## Long-range parametric amplification of THz wave with absorption loss exceeding parametric gain |

Optics Express, Vol. 21, Issue 2, pp. 2452-2462 (2013)

http://dx.doi.org/10.1364/OE.21.002452

Acrobat PDF (1718 KB)

### Abstract

Optical parametric mixing is a popular scheme to generate an idler wave at THz frequencies, although the THz wave is often absorbing in the nonlinear optical material. It is widely suggested that the useful material length for co-directional parametric mixing with strong THz-wave absorption is comparable to the THz-wave absorption length in the material. Here we show that, even in the limit of the absorption loss exceeding parametric gain, the THz idler wave can grows monotonically from optical parametric amplification over a much longer distance in a nonlinear optical material until pump depletion. The coherent production of the non-absorbing signal wave can assist the growth of the highly absorbing idler wave. We also show that, for the case of an equal input pump and signal in difference frequency generation, the quick saturation of the THz idler wave predicted from a much simplified and yet popular plane-wave model fails when fast diffraction of the THz wave from the co-propagating optical mixing waves is considered.

© 2013 OSA

## 1. Introduction

1. J. M. Yarborough, S. S. Sussman, H. E. Purhoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO_{3} without a resonator,” Appl. Phys. Lett. **15**(3), 102–105 (1969). [CrossRef]

3. M. A. Piestrup, R. N. Fleming, and R. H. Pantell, “Continuously tunable submillimeter wave source,” Appl. Phys. Lett. **26**(8), 418–421 (1975). [CrossRef]

4. K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D Appl. Phys. **35**(3), R1–R14 (2002). [CrossRef]

5. L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO_{3} in the THz range,” J. Appl. Phys. **97**, 123505 (2005), doi:. [CrossRef]

6. K. Kawase, M. Sato, K. Nakamura, T. Taniuchi, and H. Ito, “Unidirectional radiation of widely tunable THz wave using a prism coupler under noncollinear phase matching condition,” Appl. Phys. Lett. **71**(6), 753–755 (1997). [CrossRef]

10. J. B. Khurgin, D. Yang, and Y. J. Ding, “Generation of mid-infrared radiation in the highly-absorbing nonlinear medium,” J. Opt. Soc. Am. B **18**(3), 340–343 (2001). [CrossRef]

11. A. G. Stepanov, J. Hebling, and J. Kuhl, “Efficient generation of subpicosecond terahertz radiation by phase-matched optical rectification using ultrashort laser pulses with tilted pulse fronts,” Appl Phys Lett **83**, 3000–3002 doi:Doi (2003). [CrossRef]

12. T. Taniuchi and H. Nakanishi, “Collinear phase-matched terahertz-wave generation in GaP crystal using a dual-wavelength optical parametric oscillator,” J. Appl. Phys. **95**, 7588–7591, doi:Doi (2004). [CrossRef]

15. J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quant. **14**, 354–362, doi:Doi (2008). [CrossRef]

16. G. Kh. Kitaeva, “THz generation by means of optical laser,” Laser Phys. Lett. **5**, 559–576 doi: (2008). [CrossRef]

19. K. Suizu and K. Kawase, “Monochromatic-tunable terahertz-wave sources based on nonlinear frequency conversion using lithium niobate crystal,” IEEE J. Sel. Top. Quantum Electron. **14**(2), 295–306 (2008). [CrossRef]

20. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO_{3},” J. Opt. Soc. Am. B **12**(11), 2102–2116 (1995). [CrossRef]

21. D. Molter, M. Theuer, and R. Beigang, “Nanosecond terahertz optical parametric oscillator with a novel quasi phase matching scheme in lithium niobate,” Opt. Express **17**(8), 6623–6628 (2009). [CrossRef] [PubMed]

29. T. Suhara, Y. Avetisyan, and H. Ito, “Theoretical analysis of laterally emitting Terahertz-wave generation by difference-frequency generation in channel waveguides,” IEEE J. Quantum Electron. **39**(1), 166–171 (2003). [CrossRef]

