Abstract

We demonstrate picosecond terahertz (THz)-wave generation via four-wave mixing in an octagonal photonic crystal fiber (O-PCF). Perfect phase-matching is obtained at the pump wavelength of 1.55μm and a generation scheme is proposed. Using this method, THz waves can be generated in the frequency range of 7.077.74THz. Moreover, peak power of 2.55W, average power of 1.53mW, and peak conversion efficiency of more than 66.65dB at 7.42THz in a 6.25cm long fiber are realized with a pump peak power of 2kW.

© 2011 Optical Society of America

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    [CrossRef]
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2010 (3)

2008 (3)

J.-Y. Lu, C.-P. Yu, H.-C. Chang, H.-W. Chen, Y.-T. Li, C.-L. Pan, and C.-K. Sun, “Terahertz air-core microstructure fiber,” Appl. Phys. Lett. 92, 064105 (2008).
[CrossRef]

L. Ho, M. Pepper, and P. Taday, “Terahertz spectroscopy: Signatures and fingerprints,” Nat. Photon. 2, 541–543 (2008).
[CrossRef]

S. M. Abdur Razzak and Yoshinori Namihira, “Proposal for highly nonlinear dispersion-flattened octagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 20, 249–251(2008).
[CrossRef]

2007 (1)

2006 (1)

J.-S. Chiang and T.-L. Wu, “Analysis of propagation characteristics for an octagonal photonic crystal fiber (O-PCF),” Opt. Commun. 258, 170–176 (2006).
[CrossRef]

2005 (1)

K. K. Chow, C. Shu, C. Lin, and A. Bjarklev, “Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic Crystal fiber,” IEEE Photon. Technol. Lett. 17, 624–626(2005).
[CrossRef]

2004 (1)

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, 124–125 (2004).
[CrossRef]

2003 (2)

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]

J. H. Lee, W. Belardi, K. Furusawa, P. Petropoulos, Z. Yusoff, T. M. Monro, and D. J. Richardson, “Four-wave mixing based 10 Gb/s tunable wavelength conversion using a holey fiber with a high SBS threshold,” IEEE Photon. Technol. Lett. 15, 440–442 (2003).
[CrossRef]

2002 (5)

A. S. Nikoghosyan, E. M. Laziev, R. M. Martirosyan, and A. A. Hakhoumian, “Efficient ultrashort light pulse conversion in GHz-THz pulses in ZnTe, GaAs, and DAST crystals,” Proc. SPIE 4752, 40–48 (2002).
[CrossRef]

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26–33 (2002).
[CrossRef]

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634–2636 (2002).
[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. P. White, R. C. McPhedran, C. M. Sterke, N. M. Litchinitser, and B. J. Eggleton, “Resonance and scattering in microstructured optical fibers,” Opt. Lett. 27, 1977–1979 (2002).
[CrossRef]

2001 (1)

1998 (1)

1992 (2)

N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28, 2291–2301 (1992).
[CrossRef]

L. Xu, X.-C. Zhang, and D. H. Auston, “Terahertz beam generation by femtosecond optical pulses in electro-optic materials,” Appl. Phys. Lett. 61, 1784–1787 (1992).
[CrossRef]

1985 (1)

1981 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).

Auston, D. H.

N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28, 2291–2301 (1992).
[CrossRef]

L. Xu, X.-C. Zhang, and D. H. Auston, “Terahertz beam generation by femtosecond optical pulses in electro-optic materials,” Appl. Phys. Lett. 61, 1784–1787 (1992).
[CrossRef]

Belardi, W.

J. H. Lee, W. Belardi, K. Furusawa, P. Petropoulos, Z. Yusoff, T. M. Monro, and D. J. Richardson, “Four-wave mixing based 10 Gb/s tunable wavelength conversion using a holey fiber with a high SBS threshold,” IEEE Photon. Technol. Lett. 15, 440–442 (2003).
[CrossRef]

Bjarklev, A.

K. K. Chow, C. Shu, C. Lin, and A. Bjarklev, “Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic Crystal fiber,” IEEE Photon. Technol. Lett. 17, 624–626(2005).
[CrossRef]

Bösch,

Chang, H.-C.

