High-efficiency THz generation in quasi-phase matched (QPM) optically contacted GaAs (OC-GaAs) with near-Brewster angle pumping is studied numerically. The effective nonlinear coefficients deff for different incident angles and polarization directions are investigated. Compared with the normal incidence case, reflection loss of the pump energy at OC-GaAs interfaces can be reduced by propagating the pump at a near-Brewster angle (66.92°). The effect of the air-gap spacings between adjacent OC-GaAs layers to the number of optimal QPM periods and the efficiency of THz generation are calculated. In our study, the number of optimal QPM periods of OC-GaAs is increased significantly from 12 in the normal incidence configuration to 25 in the near-Brewster angle pumped configuration, while the efficiency of THz generation is enhanced by more than 16 times.
© 2007 Optical Society of America
Efficient generation of THz wave is very important to applications in many fields, such as medical imaging, noninvasive material and structure detections, and communications [1, 2, 3]. Taking the advantages of its large nonlinear coefficient and low absorption in the THz range, THz generation in quasi-phase matched (QPM) GaAs by parametric down-conversion has been extensively studied . Recently, THz wave generated in periodically-inverted diffusion-bonded GaAs stacks has been demonstrated . To bond the GaAs stacks, processes with uniform pressure up to 107 N/m 2 and temperature up to 1000°C are required . On the other hand, THz wave generation based on orientation-patterned GaAs crystal has also been reported , in which the crystal is grown by the combination of hydride vapor phase epitaxy and molecular beam epitaxy. Although this all-epitaxial growth technique can have precise control of the QPM period with a submicron resolution, it is hard to fabricate samples with relatively large clear apertures and sufficient thicknesses.
To have a large aperture QPM GaAs without the aforementioned complicated fabrication process, optically contacted GaAs (OC-GaAs) fabricated by simply stacking up 1-mm-thick, 2”-diameter (110) GaAs wafers in a clean room has been demonstrated . By pumping along the  direction of GaAs to utilize its maximum deff, THz wave generation has been observed. Although the optically contacted wafers can be stacked very close to each other that the air-gap between adjacent layers is smaller than the wavelength of the pump (λp), reflection losses from the surfaces and the interfaces limits the number of possible QPM periods. As the result, optically clear interfaces are usually difficult to obtain when the number of QPM periods exceeds 5 . Therefore, in this paper, we propose a different pumping configuration for THz generation where a TM-polarized wave is pumped near the Brewster angle of the OC-GaAs to reduce the reflection loss  both from the surfaces and interfaces. Compared with the normal incidence configuration used conventionally, the number of optimal QPM periods of the near-Brewster angle pumped configuration can be increased and a large overall enhancement in the conversion efficiency can be achieved.
Figure 1 shows the propagation and polarization configurations of a near-Brewster angle pumped QPM OC-GaAs. In our study, the pump and signal wavelengthes at λp = 3.448 μm and λs = 3.471 μm are considered because the two wavelengths avoid two-photon absorption in GaAs and are the idler wavelengths of a convenient 1064 nm pumped optical parametric amplification seeded by telecom diodes . The absorption coefficients of the pump and the THz waves at the corresponding wavelengths are αp = 0.01 cm -1 and αTHz = 0.2 cm-1 , respectively. With a QPM period of 2 mm (1-mm-thick wafer), THz wave at λTHz = 515.7 μm can be produced. The refraction indexes of the GaAs at the corresponding pump and THz wavelengths are np = 3.335 and nThz = 3.6, respectively. To account for the transmission loss between each layer, a normalized air-gap spacing D/λp between each wafer is considered.
In conventional configurations, a pump wave is incident normally to a QPM GaAs along the  axis and polarized in the [11̅1] direction to fully utilize its largest nonlinear coefficient [12, 13]. However, significant reflection losses at the surfaces and interfaces limit the possible number of QPM periods and THz conversion efficiency. Therefore, as can be seen in Fig. 1(a), a TM-polarized pump incident on the QPM OC-GaAs with an angle θi tilted from the  axis is utilized in order to minimize the reflection losses from the surfaces. The pump wave inside the GaAs layer and the generated THz wave transmitted have refraction angles of θr and θTHz, respectively. For a pump wave inside the GaAs with an angle θr, it can rotate arbitrarily along the  axis within the cone as shown in Fig. 1(b), where the rotation angle of its projection on the (110) plane from the [11̅0] axis is denoted as θro.