## 2. Different regimes of OPA/DFG with idler absorption

30. L. Lefort, K. Puech, G. W. Ross, Y. P. Svirko, and D. C. Hanna, “Optical parametric oscillation out to 6.3 μm in periodically poled lithium niobate under strong idler absorption,” Appl. Phys. Lett. **73**(12), 1610–1612 (1998). [CrossRef]

*p*,

*s*, and

*i*denote variables or parameters relevant to the pump, signal, and idler, respectively,

*κ*is the nonlinear coupling coefficient, Δ

*k*=

_{f}*k*−

_{p}*k*−

_{s}*k*is the wave vector mismatch for the co-directional mixing waves, and

_{i}*α*

_{i}is the intensity absorption coefficient of the idler wave. For what follows, the coupled-wave equations describing the variation of the pump, signal, and idler field envelopes are called the pump, signal, and idler equations, respectively. With strong idler absorption, it has been popular to neglect the signal and pump equations. The remaining idler equation can be solved to give the output idler photon flux density at z =

*L*[32

32. D. Zheng, L. A. Gordon, Y. S. Wu, R. S. Feigelson, M. M. Fejer, R. L. Byer, and K. L. Vodopyanov, “16-microm infrared generation by difference-frequency mixing in diffusion-bonded-stacked GaAs,” Opt. Lett. **23**(13), 1010–1012 (1998). [CrossRef] [PubMed]

*k*= 0:where the initial idler component is assumed to be zero in an absorptive material,

_{f}*ϕ*

_{s}(0) is the initial signal photon flux density, and 2Γ is the intensity parametric gain coefficient. Equation (1) indeed indicates power saturation of the idler wave in a material length comparable to the idler absorption length 1/

*α*. Equation (1) and its variants have been widely cited for THz OPA/DFG with strong idler absorption [12

_{i}12. T. Taniuchi and H. Nakanishi, “Collinear phase-matched terahertz-wave generation in GaP crystal using a dual-wavelength optical parametric oscillator,” J. Appl. Phys. **95**, 7588–7591, doi:Doi (2004). [CrossRef]

13. M. Cronin-Golomb, “Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production,” Opt. Lett. **29**(17), 2046–2048 (2004). [CrossRef] [PubMed]

25. 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**(5), 511–514 (2001). [CrossRef]

33. 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**(16), 1454–1456 (2002). [CrossRef] [PubMed]

37. S. Ohno, K. Miyamoto, H. Minamide, and H. Ito, “New method to determine the refractive index and the absorption coefficient of organic nonlinear crystals in the ultra-wideband THz region,” Opt. Express **18**(16), 17306–17312 (2010). [CrossRef] [PubMed]

38. S. Hayashi, K. Nawata, H. Sakai, T. Taira, H. Minamide, and K. Kawase, “High-power, single-longitudinal-mode terahertz-wave generation pumped by a microchip Nd:YAG laser [Invited],” Opt. Express **20**(3), 2881–2886 (2012). [CrossRef] [PubMed]

*could be*valid over a very short crystal length when the input amplitude of the signal is comparable to the pump one. In this regard, the condition of an equal input pump and signal is sometimes satisfied for some DFG experiment. The validity of Eq. (1) has never been rigorously and quantitatively defined within the context of relevant physical parameters. In the following, we first show that, with a variable signal and a strong pump (typical to THz OPA), the growth of the highly absorptive idler wave is not limited to a saturation length predicted by Eq. (1). We then quantitatively show that Eq. (1) can be obtained from a joint consideration of the signal and idler equations under three conditions: (1) no pump depletion, (2) absorption loss much larger than parametric gain, and (3) material length much shorter than the absorption length. Finally we show in an experiment that the fast diffraction of the THz wave in a nonlinear optical material leaves the plane-wave model invalid even in the limit of an equal input pump and signal (typical to THz DFG).

