1. Introductions

Intense monocycle terahertz (THz) electric field generation techniques allow us to perform time-domain spectroscopy and are attractive for various applications such as material characterization, sensing, imaging, telecommunication, and high-frequency devices [1,2]. Recent advances in the ultrafast pulse techniques, which are based on Ti: sapphire laser, are decisive for these broadband THz technologies. This is because the bandwidth of monocycle THz pulse has been determined directly by the excitation pulse duration [3–5]. Here, we proposed a novel THz generation technique beyond the limitation of the input optical pulse width. This generation technique is based on non-resonant χ ⁽²⁾ processes. Figure 1 shows the schematic diagram of our THz wave generation technique. When intense THz electric field generated by optical rectification lies in EO crystal, emitted THz field gives phase modulation to the optical excitation pulse. Optical pulse shape can be easily modulated in EO crystal by intense THz pulse. These simultaneous optical rectification, phase modulation processes and cascaded χ ⁽²⁾ processes, are equivalent to effective χ ⁽³⁾ process. Therefore these processes can give rise to the narrowing of optical pulse during its propagation inside the crystal, which leads to further efficient and broadband THz wave generation beyond the limitation of the input optical pulse width.

 

Fig. 1. Schematic diagram of THz generation technique beyond limitation of the input optical pulse width. Simultaneous optical rectification (OR) and optical pulse phase modulation (PM) processes bring to the narrowing of both optical and THz pulses.

Download Full Size | PDF

In order to enhance such kind of processes, a large χ ⁽²⁾ value EO crystal, which corresponds to coefficient for optical rectification and phase modulation, is required. Several conventional quadric χ ⁽²⁾ materials, such as semiconductors, dielectric and organic crystals were well characterized [6–10]. LiNbO₃ is one of the most suitable EO crystals, because of its wide-gap and high-χ ⁽²⁾ value, it enable efficient THz wave generation without conversion saturation. Index mismatching between optical and THz frequency regions determines phase matching condition for optical rectification in non-collinear configuration [11]. Recently, Hebling et al. have proposed a new technique of phase matching using femtosecond laser pulse with tilted pulsefront [12–15] and succeeded in generating THz pulses with high conversion efficiency of 5×10^-4 [16]. They have also reported large spectral shift of the transmitted excitation beam, indicating an efficient frequency conversion. This red-shifted excitation beam permits further THz wave generation beyond Manley-Rowe limit (above quantum efficiency of 1) [17]. It has been numerically evaluated in conventional EO crystal [18]. In this paper we want to mention that spectral modulation of excitation pulse permits the pulse narrowing. This non-collinear configuration is equivalent to the pulse compression technique via coherent anti-stokes Raman scattering in LiNbO₃ [19]. According to our proposed scheme, by equating phonon in this compression process with intense phonon, we can show that the pulse compression is possible. To observe such kinds of processes clearly, we use Yb-doped fiber laser as a light source. One advantage of using Yb-doped fiber laser is that, its center wavelength (1 µm) is longer than that of conventional Ti: sapphire laser (0.8 µm), so it can suppress multi-photon absorption in LiNbO₃ even under intense excitation [20]. Another one is subpicosecond pulse duration. Pulse compression of 1 µm optical pulse in optical fiber is not simple due to the dispersion. We use the commercial fiber laser with the pulse duration of 0.60 ps (full-width half-maximum). It corresponds to smaller bandwidth than phonon frequency, which allows us to observe generation efficiency enhancement and bandwidth broadening of THz wave. In the previous reports of THz generation [12–16], initial excitation beam has pulse duration around 100 fs where corresponding spectral bandwidth of initial excitation beam is above optical phonon frequency of LiNbO₃. In spite of pulse narrowing via resonant stimulated Raman scattering [21], enhanced high-frequency THz components are strongly absorbed. In this report, we experimentally measure temporal profile of THz wave from high χ ⁽²⁾ EO crystal LiNbO₃ using subpicosecond pulse from Yb-doped fiber laser. Input power dependence of generated THz wave indicates broadband THz electric filed generation beyond the excitation pulse limitation.

