Abstract

We present two solutions to the challenge of radiation loss of slot-lines at terahertz frequencies: using a slot-line in a homogeneous medium, and using a slot-line on a layered substrate. A theoretical analysis of the slot-line in a homogeneous medium as a terahertz transmission line is presented. The absorption coefficient is obtained in terms of the waveguide dimensions using the field distribution of the slot-line. Results show that the slot-line in a homogeneous medium and the slot-line on a layered substrate can be effective transmission lines for terahertz waves with 2 cm−1 and 3 cm−1 absorption due to conductor loss. Full-wave numerical simulations using the Finite Element Method (FEM) are applied to validate the theory.

© 2011 OSA

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References

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    [CrossRef] [PubMed]
  2. H. Zhan, R. Mendis, and D. M. Mittleman, “Characterization of the terahertz near-field output of parallel-plate waveguides,” J. Opt. Soc. Am. B 28(3), 558–566 (2011).
    [CrossRef]
  3. J. Liu, R. Mendis, and D. M. Mittleman, “The transition from a TEM-like mode to a plasmonic mode in parallel-plate waveguides,” Appl. Phys. Lett. 98(23), 231113 (2011).
    [CrossRef]
  4. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. D. R. Grischkowsky, M. B. Ketchen, C.-C. Chi, I. N. Duling, N. J. Halas, J.-M. Halbout, and P. G. May, “Capacitance free generation and detection of subpicosecond electrical pulses on coplanar transmission lines,” IEEE J. Quantum Electron. 24(2), 221–225 (1988).
    [CrossRef]
  9. D. Grischkowsky, I. I. I. Duling, J. C. Chen, and C. C. Chi, “Electromagnetic shock waves from transmission lines,” Phys. Rev. Lett. 59(15), 1663–1666 (1987).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  20. D. M. Pozar, “Microwave engineering (John Wiley & Sons, 2005), pp. 97-98.
  21. D. Grischkowsky, S. Keiding, M. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990).
    [CrossRef]
  22. M. Y. Frankel, R. H. Voelker, and J. N. Hilfiker, “Coplanar transmission lines on thin substrates for high-speed low-loss propagation,” IEEE Trans. Microw. Theory Tech. 42(3), 396–402 (1994).
    [CrossRef]

2011

J. Liu, R. Mendis, and D. M. Mittleman, “The transition from a TEM-like mode to a plasmonic mode in parallel-plate waveguides,” Appl. Phys. Lett. 98(23), 231113 (2011).
[CrossRef]

H. Zhan, R. Mendis, and D. M. Mittleman, “Characterization of the terahertz near-field output of parallel-plate waveguides,” J. Opt. Soc. Am. B 28(3), 558–566 (2011).
[CrossRef]

2010

2009

2004

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

2001

2000

D. Grischkowsky, “Optoelectronic characterization of transmission lines and waveguides by terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1122–1135 (2000).
[CrossRef]

1994

M. Y. Frankel, R. H. Voelker, and J. N. Hilfiker, “Coplanar transmission lines on thin substrates for high-speed low-loss propagation,” IEEE Trans. Microw. Theory Tech. 42(3), 396–402 (1994).
[CrossRef]

1991

M. Y. Frankel, S. Gupta, J. A. Valdmanis, and G. A. Mourou, “Terahertz Attenuation and dispersion characteristics of coplanar transmission lines,” IEEE Trans. Microw. Theory Tech. 39(6), 910–916 (1991).
[CrossRef]

1990

1989

C. Fattinger and D. Grischkowsky, “Observation of electromagnetic shock waves from propagating surface-dipole distributions,” Phys. Rev. Lett. 62(25), 2961–2964 (1989).
[CrossRef] [PubMed]

1988

D. R. Grischkowsky, M. B. Ketchen, C.-C. Chi, I. N. Duling, N. J. Halas, J.-M. Halbout, and P. G. May, “Capacitance free generation and detection of subpicosecond electrical pulses on coplanar transmission lines,” IEEE J. Quantum Electron. 24(2), 221–225 (1988).
[CrossRef]

1987

D. Grischkowsky, I. I. I. Duling, J. C. Chen, and C. C. Chi, “Electromagnetic shock waves from transmission lines,” Phys. Rev. Lett. 59(15), 1663–1666 (1987).
[CrossRef] [PubMed]

1984

D. K. Kleinman and D. H. Auston, “Theory of Electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20(8), 964–970 (1984).
[CrossRef]

1977

Auston, D. H.

D. K. Kleinman and D. H. Auston, “Theory of Electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20(8), 964–970 (1984).
[CrossRef]

Chen, J. C.