39. G. Kh. Kitaeva and A. N. Penin, “Parametric frequency conversion in layered nonlinear media,” J. Exp. Theor. Phys. **98**(2), 272–286 (2004). [CrossRef]

*k*= 0 and

_{f}*R*= (2Γ)/(

*α*/2) = 4Γ/

_{i}*α*

_{i}, where 2Γ is the intensity parametric gain coefficient and

*α*/2 is the effective loss of the parametric mixing process (see Eq. (4) below).

_{i}### 2.1 High-gain and short-gain-length regime

*R*

^{2}>>1 and short-gain-length Γ

*L*<< 1 limit, Eq. (2) reduces to a compact expressionwhich has the maximum value at the crystal length

*L*= 2/

*α*

_{i}. However, when the crystal length approaches 2/

*α*

_{i}, the condition Γ

*L*<< 1 is violated due to the constraint

*R*

^{2}= (4Γ/

*α*

_{i})

^{2}>> 1. Therefore, it is incorrect to conclude from this regime that the maximum idler output occurs at a length comparable to the idler absorption length or

*L*= 2/

*α*

_{i}.

### 2.2 High-gain and long-gain-length regime

*R*>>1 and long-gain-length Γ

^{2}*L*>> 1 limit, the idler output at z =

*L*becomesEquation (4) indicates an exponential growth of the idler intensity along

*z*similar to that for lossless OPA. It can be understood from Eq. (4) that 2Γ is the intensity parametric gain coefficient and

*α*

_{i}/2 is effectively the idler-absorption induced parametric loss coefficient in a high-gain OPA process. In this regime, the idler power grows exponentially until pump depletion.

### 2.3 High-loss and short-loss-length regime

*R*

^{2}<< 1 and

*α*

_{i}

*L*/2 << 1, the general solution Eq. (2) reduces to Eq. (1). Therefore, quantitatively, Eq. (1) is valid under three conditions: (1) no pump depletion, (2) absorption loss much larger than parametric gain

*R*

^{2}<< 1, (3) material length much shorter than the absorption length

*α*

_{i}

*L*/2 << 1. Condition (3) is not typical in most THz DFG experiments. For example, the THz absorption coefficient in lithium niobate is in the range of 1-100 cm

^{−1}. If one chooses

*α*

_{i}

*L*/2 = 0.1 to satisfy the condition

*α*

_{i}

*L*/2 << 1, Eq. (1) is valid only for a crystal length

*L*between 2 and 0.02 mm. This length is unrealistically short for a practical application. On the other hand, if one chooses a crystal length

*L*<< 2/

*α*

_{i}in the first place to satisfy Condition (3), the experimental result is indeed limited to the idler absorption length as a consequence of that choice, but cannot be generalized to conclude that OPA or DFG with idler absorption is limited to a crystal length comparable to the idler absorption length.

### 2.4 High-loss and long-loss-length regime

*R*

^{2}<< 1 and

*α*

_{i}

*L*/2 >> 1, the idler photon flux density at

*L*, according to Eq. (2), becomesEquation (5) is most interesting in that, in spite of the strong idler absorption

*R*

^{2}<< 1, the idler intensity increases monotonically with

*L*and does not saturate until pump depletion. This result is somewhat counter-intuitive but is a consequence of the paired signal-idler photon generation in an optical parametric process. The growth of the non-absorbing signal can assist the growth of the highly absorbing idler.

*R*= 0.2. The horizontal axis is the crystal length in units of the idler absorption length

*r*=

*ϕ*(0)/

_{s}*ϕ*

_{p}(0) = 0.01 (OPA) and 1 (DFG), where

*ϕ*

_{p}(0) is the initial pump photon flux density. As expected, pump depletion, occurring much faster for DFG (

*r*~1), results in over-estimated output power from both Eqs. (1) and (2). The saturation value of Eq. (1) is somewhat useful for estimating the maximum idler power from a DFG process with idler absorption. However, a THz wave usually diffracts away from the optical beam aperture in THz OPA/DFG. As will be shown below, given the diffraction and an equal input signal and pump, the growth distance of the idler wave is still much longer than the THz absorption length.

