We demonstrate efficient generation of THz pulses by optical rectification of 1.03 um wavelength laser pulses in LiNbO3 using tilted pulse front excitation for velocity matching between the optical and THz fields. Pulse energies of 100 nJ with a spectral bandwidth of up to 2.5 THz were obtained at a pump energy of 400 uJ and 300 fs pulse duration. This conversion efficiency of 2.5×10-4 was an order of magnitude higher than that obtained with collinear optical recitification in GaP, and far higher still than that measured using ZnTe in an optimized geometry. Using a simple model we demonstrate that two- and three-photon absorption strongly limit the THz generation efficiency at high pump fluences in ZnTe and GaP respectively.
©2007 Optical Society of America
Since its inception, terahertz time-domain spectroscopy (THz-TDS) has become a valuable tool in far-infrared-spectroscopy . Many different techniques have been developed to generate the single-cycle picosecond pulses used as signal source in THz-TDS. Commonly used are biased semiconductor antennas in combination with Ti:sapphire laser oscillators or optical rectification in ZnTe driven by a Ti:sapphire amplified laser system. Typically the pulse energies obtained by semiconductor antennas are in the range of a few fJ . In order to open up new applications in the terahertz regime such as nonlinear spectroscopy and to facilitate applications such as THz imaging and remote sensing in which most of the THz output that is generated does not reach the detector, higher pulse energies and higher average power levels - usually generated by optical rectification - are needed. The efficiency of THz generation using optical rectification is determined by several factors including the effective nonlinear constant (d eff), the length over which velocity matching between THz and optical propagation can be maintained and the THz absorption in the material.
The usual collinear velocity matching geometry precludes high-dielectric nonlinear optical crystals such as lithium niobate and other ferroelectrics, since THz waves, which take the form of phonon-polariton waves in these materials, have phase velocities far too slow to match optical group velocities. Thus the high nonlinear constants of some of these materials have not been fully exploited. Various strategies have been developed for active and passive generation of spatiotemporally shaped optical fields with components that move across a high-dielectric nonlinear crystal at the THz wave velocity [3–5]. The simplest and most effective method demonstrated to date employs a grating and lens to generate a continuous, tilted pulse front with the tilt angle adjusted for THz velocity matching [6–8]. THz pulses with energies more than 10 µJ have been demonstrated  using amplified Ti:sapphire laser systems and LiNbO3 as the nonlinear material.
In recent years, femtosecond fiber laser systems have established themselves as a more compact, efficient and user-friendly alternative to solid-state Ti:sapphire laser systems. THz generation using 1.55 µm telecommunication wavelength fiber lasers and InGaAs photoconductive switches has been demonstrated [10, 11]. For fiber lasers with a longer wavelength of 2 µm orientation-patterned GaAs has been used as an efficient THz conversion material . Another promising class of fiber lasers are Ytterbium fiber based systems at 1035 nm wavelength. Femtosecond oscillators with pulse durations in the 200 fs range have been available for some time. Recently, systems using chirped pulse amplification have become available commercially. For THz generation at a wavelength of 1035 nm, GaP is the most commonly used material for optical rectification because it allows collinear velocity matching  and it avoids direct 2-photon absorption . Using a fiber laser with 10 W average output power at 120 MHz repetition rate, average THz powers of 6.5µW (54 fJ pulse energy) have been achieved with GaP as the nonlinear material .
In this article we demonstrate efficient THz generation via optical rectification in LiNbO3 at 1035 nm using an amplified Yb bulk solid state laser with repetition rates of 1–100 kHz at varying pump levels. We compare the achieved pulse energies and spectra with those from GaP and ZnTe and we evaluate the influence of two-photon and three-photon absorption in these materials on the saturation of THz generation. We show that three-photon absorption is a limiting factor in GaP.
2. Experimental setup
Our laser system is a solid state Yb-based regenerative amplified laser system with adjustable repetition rates of 1–100 kHz and a center wavelength of 1035 nm. The average laser output power was varied from20 to 400 mWat a pulse length (FWHM) of 300 fsmeasured by intensity autocorrelation.
The THz generation efficiencies of three different materials were compared. A 2 mm thick crystal of <110> cut gallium phosphide was used in collinear geometry for optical rectification, taking advantage of the intrinsic velocity matching of the material for THz and optical frequencies at this pump wavelength. The laser polarization was parallel to the  axis of the GaP crystal. The maximum THz pulse energy at 400 µJ pump pulse energy was achieved when the pump laser spot size on the GaP crystal was 5 mm in diameter. Tighter focusing resulted in reduced THz output.
