Abstract

The propagation properties of terahertz (THz) waves passing through heavily doped semiconductor slit have been numerically investigated by using the transfer matrix method. The effects of geometrical parameters, carrier concentration, and dielectric materials filling in the slit have been considered. The contour for carrier concentration and slit width show that as slit width and carrier concentration decreases, the effective indices increase and the propagation lengths decrease. For the case of water filling in the slit, temperature has more effect on the imaginary part of propagation constant than the real part. Most of the energy stored in the slit is in the form of electric energy, which firstly decreases and then increases with the decreasing of slit width. It is expected that the semiconductor slit structure is very useful for the practical applications of THz waves in the fields of biological specimen analysis and medical diagnosis.

© 2009 OSA

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2009 (9)

X. Y. He, “Comparison of the waveguide properties of gap surface plasmon in the terahertz region and visible spectra,” J. Opt. A, Pure Appl. Opt. 11(4), 045708 (2009).

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102(18), 186402 (2009).
[PubMed]

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[PubMed]

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics 3(5), 283–286 (2009).

Y. B. Chen, “Development of mid-infrared surface plasmon resonance-based sensors with highly-doped silicon for biomedical and chemical applications,” Opt. Express 17(5), 3130–3140 (2009).
[PubMed]

R. M. Gelfand, L. Bruderer, and H. Mohseni, “Nanocavity plasmonic device for ultrabroadband single molecule sensing,” Opt. Lett. 34(7), 1087–1089 (2009).
[PubMed]

R. Mendis and M. Daniel, “Mittleman, “An investigation of the lowest-order transverse-electric (TE1) mode of the parallel-plate waveguide for THz pulse propagation,” J. Opt. Soc. Am. B 26(9), A6–A13 (2009).

X. Y. He, “Investigation of terahertz Sommerfeld propagation along conical metal wire,” J. Opt. Soc. Am. B 26(9), A23–A28 (2009).

2008 (5)

T. H. Isaac, J. Gomez., J. R. Rivas, W. L. Sambles, Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008).

S. I. Bozhevolnyi and J. Jung, “Scaling for gap plasmon based waveguides,” Opt. Express 16(4), 2676–2684 (2008).
[PubMed]

K. C. Vernon, D. K. Gramontnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103(3), 034304 (2008).

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).

H. Li, J. C. Cao, J. T. Lü, and Y. J. Han, “Monte Carlo simulation of extraction barrier width effects on terahertz quantum cascade lasers,” Appl. Phys. Lett. 92(22), 221105 (2008).

2007 (4)

M. Lee and M. C. Wanke, “Design of n-type silicon-based quantum cascade lasers for terahertz light emission,” Science 316, 64–65 (2007).
[PubMed]

R. Mendis, “THz transmission characteristics of dielectric-filled parallel-plate waveguides,” J. Appl. Phys. 101(8), 083115 (2007).

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocatities: Analysis of optical properties,” Phys. Rev. B 75(3), 035411 (2007).

P. U. Jepsen, U. Møller, and H. Merbold, “Investigation of aqueous alcohol and sugar solutions with reflection terahertz time-domain spectroscopy,” Opt. Express 15(22), 14717–14737 (2007).
[PubMed]

2006 (6)

J. A. Sánchez-Gil and J. G. Rivas, “Thermal switching of the scattering coefficients of terahertz surface plasmon polaritons impinging on a finite array of subwavelength grooves on semiconductor surfaces,” Phys. Rev. B 73(20), 205410 (2006).

S. A. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun. 258(2), 295–299 (2006).

J. A. Deibel, K. Wang, M. D. Escarra, and D. Mittleman, “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Opt. Express 14(1), 279–290 (2006).
[PubMed]

R. Mendis, “Nature of subpicosecond terahertz pulse propagation in practical dielectric-filled parallel-plate waveguides,” Opt. Lett. 31(17), 2643–2645 (2006).
[PubMed]

J. T. Lü and J. C. Cao, “Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers,” Appl. Phys. Lett. 89(21), 211115 (2006).

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006).
[PubMed]

2005 (4)

J. Q. Zhang and D. Grischkowsky, “Adiabatic compression of parallel-plate metal waveguides for sensitivity enhancement of waveguide THz time-domain spectroscopy,” Appl. Phys. Lett. 86(6), 061109 (2005).

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97(5), 053106 (2005).