## 3. Diffraction-modified plane-wave model

## 4. Experiment with equal input pump and signal

*x*direction. The two end faces of the PPLN-array crystal were optically polished and coated with anti-reflection layers at the pump and signal wavelengths.

*z*direction of the PPLN crystals. A passively Q-switched Nd:YAG microchip laser pumped a pulsed optical parametric amplifier following the Erbium-doped fiber amplifier (EDFA) to produce 9.7-μJ energy in a 360-ps width for each of the pump and signal pulse. The equal-energy signal and pump pulses were then focused to a 127-μm waist radius to the center of the PPLN array crystal for THz DFG. A Ni-metal wire mesh with uniform 45 μm × 45 μm square apertures was installed between the THz-DFG PPLN crystal and the collimating off-axis parabolic mirrors to reflect 86% of the THz wave toward the 4k Si bolometer and dump 84% of the optical waves. A 3-mm thick Germanium THz filter was installed before the 4k Si bolometer to block all the residue optical waves and transmit 35% of the THz wave into the bolometer.

*α*

_{i}= 40 cm

^{−1}, Γ = 0.53 cm

^{−1}, and

*L*= 2.5 cm. The measured absorption coefficient is consistent with the reported value for THz DFG in bulk congruent lithium niobate [21

21. D. Molter, M. Theuer, and R. Beigang, “Nanosecond terahertz optical parametric oscillator with a novel quasi phase matching scheme in lithium niobate,” Opt. Express **17**(8), 6623–6628 (2009). [CrossRef] [PubMed]

40. Y. C. Huang, T. D. Wang, Y. H. Lin, C. H. Lee, M. Y. Chuang, Y. Y. Lin, and F. Y. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express **19**(24), 24577–24582 (2011). [CrossRef] [PubMed]

41. G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of Terahertz wave brightness under nonlinear-optical detection,” J. Infrared. Millim. Te. **32**(10), 1144–1156 (2011). [CrossRef]

*α*= 40 cm

_{i}^{−1}and Γ = 0.53 cm

^{−1}, the gain-to-loss ratio is

*R*= 5.3 × 10

^{−2}, which sets our experiment in the high-loss regime. Given

*d*

_{eff}= 168☓2/π = 107 pm/V [42

42. J. Hebling, A. G. Stepanov, G. Almasi, 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]

*n*

_{p}=

*n*

_{s}= 2.14 [43

43. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, n_{e}, in congruent lithium niobate,” Opt. Lett. **22**(20), 1553–1555 (1997). [CrossRef] [PubMed]

*R*

_{Γ}calculated from Eq. (6) is 4.8 with an average

*w*of 130 μm and

*α*= 40 cm

_{i}^{−1}. Given the uncertainty in the THz material parameters for lithium niobate, the experimentally deduced

*R*

_{Γ}= 4.2 is reasonably close to the theoretically estimated

*R*

_{Γ}= 4.8.

*α*= 37 cm

_{i}^{−1}. With initial signal energy of 9.7 μJ at 1539 nm and an output THz wavelength at 200 μm, the fitted curve suggests 45-pJ peak energy at 1.5 THz generated from the 25-mm long PPLN crystal. This amount of output THz-wave energy matches well to our previously reported experimental value measured by a calibrated bolometer [40

40. Y. C. Huang, T. D. Wang, Y. H. Lin, C. H. Lee, M. Y. Chuang, Y. Y. Lin, and F. Y. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express **19**(24), 24577–24582 (2011). [CrossRef] [PubMed]

