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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 9 — Apr. 28, 2008
  • pp: 6471–6478
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Forward and backward Terahertz-wave difference-frequency generations from periodically poled lithium niobate

T. D. Wang, S. T. Lin, Y. Y. Lin, A. C. Chiang, and Y. C. Huang  »View Author Affiliations


Optics Express, Vol. 16, Issue 9, pp. 6471-6478 (2008)
http://dx.doi.org/10.1364/OE.16.006471


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Abstract

We report terahertz-wave generation in the wavelength range of 190~210 and 457~507 µm from forward and backward difference frequency generations, respectively, in a 3.2-cm long multi-grating periodically poled lithium niobate (PPLN) crystal. The grating period of the PPLN crystal varies form 63 to 70 µm in 1-µm increments. The extraordinary refractive index of lithium niobate in the THz-wave range was precisely deduced from the quasi-phase-matching condition of the difference frequency generations.

© 2008 Optical Society of America

1. Introduction

Usually, collinear phase-matching is the preferred configuration for a nonlinear frequency conversion process, because it provides the longest interaction length and more efficient power extraction from a normal-incidence crystal face. Optical rectification using a fs pump laser in a quasi-phase-matched (QPM) [13

13. J. A. Armstrong, N. Bloemergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]

] nonlinear optical material can also generate forward and backward multi-cycle THz radiations [14-16]. The mechanism of the THz-wave generation is understood as a special case of difference frequency generation in that two Fourier components of the fs laser pulse perform wave mixing [17

17. K. L. Vodopyanov, “Optical generation of narrow-band terahertz packets in periodically-inverted electro-optic crystals: conversion efficiency and optimal laser pulse format,” Opt. Express 14, 2263–2276 (2006). [CrossRef] [PubMed]

]. However in the collinear configuration the generated THz-wave quickly walks away from the short pump pulse and is mostly absorbed before existing the nonlinear optical material. On the other hand, the conventional collinearly phase-matched difference frequency generation using two coherent long-pulse pump components promises much more power and better coherence for the generated THz wave [18

18. 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]

].

2. Experimental setup

Figure 1 shows the experimental setup of the forward and backward THz difference frequency generations. A kHz-linewidth distributed-feedback diode laser (DFBDL) at 1538.98 nm and a MHz-linewidth external-cavity diode laser (ECDL) tunable between 1510 and 1610 nm provide the seed components to the first-stage Erbium-doped fiber amplifier (EDFA) and the second-stage pulsed optical parametric amplifier (OPA) for the THz difference frequency generations in the PPLN difference frequency generator (PPLN DFG). The EDFA boosts up the CW diode-laser powers to about 70 mW. A passively Q-switched Nd:YAG laser at 1064 nm pumps the OPA using a PPLN crystal as the gain medium. The PPLN-OPA crystal has a 0.78-mm thickness, 45-mm length, and 29.6-µm QPM period. The OPA pump laser generates 70-µJ pulse energy in a 500-ps pulse width repeating at a 1 kHz rate. The pump laser is focused to a waist radius of 166 µm at the center of the PPLN-OPA crystal. At 101°C, the PPLN OPA has a 12-nm or 1.6-THz bandwidth so this OPA can simultaneously amplify the two seed components from the diode lasers. After the OPA, each of the two seed components is amplified to ~8.5-µJ pulse energy in a 400-ps pulse width for pumping the THz PPLN DFG. The one-to-one power ratio in the two pump components maximizes the output power of the difference frequency generation in the low-conversion limit. The two idler waves of the OPA near 3.3 µm were completely absorbed by the BK7 substrate of the dichroic mirror (HR @1064 nm and HT @1550 nm). The two pump components near 1.5 µm were focused by a f=7.5-cm focusing lens to a 130 µm waist radius at the center of a multi-grating PPLN-DFG crystal for performing the forward and backward THz difference frequency generations. One major advantage of this broadband two-stage amplifier system is that the spatial and temporal overlap of the two pump components of the PPLN DFG is automatically achieved. In addition, the THz frequency can be easily tuned by varying the relative frequency between the two seed diode lasers. The 400-ps pulse width of the OPA output, however, gives a walkoff distance between the optical and THz pulses comparable to the 3.2-cm crystal length of the PPLN DFG.