J.-Y. Lu, C.-P. Yu, H.-C. Chang, H.-W. Chen, Y.-T. Li, C.-L. Pan, and C.-K. Sun, “Terahertz air-core microstructure fiber,” Appl. Phys. Lett. 92, 064105 (2008).
[CrossRef]

Chen, H.-W.

J.-Y. Lu, C.-P. Yu, H.-C. Chang, H.-W. Chen, Y.-T. Li, C.-L. Pan, and C.-K. Sun, “Terahertz air-core microstructure fiber,” Appl. Phys. Lett. 92, 064105 (2008).
[CrossRef]

Chiang, J.-S.

J.-S. Chiang and T.-L. Wu, “Analysis of propagation characteristics for an octagonal photonic crystal fiber (O-PCF),” Opt. Commun. 258, 170–176 (2006).
[CrossRef]

Cho, M.

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634–2636 (2002).
[CrossRef]

Chow, K. K.

K. K. Chow, C. Shu, C. Lin, and A. Bjarklev, “Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic Crystal fiber,” IEEE Photon. Technol. Lett. 17, 624–626(2005).
[CrossRef]

Coker, Ayodeji

Dawson, P.

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, 124–125 (2004).
[CrossRef]

Ding, Y. J.

Eggleton, B. J.

Ferguson, B.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26–33 (2002).
[CrossRef]

Fernelius, N.

Fiorentino, Marco

Froberg, N. M.

N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28, 2291–2301 (1992).
[CrossRef]

Furusawa, K.

J. H. Lee, W. Belardi, K. Furusawa, P. Petropoulos, Z. Yusoff, T. M. Monro, and D. J. Richardson, “Four-wave mixing based 10 Gb/s tunable wavelength conversion using a holey fiber with a high SBS threshold,” IEEE Photon. Technol. Lett. 15, 440–442 (2003).
[CrossRef]

Hakhoumian, A. A.

A. S. Nikoghosyan, E. M. Laziev, R. M. Martirosyan, and A. A. Hakhoumian, “Efficient ultrashort light pulse conversion in GHz-THz pulses in ZnTe, GaAs, and DAST crystals,” Proc. SPIE 4752, 40–48 (2002).
[CrossRef]

Han, H.

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634–2636 (2002).
[CrossRef]

Hein, G.

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, 124–125 (2004).
[CrossRef]

Ho, L.

L. Ho, M. Pepper, and P. Taday, “Terahertz spectroscopy: Signatures and fingerprints,” Nat. Photon. 2, 541–543 (2008).
[CrossRef]

Hochrein, T.

Hu, B. B.

N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28, 2291–2301 (1992).
[CrossRef]

Huang, Y.-W.

Hwang, Y.-J

Islam, M. N.

Jansen, C.

Jördens, C.

Kao, Y.-H.

Kawase, K.

Kim, J.

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634–2636 (2002).
[CrossRef]

Kimura, T.

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]

Kitayama, K.

Kleine-Ostmann, T.

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, 124–125 (2004).
[CrossRef]

Koch, M.

C. Jansen, S. Wietzke, O. Peters, M. Scheller, N. Vieweg, M. Salhi, N. Krumbholz, C. Jördens, T. Hochrein, and M. Koch, “Terahertz imaging: applications and perspectives,” Appl. Opt. 49, E48–E57 (2010).
[CrossRef] [PubMed]

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, 124–125 (2004).
[CrossRef]

Kraus, J. D.

J. D. Kraus, Radio Astronomy (Cygnus-Quasar, 1986).

Krumbholz, N.

Kumar, Prem

Kuo, C.-C

Laziev, E. M.

A. S. Nikoghosyan, E. M. Laziev, R. M. Martirosyan, and A. A. Hakhoumian, “Efficient ultrashort light pulse conversion in GHz-THz pulses in ZnTe, GaAs, and DAST crystals,” Proc. SPIE 4752, 40–48 (2002).
[CrossRef]

Lee, J. H.

