�?herenkov phase-matched monochromatic THzwave generation using difference frequency generation with a lithium niobate crystal

doi:10.1364/OE.16.007493

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�?herenkov phase-matched monochromatic THzwave generation using difference frequency generation with a lithium niobate crystal

Koji Suizu, Takayuki Shibuya, Takuya Akiba, Toshihiro Tutui, Chiko Otani, and Kodo Kawase »View Author Affiliations

Optics Express, Vol. 16, Issue 10, pp. 7493-7498 (2008)
http://dx.doi.org/10.1364/OE.16.007493

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– Abstract
1. Introduction
2. Čherenkov phase matching
3. Experimental setup
4. Results and Discussion
5. Summary
– References and links

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Abstract

We demonstrated a Čherenkov phase-matching method for monochromatic THz-wave generation using the difference frequency generation process with a lithium niobate crystal, which resulted in high conversion efficiency and wide tunability. We successfully generated monochromatic THz waves across the range 0.2–3.0 THz. We obtained efficient energy conversion in the low frequency region below 0.5 THz, and achieved a flat tuning spectrum by varying the pumping wavelength during THz-wave tuning.

1. Introduction

Terahertz (THz) waves present attractive possibilities in advanced applications including biomedical analysis and stand-off detection for hazardous materials. The development of monochromatic and tunable coherent THz-wave sources is of great interest for use in these applications. Recently, a parametric process based on second-order nonlinearities was used to generate tunable monochromatic coherent THz waves using nonlinear optical crystals [1–4

G. D. Boyd, T. J. Bridges, C. K. N. Patel, and E. Buehler, “Phase-matched submillimeter wave generation by difference-frequency mixing in ZnGeP₂ ,” Appl. Phys. Lett. 21, 553–555 (1972). [CrossRef]

]. In general, however, nonlinear optical materials have high absorption coefficients in the THz-wave region, which inhibits efficient THz-wave generation.

Avetisyan, et al., proposed surface-emitting THz-wave generation using the difference frequency generation (DFG) technique in a periodically poled lithium niobate (PPLN) waveguide to overcome these problems [5

Y. Avetisyan, Y. Sasaki, and H. Ito, “Analysis of THz-wave surface-emitted difference-frequency generation in periodically poled lithium niobate waveguide,” Appl. Phys. B 73, 511–514 (2001). [CrossRef]

]. A surface-emitted THz wave radiates from the surface of the PPLN and propagates perpendicular to the direction of the pump beam. The absorption loss is minimized because the THz wave is generated from the PPLN surface. Moreover, the phase-matching condition can be designed using PPLN with an appropriate grating period [6

Y. Sasaki, Y. Avetisyan, K. Kawase, and H. Ito, “Terahertz-wave surface-emitted difference frequency generation in slant-stripe-type periodically poled LiNbO₃ crystal,” Appl. Phys. Lett. 81, 3323–3325 (2002). [CrossRef]

]. Surface-emitted THz-wave devices have the potential for high conversion efficiency, and continuous wave THz-wave generation has been successfully demonstrated [7

Y. Sasaki, H. Yokoyama, and H. Ito, “Surface-emitted continuous-wave terahertz radiation using periodically poled lithium niobate,” Electron. Lett. 41, 712–713 (2005). [CrossRef]

]. Unfortunately, the tuning range of the THz waves is limited to about 100 GHz by the nature of PPLN [8

Y. Sasaki, Y. Avetisyan, H. Yokoyama, and H. Ito, “Surface-emitted terahertz-wave difference frequency generation in two-dimensional periodically poled lithium niobate,” Opt. Lett. 30, 2927–2929 (2005). [CrossRef] [PubMed]

], and a wide tuning range cannot be realized using the quasi-phase–matching method.