The DFG employed a multi-grating PPLN crystal with a 0.78-mm thickness. The PPLN crystal consists of 8 parallel QPM gratings with 63, 64, 65, 66, 67, 68, 69, and 70-µm domain periods. The end faces of the PPLN crystal were coated with anti-reflection dielectric layers at the two pump wavelengths (Reflectance <0.5%).

The forward THz wave was largely separated from the pump components by using a wire mesh in the down stream of the PPLN DFG. The wire mesh contains 45 µm×45 µm square apertures with a 54% filling factor. The transmittance of the wire mesh is 14% and 84% for incident waves near 200 and 1.55 µm, respectively. The residual pump laser reflected from the wire mesh is completely blocked by a 3-mm thick Ge filter and a high-density polyethylene filter in front of the bolometer. The backward THz wave was extracted by using an optically polished 3.5 cm×3.5 cm square copper reflector placed 3 cm in front of the multi-grating PPLN crystal. The copper reflector has a 5-mm diameter hole for transmitting the two pump components, but reflects nearly 94% of the THz wave incident on it. The counter-propagating configuration of the pump and THz waves in the backward THz-wave DFG provides a pump-free background for measuring the THz wave. When taking data, we scanned the wavelength of the ECDL and read the THz-wave signal from a 4K Si bolometer. When the ECDL wavelength is tuned to the quasi-phase-matching condition of the forward or backward difference frequency generation, the bolometer registers a large THz-wave signal. The bolometer signal fell back to the noise level when we blocked any of the two pump components, so generation of the forward and backward THz waves was unambiguously confirmed.

Fig. 1. Setup of the collinearly quasi-phase-matched forward and backward THz difference frequency generations in a multi-grating PPLN crystal. The two-stage amplifier, marked by a dashed-line box, generates 17-µJ pump energy in a 400-ps pulse width with two frequency components from the seeding DFBDL and the ECDL. The 17-µJ pump energy is injected to into the PPLN DFG for generating coherent THz radiation. The frequency tuning of the THz wave is achieved by varying the frequency difference between the two diode lasers matched to the QPM conditions of the DFG PPLN. (HR: high reflection, HT: high transmission, OPA: optical parametric amplifier, DFG: difference frequency generator, FP: Fabry-Perot spectrometer, ECDL: external-cavity diode laser, DFBDL: distributed-feedback diode laser, EDFA: Erbium-doped fiber amplifier.)

3. Experimental results

It can be shown from the plane-wave model that the phase-tuning curve of a highly lossy forward or backward THz-wave DFG has a Lorentzian line shape given by

ITHzjΔkL+αTHz2L2,
(1)

where ITHz is the intensity of the THz wave, Δk is the wave-vector mismatch, L is the length of the nonlinear material, αTHz is the power attenuation coefficient at THz frequencies, and j=1 is the imaginary unit. Figure 2 shows the forward THz phase-tuning curves measured by the bolometer. The solid curves are the best fits of the Lorentzian function in Eq. (1). We deduced the phase-matched wavelength of the THz radiation λTHz from the frequency conservation law, 1/λp-1/λs=1/λTHz, where λp and λs are the long- and short-wavelength pump components for the DFG, respectively. In Fig. 2(a), the phase-matched THz-radiation wavelengths were found to be 191.6, 194.4, 197.1, 199.6, 202.4, 205.0, and 206.8 µm, corresponding to the PPLN grating periods of 63, 64, 65, 66, 67, 68, and 69 µm, respectively. The best signal-to-noise ratio in the tuning curves is more than 10. The measurements were done in a laboratory atmosphere without dry-N2 purge. As shown by Fig. 2(b), the THz wave generated from the 70-µm grating near 211.5 µm was strongly absorbed by the ambient water vapor [23

23. V. B. Podobedov, D. F. Plusquellic, and G. T. Fraser, “Investigation of the water-vapor continuum in the THz region using a multipass cell,” J. Quant. Spectrosc. Radiat. Transfer91, 287–295(2005). [CrossRef]

]. We also verified the THz radiation by directly measuring its wavelength using a scanning Fabry-Perot spectrometer. The spectrometer consists of two parallel pieces of the wire mesh with a 2.5-µm scanning step along the longitudinal direction. A THz-radiation wavelength of 197.5 µm was confirmed at the output of the 65-µm period PPLN, which is in good agreement with the wavelength deduced from the frequency conservation law.

