Abstract

The phase-matching condition for broadband terahertz (THz) wave generation based on optical rectification requires that the group velocity of the optical pump beam be equal to the phase velocity of the THz wave. The design of GaP THz waveguide emitters in the form of photonic crystal fibers (PCFs) for a pump source of wavelength 1040 nm is reported. By analogy with a circular waveguide emitter, we show how the phase-matched THz wave frequency can be tuned widely by the air hole pitch and finely tuned by the air hole size. In addition, a single THz wave mode can be guided in the endlessly single-mode regime of the fiber waveguide. The layers of air holes in the PCF design not only allow tunability of the generated THz radiation but also make small emitters easy to handle.

© 2012 Optical Society of America

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2012 (2)

T. Chen, J. Sun, L. Li, J. Tang, and Y. Zhou, “Design of a photonic crystal waveguide for terahertz-wave difference-frequency generation,” IEEE Photon. Technol. Lett. 24, 921–923 (2012).
[CrossRef]

J.-S. Li and S. Zouhdi, “Fano resonance filtering characteristic of high-resistivity silicon photonic crystal slab in terahertz region,” IEEE Photon. Technol. Lett. 24, 625–627 (2012).
[CrossRef]

2011 (2)

H. Wu, H. Liu, N. Huang, Q. Sun, and J. Wen, “High-power picosecond terahertz-wave generation in photonic crystal fiber via four-wave mixing,” Appl. Opt. 50, 5338–5343 (2011).
[CrossRef]

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B 103, 45–50 (2011).
[CrossRef]

2010 (1)

F. Liu, Y.-J. Song, Q.-R. Xing, M.-L. Hu, Y.-F. Li, C.-L. Wang, L. Chai, W.-L. Zhang, A. M. Zheltikov, and C.-Y. Wang, “Broadband terahertz pulses generated by a compact femtosecond photonic crystal fiber amplifier,” IEEE Photon. Technol. Lett. 22, 814–816 (2010).
[CrossRef]

2009 (3)

2008 (3)

2007 (3)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[CrossRef]

J.-I. Nishizawa, K. Suto, T. Tanabe, K. Saito, T. Kimura, and Y. Oyama, “THz generation from GaP rod-type waveguides,” IEEE Photon. Technol. Lett. 19, 143–145 (2007).
[CrossRef]

G. Chang, C. J. Divin, J. Yang, M. A. Musheinish, S. L. Williamson, A. Galvanauskas, and T. B. Norris, “GaP waveguide emitters for high power broadband THz generation pumped by Yb-doped fiber lasers,” Opt. Express 15, 16308–16315 (2007).
[CrossRef]

2006 (2)

2005 (2)

2003 (2)

J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003).
[CrossRef]

W. Shi and Y. J. Ding, “Designs of terahertz waveguides for efficient parametric terahertz generation,” Appl. Phys. Lett. 82, 4435–4437 (2003).
[CrossRef]

2002 (4)

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech. 50, 910–928 (2002).
[CrossRef]

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

Z. Zhu and T. G. Brown, “Full–vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10, 853–864 (2002).

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]

2001 (1)

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, “A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy,” J. Appl. Phys. 89, 2357–2359 (2001).
[CrossRef]

2000 (1)

F. L. Madarasz, J. O. Dimmock, N. Dietz, and K. J. Bachmann, “Sellmeier parameters for ZnGaP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (2000).
[CrossRef]

1997 (2)

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef]

Q. Wu and X.-C. Zhang, “7 terahertz broadband GaP electro-optic sensor,” Appl. Phys. Lett. 70, 1784–1786 (1997).
[CrossRef]

1996 (1)

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

1992 (1)

L. Xu, X.-C. Zhang, and D. H. Auston, “Terahertz beam generation by femtosecond optical pulses in electro-optic materials,” Appl. Phys. Lett. 61, 1784–1786 (1992).
[CrossRef]

1990 (1)

1984 (1)

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]

1971 (1)

Adam, A. J. L.

Auston, D. H.

L. Xu, X.-C. Zhang, and D. H. Auston, “Terahertz beam generation by femtosecond optical pulses in electro-optic materials,” Appl. Phys. Lett. 61, 1784–1786 (1992).
[CrossRef]

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]

Bachmann, K. J.

F. L. Madarasz, J. O. Dimmock, N. Dietz, and K. J. Bachmann, “Sellmeier parameters for ZnGaP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (2000).
[CrossRef]

Bang, O.

Bartal, B.

Birks, T. A.

Bordas, F.

Brown, T. G.

Chai, L.

F. Liu, Y.-J. Song, Q.-R. Xing, M.-L. Hu, Y.-F. Li, C.-L. Wang, L. Chai, W.-L. Zhang, A. M. Zheltikov, and C.-Y. Wang, “Broadband terahertz pulses generated by a compact femtosecond photonic crystal fiber amplifier,” IEEE Photon. Technol. Lett. 22, 814–816 (2010).
[CrossRef]

Y. Li, Y. Yao, M. Hu, L. Chai, and C. Wang, “Improved fully vectorial effective index method for photonic crystal fibers: evaluation and enhancement,” Appl. Opt. 47, 399–406 (2008).
[CrossRef]

Chang, G.