The second material studied was LiNbO3 in combination with the tilted pulse front excitation scheme . For this experiment, the intensity front of the laser pulses was tilted by a 1800 lines/mm grating and imaged with a 60 mm focal length lens onto the input surface of the 0.6% MgO doped stoichiometric LiNbO3 (sLN) crystal (Fig. 1). A λ/2 plate was used to rotate the polarization of the pump light after the grating from horizontal to vertical polarization, parallel to the optic axis of the sLN crystal. The pump spot on the crystal surface was 2 mm in the horizontal dimension and 1 mm in the vertical.
The third material we used for this study was ZnTe. A 2 mm thick prism of ZnTe with the front surface cut along the <110> plane and the angled surface cut at 26 degrees was pumped by a tilted pulse front generated by a 830 lines per millimeter grating and a f=60 mm lens, in a similar setup to that described above. The polarization was parallel to the  axis of the ZnTe. The optimum spot size on the crystal at 400 µJ pump energy was about 6 mm in diameter.
In all cases the energy of the generated THz pulses was measured using a liquid He cooled bolometer (Infrared Labs). The bolometer was placed close enough to the generation crystals to avoid the possible effect of the change in divergence of the THz beams with varying excitation spot sizes on the detection efficiency. A wiregrid polarizer was used to attenuate the THz pulses when the THz energy exceeded the saturation limit of the bolometer. Additionally we used a LiTaO3-based pyroelectric detector (Microtech Instruments) calibrated for frequencies between 0.2 and 3 THz to obtain absolute values for the THz pulse energy at high pump fluences. An optical chopper was used in this case to modulate the THz output at a rate of 20 Hz.
3. Experimental results
3.1. Pump energy dependence of the THz output
Figure 2a shows the THz pulse energy as a function of the optical pulse energy for the three different electrooptic crystals. All these measurements were carried out at 1 kHz repetition rate using the liquid He-cooled bolometer for detection. For LiNbO3 with tilted pulse front excitation, THz pulse energies up to 100 nJ were measured using the calibrated pyroelectric detector and referenced against the bolometer voltage to obtain absolute energy values at low THz energies.
For all materials our results show a quadratic dependence on the pump energy at low pumping levels as indicated by the lines in Fig. 2a. At intermediate pump levels the dependence becomes linear in ZnTe and at high pump levels both ZnTe and GaP show strong saturation. The saturation can be attributed to two- and three-photon absorption in the respective materials. In contrast, the behavior in LiNbO3 is still quadratic at intermediate pump levels and becomes linear at high pump levels without showing saturation. Due to the large bandgap of 3.8 eV at room temperature  neither two nor three photon absorption is present in this material.
Figure 2b shows the average THz pulse energy from LiNbO3 pumped at 10–100 kHz repetition rates with constant average optical power. The average pulse energy was measured using a bolometer and a lock-in amplifier with modulation rate of 300 Hz. The result is in agreement with a quadratic fit. We found no indication of an adverse effect due to heating of the sample at higher repetition rates. Further scaling of the average pump power levels by increasing the repetition rates to MHz levels by using amplified fiber lasers should be possible.
3.2. THz spectrum and conversion efficiency
The temporal shape of the THz pulse generated with the LiNbO3 crystal was measured with electro-optic sampling using a 2 mm thick gallium phosphide crystal. Our data show the usual quasi-single cycle THz pulse form with a frequency spectrum containing spectral components up to 2.5 THz (Figure 3).
The spectrum of the pump light after the crystal was measured by an Ocean Optics USB4000 fiber coupled spectrometer with a resolution of 1.0 nm FWHM (Fig. 4). After the nonlinear interaction within the LiNbO3 crystal, the pump light spectrum shows a distinct red shift at high THz output levels. This effect was only observed when the pump light was polarized for optimum THz generation. This red shift is a consequence of the difference frequency generation process in the lithium niobate . For every THz photon with energy h̄ω T generated, one pump photon will lose the same amount of energy and its frequency will be slightly red-shifted. Because a pump photon can undergo this process multiple times, a photon efficiency of more than 100 percent is possible.
