A simple approach to generate high energy, frequency and bandwidth tunable multicycle THz pulses by optical rectification (OR) of spatially shaped femtosecond laser pulses in the lithium niobate (LN) crystal is proposed and demonstrated. A one dimensional binary shadow mask is used as a laser beam shaper. By building the mask’s image in the bulk LN crystal with various demagnifications, the frequency of THz generation was tuned in the range of 0.3 – 1.2 THz. There exist also an opportunity to tune the bandwidth of THz generation from 20 GHz to approximately 1 THz by changing the optical beam size on the crystal. The energy spectral density of narrowband THz generation is almost independent of the bandwidth and is typically 0.18 μJ/THz for ~1 W pump power at 1 kHz repetition rate.
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The terahertz band (~0.1 – 10 THz) has recently drawn much attention due to its potential for both fundamental physics and increasingly larger variety of applications . However, the applicability of terahertz (THz) sources is still critically dependent on the power available with current technology, which has prompted much research in developing compact table-top THz sources. The difference-frequency generation [2–4] and optical rectification (OR) of femtosecond laser pulses [5–9] are the widely used methods for the generation of narrowband radiation in THz frequency range. The latter method is distinguished by simplicity, but it does not lead to generation with narrow linewidth Δν << 100 GHz that is important for many applications such as high-resolution THz spectroscopy, communication and imaging. Relatively narrow generation linewidth Δν ≈20 GHz has been obtained by OR in periodically poled lithium niobate (PPLN) crystal, when special efforts to reduce THz absorption in the crystal (cryogenic cooling of PPLN  and using THz generation in surface emitting geometry ) were applied.
Recently we demonstrated  that application of wide-aperture beam in transversely patterned PPLN crystal leads to THz generation with Δν ≈14 GHz linewidth. The fs-laser beam propagates collinear to PPLN domain wall (Fig. 1(a) ) and THz-wave is generated in the direction determined by Cherenkov radiation angle θCh = cos−1(ng/nTHz), where ng = c /u is the group index, u is the group velocity of the laser pulse, c is the light velocity and nTHz is the refractive index at generated frequency. One dimensional (1-D) spatial modulation of nonlinearity in PPLN crystal serves for fulfilling the quasi-phase-matching condition in transverse direction. The main drawback of this method is that the periodical domain inverting technique may be applied only to ferroelectric materials, such as LiNbO3 or KTP. In addition, generation frequency νTHz is predetermined by the spatial period of the domain-inverted structure Λ and therefore it cannot be modified after the sample fabrication.
To overcome these problems here we demonstrate a method using a single-domain Mg-doped lithium niobate (LN) crystal which is illuminated by spatially shaped fs-laser beam. The 1-D binary shadow mask (SM) (Fig. 1(b)) is attached to the LN crystal entrance face (Fig. 1(c)) and regions marked by the black and white colors represent the dark and illuminated parts of LN crystal, respectively. The laser beam is polarized along optical z-axis to exploit the highest nonlinear coefficient d33. Obviously, the non-illuminated (dark) parts of the mask-covered LN crystal can be considered as a nonlinear medium having d33 = 0. Thus, THz generation can be considered as OR process in uniformly illuminated LN crystal having spatially modulated nonlinear coefficient d33.
In the case of SM with periodically arranged slits (Fig. 1(b)) the nonlinear coefficient d33 is a periodical function d33(y) = d33(y + Λ) of the y coordinate. Therefore, similar to the case of PPLN crystal, the reciprocal lattice vector kΛ = 2π/Λ can compensate the phase mismatching in the transverse direction (along the Y-axis). In longitudinal direction (X-axis) the phase-matching condition is always satisfied because THz-wave is radiated at Cherenkov angle with respect to direction of the optical beam propagation. Thus, the vector phase matching condition is fulfilled that promotes to high-efficient THz generation. In contract to common Cherenkov type THz generation, there is no principal limitation on the pump beam size, which is favorable for application of the modern femtosecond amplifier systems. In addition, the application of the wide-aperture beam (with large wy) leads to an increase in the number of the generated THz oscillation periods (for a given Λ) and thereby to a decrease in the THz-wave linewidth.
