America
The generation of high power narrow-band THz radiation is desirable for many applications, especially intriguing seems its application to study the nonlinear interaction of the electromagnetic radiation with material resonances in the THz frequency range . During the last ten years, several techniques for the generation of narrow-band picosecond THz pulses have been developed. The main of them are free electron lasers , photoconductive switching [3,4], and optical rectification sources utilizing femtosecond pulse trains  or shaped ultrafast laser pulses  and optical rectification in periodically poled lithium niobate (PPLN) . An alternative attractive technique exploiting the interaction of ultrashort laser pulses with a magnetized plasma for THz pulse generation is described in Ref. . Experimental data so far available  are still very preliminary, however. Free electron lasers allow to generate THz pulses with very high pulse energy (about 10 μJ), but these instruments are huge and extremely expensive, furthermore it is difficult to keep their jitter in the sub-ps range. For the case of optical rectification in PPLN, the generation of narrow-band THz pulses with energies of a few pJ has been reported . To the best of our knowledge, quantitative data for the energy of narrow-band THz pulses generated by optical rectification or photoconductive emitters pumped with pulse trains or shaped laser pulses are presented only in one previous publication .
In this letter, we demonstrate generation and frequency tuning of narrow-band, picosecond THz pulses having 1.8 pJ energy by two-beam excitation using femtosecond laser pulses in a bulk LiNbO3 crystal.
Some applications need energetic THz pulses with a special pre-defined temporal waveform or spectrum. Recently it was demonstrated that using optical rectification with shaped pump pulses , it is possible to control the temporal or spectral shape of the generated THz pulse. The same goal is achieved when a single pulse is rectified in PPLN with a special domain distribution . In the latter case, generation of a different temporal shape of course requires a new crystal with a modified domain structure. In the last chapter of this letter, we demonstrate that the two-beam excitation technique provides an opportunity for high contrast temporal shaping of the generated THz waveform.
Two-beam excitation techniques are widely used in ultrafast spectroscopy, in particular during the last ten years they have been employed by several groups for the excitation of coherent phonon-polaritons in different solids [11–14]. The main aim of these studies was the accurate characterisation of the polariton dispersion (real and imaginary parts). Obviously, when the generated polariton reaches the surface of the crystal, that part which has not been reflected at the surface transforms into a THz electromagnetic pulse propagating in free space. However, we are not aware of any work describing, characterising or employing such THz sources. F. Valée and Ch. Flytzanis  have demonstrated the transmission of a short phonon-polariton pulse through a vacuum layer separating two identical electro-optic crystals, but they did not investigate the properties of their set-up as a THz source. Thus, to the best of our knowledge, we present the first demonstration and comprehensive characterisation of free-space-propagating THz pulses generated by the two-beam excitation technique.
2. Principle of THz pulse generation and shaping
The generation of THz radiation or coherent phonon-polaritons by two-beam excitation can be considered in terms of frequency mixing  or in terms of Cherenkov radiation [17,18]. In this letter, we prefer the terms of Cherenkov radiation because in this way it is easy to consider the THz pulse shaping opportunity. A schematic illustration of the THz generation is shown in Fig.1.
The small red circles represent interference maxima formed by two ultrashort laser pulses propagating in the sample at a small angle as shown by the two red arrows. The gray tilted lines represent maxima of the generated THz fields propagating in the directions marked by the gray arrows and determined  by the ratio of the group velocity of the pump pulses to the phase velocity of the THz pulse. Unlike the Cherenkov radiation emitted by a tightly focused ultrashort pulse [19,20], which generates THz radiation propagating in a cone, the radiation generated by each interference maximum (which has a much larger extension compared to the wavelength of the generated THz radiation in the direction perpendicular to the plane of Fig. 1) is emitted as a plane-wave pair . Roughly we can assume that the Cherenkov radiation emitted by each laser interference maximum consists of a single cycle THz pulse. The superposition of the radiation emitted by all maxima determines the resulting THz waveform. The time duration of the generated THz wave form is equal to
where D is the laser spot diameter, γ = arccos(vTHz/vvis) = arccos(nvis/nTHz) is the Cherenkov angle  (see Fig. 1), νTHZ and νvis are the phase and group velocity of the THz radiation and the optical pump pulse in the crystal and nTHz = 5.12 (at 2 THz) and nvis = 2.25 are the corresponding indices of refraction. k is a coefficient taking into account that the THz intensity is proportional to the square of the THz field strength (which is proportional to the intensity of the pump). For a Gaussian profile, k=0.707. It is easy to see that a manipulation of the intensity distribution of the laser spot causes a corresponding change of the time profile of the generated THz pulse. This space-time conversion provides an opportunity for THz pulse shaping.
3. Experimental set-up
The nonlinear material used in our experiments is a nearly stoichiometric LiNbO3 crystal with 2 mol % Mg doping and shaped in such a way that the angle between the front and one of the side surfaces is equal to γ = 64 degree in order to achieve normal incidence on the surface for the incoming exciting laser beams and for the outgoing generated THz radiation (Fig. 2).