A. K. Azad, Y. Zhao, and W. Zhang, “Transmission properties of terahertz pulses through an ultrathin subwavelength silicon hole array,” Appl. Phys. Lett. 86(14), 141102 (2005).

J. T. Lü and J. C. Cao, “Confined optical phonon modes and electron-phonon interactions in wurtzite GaN/ZnO quantum wells,” Phys. Rev. B 71(15), 155304 (2005).

2004 (4)

2003 (4)

J. C. Cao, “Interband impact ionization and nonlinear absorption of terahertz radiation in semiconductor heterostructures,” Phys. Rev. Lett. 91(23), 237401 (2003).
[PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[PubMed]

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299(5607), 682–686 (2003).
[PubMed]

S. W. Gao, J. C. Cao, and S. L. Feng, “Waveguide design of long wavelength semiconductor laser based on surface plasmons,” Physica B 337(1-4), 230–236 (2003).

2002 (2)

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

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchi, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 154–157 (2002).

2001 (1)

J. C. Cao, A. Z. Li, X. L. Lei, and S. L. Feng, “Current self-oscillation and driving-frequency dependence of negative-effective-mass diodes,” Appl. Phys. Lett. 79(21), 3524–3526 (2001).

1999 (1)

C. Rønne, P. O. Åstrand, and S. R. Keiding, “THz spectroscopy of liquid H2O and D2O,” Phys. Rev. Lett. 82(14), 2888–2891 (1999).

1991 (1)

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).

Andrews, A. M.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102(18), 186402 (2009).
[PubMed]

Åstrand, P. O.

C. Rønne, P. O. Åstrand, and S. R. Keiding, “THz spectroscopy of liquid H2O and D2O,” Phys. Rev. Lett. 82(14), 2888–2891 (1999).

Atwater, H. A.

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006).
[PubMed]

Azad, A. K.

A. K. Azad, Y. Zhao, and W. Zhang, “Transmission properties of terahertz pulses through an ultrathin subwavelength silicon hole array,” Appl. Phys. Lett. 86(14), 141102 (2005).

Barnes,

T. H. Isaac, J. Gomez., J. R. Rivas, W. L. Sambles, Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008).

Barnes, W. L.

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[PubMed]

Beere, H. E.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchi, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 154–157 (2002).

Beltram, F.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchi, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 154–157 (2002).

Borghs, G.

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics 3(5), 283–286 (2009).

Bozhevolnyi, S. I.

Bradberry, G. W.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).

Bruderer, L.

Cao, J. C.

H. Li, J. C. Cao, J. T. Lü, and Y. J. Han, “Monte Carlo simulation of extraction barrier width effects on terahertz quantum cascade lasers,” Appl. Phys. Lett. 92(22), 221105 (2008).

J. T. Lü and J. C. Cao, “Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers,” Appl. Phys. Lett. 89(21), 211115 (2006).

J. T. Lü and J. C. Cao, “Confined optical phonon modes and electron-phonon interactions in wurtzite GaN/ZnO quantum wells,” Phys. Rev. B 71(15), 155304 (2005).

J. C. Cao, “Interband impact ionization and nonlinear absorption of terahertz radiation in semiconductor heterostructures,” Phys. Rev. Lett. 91(23), 237401 (2003).
[PubMed]

S. W. Gao, J. C. Cao, and S. L. Feng, “Waveguide design of long wavelength semiconductor laser based on surface plasmons,” Physica B 337(1-4), 230–236 (2003).

J. C. Cao, A. Z. Li, X. L. Lei, and S. L. Feng, “Current self-oscillation and driving-frequency dependence of negative-effective-mass diodes,” Appl. Phys. Lett. 79(21), 3524–3526 (2001).

Chen, Y. B.

Choi, S. S.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Colombelli, R.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102(18), 186402 (2009).
[PubMed]

Craighead, H. G.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299(5607), 682–686 (2003).
[PubMed]

Daniel, M.

Davies, A. G.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchi, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 154–157 (2002).

Deibel, J. A.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[PubMed]

Dionne, J. A.

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006).
[PubMed]

Dorpe, P. V.

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics 3(5), 283–286 (2009).

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[PubMed]

Erickson, D.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[PubMed]

Escarra, M. D.

Fainman, Y.

Feng, S. L.

S. W. Gao, J. C. Cao, and S. L. Feng, “Waveguide design of long wavelength semiconductor laser based on surface plasmons,” Physica B 337(1-4), 230–236 (2003).