2. Experimental setup

We used a Yb-doped fiber laser (IMRA America Inc. Co, D1000, 1040 nm, 100 kHz, output power of 1 W). Linear dispersion of laser pulse is compensated with a grating pair. The pulse duration of it, 0.60 ps, is carefully evaluated from self-correlation with pulse shape assumption of sech² function. The optical pulses split into two beams for THz generation and detection. We control wavefront and angular frequency dispersion of excitation beam with 1800/mm grating and two lenses, and focus on the stochiometric LiNbO₃ prism with 1.5 % Mg doping with spot size of 0.5 mm. One surface is cut with an angle of 62° with anti-reflection coating for near infrared beam. The generated THz pulses are guided with two off-axis parabolic mirrors and emitter’s image is transferred with half size to the surface of the (110)-oriented 1mm-thick CdTe crystal [9]. The sampling beam is focused on the same EO crystal as a sampling pulse, and the birefringence of the sampling pulse modulated by the electric field of THz pulses is measured using a quarter wave plate, Wolston prism, and two balanced Si detectors. For high-S/N measurement, we chop the pump beam at 1 kHz and modulated signal is extracted with lock-in amplifier. Absolute value of electric field can be easily calibrated from induced phase modulation θ with the formula of sin θ=2π n _opt ³ r ₄₁ t’E _THz L/λ [9], where n _opt=2.6, r ₄₁=6.8 pm/V [4], and t’=2/(n _THz ^-1) are the optical index at λ=1.04 µm, EO coefficient, THz Fresnel coefficient in CdTe, respectively. By varying the time delay between a THz pulse and a sampling pulse, the electric field amplitude of THz pulses can be detected as a function of time.

3. Experiments

The temporal evolutions of generated THz electric fields at different input laser powers are shown as gray curves in Fig. 2(a). Time interval between maximum and minimum signal at 8.5 µJ input power, is 0.66 ps. This time interval is just comparable with the sampling pulse duration 0.60 ps, implies that temporal profile becomes dull. Therefore we obtain the true profile of electric field by the deconvolution of sampling pulse. We obtained the Fourier transformed spectrum of observed profile, by dividing Fourier-transformed spectrum of the envelop function with 0.6 ps duration, and we show the inverse-Fourier-transformed profile as colored curves. Maximum electric field E_max=8.2 KV/cm corresponds to E²_max/2Z₀=90 KW/cm² with the vacuum impedance of Z ₀=120πΩ. We evaluated the power density using this relation (1/Z₀)∫E(t)² dt=67 nJ/cm² from the temporal profile. One can see that the temporal profile of electric field is dramatically changed at the maximum excitation powers. Figure 2(b) shows the time interval between maximum and minimum signal at different laser power. Since shape of THz electric field should be differential envelop shape of excitation pulse [9], this interval shows the excitation pulse duration. Time interval is 1.0 ps at low input powers, which is comparable to the envelop width of excitation electric field, 0.84 ps. However, it is decreased extensively, 0.37 ps at the maximum input power. This indicates that the narrowing of excitation pulse take’s place during THz wave generation. Figure 2(c) shows the excitation power dependence of the maximum THz electric field. Since THz electric field should be proportional to input laser power in optical rectification process, plots at low input laser power lies along slope of 1 (denoted by dashed line). Above input power of 1 µJ, however, superlinear behavior is observed. Surprisingly, output electric field at the maximum input power is one-order enhanced compared with expected one. This acceleration of generation efficiency is reasonable if we are considering the narrowing of the pulse width of excitation pulses. Since THz wave shape is equivalent to the differential envelop function of optical beam [3], optical pulse with one-third pulse duration generates THz electric field with nine times amplitude.

Let us consider these phenomena in frequency domain. THz wave ω _THz is generated by optical rectification, and optical beam ω is also modulated via both differential frequency ω - ω _THz and sum frequency ω + ω _THz generations. Consequently, the spectral bandwidth of optical pulse gets broadened, which allows the generation of higher frequency THz components. Figure 3(a) shows the power spectra of emitted THz wave at different excitation densities. Gray curves show the power spectra as shown in Fig 1(a) and we obtain calibrated spectra (bold curves) from these by dividing Frourier transformation spectrum of 0.6 ps pulse. Weighted center frequency of the power spectrum is 0.42 THz at low input power, but it extensively shifts to 1.25 THz at the maximum input power. Our experimental results imply that THz components at high frequency are strongly enhanced. Figure 3 (b) shows the optical spectra of transmitted excitation pulses from LiNbO₃. We collect whole transmitted excitation beam into 30 cm spectrometer and detect the spectra with cooled InGaAs linear image sensor. Weighted center wavelength of excitation beam is 288.6 THz at low excitation power. However, the spectral shifts towards longer wavelength proceeds above 2 µJ, and center wavelength lies at 288.2 THz at the maximum power of 8.5µJ, which corresponds to a shift of 0.4 THz frequency. These spectral changes are consistent with temporal behaviors shown in Figs. 2(b) and (c).

 

Fig. 2. (a) Temporal profile of emitted THz radiation at different excitation powers 0.95, 3.7, and 8.5 µJ. We evaluate net profile (colored curves) with the assumption of 0.60 ps sampling pulse duration from EO signal (gray curves). (b) Input power dependence of interval between maximum and minimum electric field times. c Input power dependence of the maximum electric field calibrated form EO signal. Inset shows the scheme of experimental setup.