J. H. Lee, W. Belardi, K. Furusawa, P. Petropoulos, Z. Yusoff, T. M. Monro, and D. J. Richardson, “Four-wave mixing based 10 Gb/s tunable wavelength conversion using a holey fiber with a high SBS threshold,” IEEE Photon. Technol. Lett. 15, 440–442 (2003).
[CrossRef]

Li, Y.-T.

J.-Y. Lu, C.-P. Yu, H.-C. Chang, H.-W. Chen, Y.-T. Li, C.-L. Pan, and C.-K. Sun, “Terahertz air-core microstructure fiber,” Appl. Phys. Lett. 92, 064105 (2008).
[CrossRef]

Lin, C.

K. K. Chow, C. Shu, C. Lin, and A. Bjarklev, “Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic Crystal fiber,” IEEE Photon. Technol. Lett. 17, 624–626(2005).
[CrossRef]

R. H. Stolen, Bösch, and C. Lin, “Phase matching in birefringent fibers,” Opt. Lett. 6, 213–215 (1981).
[CrossRef] [PubMed]

Litchinitser, N. M.

Lu, J.-Y.

J.-Y. Lu, C.-P. Yu, H.-C. Chang, H.-W. Chen, Y.-T. Li, C.-L. Pan, and C.-K. Sun, “Terahertz air-core microstructure fiber,” Appl. Phys. Lett. 92, 064105 (2008).
[CrossRef]

Martirosyan, R. M.

A. S. Nikoghosyan, E. M. Laziev, R. M. Martirosyan, and A. A. Hakhoumian, “Efficient ultrashort light pulse conversion in GHz-THz pulses in ZnTe, GaAs, and DAST crystals,” Proc. SPIE 4752, 40–48 (2002).
[CrossRef]

McPhedran, R. C.

Monro, T. M.

J. H. Lee, W. Belardi, K. Furusawa, P. Petropoulos, Z. Yusoff, T. M. Monro, and D. J. Richardson, “Four-wave mixing based 10 Gb/s tunable wavelength conversion using a holey fiber with a high SBS threshold,” IEEE Photon. Technol. Lett. 15, 440–442 (2003).
[CrossRef]

Namihira, Yoshinori

S. M. Abdur Razzak and Yoshinori Namihira, “Proposal for highly nonlinear dispersion-flattened octagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 20, 249–251(2008).
[CrossRef]

Nikoghosyan, A. S.

A. S. Nikoghosyan, E. M. Laziev, R. M. Martirosyan, and A. A. Hakhoumian, “Efficient ultrashort light pulse conversion in GHz-THz pulses in ZnTe, GaAs, and DAST crystals,” Proc. SPIE 4752, 40–48 (2002).
[CrossRef]

Nishizawa, J.

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]

Nowak, G. A.

Ohashi, M.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

Pan, C.-L.

J.-Y. Lu, C.-P. Yu, H.-C. Chang, H.-W. Chen, Y.-T. Li, C.-L. Pan, and C.-K. Sun, “Terahertz air-core microstructure fiber,” Appl. Phys. Lett. 92, 064105 (2008).
[CrossRef]

Park, H.

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634–2636 (2002).
[CrossRef]

Pepper, M.

L. Ho, M. Pepper, and P. Taday, “Terahertz spectroscopy: Signatures and fingerprints,” Nat. Photon. 2, 541–543 (2008).
[CrossRef]

Peters, O.

Petropoulos, P.

J. H. Lee, W. Belardi, K. Furusawa, P. Petropoulos, Z. Yusoff, T. M. Monro, and D. J. Richardson, “Four-wave mixing based 10 Gb/s tunable wavelength conversion using a holey fiber with a high SBS threshold,” IEEE Photon. Technol. Lett. 15, 440–442 (2003).
[CrossRef]

Pierz, K.

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, 124–125 (2004).
[CrossRef]

Razzak, S. M. Abdur

S. M. Abdur Razzak and Yoshinori Namihira, “Proposal for highly nonlinear dispersion-flattened octagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 20, 249–251(2008).
[CrossRef]

Richardson, D. J.