Near-infrared pulses with a pulse duration of 150 fs, a repetition rate of 200 kHz and an average power of 600 mW have been generated by a commercial mode-locked Ti:sapphire system (Mira/Rega-900 Coherent). After the amplifier, the femtosecond radiation was collimated into a narrow ( >0.5 mm diameter) beam and then split into two parts by a 50% beam splitter. Spatial and temporal superposition of the two beams with a small variable angle (0.3–2 degree) between them results in an interference pattern with variable period. The largest nonlinear tensor element (d33) of LiNbO3 was applied since the polarization of the pump beams and the optical axis of the crystal, were oriented perpendicular to the plane of Fig. 2. As a result, the polarization of the emitted THz radiation was also perpendicular to the plane of Fig. 2. The diameter of the laser spot on the sample was 500 μm. The energy of the generated THz pulses was measured by a calibrated liquid-He cooled Si-bolometer, and the temporal profile of the electric field was analyzed by a standard electro-optic sampling set-up  employing a 0.6-mm-thick ZnTe crystal as the sensor
4. Frequency tuning characteristics
The measured temporal profiles of the THz field and their normalized power spectra obtained by Fourier transformation are plotted in the left and middle panel of Fig. 3 for three different angles (0.35, 1.3, 1.9 degree) between the pump beams.
The generated THz pulses have a time duration of about 5 ps in agreement with Eq. (1). The spectra of the THz pulses reveal relatively narrow (~ 0.1 THz) peaks at 0.6, 1.9, and 2.7 THz. The right panel of Fig. 3 shows the frequencies of the generated THz pulses in dependence on the angle between the two pump pulses. The squares depict experimental data corresponding to the results shown in the middle panel and the curve exhibits the calculated dependence. The calculations have been performed without any adjustable parameters just taking into account energy and momentum conservation for polariton generation .
5. Calibrated energy measurements
According to Fig. 4, the highest energy generated by our setup was 1.8 pJ. It was achieved at 1.6 THz, and the frequency dependence shows a broad peak around this value. The THz pulse energy is larger than 1.5 pJ in a frequency range with a width of one octave. In the low frequency range, we expect that the energy of the generated THz pulse is described by an ω2 law . There are two main reasons which can result in a drop of THz generation at high frequencies: the limited spectral bandwidth of the 150 fs laser pulses and the absorption of the THz radiation in LiNbO3. At room temperature, the absorption in LiNbO3 increases rapidly at frequencies higher than 1 THz. A simple estimation taking into account the ω2 law and the limited spectral bandwidth of the 150 fs laser pulses demonstrates (red curve in Fig. 4) that these two effects can not explain the fast decrease of the THz pulse energy at high frequencies. Hence, we have to conclude that in our case the decrease of the THz pulse energy at frequencies higher than 2 THz originates mainly from THz reabsorption in the LiNbO3 crystal. The energy of the first point in Fig. 4 (open square) is probably reduced by the drop of the bolometer sensitivity at low frequencies. The energy of the generated THz pulses can be increased by cryogenic cooling of the crystal which implies a dramatic reduction of the THz absorption in LiNbO3. For example, at 1.8 THz we measured a decrease of the absorption coefficient from more than 20 cm-1 to 2 cm-1 when the crystal was cooled to 77 K. From recent experiments , we expect a 3 – 4 times corresponding increase of the pulse energy. At higher frequencies, an even higher increase of the THz energy is expected.
The pump and detection conditions applied by Y.-S. Lee et al.  using PPLN for narrow-band THz generation were very similar to ours. There were, however two important differences: they used a significantly smaller pump spot-size (resulting in a 10 times larger average intensity) and a more than three times longer crystal. Nevertheless they observed within the measurement accuracy the same (2 pJ) THz pulse energy as we. For similar pump pulses (energy, pulse duration) and for the same spot size and crystal length we should expect the same efficiency. The fact that they did not get a larger efficiency in spite of the longer interaction length and smaller spot size is probably due to the larger absorption of their congruent crystal as compared to our stochiometric one.
For optical rectification in PPLN, tuning of the THz frequency and variation of the bandwidth are possible by changing the period and the number of the domain pairs, respectively. Both changes require a new crystal. Contrary, using our two-beam excitation technique simply the angle between the pump beams and the spot-size have to be varied without any need to replace the LiNbO3 crystal, so our technique is more flexible. It should be noticed that we employed -for the sake of simplicity- a simple beam-splitter instead of a transmission grating to obtain the pump pulse pair. Thus the relative tilt of the pulse fronts (the so called pancake effect [14, 21]) can set a limit for narrowing the spectral bandwidth by using a larger pump spot. Principally, the pancake effect is negligible in our experimental configuration, since even for the largest angle (1.9 degree) we should reach this limit by applying a pump beam diameter larger than 10 mm. In practice, however, the absorption of the LiNbO3 prevents the use of such a large spot.