For a pump wave incident at θi with a polarization angle θro, the projections of the E field at the x, y, and z axes are, according to Fig. 1(b),
where . From the nonlinear susceptibility χ (2) of GaAs, the maximum effective nonlinear coefficients deff of a TM-polarized pump incident at different θi optimized with rotation angles θro are calculated and shown in Fig. 2(a), where the maximum deff is normalized to the nonlinear coefficient d 14 of GaAs. The optimal rotation angle θro is determined by rotating the pump along the cone described in Fig. 1(b) to obtained the largest deff . As can be seen, the deff decreases as θi increases, an obvious reason for adopting normal incident pump as in the conventional configuration. However, although the deff is slightly decreased when compared with the normal incidence case, the TM-polarized pump incident at an tilted angle experiences much less reflection loss from the interfaces and hence is expected to contribute to higher overall conversion efficiency when a multiple-layer QPM OC-GaAs structure is considered.
Figure 2(b) shows the transmission coefficients of the TM-polarized pump wave of the GaAs calculated with different incident angles . As can be seen, total transmission occurs at the Brewster angle of θi = 73.5°, while only 71.25 % can be transmitted for normal incidence. In spite of the higher transmission for the pump wave, total internal reflection of the THz wave (dashed curve) happens when θi > 66.92° due to the higher refractive index at the THz wavelength. As the consequence, to minimize the reflection loss of the pump while can still avoid the total internal reflection of the THz wave generated, pumping at a near-Brewster angle θi = 66.92° before the total internal reflection occurred is preferred. At θi = 66.92°, a maximum deff of 0.9014d 14 with θro = 33.58° and a transmittance above 97.8% can be reached. Note that when the incident angle is close to the Brewster angle, coupling the THz wave out from the OC-GaAs can become difficult due to the diffraction of the THz wave. This can be overcome by attaching a GaAs wedge or/and a silicon hemisphere ball-lens (n=3.4) to the last GaAs plate for better out-coupling.
In an OC-GaAs sample, the spacing of the air-gap between each layer affects the transmittance of the pump wave that can propagate into the successive wafers of the QPM structure. Figure 3 shows the transmittances of the pump wave at the interface for the normal (dashed curve) and near-Brewster angle (θi = 66.92°)(solid curve) incidences with different air-gap spacings D/λp, respectively. Apparently, while the transmittance of the pump incident at the near-Brewster angle remains at a high transmission level, the transmittance of the normal incidence case rapidly reduces as D/λp increases. It drops to its minimum of 0.3 when the spacing is equal to a quarter wavelength of the pump (D/λp = 0.25) [9, 15]. The significant reflection loss of the pump in the normal incidence case can hamper the overall efficiency of THz generation.
By solving the following coupled equations of parametric down-conversion  for each successive layer of QPM OC-GaAs with aforementioned considerations,
efficiencies of the TE- and TM-polarized THz generations with near-Brewster angle pumped QPM OC-GaAs for different numbers of QPM periods under the condition of different air-gap spacings are calculated and shown in Figs. 4(a) and (b), respectively. Here, E is the electric field, α is the absorption coefficient, κ is the coupling coefficient, Δk is the phase mismatch, and the subscripts s, p, and THz denote the signal, pump, and THz waves. The power of the THz wave generated is normalized to the power of the pump wave, where pulse energies of 10 μJ and 5 μJ for the pump and the signal waves with 0.5 ns pulsewidth are considered. As can be found, the conversion efficiency of the TE-polarized THz wave is much lower than the TM-polarized one. This is because that, at θi = 66.92° with θro = 33.58°, the maximum deff occurs at a polarization direction almost perpendicular to the TE polarization. Therefore, the THz conversion takes place solely in the direction of the TM polarization. For D/λp = 0.025 (D = 85 nm with λp = 3.4 μm), the optimal number of QMP periods for maximum TM-polarized THz conversion is about 25, yielding a conversion efficiency of 4.02×10-3.
To compare with the benchmark of the normal incidence case, Fig. 5 shows the overall (TE-and TM-polarized THz waves combined) efficiency of THz wave generation. As can be seen in Fig. 5(a), in the extreme case of no air-gap between the interfaces (D = 0, reflections only occur at the input and output surfaces but not between each layer), the efficiency of the normal incidence case (dashed blue curve) outperforms the near-Brewster angle pumped case (solid blue curve) marginally for QPM periods less than 17 contributing from the higher deff at θi = 0°. On the contrary, due to the minimized reflection losses on the input and output surfaces, the near-Brewster angle pumped case does not reaches its maximum of 4.07×10-3 until a QPM periods of 25. As the result, with higher pump power reaching into the QPM OC-GaAs, the efficiency of the near-Brewster angle pumped case eventually surpasses the normal incidence case providing an optimized number of QPM periods is chosen.