Note that the frequency of THz radiation is determined by the period Λ and therefore a set of the masks with different periods Λ is needed to obtain tunable THz generation. An alternative way is building the mask’s image in the crystal by a cylindrical lens. The variation of the image magnification M results in a modification of the structure period ΛM = ΛM and thereby to the change of the generation frequency. In this way continuously tunable THz generation can be obtained. Additional advantage of this method is avoidance of the problems related to mask fabrication in cases when M < 1.
It should be noted that in our considerations the optical beam diffraction after passage of the mask was neglected. This assumption is based on the fact that the wavelength of laser radiation in the crystal is significantly smaller than the spatial period Λ of the mask needed for THz generation, especially in low frequency THz region. In addition, there is no need for longer LN crystal because of its high THz absorption [13,14].
2. Theoretical estimations and experimental setup
The frequency of THz generation in LN crystal illuminated through a mask is determined by the same matter as for the PPLN crystal . From wave vectors diagram involving THz, optical, and primary reciprocal lattice vectors (respectively kTHz, kg, and kΛ in Fig. 1(d)) it follows that the frequency of THz radiation νTHz is given byEq. (1) ng = 2.25 (at 800 nm laser wavelength ) and nTHz from dispersion formula of the 6% Mg-doped LN crystal , we obtain that the central frequencies of narrowband THz generation are at 0.678 THz, 0.443 THz, and 0.341 THz for masks with periods of Λ = 100 μm, 154 μm, and 200 μm, respectively.
The experimental setup was similar to the one used previously . Briefly, it consists of a 100-fs Ti:Sapphire regenerative amplifier (Spitfire, Spectra-Physics) operating at 800 nm with a repetition rate of 1 kHz and a conventional THz detection system based on electro-optical sampling technique. The maximal power of the laser radiation used in present experiment was about 1 W. The THz generation takes place in the 5% Mg-doped congruently grown LN crystal (HC Photonics Inc.) having a right triangle form in the horizontal plane with sizes of 5 mm and 10 mm along the Y- and X-axis, respectively (Fig. 1(c)). The size of the LN crystal in the vertical plane (along Z-axis) was 3 mm.
The laser beam was focused by a pair of cylindrical lenses to obtain an elliptical beam spot with sizes about 4.5 mm × 2.8 mm on the surface of the mask. Experimental studies were carried out for two cases. In the first case masks with different periods (Λ = 100, 154, and 200 μm) were attached to LN crystal. In the second case the image of the last two masks (Λ = 154 μm and 200 μm) was build in the crystal using a cylindrical lens (F = 20 cm) mounted on a translation stage. By moving both the cylindrical lens and the mask, the demagnification of the image was changed. The THz-wave emitted from the crystal was directed and focused by four off-axis parabolic mirrors into a ZnTe crystal for electro-optic THz field measurement.
3. Results and discussion
First, we measured THz waveforms in a configuration when masks were attached to the entrance surface of the LN crystal. Figure 2 shows the measured THz waveforms and corresponding spectra obtained by application of the masks with periods of Λ = 100, 154, and 200 μm, respectively.
From Fig. 2(a) it is seen that the durations of multicycle THz pulses are approximately the same and it is about 60 ps for all used masks. This can be explained by following considerations. It is well known [5,6] that in the case of THz generation in PPLN crystal each domain of the periodical structure is responsible for half-cycle of the radiated THz field. In our case, the single-domain LN crystal can also be considered as a periodical structure where the nonlinear coefficient takes only d33 and 0 values representing, respectively, illuminated and non-illuminated parts of the mask covered crystal. Using this similarity we conclude that each illuminated part of the crystal is responsible for one cycle of THz oscillation. Hence, the total duration of the multicycle THz generation tim is equal to the product of the oscillation period T = 1/νTHz and the number of mask’s slits N illuminated by laser radiation. By assuming that the laser beam has a flat-top intensity distribution, the number of slits can be written as N ≈wy/Λ, where wy is the beam spot size (along the Y-axis) on the mask (Fig. 1(b)). Using it and by substituting νTHz from (1), one can easily obtain
Above relation shows that the THz pulse duration tim is determined by the optical beam spot size wyM in the crystal and it is not dependent on the mask period Λ. By substituting in Eq. (2) values M = 1 and wy ≈4.5 mm corresponding to the current experiment, the pulse duration is estimated to be tim = 66 ps. It agrees well with the measured value ~60 ps, especially taking into account the fact that neither the used optical beam nor envelop of THz pulse have a flat-top distribution.