Fig. 2. (a). Forward THz-wave phase-matching curves measured by the 4K Si bolometer for the PPLN gratings with 63, 64, 65, 66, 67, 68 and 69-µm periods. The solid curves are the best fits of the Lorentzian function in Eq. (1). (b) When taking the phase matching cure for the 70-µm period PPLN DFG, we found absorption of ambient water vapor near 211.5 µm [23].

The bolometer was specified with 100% quantum efficiency at 200 µm. From the bolometer signal, we estimated about 10-fJ THz-wave energy entering the detection cone of the bolometer. Considering the 54, 35, 72% transmittances at PPLN output face, the Ge filter, and the bolometer window, respectively, and the fast diffraction of the THz, we obtain 0.37 pJ energy of THz radiation inside the PPLN crystal.

While fixing the wavelength of the DFBDL at 1538.43 nm, we continued to scan the ECDL wavelength and read the backward THz-wave signal from the 4K Si bolometer. In Fig. 3, we plot the backward DFG tuning curves measured by the bolometer. The phase-matched THz-radiation wavelengths were found to be 456.7, 463.8, 470.2, 477.7, 484.6, 492.6, 498.8, and 507.3 µm, corresponding to the PPLN grating periods of 63, 64, 65, 66, 67, 68, 69, and 70 µm, respectively. The measurements were also done in a laboratory atmosphere without dry-N2 purge. For those measurements, the best signal-to-noise ratio in the tuning curves is also about 10.

In this experiment, the pump power for the backward THz DFG was about 2-3 orders of magnitudes lower than that for most THz-wave forward difference frequency generation in LiNbO3. By assuming 100% quantum efficiency of our Si bolometer for the backward THz photons between 450~500 µm, we estimate ~6 fJ energy of the backward THz wave entering the detection cone of the bolometer. The backward THz wave was emitted from the input face of the PPLN crystal with a radiation area approximately equal to the pump laser area. Since the 130-µm pump laser radius is several times less than the radiation wavelength, the THz wave appears to radiate from a point source from the PPLN end face covering a nearly 2π solid angle. The first f=76-mm, 2″-aperture off-axis parabolic mirror was responsible for collecting the THz radiation into the bolometer, which was placed ~7 cm from the PPLN input face due to the space constraint in our setup. This suggests that, with our current setup, only a very small fraction of the THz-wave energy collected into the sensor area of the bolometer. Further taking into account the ~50% Fresnel reflection at the PPLN surface, we conclude a minimum of 56-fJ energy of the backward THz wave was generated in the PPLN. Further improvements on the detection scheme and the detector calibration are needed to understand the conversion efficiency of this backward THz difference frequency generation. In addition, the short 400-ps pump pulse lengths only allow 200-ps buildup time for the backwardpropagating THz wave in the highly absorptive PPLN. This means the effective gain length of our backward THz DFG is only 1.2 cm, given a THz refractive index of ~5.

Fig. 3. Backward THz-wave phase matching curves measured by the 4K Si bolometer for the PPLN with 63, 64, 65, 66, 67, 68, 69 and 70-µm periods. The solid curves are the best fits of the Lorentzian function in Eq. (1).

Table 1 summaries the generated THz wavelengths and deduced refractive indices of the forward and backward THz difference frequency generations. For the forward THz-wave generation, the data for the 70-µm PPLN grating period is not available (NA) due to water absorption at the generated wavelength. The refractive index can be deduced from the QPM condition np/λp-ns/λs-1/ΛPPLNnTHz/λTHz with known material dispersion at the optical frequencies, where the + and - signs denote the forward and backward processes, respectively, ΛPPLN is the PPLN grating period, and n is the refractive index. For the PPLN DFG, nTHz is the extraordinary refractive index seen by the THz radiation.

