Abstract

We explore a class of dielectrically loaded metallic waveguides capable of supporting negative index modes in the far infrared and terahertz regime. Principles of operation, modal structure and appropriate coupling schemes are analytically and numerically investigated. The extreme simplicity of the proposed design, along with the non-conventional and counter intuitive electromagnetic properties of this family of waveguides, makes these structures excellent candidates for the practical realization of negative index far infrared and terahertz devices with new and interesting functionalities. Generalizations and extensions of the suggested design are also discussed.

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968) (published in Russian in 1967).
  2. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
    [CrossRef] [PubMed]
  3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
    [CrossRef]
  4. O. Siddiqui, M. Mojahedi, and G. V. Eleftheriades, “Periodically loaded transmission line with effective negative refractive index and negative group velocity,” IEEE Trans. Antenn. Propag. 51(10), 2619–2625 (2003).
    [CrossRef]
  5. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
    [CrossRef]
  6. G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microw. Theory Tech. 50(12), 2702–2712 (2002).
    [CrossRef]
  7. P. J. B. Clarricoats and R. A. Waldron, “Non-periodic slow-wave and backward-wave structures,” Electron. Control 8, 455 (1960).
  8. R. E. Collin, Field Theory of Guided Waves, 2nd ed., (New York, IEEE Press, 1991) Chap. 9: periodic structures.
  9. P. J. B. Clarricoats, “Backward waves in waveguides containing dielectrics,” Proc. IEE 108, 496–501 (1961).
  10. P. J. B. Clarricoats and A. B. Birtles, “Circular Waveguide Backward-wave Experiments,” J. Electron Contr. 15, 325–330 (1963).
  11. R. A. Waldron, “Theory and potential applications of backward-waves in non-periodic inhomogeneous waveguides,” Proc. IEE 111, 1659–1667 (1964).
  12. M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
    [CrossRef] [PubMed]
  13. G. N. Tsandoulas, “Propagation in Dielectric-Lined Square Waveguides,” IEEE Trans. Microw. Theory Tech. 23(5), 406–410 (1975).
    [CrossRef]
  14. K. Okamoto, Fundamentals of Optical Waveguides, (Academic Press, New York, 2000), Chap. 3: optical fibers.
  15. C. S. Lee, S. W. Lee, and S. L. Chuang, “Plot of Modal Field Distribution in Rectangular and Circular Waveguides,” IEEE Trans. Microw. Theory Tech. 33(3), 271–274 (1985).
    [CrossRef]
  16. E. F. F. Gillespie, “Power flow and negative impedance in the dielectric rod waveguide,” Proc. Inst. Electr. Eng. 107c, 198–201 (1960).
  17. S. Mokhov, R. El-Ganainy, and D. N. Christodoulides, “Power circulation via negative energy-flux wormholes in optical nanowaveguides,” Opt. Express 14(8), 3255–3262 (2006).
    [CrossRef] [PubMed]
  18. P. H. Bolivar, M. Brucherseifer, J. Gómez Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant materials at Terahertz Frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
    [CrossRef]
  19. R. F. Potter, “Germanim (Ge),” in Handbook of Optical Constants of Solids, E.D. Palik, ed., (Academic, Orlando, Fla., 1985).
  20. S. H. Nam, A. J. Taylor, and A. Efimov, “Subwavelength hybrid terahertz waveguides,” Opt. Express 17(25), 22890–22897 (2009).
    [CrossRef]

2009 (1)

2007 (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

2006 (1)

2004 (1)

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[CrossRef] [PubMed]

2003 (2)

O. Siddiqui, M. Mojahedi, and G. V. Eleftheriades, “Periodically loaded transmission line with effective negative refractive index and negative group velocity,” IEEE Trans. Antenn. Propag. 51(10), 2619–2625 (2003).
[CrossRef]

P. H. Bolivar, M. Brucherseifer, J. Gómez Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant materials at Terahertz Frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[CrossRef]

2002 (1)

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microw. Theory Tech. 50(12), 2702–2712 (2002).
[CrossRef]