From the experimentally determined red shift, it is possible to estimate the THz conversion efficiency . We calculate the total shift Δλ̄ in the spectrum by calculating the difference of the first moments λ̄ of the spectra S(λ) 
We obtain λ̄=1036.7 nm for the red shifted spectrum (solid line in Fig. 4) and λ̄=1033.7 for the spectrum with crossed polarization (no THz generation) of the pump pulse resulting in a difference Δλ̄ of 3.0 nm. Similarly, we calculate the first spectral moment of the THz pulse from Fig. 3, resulting in a value of 0.92 THz. At 100 % photon efficiency, this corresponds to a wavelength shift in the optical spectrum of
Comparing this to the observed optical wavelength shift of 3.0 nm, we calculate a photon efficency of η=90%. From this number, the generated THz pulse energy can be estimated by calculating the number of THz photons N THz photon and multiplying by the THz photon energy. We obtain a value of
for ν THz=0.92 THz, ν vis=290 THz and E vis pulse=400µJ. This is a factor of 11 higher than the observed THz pulse energy measured with the pyroelectric detector. This difference can be explained by THz absorption in the generation crystal and reflection loss at the output interface of the crystal. The THz intensity within the crystal is attenuated to a level of 20 percent after a propagation distance of about 1 mm (α≈15cm-1). Further, the reflection loss at the output surface (n LN≈5) of the generation crystal is 44 percent resulting in a total output efficiency of roughly 10 percent, in agreement with our experimental findings.
At low pump pulse energies, the THz output from all three materials showed a quadratic dependence on the pump intensity, as expected for a second order difference frequency generation process. At intermediate pump energies, the dependence became linear and at high pump energies saturation of the THz generation was observed both in ZnTe and GaP. The observed saturation is similar to the results for ZnTe reported by Löffler et al .
This effect can be explained by multi-photon absorption processes of the pump beam in the generation medium. A generalized Beer absorption law taking into account multi-photon absorption can be written as:
where I(z) is the pump pulse intensity as a function of the position z in the crystal and α,β,γ,δ are the absorption coefficients for the one- and multi-photon processes in ascending order.
The THz field generated in the crystal is proportional to the pump intensity I(z) and the nonlinear susceptibility. We assume that each absorption process creates a free carrier, which in turn absorbs the THz radiation inside the generation crystal. Taking into account these processes, the change of the THz electric field strength along the propagation axis z is given by
Here d eff is the effective nonlinear constant and a THz is a proportionality constant for the THz absorption by the free carriers. The THz absorption is assumed to be proportional to the carrier concentration.
Using this model for ZnTe, it was possible to obtain a convincing fit by taking into account only two-photon absorption and the published value for the two-photon absorption coefficient β=4.2 cm/GW . The value of the THz absorption factor a THz was 2×10-22 cm2.
In the case of GaP, it was necessary to consider 3-photon absorption in Equation (5). Figure 5a shows the saturation behavior for GaP and a fit using the value of β=0.05 cm/GW and γ=0.042 cm3/GW2 given for the 3-photon process in . The value for the indirect 2-photon absorption β differs substantially from the value of 1.7 cm/GWpublished in the same reference. However, theory predicts only a value of 0.2 cm/GW for the indirect 2-photon process  which is closer to our fit parameter. For the fit to the GaP data it was necessary to use a four times larger value for the free carrier absorption coefficient a THz in comparison to ZnTe.
Because lithium niobate has a bandgap of 3.8 eV at room temperature, at the pump wavelength of 1.03 micrometers only 4-photon absorption should be possible in a perfectly pure material . Figure 5b shows a fit to our experimental data using the above model considering 4-photon absorption with δ=10-7cm5/GW3 and a THz=2×10-21cm2. The fits obtained with this model are in good qualitative agreement with our data but the fitting procedure is only sensitive to the product of δ and a THz. Thus an independent measurement of δ by nonlinear transmission experiments is needed for the determination of the contribution of free carrier absorption in optical rectification.
We have demonstrated 2.5×10-4 optical-to-THz conversion efficiency in LiNbO3 using a Yb-based amplified laser system at 1035 nm wavelength with a tilted pulse front for velocity matching in the crystal. The observed spectral shift of the pump pulse by the difference frequency generation process is an indicator of even higher conversion efficiency achieved by the tilted pulse front technique within the crystal. Absorption and reflection loss at the output face account for the discrepancy between the observed internal and external THz generation efficiency.