J. C. Cao, A. Z. Li, X. L. Lei, and S. L. Feng, “Current self-oscillation and driving-frequency dependence of negative-effective-mass diodes,” Appl. Phys. Lett. 79(21), 3524–3526 (2001).

Ferguson, B.

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

Foquet, M.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299(5607), 682–686 (2003).
[PubMed]

Friberg, A. T.

Gao, S. W.

S. W. Gao, J. C. Cao, and S. L. Feng, “Waveguide design of long wavelength semiconductor laser based on surface plasmons,” Physica B 337(1-4), 230–236 (2003).

Gelfand, R. M.

Gomez., J.

T. H. Isaac, J. Gomez., J. R. Rivas, W. L. Sambles, Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008).

Gramontnev, D. K.

K. C. Vernon, D. K. Gramontnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103(3), 034304 (2008).

Grischkowsky, D.

J. Q. Zhang and D. Grischkowsky, “Adiabatic compression of parallel-plate metal waveguides for sensitivity enhancement of waveguide THz time-domain spectroscopy,” Appl. Phys. Lett. 86(6), 061109 (2005).

J. Q. Zhang and D. Grischkowsky, “Waveguide terahertz time-domain spectroscopy of nanometer water layers,” Opt. Lett. 29(14), 1617–1619 (2004).
[PubMed]

Han, Y. J.

H. Li, J. C. Cao, J. T. Lü, and Y. J. Han, “Monte Carlo simulation of extraction barrier width effects on terahertz quantum cascade lasers,” Appl. Phys. Lett. 92(22), 221105 (2008).

He, X. Y.

X. Y. He, “Investigation of terahertz Sommerfeld propagation along conical metal wire,” J. Opt. Soc. Am. B 26(9), A23–A28 (2009).

X. Y. He, “Comparison of the waveguide properties of gap surface plasmon in the terahertz region and visible spectra,” J. Opt. A, Pure Appl. Opt. 11(4), 045708 (2009).

Hendry, E.

T. H. Isaac, J. Gomez., J. R. Rivas, W. L. Sambles, Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008).

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).

Hu, Q.

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97(5), 053106 (2005).

Iotti, R. C.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchi, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 154–157 (2002).

Isaac, T. H.

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).

T. H. Isaac, J. Gomez., J. R. Rivas, W. L. Sambles, Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008).

Jepsen, P. U.

Jung, J.

Kaivola, M.

Kang, J. H.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Keiding, S. R.

C. Rønne, P. O. Åstrand, and S. R. Keiding, “THz spectroscopy of liquid H2O and D2O,” Phys. Rev. Lett. 82(14), 2888–2891 (1999).

Kim, D. S.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Klang, P.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102(18), 186402 (2009).
[PubMed]

Klug, M.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[PubMed]

Kohen, S.

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97(5), 053106 (2005).

Köhler, R.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchi, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 154–157 (2002).

Koo, S. M.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Korlach, J.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299(5607), 682–686 (2003).
[PubMed]

Kurokawa, Y.

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocatities: Analysis of optical properties,” Phys. Rev. B 75(3), 035411 (2007).

Lagae, L.

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics 3(5), 283–286 (2009).

Lee, M.

M. Lee and M. C. Wanke, “Design of n-type silicon-based quantum cascade lasers for terahertz light emission,” Science 316, 64–65 (2007).
[PubMed]

Lei, X. L.

J. C. Cao, A. Z. Li, X. L. Lei, and S. L. Feng, “Current self-oscillation and driving-frequency dependence of negative-effective-mass diodes,” Appl. Phys. Lett. 79(21), 3524–3526 (2001).

Levene, M. J.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299(5607), 682–686 (2003).
[PubMed]

Lezec, H. J.

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006).
[PubMed]

Li, A. Z.

J. C. Cao, A. Z. Li, X. L. Lei, and S. L. Feng, “Current self-oscillation and driving-frequency dependence of negative-effective-mass diodes,” Appl. Phys. Lett. 79(21), 3524–3526 (2001).

Li, H.

H. Li, J. C. Cao, J. T. Lü, and Y. J. Han, “Monte Carlo simulation of extraction barrier width effects on terahertz quantum cascade lasers,” Appl. Phys. Lett. 92(22), 221105 (2008).

Lindberg, J.

Lindfors, K.

Linfield, E. H.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchi, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 154–157 (2002).

Lipson, M.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[PubMed]

Lü, J. T.