The maximum energy of the THz pulses generated by the two-beam excitation method at room temperature is 17 times smaller than that generated by the tilted pulse front technique  using similar experimental contitions. The difference originates from the effect that has previously been shown to explain the higher efficiency of the tilted pulse front excitation in comparison to rectification in PPLN . The tilted pulse front excitation essentially generates a single cycle THz pulse, while two-beam excitation (or PPLN) creates a THz pulse train consisting of a number of periods equal to the number of interference fringes (or domain pairs). The ratio of the THz energies generated by the two methods is in agreement with the expected value within a factor of two. It should be noticed that the spectral energy densities of the THz pulses generated by the two-beam excitation technique and by the tilted pulse front method have similar values (~ 18 pJ/THz). So for applications where the spectral energy density rather than the generated electric field strength of the THz pulse is important, the two-beam excitation technique is preferable because of its comfortable tunability.
Besides cryogenic cooling of the LiNbO3 crystal there exist a few possibilities for further increase of the THz pulse energy generated by the two-beam excitation technique.
- The total available THz energy can be raised by a factor of 2 just by exploiting the second THz beam generated by the two-beam excitation (see Fig. 1), which was absorbed in the LiNbO3 crystal in the case of our experiments performed so far.
- Choice of a LiNbO3 crystal with an optimized Mg doping level . Mg doping is used to suppress photorefraction but it also affects the THz absorption in the crystal.
- Increase of the laser pump intensity keeping the laser spot size constant. This can be done until the intensity reaches the optical damage threshold (a few times 1010 W/cm2) of the crystal.
- When the laser intensity is near to the optical damage threshold, the THz pulse energy can be increased further by simultaneous up scaling of the laser pulse energy and the laser spot size in order to keep the laser intensity below the damage threshold. The increase of the laser spot size in the direction perpendicular to the interference fringes leads to a narrowing of the generated THz pulse spectrum, whereas a larger laser spot size in the perpendicular direction does not change the THz pulse spectrum.
- Increase of the crystal length. For this purpose a rectangularly shaped crystal has to be chosen (in contrast to the crystal with an angle of 64 degrees between the front and side surfaces applied in the present study). In this case, a prism or grating THz output coupler  should be employed to prevent total reflection at the side surface of the LiNbO3.
6. Temporal waveform shaping
A demonstration of THz waveform shaping accomplished by changing the spatial intensity distribution of the pump beams is presented in Fig. 5. The first column depicts schematic drawings of simple mask set-ups resulting in different transverse pump intensity profiles. For illustration the second column shows the measured or calculated pump laser intensity distributions on the front surface of the crystal. (The first two lines present real photos of the laser spot taken by a digital camera. In lines 3–5 the pictures have been obtained from the photo of the undisturbed laser spot taking into account the effect of the used shields or slit. The third column in Fig. 5 represents the generated THz waveforms detected by an electro-optic sampling set-up. The THz waveform, generated by undisturbed laser beams is shown in the first line of Fig. 5. The second line demonstrates the effect of inserting vertically a 80 μm wire in front of the crystal to block the central part of the laser spot. The pronounced temporal shaping of the THz wave originates from the spatial-temporal correspondence mentioned in chapter 2: blocking of the central part of the interference pattern results in a minimum in the central part of the THz temporal waveform. We also performed measurements for blocking approximately half of the laser spot by a vertical shield. When the shield was placed on that side where the THz radiation was measured (see third line in Fig. 5) the generated THz waveform reveals a sharp rising and a slow trailing edge. When the shield was placed on the opposite side (see fourth line in Fig. 5) the generated THz waveform has a slowly rising edge and a sharp trailing edge. For the last case (see line five in Fig. 5), the two sides of the laser spot were cut by a slit resulting in a sharp rising and trailing edge. It should be noticed that the LiNbO3 was tuned to a slightly different THz frequency in this case.
Finally, we should mention that more complicated temporal profiles of the generated THz radiation can be achieved by applying a liquid crystal modulator  in close proximity to the LiNbO3 crystal or imaging the surface of the liquid crystal modulator into the LiNbO3 crystal. The liquid crystal modulator could provide an opportunity for fast manipulation of the generated THz waveforms, which could allow signal processing in quantum communication systems .
Narrow-band picosecond THz pulses have been generated by optical rectification utilizing an optical source with a periodic intensity distribution created by two ultrashort laser pulses propagating in a bulk LiNbO3 crystal. This novel technique, which is distinguished by attractive frequency tuning and pulse shaping properties, yields approximately the same THz conversion efficiency as optical rectification in PPLN. The bandwidth of the THz pulses obtained in our first experiments was 0.1 THz and the central frequency was tunable across the 0.5–3 THz region. The bandwidth is expected to be narrowed further by simply using a larger spot size. Easy and reliable THz pulse shaping exploiting the space-time intensity distribution conversion has been demonstrated
Note added in proof
After submission of our manuscript, similar work has been published .
This work was supported by the Hungarian Scientific Research Fund under Grant No. T 038372. A.G.S. and J.H. acknowledge funding of their stays in Stuttgart by the Max-Planck-Institute for Solid State Research.
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