Tilted pulse front excitation using LiNbO3 produces at least one order of magnitude higher THz pulse energies than collinear optical rectification in GaP. Strong saturation of the THz generation in ZnTe and in GaP was observed at moderate to high pump intensities. This can be explained by two- and three-photon absorption in these materials using a simple model. In GaP the limiting process seems to be a combination of indirect two photon and direct three-photon absorption. Due to the large band gap of 3.8 eV, the saturation threshold in LiNbO3 is much higher. Generally, saturation through multi-photon processes limits the pump pulse intensities when using optical rectification as a source.
The combination of the tilted pulse front technique in LiNbO3 with compact and robust fiber laser sources with µJ pulse energies and high repetition rates is very promising for the development of high average power THz sources. This approach may enable new applications of THz spectroscopy in imaging and remote sensing.
This work is supported in part by ONR grant no. N00014-06-1-0463.
References and links
1. Ch. Fattinger and D. Grischkowsky, “Terahertz Beams,” Appl. Phys. Lett. 54, 490–492 (1989). [CrossRef]
2. M. Herrmann, M. Tanic, and K. Sakai, “Generation and detection of terahertz pulsed radiation with photoconductive antennas and its application to imaging,” Meas. Sci. Technol 13, 1739–1745 (2002). [CrossRef]
3. R. M. Koehl and K. A. Nelson, “Terahertz polaritonics: automated spatiotemporal control over propagating lattice waves,” Chem. Phys. 267, 151–159 (2001). [CrossRef]
5. T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317–350 (2007). [CrossRef]
6. J. Hebling, G. Almási, I. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large area THz-pulse generation,” Opt. Express 10, 1161–1166 (2002). [PubMed]
7. J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004). [CrossRef]
8. B. Bartal, I. Z. Kozma, A.G. Stepanov, G. Almási, J. Kuhl, E. Riedle, and J. Hebling, “Toward generation of mJ range sub-ps THz pulses by optical rectification,” App. Phys. B 86, 419–423 (2007). [CrossRef]
9. K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 mJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007). [CrossRef]
10. M. Suzuki and M. Tonouchi, “Fe-implanted InGaAs photoconductive terahertz detectors triggered by 1.56 m femtosecond optical pulses,” Appl. Phys. Lett. 86, 163504 (2005). [CrossRef]
11. J. Mangeney, L. Joulaud, P. Crozat, H. Bernas, K. Blary, and J. F. Lampin, “Terahertz radiation from heavy-ion-irradiated In0.53Ga0.47As photoconductive antenna excited at 1.55 mm,” Appl. Phys. Lett. 87, 193510 (2005). [CrossRef]
12. G. Imeshev, M. E. Fermann, K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, D. Bliss, and C. Lynch, “High-power source of THz radiation based on orientation-patterned GaAs pumped by a fiber laser,” Opt. Express 14, 4439–4444 (2006). [CrossRef] [PubMed]
13. Q. Wu and X.-C. Zhang, “7 terahertz broadband GaP electro-optic sensor,” Appl. Phys. Lett. 70, 1784–1786 (1997). [CrossRef]
14. Y. J. Ding, “Efficient generation of high-power quasi-single-cycle terahertz pulses from a single infrared beam in a second-order nonlinear medium,” Opt. Lett. 29, 2650–2652 (2004). [CrossRef] [PubMed]
15. G. Chang, C. J. Divin, C-H. Liu, S. L. Williamson, A. Galvanauskas, and T. B. Norris, “Power scalable compact THz system based on an ultrafast Yb-doped fiber amplifier,” Opt. Express 14, 7909–7913 (2006). [CrossRef] [PubMed]
16. D. Redfield and W. J. Burke, “Optical absorption edge of LiNbO3,” J. Appl. Phys. 45, 4566–4571 (1974). [CrossRef]
17. Y. R. Shen, The principles of nonlinear optics (Wiley2002).
18. A. G. Stepanov, A. A. Melnikov, V. O. Kompanets, and S. V. Chekalin, “Spectral modification of femtosecond laser pulses in the process of highly efficient generation of terahertz radiation via optical rectification,” JETP Lett 85, 227–230 (2007). [CrossRef]
20. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, J. Opt. Soc. Am. B, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B9, 405–414 (1992). [CrossRef]
21. V. Nathan and A. H. Guenther, “Review Of Multiphoton Absorption in Crystalline Solids,” J. Opt. Soc. Am. B 2, 294–316 (1985). [CrossRef]
22. J. H. Yee and H. H. M. Chau, Opt. Commun., “Two-photon indirect transition in GaP crystal,” Opt. Commun.10, 56–58 (1974). [CrossRef]
23. S. R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996). [CrossRef]