J. H. Lee, W. Belardi, K. Furusawa, P. Petropoulos, Z. Yusoff, T. M. Monro, and D. J. Richardson, “Four-wave mixing based 10 Gb/s tunable wavelength conversion using a holey fiber with a high SBS threshold,” IEEE Photon. Technol. Lett. 15, 440–442 (2003).
[CrossRef]

Saito, K.

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]

Salhi, M.

Scheller, M.

Seikai, S.

Setti, V.

L. Vincetti, V. Setti, and M. Zoboli, “Terahertz tube lattice fibers with octagonal symmetry,” IEEE Photon. Technol. Lett. 22, 972–974 (2010).
[CrossRef]

Sharping, Jay E.

Shi, W.

Shibata, N.

Shu, C.

K. K. Chow, C. Shu, C. Lin, and A. Bjarklev, “Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic Crystal fiber,” IEEE Photon. Technol. Lett. 17, 624–626(2005).
[CrossRef]

Sterke, C. M.

Stolen, R. H.

Suizu, K.

Sun, C.-K.

Y.-W. Huang, T.-F. Tseng, C.-C Kuo, Y.-J Hwang, and C.-K. Sun, “Fiber-based swept-source terahertz radar,” Opt. Lett. 35, 1344–1346 (2010).
[CrossRef] [PubMed]

J.-Y. Lu, C.-P. Yu, H.-C. Chang, H.-W. Chen, Y.-T. Li, C.-L. Pan, and C.-K. Sun, “Terahertz air-core microstructure fiber,” Appl. Phys. Lett. 92, 064105 (2008).
[CrossRef]

Sutherland, R. L.

R. L. Sutherland, Handbook of Nonlinear Optics (Dekker, 2003).
[CrossRef]

Suto, K.

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]

Taday, P.

L. Ho, M. Pepper, and P. Taday, “Terahertz spectroscopy: Signatures and fingerprints,” Nat. Photon. 2, 541–543 (2008).
[CrossRef]

Tanabe, T.

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]

Tseng, T.-F.

Vieweg, N.

Vincetti, L.

L. Vincetti, V. Setti, and M. Zoboli, “Terahertz tube lattice fibers with octagonal symmetry,” IEEE Photon. Technol. Lett. 22, 972–974 (2010).
[CrossRef]

Vodopyanov, K.

White, T. P.

Wietzke, S.

Wu, T.-L.

J.-S. Chiang and T.-L. Wu, “Analysis of propagation characteristics for an octagonal photonic crystal fiber (O-PCF),” Opt. Commun. 258, 170–176 (2006).
[CrossRef]

Xia, T. J.

Xu, L.

L. Xu, X.-C. Zhang, and D. H. Auston, “Terahertz beam generation by femtosecond optical pulses in electro-optic materials,” Appl. Phys. Lett. 61, 1784–1787 (1992).
[CrossRef]

Yu, C.-P.

J.-Y. Lu, C.-P. Yu, H.-C. Chang, H.-W. Chen, Y.-T. Li, C.-L. Pan, and C.-K. Sun, “Terahertz air-core microstructure fiber,” Appl. Phys. Lett. 92, 064105 (2008).
[CrossRef]

Yusoff, Z.

J. H. Lee, W. Belardi, K. Furusawa, P. Petropoulos, Z. Yusoff, T. M. Monro, and D. J. Richardson, “Four-wave mixing based 10 Gb/s tunable wavelength conversion using a holey fiber with a high SBS threshold,” IEEE Photon. Technol. Lett. 15, 440–442 (2003).
[CrossRef]

Zhang, X.-C.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26–33 (2002).
[CrossRef]

L. Xu, X.-C. Zhang, and D. H. Auston, “Terahertz beam generation by femtosecond optical pulses in electro-optic materials,” Appl. Phys. Lett. 61, 1784–1787 (1992).
[CrossRef]

N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28, 2291–2301 (1992).
[CrossRef]

Zoboli, M.