We developed a Čherenkov phase-matching method for monochromatic THz-wave generation using the DFG process with a lithium niobate crystal, which resulted in both high conversion efficiency and wide tunability. Although THz-wave generation by Čherenkov phase matching has been demonstrated using femtosecond pumping pulses [9–11

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984). [CrossRef]

], producing very high peak power [12

K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 µJ ultrashort THz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007). [CrossRef]

], these THz-wave sources are not monochromatic. Our method generates monochromatic and tunable THz waves using a nanosecond pulsed laser source.

2. Čherenkov phase matching

The Čherenkov phase-matching condition is satisfied when the velocity of the polarization wave inside the nonlinear crystal is greater than the velocity of the radiated wave outside. The radiation angle θ is determined by the refractive index of the pumping wave in the crystal, n_opt, and that of THz-wave in the crystal, n_THz [13

R. L. Sutherland, Handbook of Nonlinear Optics , Chap. 2. Marcel Dekker, New York (2003). [CrossRef]

\cos θ = \frac{\frac{λ_{THz}}{n_{THz}}}{2 L_{c}} = \frac{\frac{λ_{THz}}{n_{THz}}}{\frac{λ_{1} λ_{2}}{(n_{1} λ_{2} - n_{2} λ_{1})}} \approx \frac{n_{opt}}{n_{THz}},

(1)

where λ is a wavelength of the contributing waves in the DFG process (ω₁–ω₂=ω_THz) and L_c is the coherence length of the surface-emitted process (L_c=π/Δk, where Δk=k₁–k₂ and k is the wave number). We approximate the refractive index of the optical wave as n₁≈n₂=n_opt because λ₁ and λ₂ have almost the same value for THz-wave generation. Equation (1) implies that n_THz should be larger than n_opt. The lithium niobate crystal has a refractive index of about 2.1 in the near infrared region, and has a refractive index of about 5.1 in the THz-wave region. The generated THz-wave is totally reflected at the interface of air and the lithium niobate crystal. The silicon prevents total internal reflection of THz waves at the interface of air and the lithium niobate crystal, as shown in Fig. 1.

Fig. 1. Schematic of Čherenkov phase-matched monochromatic THz-wave generation. The phase-matching condition is satisfied when 2L_c=λ_THz/n_THz.

The radiation angle hardly changes during THz-frequency tuning because the silicon has low refractive index dispersion in the THz-wave region [14

D. Grischkowsky, S. Keiding, M. van Exter, and Ch. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990). [CrossRef]

] and the optical wavelength requires only slight tuning. The change in radiation angle is less than 0.01° for a fixed pumping wavelength. The actual angle change of the THz wave is significantly better than for the THz parametric oscillator (TPO) with a Si prism coupler [15

K. Kawase, J. Shikata, H. Minamide, K. Imai, and H. Ito, “Arrayed silicon prism coupler for a terahertz-wave parametric oscillator,” Appl. Opt. 40, 1423–1426 (2001). [CrossRef]

], which has an angle change of about 1.5° in the 0.7–3 THz tuning range.

3. Experimental setup

We demonstrated the method described above using the experimental setup shown in Fig. 2. The frequency-doubled Nd:YAG laser, which has pulse duration of 15 ns, a pulse energy of 12 mJ when operating at 532 nm, and a repetition rate of 50 Hz, was used as the pump source for a dual-wavelength potassium titanium oxide phosphate (KTP) optical parametric oscillator (OPO). The KTP-OPO, which consists of two KTP crystals with independently controlled angles, is capable of dual-wavelength operation with independent tuning of each wavelength [16

H. Ito, K. Suizu, T. Yamashita, and T. Sato, “Random frequency accessible broad tunable terahertz-wave source using phase-matched 4-dimethylamino-N-methyl-4-stilbazolium tosylate (DAST) crystal,” Jpn. J. Appl. Phys. 46, 7321–7324 (2007). [CrossRef]

,17

K. Suizu, T. Shibuya, S. Nagano, T. Akiba, K. Edamatsu, H. Ito, and K. Kawase, “Pulsed high peak power millimeter wave generation via difference frequency generation using periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L982–L984 (2007). [CrossRef]