Table 1. Summary of the forward and backward THz difference frequency generations

table-icon
View This Table

Figures 4(a) and 4(b) show the measured extraordinary refractive indices (dots) versus the forward and backward THz-wave wavelengths, respectively. For comparison, we also overlay on the same plots the fitting curves of the THz-wave refractive index from Refs. [24

24. L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505–123511 (2005). [CrossRef]

, 25

25. E. D. Palik, Handbook of Optical Constants of Solids, 695–702 (Academic, New York, 1991).

]. In Fig. 4(a), the fitting curve from Ref. [24

24. L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505–123511 (2005). [CrossRef]

] matches reasonably well to our measured data. In Fig. 4(b), the experimental data are in a good agreement with Ref. [25

25. E. D. Palik, Handbook of Optical Constants of Solids, 695–702 (Academic, New York, 1991).

]. Usually it is relatively difficult to precisely measure the refractive index of a material at the THz frequency. The quasi-phase-matched difference generations offer a convenient and precise way of characterizing material dispersion at THz frequencies.

Fig. 4. The THz extraordinary refractive indices deduced from the (a) forward and (b) backward THz-wave difference frequency generations. The fitting curves from Refs. [24, 25] are also shown for comparison.

4. Discussion and conclusion

Although the QPM technique holds some promise to increase the gain length for parametric THz-wave generation from LiNbO3, future work is necessary to make a direct comparison between the collinear and non-collinear phase-matching schemes under the same pump power and radiation wavelength. As an attempt to achieve backward parametric oscillation, we also used a single high-power source to pump the PPLN crystal but only generated high-order phase-matched forward mid-infrared radiation. Apparently, in our PPLN crystal, the net gain of the backward parametric process for THz-wave generation is much lower than that of the forward parametric process for mid-infrared generation. Forced nonlinear dipole radiation with a more intense seed signal for the DFG could be an approach to achieve backward-wave oscillation at the THz frequencies.

Acknowledgments

We appreciate some fruitful discussion with Fan-Yi Lin. This work was supported by the National Science Council of Taiwan under Contract NSC 95-2112-M-007-027-MY2. Y. C. Huang’s e-mail address is ychuang@ee.nthu.edu.tw.

References and links

1.

C. Rønne, P. Åstrand, and S. R. Keiding, “THz spectroscopy of liquid H2O and D2O,” Phys. Rev. Lett. 82, 2888–2891 (1999). [CrossRef]

2.

E. Knoesel, M. Bonn, J. Shan, and T. F. Heinz, “Charge transport and carrier dynamics in liquids probed by THz Time-Domain Spectroscopy,” Phys. Rev. Lett. 86, 340–343 (2001). [CrossRef] [PubMed]

3.

K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fringeprints,” Opt. Express. 11, 2549–2554 (2003). [CrossRef] [PubMed]

4.

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996). [CrossRef]

5.

P. R. Smith, D. H. Auston, and M. C. Nuss, “Subpicosecond photoconducting dipole antennas,” IEEE J. Quantum Electron. 24, 255–256 (1988). [CrossRef]

6.

X.-C., B. B. Hu, J. T. Darrow, and D. H. Auston, “Generation of femtosecond electromagnetic pulses from semiconductor surface,” Appl. Phys. Lett. 56, 1011–1013 (1990). [CrossRef]

7.

D. H. Levy, Free Electron Lasers and Other Advanced Sources of Light, (National Academy Press Washington, DC, 1994) 24–31.

8.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-hetrostructure laser,” Nature 417, 156–159 (2002). [CrossRef] [PubMed]

9.

M. A. Piestrup, R. N. Fleming, and R. H. Pantell, “Continuously tunable submillimeter wave source,” Appl. Phys. Lett. 26, 418–419 (1975). [CrossRef]

10.