Chen, T.

T. Chen, J. Sun, L. Li, J. Tang, and Y. Zhou, “Design of a photonic crystal waveguide for terahertz-wave difference-frequency generation,” IEEE Photon. Technol. Lett. 24, 921–923 (2012).
[CrossRef]

Cheung, K. P.

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]

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]

Coleman, P. D.

Dietz, N.

F. L. Madarasz, J. O. Dimmock, N. Dietz, and K. J. Bachmann, “Sellmeier parameters for ZnGaP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (2000).
[CrossRef]

Dimmock, J. O.

F. L. Madarasz, J. O. Dimmock, N. Dietz, and K. J. Bachmann, “Sellmeier parameters for ZnGaP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (2000).
[CrossRef]

Ding, Y. J.

W. Shi and Y. J. Ding, “Designs of terahertz waveguides for efficient parametric terahertz generation,” Appl. Phys. Lett. 82, 4435–4437 (2003).
[CrossRef]

Divin, C. J.

Fan, S.

Faraon, A.

K. Rivoire, A. Faraon, and J. Vuckovic, “Gallium phosphide photonic crystal nanocavities in the visible,” Appl. Phys. Lett. 93, 063103 (2008).
[CrossRef]

Fattinger, Ch.

Fejer, M. M.

Ferguson, B.

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

Galvanauskas, A.

Giessen, H.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B 103, 45–50 (2011).
[CrossRef]

Grischkowsky, D.

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]

Han, P. Y.

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, “A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy,” J. Appl. Phys. 89, 2357–2359 (2001).
[CrossRef]

Hatami, F.

Hebling, J.

Hegenbarth, R.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B 103, 45–50 (2011).
[CrossRef]

Heinz, T. F.

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

Hoffmann, M. C.

Hoos, F.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B 103, 45–50 (2011).
[CrossRef]

Hu, M.

Hu, M.-L.

F. Liu, Y.-J. Song, Q.-R. Xing, M.-L. Hu, Y.-F. Li, C.-L. Wang, L. Chai, W.-L. Zhang, A. M. Zheltikov, and C.-Y. Wang, “Broadband terahertz pulses generated by a compact femtosecond photonic crystal fiber amplifier,” IEEE Photon. Technol. Lett. 22, 814–816 (2010).
[CrossRef]

Huang, N.

Jepsen, P. U.

Keiding, S.

Kersting, R.

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, “A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy,” J. Appl. Phys. 89, 2357–2359 (2001).
[CrossRef]

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.

J.-I. Nishizawa, K. Suto, T. Tanabe, K. Saito, T. Kimura, and Y. Oyama, “THz generation from GaP rod-type waveguides,” IEEE Photon. Technol. Lett. 19, 143–145 (2007).
[CrossRef]

Kleinman, D. A.

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]

Knight, J. C.

Kono, S.

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, “A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy,” J. Appl. Phys. 89, 2357–2359 (2001).
[CrossRef]

Kuhlmey, B. T.

Li, J.-S.

J.-S. Li and S. Zouhdi, “Fano resonance filtering characteristic of high-resistivity silicon photonic crystal slab in terahertz region,” IEEE Photon. Technol. Lett. 24, 625–627 (2012).
[CrossRef]

Li, L.

T. Chen, J. Sun, L. Li, J. Tang, and Y. Zhou, “Design of a photonic crystal waveguide for terahertz-wave difference-frequency generation,” IEEE Photon. Technol. Lett. 24, 921–923 (2012).
[CrossRef]

Li, Y.

Li, Y.-F.

F. Liu, Y.-J. Song, Q.-R. Xing, M.-L. Hu, Y.-F. Li, C.-L. Wang, L. Chai, W.-L. Zhang, A. M. Zheltikov, and C.-Y. Wang, “Broadband terahertz pulses generated by a compact femtosecond photonic crystal fiber amplifier,” IEEE Photon. Technol. Lett. 22, 814–816 (2010).
[CrossRef]

Lin, Z.

Liu, F.

F. Liu, Y.-J. Song, Q.-R. Xing, M.-L. Hu, Y.-F. Li, C.-L. Wang, L. Chai, W.-L. Zhang, A. M. Zheltikov, and C.-Y. Wang, “Broadband terahertz pulses generated by a compact femtosecond photonic crystal fiber amplifier,” IEEE Photon. Technol. Lett. 22, 814–816 (2010).
[CrossRef]

Liu, H.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Madarasz, F. L.

F. L. Madarasz, J. O. Dimmock, N. Dietz, and K. J. Bachmann, “Sellmeier parameters for ZnGaP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (2000).
[CrossRef]

Masselink, W. T.

Metzger, B.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B 103, 45–50 (2011).
[CrossRef]

Mortensen, N. A.