H. Li, J. C. Cao, J. T. Lü, and Y. J. Han, “Monte Carlo simulation of extraction barrier width effects on terahertz quantum cascade lasers,” Appl. Phys. Lett. 92(22), 221105 (2008).

J. T. Lü and J. C. Cao, “Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers,” Appl. Phys. Lett. 89(21), 211115 (2006).

J. T. Lü and J. C. Cao, “Confined optical phonon modes and electron-phonon interactions in wurtzite GaN/ZnO quantum wells,” Phys. Rev. B 71(15), 155304 (2005).

Maier, S. A.

S. A. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun. 258(2), 295–299 (2006).

Mendis, R.

Merbold, H.

Mittleman, D.

Mittleman, D. M.

K. L. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
[PubMed]

Miyazaki, H. T.

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocatities: Analysis of optical properties,” Phys. Rev. B 75(3), 035411 (2007).

Mohseni, H.

Møller, U.

Moore, S. D.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[PubMed]

Neutens, P.

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics 3(5), 283–286 (2009).

Nezhad, M. P.

Park, D. J.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Park, G. S.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Park, H. R.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Park, N. K.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Park, Q. H.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Pile, D. F. P.

K. C. Vernon, D. K. Gramontnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103(3), 034304 (2008).

Planken, P. C. M.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Ritchi, D. A.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchi, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 154–157 (2002).

Rivas, J. G.

J. A. Sánchez-Gil and J. G. Rivas, “Thermal switching of the scattering coefficients of terahertz surface plasmon polaritons impinging on a finite array of subwavelength grooves on semiconductor surfaces,” Phys. Rev. B 73(20), 205410 (2006).

Rivas, J. R.

T. H. Isaac, J. Gomez., J. R. Rivas, W. L. Sambles, Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008).

Rønne, C.

C. Rønne, P. O. Åstrand, and S. R. Keiding, “THz spectroscopy of liquid H2O and D2O,” Phys. Rev. Lett. 82(14), 2888–2891 (1999).

Rossi, F.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchi, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 154–157 (2002).

Sagnes, I.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102(18), 186402 (2009).
[PubMed]

Sambles, J. R.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).

Sambles, W. L.

T. H. Isaac, J. Gomez., J. R. Rivas, W. L. Sambles, Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008).

Sánchez-Gil, J. A.

J. A. Sánchez-Gil and J. G. Rivas, “Thermal switching of the scattering coefficients of terahertz surface plasmon polaritons impinging on a finite array of subwavelength grooves on semiconductor surfaces,” Phys. Rev. B 73(20), 205410 (2006).

Schmidt, B. S.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[PubMed]

Seo, M. A.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Setala, T.

Sirtori, C.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102(18), 186402 (2009).
[PubMed]

Strasser, G.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102(18), 186402 (2009).
[PubMed]

Suwal, O. K.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

Tetz, K.

Todorov, Y.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102(18), 186402 (2009).
[PubMed]

Tredicucci, A.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchi, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 154–157 (2002).

Turner, S. W.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299(5607), 682–686 (2003).
[PubMed]

Vernon, K. C.

K. C. Vernon, D. K. Gramontnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103(3), 034304 (2008).

Vlaminck, I. D.

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics 3(5), 283–286 (2009).

Wang, K.

Wang, K. L.

K. L. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
[PubMed]

Wanke, M. C.

M. Lee and M. C. Wanke, “Design of n-type silicon-based quantum cascade lasers for terahertz light emission,” Science 316, 64–65 (2007).
[PubMed]

Webb, W. W.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299(5607), 682–686 (2003).
[PubMed]

Williams, B. S.

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97(5), 053106 (2005).

Yang, A. H. J.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[PubMed]

Yang, F.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).

Zhang, J. Q.

J. Q. Zhang and D. Grischkowsky, “Adiabatic compression of parallel-plate metal waveguides for sensitivity enhancement of waveguide THz time-domain spectroscopy,” Appl. Phys. Lett. 86(6), 061109 (2005).

J. Q. Zhang and D. Grischkowsky, “Waveguide terahertz time-domain spectroscopy of nanometer water layers,” Opt. Lett. 29(14), 1617–1619 (2004).
[PubMed]

Zhang, W.

A. K. Azad, Y. Zhao, and W. Zhang, “Transmission properties of terahertz pulses through an ultrathin subwavelength silicon hole array,” Appl. Phys. Lett. 86(14), 141102 (2005).