D. Grischkowsky, I. I. I. Duling, J. C. Chen, and C. C. Chi, “Electromagnetic shock waves from transmission lines,” Phys. Rev. Lett. 59(15), 1663–1666 (1987).
[CrossRef] [PubMed]

Chi, C. C.

D. Grischkowsky, I. I. I. Duling, J. C. Chen, and C. C. Chi, “Electromagnetic shock waves from transmission lines,” Phys. Rev. Lett. 59(15), 1663–1666 (1987).
[CrossRef] [PubMed]

Chi, C.-C.

D. R. Grischkowsky, M. B. Ketchen, C.-C. Chi, I. N. Duling, N. J. Halas, J.-M. Halbout, and P. G. May, “Capacitance free generation and detection of subpicosecond electrical pulses on coplanar transmission lines,” IEEE J. Quantum Electron. 24(2), 221–225 (1988).
[CrossRef]

Darcie, T. E.

Duling, I. I. I.

D. Grischkowsky, I. I. I. Duling, J. C. Chen, and C. C. Chi, “Electromagnetic shock waves from transmission lines,” Phys. Rev. Lett. 59(15), 1663–1666 (1987).
[CrossRef] [PubMed]

Duling, I. N.

D. R. Grischkowsky, M. B. Ketchen, C.-C. Chi, I. N. Duling, N. J. Halas, J.-M. Halbout, and P. G. May, “Capacitance free generation and detection of subpicosecond electrical pulses on coplanar transmission lines,” IEEE J. Quantum Electron. 24(2), 221–225 (1988).
[CrossRef]

Exter, M.

Fan, S.

Fattinger, C.

D. Grischkowsky, S. Keiding, M. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990).
[CrossRef]

C. Fattinger and D. Grischkowsky, “Observation of electromagnetic shock waves from propagating surface-dipole distributions,” Phys. Rev. Lett. 62(25), 2961–2964 (1989).
[CrossRef] [PubMed]

Fejer, M. M.

Frankel, M. Y.

M. Y. Frankel, R. H. Voelker, and J. N. Hilfiker, “Coplanar transmission lines on thin substrates for high-speed low-loss propagation,” IEEE Trans. Microw. Theory Tech. 42(3), 396–402 (1994).
[CrossRef]

M. Y. Frankel, S. Gupta, J. A. Valdmanis, and G. A. Mourou, “Terahertz Attenuation and dispersion characteristics of coplanar transmission lines,” IEEE Trans. Microw. Theory Tech. 39(6), 910–916 (1991).
[CrossRef]

Grischkowsky, D.

R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001).
[CrossRef] [PubMed]

D. Grischkowsky, “Optoelectronic characterization of transmission lines and waveguides by terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1122–1135 (2000).
[CrossRef]

D. Grischkowsky, S. Keiding, M. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990).
[CrossRef]

C. Fattinger and D. Grischkowsky, “Observation of electromagnetic shock waves from propagating surface-dipole distributions,” Phys. Rev. Lett. 62(25), 2961–2964 (1989).
[CrossRef] [PubMed]

D. Grischkowsky, I. I. I. Duling, J. C. Chen, and C. C. Chi, “Electromagnetic shock waves from transmission lines,” Phys. Rev. Lett. 59(15), 1663–1666 (1987).
[CrossRef] [PubMed]

Grischkowsky, D. R.

D. R. Grischkowsky, M. B. Ketchen, C.-C. Chi, I. N. Duling, N. J. Halas, J.-M. Halbout, and P. G. May, “Capacitance free generation and detection of subpicosecond electrical pulses on coplanar transmission lines,” IEEE J. Quantum Electron. 24(2), 221–225 (1988).
[CrossRef]

Gupta, S.

M. Y. Frankel, S. Gupta, J. A. Valdmanis, and G. A. Mourou, “Terahertz Attenuation and dispersion characteristics of coplanar transmission lines,” IEEE Trans. Microw. Theory Tech. 39(6), 910–916 (1991).
[CrossRef]

Halas, N. J.

D. R. Grischkowsky, M. B. Ketchen, C.-C. Chi, I. N. Duling, N. J. Halas, J.-M. Halbout, and P. G. May, “Capacitance free generation and detection of subpicosecond electrical pulses on coplanar transmission lines,” IEEE J. Quantum Electron. 24(2), 221–225 (1988).
[CrossRef]

Halbout, J.-M.

D. R. Grischkowsky, M. B. Ketchen, C.-C. Chi, I. N. Duling, N. J. Halas, J.-M. Halbout, and P. G. May, “Capacitance free generation and detection of subpicosecond electrical pulses on coplanar transmission lines,” IEEE J. Quantum Electron. 24(2), 221–225 (1988).
[CrossRef]

Heshmat, B.