Nonetheless, air-gaps in the interfaces inevitably exist. For the case of D/λp = 0.025, the efficiencies of the near-Brewster angle pumped case and the normal incidence case are shown in Fig. 5(a) with the solid cyan and dashed cyan curves, respectively. Figure 5(b) zooms the low-efficiency region of Fig. 5(a) to show the details of the normal incidence case. As the air-gap is taken into account, which introduces reflection loss of the pump wave before entering the successive layer, the efficiency of the normal incidence case drops severely compared to the near-Brewster angle pump case. Suffering from the great loss in reflection, the normal incidence case reaches its maximum efficiency of only 0.251×10-3 at a QPM periods of 12. At the same time, by simply changing the incident angle of the pump to the near-Brewster angle θi = 66.92°, a gain of 6 times can be obtained with the same number of QPM periods. With the possibility to increase the QPM periods to 25, a gain of more than 16 times for the near-Brewster angle case can eventually be reached.
In conclusion, the advantages of pumping a QPM OC-GaAs sample with the TM-polarized pump incident at a near-Brewster angle is discussed and studied. Although the effective nonlinear coefficient may be slightly lower compared with the normal incidence case, significant reduction in the reflection losses on both the surfaces and interfaces benefits not only in the possibility of increasing the QPM periods, but also in the overall conversion efficiency. Under the near-Brewster angle pumping configuration studied, the QPM OC-GaAs can be a promising device for efficient THz wave generation that it has the advantages of high conversion efficiency, large aperture, and better yet, easy process in fabrication.
The authors are grateful to S. Y. Shaw for helpful discussions. This work was supported in part by the National Science Council of Taiwan under contract NSC 95-2112-M-007-011 and National Tsing Hua University under project code 96N2534E1.
References and links
1. P. H. Siegel, ”Terahertz technology in biology and medicine,” IEEE T. Microw. Theory 52, 2438–2447 (2004). [CrossRef]
2. H. Feng, F. John, G. Dale, B. Robert, and Z. David, ”Noninvasive study of explosive materials by time domain spectroscopy and FTIR,” in AIP conference proceedings 760, 578–585 (2005). [CrossRef]
3. T. Kleine-Ostmann, K. Pierz, G. Hein, P. Dawson, and M. Koch, ”Audio signal transmission over THz communication channel using semiconductor modulator,” Electron. Lett. 40, 124–126 (2004). [CrossRef]
4. 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]
5. Y. S. Lee, W. C. Hurlbut, K. L. Vodopyanov, M. M. Fejer, and V. G. Kozlov, ”Coherent detection of multi-cycle terahertz pulses generated in periodically inverted GaAs structures,” Proc. SPIE 6455, 64550G (2007). [CrossRef]
6. D. Zheng, ”Tunable infrared generation with diffusion-bonded-stacked gallium arsenide,” PhD thesis, Stanford University GL8900 (1998).
7. K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y. S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, ”Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006). [CrossRef]
8. Y. S. Lee, W. C. Hurlbut, K. L. Vodopyanov, M. M. Fejer, and V. G. Kozlov, ”Generation of multicycle terahertz pulses via optical rectification in periodically inverted GaAs structures,” Appl. Phys. Lett. 89, 181104 (2006). [CrossRef]
9. A. Szilagyi, A. Hordvik, and H. Schlossberg, ”A quasi-phase-matching technique for efficient optical mixing and frequency doubling,” J. of Appl. Phys. 47, 2025–2032 (1976). [CrossRef]
10. A. C. Chiang, T. D. Wang, Y. Y. Lin, C. W. Lau, B. C. Wong, Y. C. Huang, J. T. Shy, Y. P. Lan, Y. F. Chen, and P. H. Tsao, ”Pulsed optical parametric generation, amplification, and oscillation in monolithic periodically poled lithium niobate crystals,” IEEE J. of Quantum Electron. 40, 791–799 (2004). [CrossRef]
11. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, ”Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990). [CrossRef]
12. K. L. Vodopyanov, O. Levi, P. S. Kuo, T. J. Pinguet, J. S. Harris, and M. M. Fejer, ”Optical parametric oscillation in quasi-phase-matched GaAs,” Opt. Lett. 29, 1912–1914 (2004). [CrossRef] [PubMed]
13. Q. Chen, M. Tani, Z. Jiang, and X. C. Zhang, ”Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am B 18, 823–831 (2001). [CrossRef]
14. B. Wyncke and F. Brehat, ”Calculation of the effective second-order non-linear coefficients along the phase matching directions in acentric orthorhombic biaxial crystals,” J. of Phys. B: At. Mol. Opt. Phys. 22, 363–376 (1989). [CrossRef]
15. E. Hecht, Optics, 4th ed. (Academic, Adelphi, 2002).
16. X. Liu and H. Zhang, ”Exact analytical solutions and their applications for interacting waves in quadratic nonlinear medium,” Opt. Express 10, 83–97 (2002). [PubMed]