A new scheme of optical rectification (OR) of femtosecond laser pulses in a periodically poled lithium niobate (PPLN) crystal, which generates high energy and bandwidth tunable multicycle THz pulses, is proposed and demonstrated. We show that the number of the oscillation cycles of the THz electric field and therefore bandwidth of generated THz spectrum can easily and smoothly be tuned from a few tens of GHz to a few THz by changing the pump optical spot size on PPLN crystal. The minimal bandwidth is 17 GHz that is smallest ever of reported in scheme of THz generation by OR at room temperature. Similar to the case of Cherenkov-type OR in single-domain LiNbO3, the spectrum of THz generation extends from 0.1 THz to 3 THz when laser beam is focused to a size close to half-period of PPLN structure. The energy spectral density of narrowband THz generation is almost independent of the bandwidth and is typically 220 nJ/THz for ~1 W pump power at 1 kHz repetition rate.
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During the last decade significant progress has been made for near-single-cycle terahertz (THz) pulse generation with ultrafast lasers [1–3]. The spectrum of such THz pulses covers a wide frequency range (0.2–10 THz) that is favorable for broadband spectroscopic applications. However for many applications, multicycle THz pulses would be preferred rather than typical single-cycle pulses. For example, using narrowband THz radiation in free-space imaging and telecommunication systems allows escaping the THz absorption of water vapor , and some new sensing techniques are intended for operation with narrowband THz sources . Besides, multicycle THz pulses can excite a selected resonance transition of the material without influencing neighboring modes.
Utilizing the broad spectra of ultrafast lasers, one possibility to generate narrowband THz radiation is based on mixing two time-delayed, linearly-chirped pulses in a dipole antenna [6, 7] or in a nonlinear crystal, such as ZnTe . The chirp-and-delay approach yields a quasi-sinusoidal optical intensity modulation at beat frequency of the mixed laser pulses. By combining this method with tilted-pulse-front pumping (TPFP) technique, tunable THz pulses were generated in LiNbO3 crystal  in the range from 0.3 to 1.3 THz with typical bandwidth Δf ≈100 GHz. Despite record power of narrowband THz radiation has been obtained, a necessity of using both large tilt angle δ ≈63° and two time-delayed, linearly chirped pulses complicates THz generation scheme. Besides, there are some applications (e.g. effective excitation of gas media with narrow resonance transitions, THz-wave heterodyne detection systems, THz radar based on Doppler effect) where exploiting THz radiation with bandwidth Δf << 100 GHz is desirable.
The simplest technique of narrowband THz generation is based on optical rectification (OR) of the ultrashort laser pulses in periodically poled lithium niobate (PPLN) crystal . The generated THz waveform corresponds to the domain structure of the PPLN crystal with a bandwidth inversely proportional to the crystal length [10, 11]. In initial experiments the bandwidth of THz radiation was relatively large Δf = 110 GHz because strong THz-wave absorption limits the effective length of the crystal. Later this value of Δf was decreased down to Δf = 18 GHz by reducing THz absorption by cryogenic cooling of PPLN sample .
An alternative way to decrease THz-wave decay in PPLN crystal is the use of OR in surface-emitting geometry (SEG). In this case THz-wave is emitted perpendicularly to direction of the laser pulse propagation. By concentrating laser beam close to lateral surface of the rectangular form PPLN sample, the THz-wave path length in crystal is significantly reduced, resulting in decrease of THz-wave decay. With this method the generation of quasi-monochromatic THz-wave (centered at f0 = 0.95 THz) with a bandwidth of Δf = 50 GHz has been obtained at room temperature . The main disadvantage of OR in SEG is the necessity of using the laser beam with small size w in the direction of THz-wave emission [11, 13]. The extended laser beam size results in phase-mismatching, if w > wc = λTHz/2nTHz, where λTHz is the wavelength of THz radiation in vacuum, nTHz is the refractive index of the crystal in THz region. For example, to generate THz radiation with wavelength λTHz = 300 μm, the laser beam has to be focused to a line (by cylindrical lens) having w < wc = 29 μm thickness. Obviously, it limits the effective length of the crystal due to strong laser beam divergence. Besides, it can lead to damage of the crystal if high-energy femtosecond laser pulses are used.