]. The OPO has a tunable range of 1300 to 1600 nm. The maximum output energy of 2 mJ was obtained for a pumping energy of less than 12 mJ. The 5 mol% MgO-doped lithium niobate crystal (MgO:LiNbO₃) used in the experiment was cut from a 5 × 65 × 6 mm wafer, and the x-surfaces at both ends were mirror-polished. An array of seven Si prism couplers was placed on the y-surface of the MgO:LiNbO₃ crystal. The y-surface was also mirror-polished to minimize the coupling gap between the prism base and the crystal surface, and to prevent scattering of the pump beam, which excites a free carrier at the Si prism base. To increase the power density, the pump beam diameter was reduced to 0.3 mm. The polarizations of the pump and THz waves were both parallel to the Z-axis of the crystals. The THz-wave output was measured with a fixed 4 K Si bolometer.

Fig. 2. Experimental setup for Čherenkov phase-matching monochromatic THz-wave generation.

4. Results and Discussion

The THz-wave output map for various pumping wavelengths and corresponding THz-wave frequencies is shown in Fig. 3. The magnitude of the map denotes the output voltage of a Si bolometer with a gain of 200. The noise level of the bolometer was about 10 mV and is shown as the blue region in the figure. The regions where 100 mV and 1 V of output voltage were obtained are green and red, respectively. The blue, green, and red curves are contour plots for 10 mV, 100 mV, and 1 V, respectively. As seen in the figure, wide tunability in the range 0.2–3.0 THz was obtained by choosing the proper pumping wavelength. Especially for lower frequency below 1.0 THz, this was very efficient compared to our previous TPO systems that used 1470 nm pumping.

Fig. 3. THz-wave output mapping for various pumping wavelengths and corresponding THz-wave frequencies. The X-axis and Y-axis denote pumping wavelength λ₁ and THz-wave frequency, respectively. The magnitude of the map values indicates the output voltage of the detector. Blue, green, and red curves are contour plots of 10 mV, 100 mV, and 1 V, respectively, of the detector output voltage.

Figure 4 shows cross sections of the THz-wave output map of Fig. 3. We converted the output voltage of the Si bolometer to the actual THz-wave energy, using the fact that 10 V≈110 pJ/pulse for low repetition rate detection, pulsed heating of the Si device, and an amplifier gain of 200 at the bolometer. The highest THz-wave energy obtained was about 80 pJ, and the energy conversion efficiency from the λ₁ wave (1 mJ/pulse) was about 10^-5%. This value is comparable to that obtained with our previous TPO systems, despite the low excitation energy of only 1 mJ. The figures clearly show the strong dependence of THz-wave output energy on the pumping wavelength. In the case of 0.8 THz generation, the output energy had a dip at a pumping wavelength of approximately 1400 nm as shown in Fig. 4(a). We obtained extremely high energy in the low-frequency region below 0.3 THz (millimeter wave region) using 1470 nm pumping. The reason for this is not clear, and the dispersion of pumping waves cannot explain the results; thus, an explanation is left for future research. The important result is that we can obtain a flat output spectrum in the range 0.2–2 THz by varying the pumping wavelength.

Fig. 4. THz-wave output mapping for various pumping wavelengths and corresponding THz-wave frequencies. The X-axis and Y-axis denote the pumping wavelength λ₁ and THz-wave frequency, respectively. The magnitude of the map denotes the output voltage of the detector. Blue, green, and red curves are the contour plots of 10 mV, 100 mV, and 1 V, respectively, of the detector output voltage.