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

1985 (1)

C. S. Lee, S. W. Lee, and S. L. Chuang, “Plot of Modal Field Distribution in Rectangular and Circular Waveguides,” IEEE Trans. Microw. Theory Tech. 33(3), 271–274 (1985).
[CrossRef]

1975 (1)

G. N. Tsandoulas, “Propagation in Dielectric-Lined Square Waveguides,” IEEE Trans. Microw. Theory Tech. 23(5), 406–410 (1975).
[CrossRef]

1963 (1)

P. J. B. Clarricoats and A. B. Birtles, “Circular Waveguide Backward-wave Experiments,” J. Electron Contr. 15, 325–330 (1963).

1960 (2)

P. J. B. Clarricoats and R. A. Waldron, “Non-periodic slow-wave and backward-wave structures,” Electron. Control 8, 455 (1960).

E. F. F. Gillespie, “Power flow and negative impedance in the dielectric rod waveguide,” Proc. Inst. Electr. Eng. 107c, 198–201 (1960).

Birtles, A. B.

P. J. B. Clarricoats and A. B. Birtles, “Circular Waveguide Backward-wave Experiments,” J. Electron Contr. 15, 325–330 (1963).

Bolivar, P. H.

P. H. Bolivar, M. Brucherseifer, J. Gómez Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant materials at Terahertz Frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[CrossRef]

Brucherseifer, M.

P. H. Bolivar, M. Brucherseifer, J. Gómez Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant materials at Terahertz Frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[CrossRef]

Christodoulides, D. N.

Chuang, S. L.

C. S. Lee, S. W. Lee, and S. L. Chuang, “Plot of Modal Field Distribution in Rectangular and Circular Waveguides,” IEEE Trans. Microw. Theory Tech. 33(3), 271–274 (1985).
[CrossRef]

Clarricoats, P. J. B.

P. J. B. Clarricoats and A. B. Birtles, “Circular Waveguide Backward-wave Experiments,” J. Electron Contr. 15, 325–330 (1963).

P. J. B. Clarricoats and R. A. Waldron, “Non-periodic slow-wave and backward-wave structures,” Electron. Control 8, 455 (1960).

de Maagt, P.

P. H. Bolivar, M. Brucherseifer, J. Gómez Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant materials at Terahertz Frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[CrossRef]

Ederra, I.

P. H. Bolivar, M. Brucherseifer, J. Gómez Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant materials at Terahertz Frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[CrossRef]

Efimov, A.

Eleftheriades, G. V.

O. Siddiqui, M. Mojahedi, and G. V. Eleftheriades, “Periodically loaded transmission line with effective negative refractive index and negative group velocity,” IEEE Trans. Antenn. Propag. 51(10), 2619–2625 (2003).
[CrossRef]

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microw. Theory Tech. 50(12), 2702–2712 (2002).
[CrossRef]

El-Ganainy, R.

Fink, Y.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[CrossRef] [PubMed]

Gillespie, E. F. F.

E. F. F. Gillespie, “Power flow and negative impedance in the dielectric rod waveguide,” Proc. Inst. Electr. Eng. 107c, 198–201 (1960).

Gómez Rivas, J.

P. H. Bolivar, M. Brucherseifer, J. Gómez Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant materials at Terahertz Frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[CrossRef]

Gonzalo, R.

P. H. Bolivar, M. Brucherseifer, J. Gómez Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant materials at Terahertz Frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Holker, M.

P. H. Bolivar, M. Brucherseifer, J. Gómez Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant materials at Terahertz Frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[CrossRef]

Ibanescu, M.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[CrossRef] [PubMed]

Iyer, A. K.

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microw. Theory Tech. 50(12), 2702–2712 (2002).
[CrossRef]

Joannopoulos, J. D.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[CrossRef] [PubMed]

Johnson, S. G.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[CrossRef] [PubMed]

Kremer, P. C.

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microw. Theory Tech. 50(12), 2702–2712 (2002).
[CrossRef]

Lee, C. S.