L. Vincetti, V. Setti, and M. Zoboli, “Terahertz tube lattice fibers with octagonal symmetry,” IEEE Photon. Technol. Lett. 22, 972–974 (2010).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

L. Xu, X.-C. Zhang, and D. H. Auston, “Terahertz beam generation by femtosecond optical pulses in electro-optic materials,” Appl. Phys. Lett. 61, 1784–1787 (1992).
[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]

J.-Y. Lu, C.-P. Yu, H.-C. Chang, H.-W. Chen, Y.-T. Li, C.-L. Pan, and C.-K. Sun, “Terahertz air-core microstructure fiber,” Appl. Phys. Lett. 92, 064105 (2008).
[CrossRef]

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634–2636 (2002).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic diagram of the whole structure. (b) The specific structure of the O-PCF.

Fig. 2
Fig. 2

Schematic of (a) energy-conservation diagram and the phase-matching conditions for (b).

Fig. 3
Fig. 3

Signal wavelength λ 2 (dashed curve) and related THz- frequency (solid curve) depend on λ 1 for phase-matching.

Fig. 4
Fig. 4

Scheme of the generation used to investigate FWM in PCFs. L1, L2: YDL; PC1, PC2: fiber polarization controllers; O-PCF: an octagonal PCF.

Fig. 5
Fig. 5

By changing the length of O-PCF ranging from 5.30 cm to 7.30 cm , the peak power of 7.42 THz -wave at zero-dispersion wavelength 1.55 μm has a maximum value of 2.55 W at 6.25 cm .

Fig. 6
Fig. 6

At the length of 6.25 cm with O-PCF, the peak power of the THz-wave ranging from 7.07 THz to 7.74 THz is obtained.

Fig. 7
Fig. 7

Conversion efficiency versus THz-frequency detuned from 7.07 THz to 7.74 THz .

Fig. 8
Fig. 8

Temporal domain pulse of the THz-wave detuned at 7.07 7.74 THz with a 2 kW pump beam λ 1 ( 1.55 μm ) along a 6.25 cm long O-PCF.

Equations (11)

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A 1 z + β 11 A 1 t + i 2 β 21 2 A 1 t 2 1 2 α 1 A 1 = i γ 1 [ ( | A 1 | 2 + 2 | A 2 | 2 + 2 | A 3 | 2 ) A 1 + 2 A 1 * A 2 A 3 exp ( i Δ k z ) ,
A 2 z + β 12 A 2 t + i 2 β 22 2 A 2 t 2 1 2 α 2 A 2 = i γ 2 [ ( | A 2 | 2 + 2 | A 1 | 2 + 2 | A 3 | 2 ) A 2 + 2 A 1 2 A 3 * exp ( i Δ k z ) ,
A 3 z + β 13 A 3 t + i 2 β 23 2 A 3 t 2 1 2 α 3 A 3 = i γ 3 [ ( | A 3 | 2 + 2 | A 1 | 2 + 2 | A 2 | 2 ) A 3 + 2 A 1 2 A 2 * exp ( i Δ k z ) .
A 1 z + i 2 β 21 2 A 1 T 2 1 2 α 1 A 1 = i γ 1 [ ( | A 1 | 2 + 2 | A 2 | 2 + 2 | A 3 | 2 ) A 1 + 2 A 1 * A 2 A 3 exp ( i Δ k z ) ,
A 2 z + h 2 A 2 T + i 2 β 22 2 A 2 T 2 1 2 α 2 A 2 = i γ 2 [ ( | A 2 | 2 + 2 | A 1 | 2 + 2 | A 3 | 2 ) A 2 + 2 A 1 2 A 3 * exp ( i Δ k z ) ,
A 3 z + h 3 A 3 T + i 2 β 23 2 A 3 T 2 1 2 α 3 A 3 = i γ 3 [ ( | A 3 | 2 + 2 | A 1 | 2 + 2 | A 2 | 2 ) A 3 + 2 A 1 2 A 2 * exp ( i Δ k z ) ,
ω THz = 2 ω 1 ω 2 ,
2 k 1 k 2 k THz + 2 γ P 1 = 0 ,
λ THz = λ 1 λ 2 2 λ 2 λ 1 ,
λ THz = π n THz 2 π n 1 λ 2 π n 2 λ 1 + γ P 1 λ 1 λ 2 λ 1 λ 2 ,
V eff = k Λ F 1 / 2 ( n eff 2 n o 2 ) 1 / 2 ,

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