## 5. Conclusion

40. Y. C. Huang, T. D. Wang, Y. H. Lin, C. H. Lee, M. Y. Chuang, Y. Y. Lin, and F. Y. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express **19**(24), 24577–24582 (2011). [CrossRef] [PubMed]

*R*

^{2}<< 1 and short crystal length

*L*<< 2/

*α*

_{i}. The only assumptions made to derive Eq. (2) are: (1) the slowly varying envelope approximation, (2) plane-wave like fields, and (3) an undepleted pump. When the signal-to-pump ratio

*r*approaches 1 for DFG, pump depletion can occur quickly in a short crystal and the valid regime of Eq. (2) merges with that of Eq. (1) in the short-crystal limit. However, in practice, the THz wave in THz DFG can diffract much faster than the optical mixing waves for an optical beam size comparable to the THz wavelength. Consequently, the pump-depletion induced idler saturation does not occur in a short crystal as predicted by Eq. (1). By using equal-amplitude pump and signal as the inputs to a co-directional THz difference frequency generator, we show the growth of an idler wave at 1.5 THz over a crystal length exceeding 40 idler absorption lengths. In this experiment, the effective parametric loss is nearly 20 times the parametric gain.

## Acknowledgments

## References and links

1. | J. M. Yarborough, S. S. Sussman, H. E. Purhoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO |

2. | B. C. Johnson, H. E. Puthoff, J. Soohoo, and S. S. Sussman, “Power and linewidth of tunable stimulated far-infrared emission in LiNbO |

3. | M. A. Piestrup, R. N. Fleming, and R. H. Pantell, “Continuously tunable submillimeter wave source,” Appl. Phys. Lett. |

4. | K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D Appl. Phys. |

5. | L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO |

6. | K. Kawase, M. Sato, K. Nakamura, T. Taniuchi, and H. Ito, “Unidirectional radiation of widely tunable THz wave using a prism coupler under noncollinear phase matching condition,” Appl. Phys. Lett. |

7. | K. Kawase, M. Sato, T. Taniuchi, and H. Ito, “Coherent tunable THz-wave generation from LiNbO |

8. | K. Kawase, J. Shikata, H. Minamide, K. Imai, and H. Ito, “Arrayed silicon prism coupler for a terahertz-wave parametric oscillator,” Appl. Opt. |

9. | K. Suizu, T. Tsutsui, T. Shibuya, T. Akiba, and K. Kawase, “Cherenkov phase matched THz-wave generation with surfing configuration for bulk lithium nobate crystal,” Opt. Express |

10. | J. B. Khurgin, D. Yang, and Y. J. Ding, “Generation of mid-infrared radiation in the highly-absorbing nonlinear medium,” J. Opt. Soc. Am. B |

11. | A. G. Stepanov, J. Hebling, and J. Kuhl, “Efficient generation of subpicosecond terahertz radiation by phase-matched optical rectification using ultrashort laser pulses with tilted pulse fronts,” Appl Phys Lett |

12. | T. Taniuchi and H. Nakanishi, “Collinear phase-matched terahertz-wave generation in GaP crystal using a dual-wavelength optical parametric oscillator,” J. Appl. Phys. |

13. | M. Cronin-Golomb, “Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production,” Opt. Lett. |

14. | K. Kawase, K. Suizu, and S. Hayashi, and T. Shibuya” Nonlinear optical terahertz wave sources,” Opt. Spectroscopy |

15. | J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quant. |

16. | G. Kh. Kitaeva, “THz generation by means of optical laser,” Laser Phys. Lett. |

17. | J. A. L’huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate – Part 1: Theory,” Appl. Phys. B. |

18. | J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, R. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate – Part 2: Experiments,” Appl. Phys. B. |

19. | K. Suizu and K. Kawase, “Monochromatic-tunable terahertz-wave sources based on nonlinear frequency conversion using lithium niobate crystal,” IEEE J. Sel. Top. Quantum Electron. |