Čherenkov phase matching inherently requires a waveguide structure for nonlinear polarization waves in the crystal to suppress phase mismatching in the direction perpendicular to the guiding mode (i.e., normal to the crystal surface) [13

R. L. Sutherland, Handbook of Nonlinear Optics , Chap. 2. Marcel Dekker, New York (2003). [CrossRef]

]. If we reduce the width of the pumping beams in the direction of THz-wave propagation to about one-half of the THz wavelength, (i.e., about 10 µm for 3 THz) by taking into account the refractive index of MgO:LiNbO₃ in the THz-wave region, no need exists to consider phase matching in that direction [18

K. Suizu, Y. Suzuki, Y. Sasaki, H. Ito, and Y. Avetisyan, “Surface-emitted terahertz-wave generation by ridged periodically poled lithium niobate and enhancement by mixing of two terahertz waves,” Opt. Lett. 31, 957–959 (2006). [CrossRef] [PubMed]

]. In our case, the waist of the pump beams in the MgO:LiNbO₃ was about 300 µm, which corresponds to about five cycles of THz waves at 1.0 THz, and one cycle of THz waves at 0.2 THz. Although the experimental conditions did not satisfy the requirement for Čherenkov phase matching, we did successfully detect Čherenkov-radiated THz waves, which originated in the higher absorbance area of the crystal at the THz-wave region. The THz waves generated far from the crystal surface would be attenuated and no significant phase mismatch would occur. This also remains an area for future study.

By shaping the pumping beams with a focused cylindrical lens or by adopting the waveguide structure of the crystal [19

Y. Sasaki, Y. Suzuki, K. Suizu, H. Ito, S. Yamaguchi, and M. Imaeda, “Surface-emitted terahertz-wave difference-frequency generation in periodically poled lithium niobate ridge-type waveguide,” Jpn. J. Appl. Phys. 45, L367–369 (2006). [CrossRef]

], we could neglect phase mismatches and obtain a higher power density of the pumping beams, resulting in higher conversion efficiency.

5. Summary

We demonstrated a Čherenkov phase-matching method for monochromatic THz-wave generation using the DFG process with a lithium niobate crystal, which resulted in both high conversion efficiency and wide tunability. We successfully generated monochromatic THz-waves with wide tunability in the range 0.2–3.0 THz. We obtained efficient energy conversion in the low-frequency region below 0.5 THz, and we achieved a flat tuning spectrum by varying the pumping wavelength during THz-wave tuning. The highest THz-wave energy was about 80 nJ/pulse, and this energy could be obtained for the broad spectral region in the range 0.2–2.0 THz.

Acknowledgments

The authors thank Dr. J. Shikata of the Research Institute of Electrical Communication, Tohoku University, for useful discussions, C. Takyu for his excellent work coating the crystal surface, and T. Shoji for polishing the crystals superbly. This work was supported in part by the National Institute of Communications Technology, Japan.