Musheinish, M. A.

Nahata, A.

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

Negel, J.-P.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B 103, 45–50 (2011).
[CrossRef]

Nelson, K. A.

Nielsen, K.

Nishizawa, J.-I.

J.-I. Nishizawa, K. Suto, T. Tanabe, K. Saito, T. Kimura, and Y. Oyama, “THz generation from GaP rod-type waveguides,” IEEE Photon. Technol. Lett. 19, 143–145 (2007).
[CrossRef]

Norris, T. B.

Oyama, Y.

J.-I. Nishizawa, K. Suto, T. Tanabe, K. Saito, T. Kimura, and Y. Oyama, “THz generation from GaP rod-type waveguides,” IEEE Photon. Technol. Lett. 19, 143–145 (2007).
[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]

Parsons, D. F.

Planken, P. C. M.

Rasmussen, H. K.

Renversez, G.

Rivoire, K.

Ruan, Z.

Russell, P. St. J.

Saito, K.

J.-I. Nishizawa, K. Suto, T. Tanabe, K. Saito, T. Kimura, and Y. Oyama, “THz generation from GaP rod-type waveguides,” IEEE Photon. Technol. Lett. 19, 143–145 (2007).
[CrossRef]

Shi, W.

W. Shi and Y. J. Ding, “Designs of terahertz waveguides for efficient parametric terahertz generation,” Appl. Phys. Lett. 82, 4435–4437 (2003).
[CrossRef]

Siegel, P. H.

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech. 50, 910–928 (2002).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Song, Y.-J.

F. Liu, Y.-J. Song, Q.-R. Xing, M.-L. Hu, Y.-F. Li, C.-L. Wang, L. Chai, W.-L. Zhang, A. M. Zheltikov, and C.-Y. Wang, “Broadband terahertz pulses generated by a compact femtosecond photonic crystal fiber amplifier,” IEEE Photon. Technol. Lett. 22, 814–816 (2010).
[CrossRef]

Steinmann, A.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B 103, 45–50 (2011).
[CrossRef]

Sun, J.

T. Chen, J. Sun, L. Li, J. Tang, and Y. Zhou, “Design of a photonic crystal waveguide for terahertz-wave difference-frequency generation,” IEEE Photon. Technol. Lett. 24, 921–923 (2012).
[CrossRef]

Sun, Q.

Suto, K.

J.-I. Nishizawa, K. Suto, T. Tanabe, K. Saito, T. Kimura, and Y. Oyama, “THz generation from GaP rod-type waveguides,” IEEE Photon. Technol. Lett. 19, 143–145 (2007).
[CrossRef]

Tanabe, T.

J.-I. Nishizawa, K. Suto, T. Tanabe, K. Saito, T. Kimura, and Y. Oyama, “THz generation from GaP rod-type waveguides,” IEEE Photon. Technol. Lett. 19, 143–145 (2007).
[CrossRef]

Tang, J.

T. Chen, J. Sun, L. Li, J. Tang, and Y. Zhou, “Design of a photonic crystal waveguide for terahertz-wave difference-frequency generation,” IEEE Photon. Technol. Lett. 24, 921–923 (2012).
[CrossRef]

Tani, M.

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, “A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy,” J. Appl. Phys. 89, 2357–2359 (2001).
[CrossRef]

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[CrossRef]

Usami, M.

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, “A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy,” J. Appl. Phys. 89, 2357–2359 (2001).
[CrossRef]

Valdmanis, J. A.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of (a)  PCF GaP waveguide emitter and (b)  circular GaP waveguide emitter for THz wave generation. The gray area is GaP, and the white circles are air holes. One missing air hole forms the core of the PCF waveguide emitter. Both emitters are 110-cut with 110 axis along the propagation direction.

Fig. 2.
Fig. 2.

Dependence of the refractive index of the THz wave on frequency in a circular waveguide emitter as a function of (a) core diameter D with air cladding and (b) cladding index with D=600μm. The refractive index of the THz wave in bulk GaP and the group index of pump light at 1.04 μm are also shown.

Fig. 3.
Fig. 3.

Dependence of the refractive index of the THz wave on frequency in a PCF waveguide emitter as a function of (a) pitch Λ with d/Λ=0.4 and (b) d/Λ with Λ=300μm. The refractive index of the THz wave in bulk GaP and the group index of pump light at 1.04 μm are also shown.

Fig. 4.
Fig. 4.

Comparison of (a) phase matching and (b) simulated intensity spectra of generated THz radiation between circular and PCF waveguide emitters for two sets of parameters.

Fig. 5.
Fig. 5.

Ey component distribution of the y-polarized fundamental mode at 1.5 THz for a PCF waveguide emitter with Λ=200μm and d/Λ=0.2.

Equations (1)

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|ETHz(ΩTHz,L)|2=ΩTHz2deff2E04τ2L28πc2nTHz2exp[τ2ΩTHz24]sinc2[ΔkL2],

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