K. Kawase, M. Sato, T. Taniuchi, and H. Ito, “Coherent THz-wave generation from LiNbO3 with monolithic grating coupler,” Appl. Phy. Lett. 68, 2483–2485 (1996). [CrossRef]

11.

J. Shikata, M. Sato, T. Taniuchi, and H. Ito, “Enhancement of Terahertz-wave output from LiNbO3 optical parametric oscillator by cryogenic cooling,” Opt. Lett. 24, 202–204 (1999). [CrossRef]

12.

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

13.

J. A. Armstrong, N. Bloemergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]

14.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 78, 2505–2507 (2000). [CrossRef]

15.

C. Weiss, G. Torosyan, J. P. Meyn, R. Wallenstein, R. Beigang, and Y. Avetisyan, “Tuning characteristics of narrowband THz radiation generated via optical rectification in periodically poled lithium niobate,” Opt. Express 8, 497–502 (2001). [CrossRef] [PubMed]

16.

N. E. Yu, C. Jung, C. S. Kee, Y. L. Lee, B. A. Yu, D. K. Ko, and J. Lee, “Backward terahertz generation in periodically poled lithium niobate crystal via difference frequency generation,” Jpn. J. Appl. Phys. 46, 1501–1504 (2007). [CrossRef]

17.

K. L. Vodopyanov, “Optical generation of narrow-band terahertz packets in periodically-inverted electro-optic crystals: conversion efficiency and optimal laser pulse format,” Opt. Express 14, 2263–2276 (2006). [CrossRef] [PubMed]

18.

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]

19.

Y. J. Ding and J. B. Khurgin, “A new scheme for efficient generation of coherent and incoherent submillimeter to THz wave in periodically-poled lithium niobate,” Opt. Commun. 148, 105–109 (1998). [CrossRef]

20.

S. E. Harris, “Proposed Backward Wave Oscillation in the Infrared,” Appl. Phys. Lett. 9, 114–115 (1966). [CrossRef]

21.

C. Canalias and V. Pasiskevicius, “Mirror-less optical parametric oscillator,” Nat. Photonics 1, 459–462 (2007). [CrossRef]

22.

W. Shi and Y. J. Ding, “Backward parametric oscillation in second-order nonlinear medium,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper QTuF7.

23.

V. B. Podobedov, D. F. Plusquellic, and G. T. Fraser, “Investigation of the water-vapor continuum in the THz region using a multipass cell,” J. Quant. Spectrosc. Radiat. Transfer91, 287–295(2005). [CrossRef]

24.

L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505–123511 (2005). [CrossRef]

25.

E. D. Palik, Handbook of Optical Constants of Solids, 695–702 (Academic, New York, 1991).

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

ToC Category:
Nonlinear Optics

History
Original Manuscript: March 27, 2008
Revised Manuscript: April 18, 2008
Manuscript Accepted: April 18, 2008
Published: April 22, 2008

Citation
T. D. Wang, S. T. Lin, Y. Y Lin, A. C. Chiang, and Y. C. Huang, "Forward and backward terahertz-wave difference-frequency generations from periodically poled lithium niobate," Opt. Express 16, 6471-6478 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6471