Hilfiker, J. N.

M. Y. Frankel, R. H. Voelker, and J. N. Hilfiker, “Coplanar transmission lines on thin substrates for high-speed low-loss propagation,” IEEE Trans. Microw. Theory Tech. 42(3), 396–402 (1994).
[CrossRef]

Hong, C.

Keiding, S.

Ketchen, M. B.

D. R. Grischkowsky, M. B. Ketchen, C.-C. Chi, I. N. Duling, N. J. Halas, J.-M. Halbout, and P. G. May, “Capacitance free generation and detection of subpicosecond electrical pulses on coplanar transmission lines,” IEEE J. Quantum Electron. 24(2), 221–225 (1988).
[CrossRef]

Kleinman, D. K.

D. K. Kleinman and D. H. Auston, “Theory of Electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20(8), 964–970 (1984).
[CrossRef]

Liu, J.

J. Liu, R. Mendis, and D. M. Mittleman, “The transition from a TEM-like mode to a plasmonic mode in parallel-plate waveguides,” Appl. Phys. Lett. 98(23), 231113 (2011).
[CrossRef]

May, P. G.

D. R. Grischkowsky, M. B. Ketchen, C.-C. Chi, I. N. Duling, N. J. Halas, J.-M. Halbout, and P. G. May, “Capacitance free generation and detection of subpicosecond electrical pulses on coplanar transmission lines,” IEEE J. Quantum Electron. 24(2), 221–225 (1988).
[CrossRef]

Mendis, R.

Mittleman, D. M.

H. Zhan, R. Mendis, and D. M. Mittleman, “Characterization of the terahertz near-field output of parallel-plate waveguides,” J. Opt. Soc. Am. B 28(3), 558–566 (2011).
[CrossRef]

J. Liu, R. Mendis, and D. M. Mittleman, “The transition from a TEM-like mode to a plasmonic mode in parallel-plate waveguides,” Appl. Phys. Lett. 98(23), 231113 (2011).
[CrossRef]

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

Mourou, G. A.

M. Y. Frankel, S. Gupta, J. A. Valdmanis, and G. A. Mourou, “Terahertz Attenuation and dispersion characteristics of coplanar transmission lines,” IEEE Trans. Microw. Theory Tech. 39(6), 910–916 (1991).
[CrossRef]

Pahlevaninezhad, H.

Ruan, Z.

Valdmanis, J. A.

M. Y. Frankel, S. Gupta, J. A. Valdmanis, and G. A. Mourou, “Terahertz Attenuation and dispersion characteristics of coplanar transmission lines,” IEEE Trans. Microw. Theory Tech. 39(6), 910–916 (1991).
[CrossRef]

Veronis, G.

Vodopyanov, K. L.

Voelker, R. H.

M. Y. Frankel, R. H. Voelker, and J. N. Hilfiker, “Coplanar transmission lines on thin substrates for high-speed low-loss propagation,” IEEE Trans. Microw. Theory Tech. 42(3), 396–402 (1994).
[CrossRef]

Wang, K.

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

Yariv, A.

Yeh, P.

Zhan, H.

Appl. Phys. Lett.

J. Liu, R. Mendis, and D. M. Mittleman, “The transition from a TEM-like mode to a plasmonic mode in parallel-plate waveguides,” Appl. Phys. Lett. 98(23), 231113 (2011).
[CrossRef]

IEEE J. Quantum Electron.

D. R. Grischkowsky, M. B. Ketchen, C.-C. Chi, I. N. Duling, N. J. Halas, J.-M. Halbout, and P. G. May, “Capacitance free generation and detection of subpicosecond electrical pulses on coplanar transmission lines,” IEEE J. Quantum Electron. 24(2), 221–225 (1988).
[CrossRef]

D. K. Kleinman and D. H. Auston, “Theory of Electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20(8), 964–970 (1984).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

D. Grischkowsky, “Optoelectronic characterization of transmission lines and waveguides by terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1122–1135 (2000).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

M. Y. Frankel, R. H. Voelker, and J. N. Hilfiker, “Coplanar transmission lines on thin substrates for high-speed low-loss propagation,” IEEE Trans. Microw. Theory Tech. 42(3), 396–402 (1994).
[CrossRef]

M. Y. Frankel, S. Gupta, J. A. Valdmanis, and G. A. Mourou, “Terahertz Attenuation and dispersion characteristics of coplanar transmission lines,” IEEE Trans. Microw. Theory Tech. 39(6), 910–916 (1991).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Nature

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

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

C. Fattinger and D. Grischkowsky, “Observation of electromagnetic shock waves from propagating surface-dipole distributions,” Phys. Rev. Lett. 62(25), 2961–2964 (1989).
[CrossRef] [PubMed]

D. Grischkowsky, I. I. I. Duling, J. C. Chen, and C. C. Chi, “Electromagnetic shock waves from transmission lines,” Phys. Rev. Lett. 59(15), 1663–1666 (1987).
[CrossRef] [PubMed]

Other

J. V. Jelley, Cherenlov radiation and its applications (Pergamon, New York, 1958).

J. D. Jackson, Classical electrodynamics (John Wiley & Sons, 1999), pp. 352–356.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Modeling the flow of light, 2nd Edition (Princeton Univ. Press,2008), Chap. 4.