20. | L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO |

21. | D. Molter, M. Theuer, and R. Beigang, “Nanosecond terahertz optical parametric oscillator with a novel quasi phase matching scheme in lithium niobate,” Opt. Express |

22. | C. Weiss, G. Torosyan, Y. Avetisyan, and R. Beigang, “Generation of tunable narrow-band surface-emitted terahertz radiation in periodically poled lithium niobate,” Opt. Lett. |

23. | Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique,” Opt. Lett. |

24. | 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. |

25. | 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. |

26. | Y. Sasaki, Y. Avetisyan, K. Kawase, and H. Ito, “Terahertz-wave surface-emitted difference-frequency generation in slant-stripe-type periodically poled LiNbO |

27. | 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. |

28. | Y. Sasaki, H. Yokoyama, and H. Ito, “Surface-emitted continuous-wave terahertz radiation using periodically poled lithium niobate,” Electron. Lett. |

29. | T. Suhara, Y. Avetisyan, and H. Ito, “Theoretical analysis of laterally emitting Terahertz-wave generation by difference-frequency generation in channel waveguides,” IEEE J. Quantum Electron. |

30. | L. Lefort, K. Puech, G. W. Ross, Y. P. Svirko, and D. C. Hanna, “Optical parametric oscillation out to 6.3 μm in periodically poled lithium niobate under strong idler absorption,” Appl. Phys. Lett. |

31. | A. Yariv and P. Yeh, |

32. | D. Zheng, L. A. Gordon, Y. S. Wu, R. S. Feigelson, M. M. Fejer, R. L. Byer, and K. L. Vodopyanov, “16-microm infrared generation by difference-frequency mixing in diffusion-bonded-stacked GaAs,” Opt. Lett. |

33. | 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. |

34. | K. Zhong, J. Yao, D. Xu, Z. Wang, Z. Li, H. Zhang, and P. Wang, “Enhancement of terahertz wave difference frequency generation based on a compact walk-off compensated KTP OPO,” Opt. Commun. |

35. | 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. |

36. | K. Kawase, M. Mizuno, S. Sohma, H. Takahashi, T. Taniuchi, Y. Urata, S. Wada, H. Tashiro, and H. Ito, “Difference-frequency terahertz-wave generation from 4-dimethylamino-N-methyl-4-stilbazolium-tosylate by use of an electronically tuned Ti:sapphire laser,” Opt. Lett. |

37. | S. Ohno, K. Miyamoto, H. Minamide, and H. Ito, “New method to determine the refractive index and the absorption coefficient of organic nonlinear crystals in the ultra-wideband THz region,” Opt. Express |

38. | S. Hayashi, K. Nawata, H. Sakai, T. Taira, H. Minamide, and K. Kawase, “High-power, single-longitudinal-mode terahertz-wave generation pumped by a microchip Nd:YAG laser [Invited],” Opt. Express |

39. | G. Kh. Kitaeva and A. N. Penin, “Parametric frequency conversion in layered nonlinear media,” J. Exp. Theor. Phys. |

40. | Y. C. Huang, T. D. Wang, Y. H. Lin, C. H. Lee, M. Y. Chuang, Y. Y. Lin, and F. Y. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express |

41. | G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of Terahertz wave brightness under nonlinear-optical detection,” J. Infrared. Millim. Te. |

42. | J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B. |

43. | D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, n |

**OCIS Codes**

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: November 28, 2012

Manuscript Accepted: January 14, 2013

Published: January 24, 2013

**Citation**

Tsong-Dong Wang, Yen-Chieh Huang, Ming-Yun Chuang, Yen-Hou Lin, Ching-Han Lee, Yen-Yin Lin, Fan-Yi Lin, and Galiya Kh. Kitaeva, "Long-range parametric amplification of THz wave with absorption loss exceeding parametric gain," Opt. Express **21**, 2452-2462 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-2452