In this paper we consider a new configuration of narrowband THz generation by OR in PPLN crystal having a triangular prism form (Fig. 1 ). The cross-section of PPLN sample in XY-plane has a form of right angle triangle with legs oriented along crystallographic X- and Y-axis. The femtosecond laser beam propagates parallel to domain walls of the PPLN crystal (X-axis) and is polarized along the optical Z-axis. Similar to the case of OR in single domain LiNbO3 crystal, the THz emission from every domain of the PPLN structure takes place in 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 velocity of light in vacuum. The periodical domain-inverted structure in the PPLN crystal serves to obtain a constructive interference of THz fields radiated by separate PPLN’s domains. The resultant THz radiation is a quasi-monochromatic wave with central frequency fTHz determined by spatial period Λ of PPLN crystal and with bandwidth Δf, which is inversely proportional to the number of PPLN’s domains N involved in the generation process. Small variations of the frequency fTHz are possible by changing both the direction of the optical beam propagation and temperature of the crystal. However, to significantly change the generation frequency fTHz, a new PPLN crystal with different period Λ is needed.
The interesting feature of the proposed scheme is the ability to control easily the bandwidth of the generated THz-wave Δf through change of the laser beam size dy along the Y-axis of the PPLN crystal. As it is seen in Fig. 1(b), decrease of the beam size dy leads to reduction of the PPLN domain number N ≈2dy /Λ involved in THz generation and therefore increases the bandwidth Δf. In such way the transformation of THz radiation from narrowband to broadband is possible. A maximal bandwidth of a few THz order is expected in case of dy ≈Λ/2, corresponding to Cherenkov-type OR of femtosecond pulse in a single-domain LiNbO3.
Note that maximal size of the laser beam dy along Y-axis is limited only by corresponding size of the entrance face of PPLN sample and in our case it is about 4.5 mm. As for beam size along optical Z-axis, it also can be large, since now MgO-doped PPLN crystals with thickness of 3 mm are commercially available (HC Photonics Inc.) and fabrication of even 5-mm-thick samples has been reported . The opportunity of using a wide-aperture laser beam is very important, because high-energy laser pulses (delivered by fs-amplified systems) can be applied without damage of the crystal.
2. Crystal design and experiment
To calculate the spatial period of PPLN crystal, the OR is considered as difference frequency generation between spectral components of Fourier transform-limited laser pulse. Because optical beam propagates parallel to domain walls of the PPLN crystal, the wave vector diagram forms right-angled triangular (Fig. 1(d)) and therefore phase matching condition can be written in the following form
Using Eq. (1) the frequency of THz radiation fTHz = ωTHz/2π is given by
By substituting ng = 2.25 (at 800 nm laser wavelength ) and nTHz ≈5.15  we obtain a simple relation Λ ≈0.216λTHz between the spatial period of PPLN crystal and the wavelength of THz radiation. For example, if THz generation at λTHz = 356.6 μm (fTHz = 0.84 THz) is required, Λ should be approximately equal to 77 μm.
The experimental setup 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 1.5 W. The THz generation takes place in congruently grown 5% MgO-doped PPLN crystal having a spatial period Λ = 77 μm. The period Λ was chosen to obtain a THz radiation at 0.84 THz frequency, which corresponds to one of transmission windows of THz-wave propagation in ambient air. The PPLN sample (HC Photonics Inc.) having a triangular prism form was made from a 3-mm-thick Z-cut rectangular plate by cutting it at Cherenkov radiation angle θCh ≈63°. The directions of the optical beam and THz-wave propagation were perpendicular to the faces of PPLN triangular prism and the angle between them was θCh ≈63° (Fig. 1(c)). The angles between other faces of the triangular PPLN prism were 90° and 27°.
The laser beam having ~6 mm diameter was focused by a cylindrical lens (F = 200 mm) at the entrance face of the crystal with 4.5 mm and 3 mm sizes along Y- and Z-axis, respectively (Fig. 1(b)). By moving the cylindrical lens the beam size along Y-axis on the surface of the crystal dy is varied from 4.5 mm to approximately 40 μm, whereas the beam size dz along Z-axis was kept nearly 2 times larger than the corresponding size of the PPLN crystal. Because of high power availability of the pump source, we did not care of its complete usage.
3. Results and discussion
The THz-wave emitted from PPLN crystal was collimated and focused by four off-axis parabolic mirrors into a ZnTe crystal for electro-optic sampling measurement. As it was expected the multicycle THz pulse with longest duration is generated when optical beam size dy is maximal, i.e. when optical beam spot fully covers the entrance face of the PPLN crystal. The spectrum of THz generation is centered at 0.85 THz, which agrees well with the calculated value. The full width at 3-dB-level is nearly 17 GHz that is smallest of ever reported using PPLN crystals at room temperature.