Download Full Size | PDF

Assuming that such a strong modulation of excitation beam is related to the THz wave generation, photon number of generated THz pulse should approach that of excitation pulse, i.e. quantum efficiency approaching to one. One can consider that conversion efficiency is rather saturated due to inverse process, according to well-known Manley-Rowe relation [4]. However, pulse narrowing via cascaded processes opens a new channel for high-frequency THz components generation in sequence, and further frequency conversion is permitted. We evaluate the conversion efficiency from Fig. 3(b), assuming that whole energy shift of excitation beam corresponds to convert into THz wave. Evaluated conversion efficiency is 1.4×10^-3 at maximum input power of 8.5 µJ and corresponding quantum efficiency is very closed to the ratio of weighted center frequencies 0.4 THz/1.25 THz=0.3, Note here that the experimentally evaluated output power is 0.67 nJ with the assumption of 1×1 mm² spot size, and conversion efficiency is 7.8×10^-5 (corresponding quantum efficiency is 0.017), one-order different from that evaluated from spectral shift. This discrepancy is probably due to Fresnel loss, absorption in LiNbO3 above 3 THz, steep diffraction out of the emitter, and frequency components are undetectable above 2 THz with our EO sampling technique.

 

Fig. 3. (a) Power spectra of THz radiation from LiNbO₃ at different excitation powers. (b) Optical spectra of transmitted excitation pulses through LiNbO₃ at corresponding excitation densities. These spectra are normalized by their area.

Download Full Size | PDF

We also measured spatial distribution of THz wave on the surface of LiNbO₃ crystal. We controlled the position of emitter’s image on the detector by moving one parabolic mirror horizontally. Figure 4 shows the power density (upper) and interval of maximum and minimum times (lower) of THz electric field emitted from different positions of LiNbO₃ surface. Power density is evaluated from the time integration of measured E ², and normalized by the square of input power. At low input power, spatial distribution of the power density should be independent of it. We set the origin at peak power density position at 0.8 µJ input power. At this position THz wave is the most efficiently generated via optical rectification, where one edge of excitation beam approaches to the surface of prism. By increasing input power, emitted THz electric field is enhanced at the location of d=0.6 mm. This shift implies that long propagation of excitation beam with intense THz electric field brings in a strong phase modulation of excitation pulse. Coincidently, spatial modulation of excitation pulse may occur and increases the excitation power density and causes the enhancement in THz wave generation efficiency. Similar results have been reported in LiNbO₃ using Ti: sapphire laser [22]. However, Figure 4 shows the that enhancement of THz wave generation coincides with the time interval of narrowing of THz profile. Considering that the envelop shape of excitation pulse determines the THz pulse profile, this time interval narrowing directly shows the optical pulse narrowing caused by cascaded χ ⁽²⁾ process. Both modulations bring in the enhancement of THz wave generation efficiency.

 

Fig. 4. The position dependence of THz radiation on the surface of LiNbO3. Upper shows the output power densities of THz radiation, which is normalized by the square of input power. Lower shows corresponding time intervals between maximum and minimum electric field locations. We set the original where power density is the maximum at 0.8 µJ. We measured THz electric fields as shown in Figs. 1 and 2(a) at the position of d=0.6 mm.

Download Full Size | PDF

Large spectral broadening of THz pulse clearly shows the narrowing of excitation pulse width in Fig. 3(a). Nevertheless, spectral modulation of excitation beam is not so large in Fig. 3(b). This is due to that the excitation laser pulse has higher-order dispersion, which cannot be compensated with a grating pair. Bandwidth of spectral limited pulse with 0.60 ps duration is 0.53 THz in spite of spectral width 1.8 THz of our laser pulse. Of course the profile of THz wave is simply determined by optical pulse duration, and is independent of the pulse dispersion [3]. If this higher order dispersion is compensated via cascaded χ ⁽²⁾ process, small spectral modulation with envelop shape of excitation pulse becomes narrow. This mechanism is not clear now. Looking back on the reports of pulse compression via second-harmonic generation process [23], we believe that pulse compression via cascaded χ ⁽²⁾ process should occurs with broadband THz wave generation even using spectral limited excitation pulse.

4. Summary

We have experimentally demonstrated broadband THz wave generation beyond the excitation pulse limitation with extensive phase modulation via cascaded χ ⁽²⁾ process. Our result indicates that subpicosecond excitation pulse, which seems rather unfavorable in THz technologies, suffices monocycle THz wave generation with the bandwidth above several THz frequencies. Yb-doped fiber laser we used here is attractive in the viewpoint of compact, high-power and high-efficiency excitation light source. Releasing pulse-width limitation of laser enables compact and convenient light souse of intense THz pulse. This opens novel THz sensing based on nonlinear spectroscopy, THz EO devices, and real-time large-aperture imaging.