Zhang, X. C.

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

Zhao, Y.

A. K. Azad, Y. Zhao, and W. Zhang, “Transmission properties of terahertz pulses through an ultrathin subwavelength silicon hole array,” Appl. Phys. Lett. 86(14), 141102 (2005).

Appl. Phys. Lett. (6)

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).

J. C. Cao, A. Z. Li, X. L. Lei, and S. L. Feng, “Current self-oscillation and driving-frequency dependence of negative-effective-mass diodes,” Appl. Phys. Lett. 79(21), 3524–3526 (2001).

J. T. Lü and J. C. Cao, “Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers,” Appl. Phys. Lett. 89(21), 211115 (2006).

H. Li, J. C. Cao, J. T. Lü, and Y. J. Han, “Monte Carlo simulation of extraction barrier width effects on terahertz quantum cascade lasers,” Appl. Phys. Lett. 92(22), 221105 (2008).

J. Q. Zhang and D. Grischkowsky, “Adiabatic compression of parallel-plate metal waveguides for sensitivity enhancement of waveguide THz time-domain spectroscopy,” Appl. Phys. Lett. 86(6), 061109 (2005).

A. K. Azad, Y. Zhao, and W. Zhang, “Transmission properties of terahertz pulses through an ultrathin subwavelength silicon hole array,” Appl. Phys. Lett. 86(14), 141102 (2005).

J. Appl. Phys. (3)

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97(5), 053106 (2005).

R. Mendis, “THz transmission characteristics of dielectric-filled parallel-plate waveguides,” J. Appl. Phys. 101(8), 083115 (2007).

K. C. Vernon, D. K. Gramontnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103(3), 034304 (2008).

J. Opt. A, Pure Appl. Opt. (1)

X. Y. He, “Comparison of the waveguide properties of gap surface plasmon in the terahertz region and visible spectra,” J. Opt. A, Pure Appl. Opt. 11(4), 045708 (2009).

J. Opt. Soc. Am. B (2)

Nano Lett. (1)

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006).
[PubMed]

Nat. Mater. (1)

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

Nat. Photonics (2)

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics 3(5), 283–286 (2009).

Nature (4)

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[PubMed]

K. L. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
[PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchi, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 154–157 (2002).

Opt. Commun. (1)

S. A. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun. 258(2), 295–299 (2006).

Opt. Express (6)

Opt. Lett. (3)

Phys. Rev. B (5)

J. T. Lü and J. C. Cao, “Confined optical phonon modes and electron-phonon interactions in wurtzite GaN/ZnO quantum wells,” Phys. Rev. B 71(15), 155304 (2005).

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocatities: Analysis of optical properties,” Phys. Rev. B 75(3), 035411 (2007).

J. A. Sánchez-Gil and J. G. Rivas, “Thermal switching of the scattering coefficients of terahertz surface plasmon polaritons impinging on a finite array of subwavelength grooves on semiconductor surfaces,” Phys. Rev. B 73(20), 205410 (2006).

T. H. Isaac, J. Gomez., J. R. Rivas, W. L. Sambles, Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008).

Phys. Rev. Lett. (3)

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102(18), 186402 (2009).
[PubMed]

J. C. Cao, “Interband impact ionization and nonlinear absorption of terahertz radiation in semiconductor heterostructures,” Phys. Rev. Lett. 91(23), 237401 (2003).
[PubMed]

C. Rønne, P. O. Åstrand, and S. R. Keiding, “THz spectroscopy of liquid H2O and D2O,” Phys. Rev. Lett. 82(14), 2888–2891 (1999).

Physica B (1)

S. W. Gao, J. C. Cao, and S. L. Feng, “Waveguide design of long wavelength semiconductor laser based on surface plasmons,” Physica B 337(1-4), 230–236 (2003).

Science (2)

M. Lee and M. C. Wanke, “Design of n-type silicon-based quantum cascade lasers for terahertz light emission,” Science 316, 64–65 (2007).
[PubMed]

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299(5607), 682–686 (2003).
[PubMed]

Other (1)

H. Raether, “Surface plasmons on smooth and rough surfaces and on gratings,” (Springer, Berlin, 1988).

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Figures (6)

Fig. 1
Fig. 1

Geometry of an infinitely long slit under illumination of THz waves. The slit width is w, which is filled with gain dielectric material in region 2 and bounded by semi-infinite regions of heavily doped InSb in region 1 and 3.