References and links

1.	G. D. Boyd, T. J. Bridges, C. K. N. Patel, and E. Buehler, “Phase-matched submillimeter wave generation by difference-frequency mixing in ZnGeP₂ ,” Appl. Phys. Lett. 21, 553–555 (1972). [CrossRef]
2.	A. Rice, Y. Jin, X. F. Ma, X. C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from <110> zinc-blende crystals,” Appl. Phys. Lett. 64, 1324–1326 (1994). [CrossRef]
3.	W. Shi, Y. J. Ding, N. Fernelius, and K. Vodopyanov, “Efficient, tunable, and coherent 0.18–5.27-THz source based on GaSe crystal,” Opt. Lett. 27, 1454–1456 (2002). [CrossRef]
4.	T. Tanabe, K. Suto, J. Nishizawa, K. Saito, and T. Kimura, “Tunable terahertz wave generation in the 3- to 7-THz region from GaP,” Appl. Phys. Lett. 83, 237–239 (2003). [CrossRef]
5.	Y. Avetisyan, Y. Sasaki, and H. Ito, “Analysis of THz-wave surface-emitted difference-frequency generation in periodically poled lithium niobate waveguide,” Appl. Phys. B 73, 511–514 (2001). [CrossRef]
6.	Y. Sasaki, Y. Avetisyan, K. Kawase, and H. Ito, “Terahertz-wave surface-emitted difference frequency generation in slant-stripe-type periodically poled LiNbO₃ crystal,” Appl. Phys. Lett. 81, 3323–3325 (2002). [CrossRef]
7.	Y. Sasaki, H. Yokoyama, and H. Ito, “Surface-emitted continuous-wave terahertz radiation using periodically poled lithium niobate,” Electron. Lett. 41, 712–713 (2005). [CrossRef]
8.	Y. Sasaki, Y. Avetisyan, H. Yokoyama, and H. Ito, “Surface-emitted terahertz-wave difference frequency generation in two-dimensional periodically poled lithium niobate,” Opt. Lett. 30, 2927–2929 (2005). [CrossRef] [PubMed]
9.	D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984). [CrossRef]
10.	D. A. Kleinman and D. H. Auston, “Theory of electro-optic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20, 964–970 (1984). [CrossRef]
11.	J. Hebling, G. Almasi, I. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large area THz pulse generation,” Opt. Express 10, 1161–1166 (2002). [PubMed]
12.	K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 µJ ultrashort THz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007). [CrossRef]
13.	R. L. Sutherland, Handbook of Nonlinear Optics , Chap. 2. Marcel Dekker, New York (2003). [CrossRef]
14.	D. Grischkowsky, S. Keiding, M. van Exter, and Ch. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990). [CrossRef]
15.	K. Kawase, J. Shikata, H. Minamide, K. Imai, and H. Ito, “Arrayed silicon prism coupler for a terahertz-wave parametric oscillator,” Appl. Opt. 40, 1423–1426 (2001). [CrossRef]
16.	H. Ito, K. Suizu, T. Yamashita, and T. Sato, “Random frequency accessible broad tunable terahertz-wave source using phase-matched 4-dimethylamino-N-methyl-4-stilbazolium tosylate (DAST) crystal,” Jpn. J. Appl. Phys. 46, 7321–7324 (2007). [CrossRef]
17.	K. Suizu, T. Shibuya, S. Nagano, T. Akiba, K. Edamatsu, H. Ito, and K. Kawase, “Pulsed high peak power millimeter wave generation via difference frequency generation using periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L982–L984 (2007). [CrossRef]
18.	K. Suizu, Y. Suzuki, Y. Sasaki, H. Ito, and Y. Avetisyan, “Surface-emitted terahertz-wave generation by ridged periodically poled lithium niobate and enhancement by mixing of two terahertz waves,” Opt. Lett. 31, 957–959 (2006). [CrossRef] [PubMed]
19.	Y. Sasaki, Y. Suzuki, K. Suizu, H. Ito, S. Yamaguchi, and M. Imaeda, “Surface-emitted terahertz-wave difference-frequency generation in periodically poled lithium niobate ridge-type waveguide,” Jpn. J. Appl. Phys. 45, L367–369 (2006). [CrossRef]

OCIS Codes
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(190.4223) Nonlinear optics : Nonlinear wave mixing

ToC Category:
Nonlinear Optics

History
Original Manuscript: November 12, 2007
Revised Manuscript: December 27, 2007
Manuscript Accepted: December 27, 2007
Published: May 9, 2008

Citation
Koji Suizu, Takayuki Shibuya, Takuya Akiba, Toshihiro Tutui, Chiko Otani, and Kodo Kawase, "�?herenkov phase-matched monochromatic THzwave generation using difference frequency generation with a lithium niobate crystal," Opt. Express 16, 7493-7498 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-7493