The change of both the temporal form of multicycle THz pulse generation and corresponding amplitude spectrum with decrease of the beam size dy are shown in Fig. 2 . As it is seen from Fig. 2, the number of half-circles of THz generation approximately equals to number of domains of PPLN structure N ≈2dy /Λ. For this reason the spectral width of generated THz-wave is increased with decrease of the optical beam size dy (Fig. 2(b)). The near-single-cycle THz pulse is generated when the beam is focused to dy ≈40 μm size, which is close to the size of the separate PPLN domain. The corresponding spectrum covers a broad frequency range from 0.1 THz to nearly 3 THz as is illustrated in the inset of Fig. 2(b).
It is also interesting to measure the average power of multicycle THz generation PTHz and investigate its dependence on pump intensity Io. During these measurements the laser beam was focused by cylindrical lens to size dy ≈3 mm. To measure the THz power we used a pyroelectric detector SPI-A-62 (Spectrum Detector Inc.), whose voltage response Rv was calibrated by manufacturer at 30 THz and according to specification, the expected value of Rv at 0.85 THz is approximately 2 times smaller. Using it we estimate PTHz ≈8 μW for pump intensity Io = 0.067 TW/cm2 (pump power P ≈950 mW for elliptical form of the beam spot with sizes dy ≈3 mm and dz ≈6 mm) that corresponds to THz pulse energy of 8 nJ at 1 kHz repetition rate. The Fig. 3(a) shows the temporal forms of THz pulses measured at various pump powers Po. Evidently, the change of the pump power does not affect the shape of multicycle THz pulse and it only results in a change of the amplitude. The dependence of THz power PTHz on pump intensity Io is presented in Fig. 3(b). It is seen that the experimental points can be approximately fitted by the PTHz ∝ (Io) 1.8 dependence (the solid line in Fig. 3(b)). The deviation from quadratic pump power dependence is probably related to three-photon absorption of the pump radiation in the crystal [17,18] or other loss mechanisms, originated at high peak intensities of the femtosecond pump pulse.
As we have seen previously (Fig. 2(b)) the decrease of the beam size dy results in increase of the spectral width of generated THz radiation. It is also interesting to investigate the dependence of generated THz energy on beam size dy for fixed pump power. The duration of multicycle THz pulse tp is proportional to beam size dy, whereas pump intensity Io ∝ 1/ dy. According to above measurements, the average THz power PTHz and therefore the peak THz power Pimp depends on pump intensity Io as Pimp ∝ (Io)1.8. Therefore, we can expect that the energy of THz pulse eTHz = Pimptp will be proportional to (1/dy)0.8.
The measured dependence of eTHz on optical beam size dy is presented in Fig. 4 . During measurements the pump power held constant at 150 mW and the beam size dy varied by moving the cylindrical lens. It is seen that the experimental points are close to expected dependence eTHz ∝(1/dy)0.8 (solid line in Fig. 4). Because the bandwidth of generated THz-wave is Δf ∝ 1/dy, the energy spectral density slightly varies with change of the beam size dy and it is typically about S = 220 nJ/THz for pump power ~1 W. The obtained value of the spectral density S is by four orders of magnitude larger than that of reported in  and , but it is 50 times smaller in comparison to recently published data , when a combination of chirped pulse beating with TPFP techniques and pump power ~6 W were used. Nevertheless, the spectral density 220 nJ/THz obtained in present work is quite sufficient for many applications, especially when taking into account simplicity of THz generator and its ability to easily tune the spectral width of generated THz radiation. Additional increase of the spectral density can be obtained by cryogenic cooling of MgO:PPLN crystal to reduce the THz decay and by using of higher pump power.
In applications related to nonlinear phenomena the THz electrical field strength ETHz is important. From measured dependence of THz energy eTHz on optical beam size dy we can calculate the dependence of electrical field ETHz on dy for a given area of THz beam A. The results of calculations for THz beam area of A = 7 mm2 are presented in the inset of Fig. 4. The amplitude of multicycle THz pulse generation is only in order of a few kV/cm. The amplitude of the electrical field ETHz can be increased if focused THz beam is used. Generally, the presented method of THz generation is more useful for application cases, where the spectral energy density rather than the generated electric field is important.
In conclusion, the operating principle and the demonstration of narrowband THz generation with controllable bandwidth was presented. We achieved 17 GHz bandwidth which to our best knowledge is the smallest reported bandwidth in THz generation schemes by OR, and the bandwidth could easily and smoothly be tuned from 17 GHz to a few THz by varying the pump spot size on the PPLN crystal. Future improvements in conversion efficiency and tuning of generation bandwidth can be achieved by cooling the MgO:PPLN crystal to reduce the THz decay. Our method offers an efficient and easy way to the design and implementation of narrowband THz source with tunable bandwidth.
This work is partially supported by Grant-in-Aid A222460430, Core to Core, JSPS, and Industry-Academia Collaborative R&D, JST.
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