Fig. 2
Fig. 2

The effective indices and propagation lengths of GSPPs mode versus slit width for different dielectric materials, the radiation frequency is 1.0 THz; the carrier concentration of InSb is 8.0×1016 cm−3. (a) The dielectric materials filling in the slit are air, polyethylene, water, and GaAs, respectively. (b) The dielectric materials filling in the slit is GaAs, the real part of dielectric constant keeps 3.4, the imaginary part are 0.0, 0.02, 0.05, 0.10, 0.20 and 0.50, respectively.

Figures 3(a) and 3(b)
Figures 3(a) and 3(b)

show the effective indices and propagation lengths of GSPPs mode versus slit width, respectively. The radiation frequency is 1.0 THz, the carrier concentration are 2.0×1016 cm−3, 4.0×1016 cm−3, 6.0×1016 cm−3, and 8.0×1016 cm−3, respectively, air is filled in the slit. The insets show the effective indices and propagation lengths contour for slit width and carrier concentration.

Fig. 4
Fig. 4

The GSPPs mode of effective indices and propagation lengths versus slit width, the dielectric material filling in the slit is water with different radiation frequencies and temperatures, the doping concentration of InSb is 8.0×1016 cm−3. (a) The water temperature is 292.3 K, the radiation frequencies are 0.1 THz, 0.3 THz, 0.5 THz, and 1.0 THz, respectively. (b) The water temperature are 278.8 K, 292.3 K, 315.0 K, and 366.7 K, respectively.

Fig. 5
Fig. 5

The field distribution of electric component of GSPPs mode along the x-direction. The slit material is heavily doped InSb with carrier concentration of 8.0×1016 cm−3, the radiation frequency is 1.0 THz. (a) The dielectric materials filling in the slit are air, polyethylene, water, and GaAs, respectively, the slit width is 20 μm . (b) The slit width are 1.0 μm , 10.0 μm , 20.0 μm , 50.0 μm , 100.0 μm , and 200.0 μm , respectively, air is filled in the slit.

Fig. 6
Fig. 6

The electric and magnetic energy densities in the metal and slit versus frequency for different slit width are shown in Fig. 6(a)-6(d), respectively. Air is filled in the slit; the carrier concentration of InSb is 8.0×1016 cm−3; the slit width are 1 μm , 2 μm , 10 μm , 20 μm , 50 μm , and 100 μm , respectively.

Equations (22)

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γ2γ3γNε1ε2εN1[HN+HN]N,N1=(M11M12M21M22)[H1+H1]2,1,
(M11M12M21M22)=MN1MN2M1,
Mi=(εi1εiεi1εi)(γiγiγi1γi1)(exp(γidi)00exp(γidi)),
γj2=β2k02εi,i=1,2,3,
Exm(r,ω)=exp(α1,3|x|)×exp(i(βzωt)),
Hym(r,ω)=ωε0εmβexp(α1,3|x|)×exp(i(βzωt)),
Ezm(r,ω)=iα1,3β|x|xexp(α1,3|x|)×exp(i(βzωt)),
(|x|<w/2)
Exd(r,ω)=2cosh(α2|x|)×exp(i(βzωt)),
Hyd(r,ω)=2ωε0ε2βcosh(α2|x|)×exp(i(βzωt)),
Ezd(r,ω)=2iα2βsinh(α2|x|)×exp(i(βzωt)),
uei(x,ω)=14ε0εi|εm(ω)εiexp(kmT/2)cosh(kiT/2)|2|A|2(|cosh(kix)|2+|kiksinh(kix)2|),
umi(x,ω)=14ε0|ωεm(ω)ckexp(kmT/2)cosh(kiT/2)|2|A|2(|cosh(kix)|2),
uem(x,ω)=14ε0Re((ωεm(ω))ω)|Aexp(km|x|)|2(1.0+|kmk|2),
umm(x,ω)=14ε0|Aωεm(ω)ckexp(km|x|)|2,
ε(ω)=(εωp2ω2+ωτ2)+iωτωp2ω(ω2+ωτ2),
ε(ω)=ε+εsε11+iωτD+ε1ε1+iωτ2,
εs=87.91e0.00458T,
ε(ω)=ε+ine2τωm(1iωτ),
δsemic0ω(Re(εsemi)+1Re(εsemi)2)1/2.
neff=Re(β)/k0,
L=[2Im(β)]1.

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