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References

  1. C. Rønne, P. ?strand, and S. R. Keiding, "THz spectroscopy of liquid H2O and D2O," Phys. Rev. Lett. 82, 2888-2891 (1999). [CrossRef]
  2. E. Knoesel, M. Bonn, J. Shan, and T. F. Heinz, "Charge transport and carrier dynamics in liquids probed by THz Time-Domain Spectroscopy," Phys. Rev. Lett. 86, 340-343 (2001). [CrossRef] [PubMed]
  3. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, "Non-destructive terahertz imaging of illicit drugs using spectral fringeprints," Opt. Express. 11, 2549-2554 (2003). [CrossRef] [PubMed]
  4. Q. Wu, T. D. Hewitt, and X.-C. Zhang, "Two-dimensional electro-optic imaging of THz beams," Appl. Phys. Lett. 69, 1026-1028 (1996). [CrossRef]
  5. P. R. Smith, D. H. Auston, and M. C. Nuss, "Subpicosecond photoconducting dipole antennas," IEEE J. Quantum Electron. 24, 255-256 (1988). [CrossRef]
  6. X.-C. Zhang, B. B. Hu, J. T. Darrow, and D. H. Auston, "Generation of femtosecond electromagnetic pulses from semiconductor surface," Appl. Phys. Lett. 56, 1011-1013 (1990). [CrossRef]
  7. D. H. Levy, Free Electron Lasers and other advanced Sources of Light, (National Academy Press Washington, DC, 1994) 24-31.
  8. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti and F. Rossi, "Terahertz semiconductor-hetrostructure laser," Nature 417, 156-159 (2002). [CrossRef] [PubMed]
  9. M. A. Piestrup, R. N. Fleming, and R. H. Pantell, "Continuously tunable submillimeter wave source," Appl. Phys. Lett. 26, 418-419 (1975). [CrossRef]
  10. K. Kawase, M. Sato, T. Taniuchi, and H. Ito, "Coherent THz-wave generation from LiNbO3 with monolithic grating coupler," Appl. Phy. Lett. 68, 2483-2485 (1996). [CrossRef]
  11. J. Shikata, M. Sato, T. Taniuchi, and H. Ito, "Enhancement of Terahertz-wave output from LiNbO3 optical parametric oscillator by cryogenic cooling," Opt. Lett. 24, 202-204 (1999). [CrossRef]
  12. K. Kawase, J. Shikata, H. Minamide, K. Imai, and H. Ito, "Arrayed silicon prism coupler for THz-wave parametric oscillator," Appl. Opt. 40, 1423-1426 (2001). [CrossRef]
  13. J. A. Armstrong, N. Bloemergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962). [CrossRef]
  14. Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, "Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate," Appl. Phys. Lett. 78, 2505-2507 (2000). [CrossRef]
  15. C. Weiss, G. Torosyan, J. P. Meyn, R. Wallenstein, R. Beigang, and Y. Avetisyan, "Tuning characteristics of narrowband THz radiation generated via optical rectification in periodically poled lithium niobate," Opt. Express 8, 497-502 (2001). [CrossRef] [PubMed]
  16. N. E. Yu, C. Jung, C. S. Kee, Y. L. Lee, B. A. Yu, D. K. Ko, and J. Lee, "Backward terahertz generation in periodically poled lithium niobate crystal via difference frequency generation," Jpn. J. Appl. Phys. 46, 1501-1504 (2007). [CrossRef]
  17. K. L. Vodopyanov, "Optical generation of narrow-band terahertz packets in periodically-inverted electro-optic crystals: conversion efficiency and optimal laser pulse format," Opt. Express 14, 2263-2276 (2006). [CrossRef] [PubMed]
  18. 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]
  19. Y. J. Ding and J. B. Khurgin, "A new scheme for efficient generation of coherent and incoherent submillimeter to THz wave in periodically-poled lithium niobate," Opt. Commun. 148, 105-109 (1998). [CrossRef]
  20. S. E. Harris, "Proposed Backward Wave Oscillation in the Infrared," Appl. Phys. Lett. 9, 114-115 (1966). [CrossRef]
  21. C. Canalias and V. Pasiskevicius, "Mirror-less optical parametric oscillator," Nat. Photonics 1, 459-462 (2007). [CrossRef]
  22. W. Shi, and Y. J. Ding, "Backward parametric oscillation in second-order nonlinear medium," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper QTuF7.
  23. V. B. Podobedov, D. F. Plusquellic, and G. T. Fraser, "Investigation of the water-vapor continuum in the THz region using a multipass cell," J. Quant. Spectrosc. Radiat. Transf. 91, 287-295 (2005). [CrossRef]
  24. L. Pálfalvi, J. Hebling, J. Kuhl, ?. Péter, and K. Polgár, "Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range," J. Appl. Phys. 97, 123505-123511 (2005). [CrossRef]
  25. E. D. Palik, Handbook of Optical Constants of Solids, 695-702 (Academic, New York, 1991).

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