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### References

- J. M. Yarborough, S. S. Sussman, H. E. Purhoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO3 without a resonator,” Appl. Phys. Lett.15(3), 102–105 (1969). [CrossRef]
- B. C. Johnson, H. E. Puthoff, J. Soohoo, and S. S. Sussman, “Power and linewidth of tunable stimulated far-infrared emission in LiNbO3,” Appl. Phys. Lett.18(5), 181–183 (1971). [CrossRef]
- M. A. Piestrup, R. N. Fleming, and R. H. Pantell, “Continuously tunable submillimeter wave source,” Appl. Phys. Lett.26(8), 418–421 (1975). [CrossRef]
- K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D Appl. Phys.35(3), R1–R14 (2002). [CrossRef]
- 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 (2005), doi:. [CrossRef]
- K. Kawase, M. Sato, K. Nakamura, T. Taniuchi, and H. Ito, “Unidirectional radiation of widely tunable THz wave using a prism coupler under noncollinear phase matching condition,” Appl. Phys. Lett.71(6), 753–755 (1997). [CrossRef]
- K. Kawase, M. Sato, T. Taniuchi, and H. Ito, “Coherent tunable THz-wave generation from LiNbO3 with monolithic grating coupler,” Appl. Phys. Lett.68(18), 2483–2485 (1996). [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(9), 1423–1426 (2001). [CrossRef] [PubMed]
- K. Suizu, T. Tsutsui, T. Shibuya, T. Akiba, and K. Kawase, “Cherenkov phase matched THz-wave generation with surfing configuration for bulk lithium nobate crystal,” Opt. Express17(9), 7102–7109 (2009). [CrossRef] [PubMed]
- J. B. Khurgin, D. Yang, and Y. J. Ding, “Generation of mid-infrared radiation in the highly-absorbing nonlinear medium,” J. Opt. Soc. Am. B18(3), 340–343 (2001). [CrossRef]
- A. G. Stepanov, J. Hebling, and J. Kuhl, “Efficient generation of subpicosecond terahertz radiation by phase-matched optical rectification using ultrashort laser pulses with tilted pulse fronts,” Appl Phys Lett83, 3000–3002 doi:Doi (2003). [CrossRef]
- T. Taniuchi and H. Nakanishi, “Collinear phase-matched terahertz-wave generation in GaP crystal using a dual-wavelength optical parametric oscillator,” J. Appl. Phys. 95, 7588–7591, doi:Doi (2004). [CrossRef]
- M. Cronin-Golomb, “Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production,” Opt. Lett.29(17), 2046–2048 (2004). [CrossRef] [PubMed]
- K. Kawase, K. Suizu, and S. Hayashi, and T. Shibuya” Nonlinear optical terahertz wave sources,” Opt. Spectroscopy 108, 841–845, doi:Doi (2010). [CrossRef]
- J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quant. 14, 354–362, doi:Doi (2008). [CrossRef]
- G. Kh. Kitaeva, “THz generation by means of optical laser,” Laser Phys. Lett. 5, 559–576 doi: (2008). [CrossRef]
- J. A. L’huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate – Part 1: Theory,” Appl. Phys. B.86(2), 185–196 (2007). [CrossRef]
- J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, R. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate – Part 2: Experiments,” Appl. Phys. B.86(2), 197–208 (2007). [CrossRef]
- K. Suizu and K. Kawase, “Monochromatic-tunable terahertz-wave sources based on nonlinear frequency conversion using lithium niobate crystal,” IEEE J. Sel. Top. Quantum Electron.14(2), 295–306 (2008). [CrossRef]
- L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B12(11), 2102–2116 (1995). [CrossRef]
- D. Molter, M. Theuer, and R. Beigang, “Nanosecond terahertz optical parametric oscillator with a novel quasi phase matching scheme in lithium niobate,” Opt. Express17(8), 6623–6628 (2009). [CrossRef] [PubMed]