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References

G. D. Boyd, T. J. Bridges, C. K. N. Patel, and E. Buehler, " Phase-matched submillimeter wave generation by difference-frequency mixing in ZnGeP2," Appl. Phys. Lett. 21, 553-555 (1972). [CrossRef]
A. Rice, Y. Jin, X. F. Ma, X. C. Zhang, D. Bliss, J. Larkin, and M. Alexander, "Terahertz optical rectification from �?�110�?� zinc-blende crystals," Appl. Phys. Lett. 64, 1324-1326 (1994). [CrossRef]
W. Shi, Y. J. Ding, N. Fernelius, and K. Vodopyanov, "Efficient, tunable, and coherent 0.18-5.27-THz source based on GaSe crystal," Opt. Lett. 27, 1454-1456 (2002). [CrossRef]
T. Tanabe, K. Suto, J. Nishizawa, K. Saito, and T. Kimura, "Tunable terahertz wave generation in the 3- to 7-THz region from GaP," Appl. Phys. Lett. 83, 237-239 (2003). [CrossRef]
Y. Avetisyan, Y. Sasaki, and H. Ito, "Analysis of THz-wave surface-emitted difference-frequency generation in periodically poled lithium niobate waveguide," Appl. Phys. B 73, 511-514 (2001). [CrossRef]
Y. Sasaki, Y. Avetisyan, K. Kawase, and H. Ito, "Terahertz-wave surface-emitted difference frequency generation in slant-stripe-type periodically poled LiNbO3 crystal," Appl. Phys. Lett. 81, 3323-3325 (2002). [CrossRef]
Y. Sasaki, H. Yokoyama, and H. Ito, "Surface-emitted continuous-wave terahertz radiation using periodically poled lithium niobate," Electron. Lett. 41, 712-713 (2005). [CrossRef]
Y. Sasaki, Y. Avetisyan, H. Yokoyama, and H. Ito, "Surface-emitted terahertz-wave difference frequency generation in two-dimensional periodically poled lithium niobate," Opt. Lett. 30, 2927-2929 (2005). [CrossRef] [PubMed]
D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, "Cherenkov radiation from femtosecond optical pulses in electro-optic media," Phys. Rev. Lett. 53, 1555-1558 (1984). [CrossRef]
D. A. Kleinman and D. H. Auston, "Theory of electro-optic shock radiation in nonlinear optical media," IEEE J. Quantum Electron. 20, 964-970 (1984). [CrossRef]
J. Hebling, G. Almasi, I. Kozma, and J. Kuhl, "Velocity matching by pulse front tilting for large area THz-pulse generation," Opt. Express 10, 1161-1166 (2002). [PubMed]
K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, "Generation of 10 μJ ultrashort THz pulses by optical rectification," Appl. Phys. Lett. 90, 171121 (2007). [CrossRef]
R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York 2003), Chap. 2. [CrossRef]
D. Grischkowsky, S. Keiding, M. van Exter, and Ch. Fattinger, "Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors," J. Opt. Soc. Am. B 7, 2006-2015 (1990). [CrossRef]
K. Kawase, J. Shikata, H. Minamide, K. Imai, and H. Ito, "Arrayed silicon prism coupler for a terahertz-wave parametric oscillator," Appl. Opt. 40, 1423-1426 (2001). [CrossRef]
H. Ito, K. Suizu, T. Yamashita, and T. Sato, "Random frequency accessible broad tunable terahertz-wave source using phase-matched 4-dimethylamino-N-methyl-4-stilbazolium tosylate (DAST) crystal," Jpn. J. Appl. Phys. 46, 7321-7324 (2007). [CrossRef]
K. Suizu, T. Shibuya, S. Nagano, T. Akiba, K. Edamatsu, H. Ito, and K. Kawase, "Pulsed high peak power millimeter wave generation via difference frequency generation using periodically poled lithium niobate," Jpn. J. Appl. Phys. 46, L982-L984 (2007). [CrossRef]
K. Suizu, Y. Suzuki, Y. Sasaki, H. Ito, and Y. Avetisyan, "Surface-emitted terahertz-wave generation by ridged periodically poled lithium niobate and enhancement by mixing of two terahertz waves," Opt. Lett. 31, 957-959 (2006). [CrossRef] [PubMed]
Y. Sasaki, Y. Suzuki, K. Suizu, H. Ito, S. Yamaguchi, and M. Imaeda, "Surface-emitted terahertz-wave difference-frequency generation in periodically poled lithium niobate ridge-type waveguide," Jpn. J. Appl. Phys. 45, L367-369 (2006). [CrossRef]

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