The Fourier spectra corresponding to measured THz waveforms are presented in Fig. 2(b). It is seen that the central frequencies generated with masks having periods of Λ = 100, 154, and 200 μm are respectively 0.668, 0.435, and 0.334 THz, agreeing well with the calculated ones (0.678, 0.443, and 0.341 THz). The spectral bandwidth (at 1/√2 value of the maximum) is about Δν = 20 GHz for masks with periods of Λ = 200 μm and 154 μm, and it is about Δν = 25 GHz for the mask with a period Λ = 100 μm. In the latter case the increase of the bandwidth Δν is probably related to the increase of THz absorption in the LN crystal. The same reason is probably responsible also for the decay of the spectral amplitudes at higher frequencies.
To obtain frequency tunable THz generation, we modified the experimental setup in such a way that the mask image was built in the crystal with variable magnification M. The dependencies of the generated frequency νTHz on image magnification M for the masks with spatial periods of 154 μm and 200 μm are presented in Fig. 3 .
Figure 3 shows that tunable radiation between 0.34 - 1.3 THz region can be obtained when magnification M is varied from 1 to 0.25. As it is illustrated in the inset of Fig. 3, the increase of the generation frequency is accompanied by broadening of the bandwidth Δν . It is related to a decrease of the beam size wyM in the crystal with decreasing magnification M. Results of the measurements show that in contrast to absolute bandwidth Δν, the relative bandwidth δ = Δν/νTHz is not changed significantly with change of the magnification M. Typically, it is in the range of δ = (6-8)% when M is varied from 1 to 0.25, equivalent to frequency generation change from 0.34 THz to 1.3 THz. Though the relative bandwidth has to be δ = const according to Eq. (2), the strong THz absorption in the crystal violates this relationship.
A calibrated pyroelectric detector SPI-A-62 (Spectrum Detector) was used for measuring the average power and estimation of THz pulse energy. A silicon plate and black polyethylene film were placed in front of the detector in order to block the optical radiation. In configuration when optical beam spot size on the mask (attached to the crystal and having Λ = 200 μm) was 2.5 mm and used pump power ~1 W, the power of narrowband (νTHz = 0.34 THz, Δν = 37 GHz) THz radiation was about 6.5 μW. Taking into account the repetition rate (1 kHz) of the pump pulses, the multi-cycle THz pulse energy is estimated to be 6.5 nJ. It corresponds to peak power of 110 W and focused electric field strength of about 3 kV/cm. Though pump-to-THz energy conversion efficiency is only 6.5 × 10-4%, the estimated energy spectral density ≈0.18 μJ/THz is quite sufficient for many applications and it is by three orders of magnitude larger than earlier reported values in  and .
Recently , powerful narrowband THz generation with spectral density of 10 μJ/THz was obtained by combining the chirped pulse beating (CPB) method  and tilted-pulse-front pumping (TPFP) technique . Because CPB method allows fully adjusting the bandwidths of pump and THz spectra, its application in our scheme will lead to significant increase of the generation efficiency as well. Besides, we intend to use cryogenic cooling of the crystal which will increase THz power due to significant reduction of THz absorption. Nevertheless, even in the present stage, the developed THz generator can find many applications, especially taking into account its simplicity and ability to easily tune the frequency and spectral bandwidth of generated THz radiation.
In summary, we have developed a simple and promising technique for frequency tunable and bandwidth adjustable THz generation by using spatially pre-shaped fs-laser pulses. By illuminating the lithium niobate crystal through 1-D shadow mask, the multicycle THz pulses with an average power level of 6.5 μW and energy spectral density of 0.18 μJ/THz have been generated at a 1 kHz repetition rate. This initial demonstration was conducted using simple periodical masks, however, application of reconfigurable masks will lead to generation of temporally shaped THz pulses needed for communications, signal processing and materials control [7,8]. Finally, by employing the CPB method and cryogenic cooling the LN crystal, we hope to generate THz radiation at power levels suitable for THz nonlinear spectroscopy.
This work is partially supported by JSPS, Grant-in-Aid A222460430, and Industry-Academia Collaborative R&D, JST. The first author would like to thank Prof. T. Suhara for helpful discussions.
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