P. Yeh, Optical waves in layered media (Wiley,1988), Chap.6.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley,1984), Chap. 6.

D. M. Pozar, “Microwave engineering (John Wiley & Sons, 2005), pp. 97-98.

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Figures (7)

Fig. 1
Fig. 1

(a) Conventional slot-line, (b) slot-line in a homogeneous medium, and (c) slot-line on a layered substrate.

Fig. 2
Fig. 2

(a) Slot-Line in a homogeneous medium, (b,c) mapping the cross section of the slot-line (b) to the cross section of a parallel-plate waveguide (c), dotted-lines show the constant potential curves.

Fig. 3
Fig. 3

(a) Equipotential curves and electric field vector (blue arrows), (b) electric field amplitude square.

Fig. 4
Fig. 4

Approximation of two thin planar plates with two branches of a hyperbola

Fig. 5
Fig. 5

(a) Electric field amplitude associated with a localized mode at the surface of a layered substrate, (b) the electric field distribution for a slot-line on a periodic Si/SiO2 layered substrate (d1 = 13.8 μm, d2 = 37.5 μm, s = 10 μm, w = 500 μm) from a 3D full-wave FEM simulations.

Fig. 6
Fig. 6

The electric field amplitude from a 3D full-wave simulations with FEM using the Ansoft HFSS for (a) a slot-line on a half-space GaAs substrate, (b) a slot-line in GaAs, and (c) slot-line on a periodic Si/SiO2 layered substrate (d1 = 13.8 μm, d2 = 37.5 μm), all with s = 20 μm, w = 500 μm.

Fig. 7
Fig. 7

(a) The conductor loss vs. separation s, for slot-line made out of gold in GaAs, obtained from the theory (solid blue line) and from the simulations (dashed-line with green squares), and for a slot-line on a quarter-wave stack of Si/SiO2, obtained from the simulations (dotted-line with purple circles), (b) the conductor loss for slot-line in GaAs vs. u0, for s = 10μm.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

f(z)= Sin 1 ( z s/2 ).
V= 2 V 0 π e{ f(z) }= 2 V 0 π e{ Sin 1 ( x+iy s/2 ) },
( x s/2Sin( π 2 V V 0 ) ) 2 ( y s/2Cos( π 2 V V 0 ) ) 2 =1.
E =V,
E = V 0 s/2( Cos 2 ( u )+Sin h 2 ( v ) ) ( Cos( u )Cosh( v ) x Sin( u )Sinh( v ) y ),
H = 1 η z × E ,
{ u=e{ Sin 1 ( x+iy s/2 ) } v=m{ Sin 1 ( x+iy s/2 ) } ,
H = H || e ξ/δ e iξ/δ ,
E c μ c ω 2σ ( 1i )( n × H || ) e ξ/δ e iξ/δ ,
δ= 2 ω μ c σ ,
d P loss dA = μ c ωδ 4 | H || | 2 .
P loss L = μ c ωδ 4 C H || 2 dl= μ c ωδ 4 C E 2 η 2 dl ,
{ x= s 2 Sin( u 0 )Cosh( v ) y= s 2 Cos( u 0 )Sinh( v ) ,
P loss L = μ c ωδ 4 [ 4 V 0 2 η 2 ( 2 s ) 0 v 0 dv Cos 2 ( u 0 )+Sin h 2 ( v ) ],
v 0 =Cos h 1 ( w/s ).
P 0 = 1 2 e{ S ' ( E × H ). ds },
P 0 = V 0 2 2η ( 2 u 0 )( 2 v 0 ).
α= P l 2 P 0 = P loss /L 2 P 0 ,
α= μ c ωδ η [ 1 2s u 0 v 0 0 v 0 dv Cos 2 ( u 0 )+Sin h 2 ( v ) ],
E k ( x,y,z )= E 0 ( x,y ) e i k z z ,
E k ( x,y,z )= u k y ( x,y ). e i k y y e i k z z ,
ω m = n 1 + n 2 4 n 1 n 2 2πc a ,

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