- C. Weiss, G. Torosyan, Y. Avetisyan, and R. Beigang, “Generation of tunable narrow-band surface-emitted terahertz radiation in periodically poled lithium niobate,” Opt. Lett.26(8), 563–565 (2001). [CrossRef] [PubMed]
- Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique,” Opt. Lett.35(15), 2508–2510 (2010). [CrossRef] [PubMed]
- 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(7), 957–959 (2006). [CrossRef] [PubMed]
- 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(5), 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).
- 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(21), 2927–2929 (2005). [CrossRef] [PubMed]
- Y. Sasaki, H. Yokoyama, and H. Ito, “Surface-emitted continuous-wave terahertz radiation using periodically poled lithium niobate,” Electron. Lett.41(12), 712–713 (2005). [CrossRef]
- T. Suhara, Y. Avetisyan, and H. Ito, “Theoretical analysis of laterally emitting Terahertz-wave generation by difference-frequency generation in channel waveguides,” IEEE J. Quantum Electron.39(1), 166–171 (2003). [CrossRef]
- L. Lefort, K. Puech, G. W. Ross, Y. P. Svirko, and D. C. Hanna, “Optical parametric oscillation out to 6.3 μm in periodically poled lithium niobate under strong idler absorption,” Appl. Phys. Lett.73(12), 1610–1612 (1998). [CrossRef]
- A. Yariv and P. Yeh, Photonics, 6th Ed. (Oxford University Press, New York, Oxford, 2007).
- D. Zheng, L. A. Gordon, Y. S. Wu, R. S. Feigelson, M. M. Fejer, R. L. Byer, and K. L. Vodopyanov, “16-microm infrared generation by difference-frequency mixing in diffusion-bonded-stacked GaAs,” Opt. Lett.23(13), 1010–1012 (1998). [CrossRef] [PubMed]
- 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(16), 1454–1456 (2002). [CrossRef] [PubMed]
- K. Zhong, J. Yao, D. Xu, Z. Wang, Z. Li, H. Zhang, and P. Wang, “Enhancement of terahertz wave difference frequency generation based on a compact walk-off compensated KTP OPO,” Opt. Commun.283(18), 3520–3524 (2010). [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(40), L982–L984 (2007). [CrossRef]
- K. Kawase, M. Mizuno, S. Sohma, H. Takahashi, T. Taniuchi, Y. Urata, S. Wada, H. Tashiro, and H. Ito, “Difference-frequency terahertz-wave generation from 4-dimethylamino-N-methyl-4-stilbazolium-tosylate by use of an electronically tuned Ti:sapphire laser,” Opt. Lett.24(15), 1065–1067 (1999). [CrossRef] [PubMed]
- S. Ohno, K. Miyamoto, H. Minamide, and H. Ito, “New method to determine the refractive index and the absorption coefficient of organic nonlinear crystals in the ultra-wideband THz region,” Opt. Express18(16), 17306–17312 (2010). [CrossRef] [PubMed]
- S. Hayashi, K. Nawata, H. Sakai, T. Taira, H. Minamide, and K. Kawase, “High-power, single-longitudinal-mode terahertz-wave generation pumped by a microchip Nd:YAG laser [Invited],” Opt. Express20(3), 2881–2886 (2012). [CrossRef] [PubMed]
- G. Kh. Kitaeva and A. N. Penin, “Parametric frequency conversion in layered nonlinear media,” J. Exp. Theor. Phys.98(2), 272–286 (2004). [CrossRef]
- Y. C. Huang, T. D. Wang, Y. H. Lin, C. H. Lee, M. Y. Chuang, Y. Y. Lin, and F. Y. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express19(24), 24577–24582 (2011). [CrossRef] [PubMed]
- G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of Terahertz wave brightness under nonlinear-optical detection,” J. Infrared. Millim. Te.32(10), 1144–1156 (2011). [CrossRef]
- J. Hebling, A. G. Stepanov, G. Almasi, 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]
- D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett.22(20), 1553–1555 (1997). [CrossRef] [PubMed]

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