C. S. Lee, S. W. Lee, and S. L. Chuang, “Plot of Modal Field Distribution in Rectangular and Circular Waveguides,” IEEE Trans. Microw. Theory Tech. 33(3), 271–274 (1985).
[CrossRef]

Lee, S. W.

C. S. Lee, S. W. Lee, and S. L. Chuang, “Plot of Modal Field Distribution in Rectangular and Circular Waveguides,” IEEE Trans. Microw. Theory Tech. 33(3), 271–274 (1985).
[CrossRef]

Luo, C.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[CrossRef] [PubMed]

Mojahedi, M.

O. Siddiqui, M. Mojahedi, and G. V. Eleftheriades, “Periodically loaded transmission line with effective negative refractive index and negative group velocity,” IEEE Trans. Antenn. Propag. 51(10), 2619–2625 (2003).
[CrossRef]

Mokhov, S.

Nam, S. H.

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Reynolds, A. L.

P. H. Bolivar, M. Brucherseifer, J. Gómez Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant materials at Terahertz Frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Roundy, D.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[CrossRef] [PubMed]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

Siddiqui, O.

O. Siddiqui, M. Mojahedi, and G. V. Eleftheriades, “Periodically loaded transmission line with effective negative refractive index and negative group velocity,” IEEE Trans. Antenn. Propag. 51(10), 2619–2625 (2003).
[CrossRef]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Taylor, A. J.

Tsandoulas, G. N.

G. N. Tsandoulas, “Propagation in Dielectric-Lined Square Waveguides,” IEEE Trans. Microw. Theory Tech. 23(5), 406–410 (1975).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Waldron, R. A.

P. J. B. Clarricoats and R. A. Waldron, “Non-periodic slow-wave and backward-wave structures,” Electron. Control 8, 455 (1960).

Electron. Control (1)

P. J. B. Clarricoats and R. A. Waldron, “Non-periodic slow-wave and backward-wave structures,” Electron. Control 8, 455 (1960).

IEEE Trans. Antenn. Propag. (1)

O. Siddiqui, M. Mojahedi, and G. V. Eleftheriades, “Periodically loaded transmission line with effective negative refractive index and negative group velocity,” IEEE Trans. Antenn. Propag. 51(10), 2619–2625 (2003).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (5)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microw. Theory Tech. 50(12), 2702–2712 (2002).
[CrossRef]

G. N. Tsandoulas, “Propagation in Dielectric-Lined Square Waveguides,” IEEE Trans. Microw. Theory Tech. 23(5), 406–410 (1975).
[CrossRef]

C. S. Lee, S. W. Lee, and S. L. Chuang, “Plot of Modal Field Distribution in Rectangular and Circular Waveguides,” IEEE Trans. Microw. Theory Tech. 33(3), 271–274 (1985).
[CrossRef]

P. H. Bolivar, M. Brucherseifer, J. Gómez Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant materials at Terahertz Frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[CrossRef]

J. Electron Contr. (1)

P. J. B. Clarricoats and A. B. Birtles, “Circular Waveguide Backward-wave Experiments,” J. Electron Contr. 15, 325–330 (1963).

Nat. Photonics (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

Opt. Express (2)

Phys. Rev. Lett. (2)

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Proc. Inst. Electr. Eng. (1)

E. F. F. Gillespie, “Power flow and negative impedance in the dielectric rod waveguide,” Proc. Inst. Electr. Eng. 107c, 198–201 (1960).

Other (6)

R. F. Potter, “Germanim (Ge),” in Handbook of Optical Constants of Solids, E.D. Palik, ed., (Academic, Orlando, Fla., 1985).

R. A. Waldron, “Theory and potential applications of backward-waves in non-periodic inhomogeneous waveguides,” Proc. IEE 111, 1659–1667 (1964).

K. Okamoto, Fundamentals of Optical Waveguides, (Academic Press, New York, 2000), Chap. 3: optical fibers.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968) (published in Russian in 1967).

R. E. Collin, Field Theory of Guided Waves, 2nd ed., (New York, IEEE Press, 1991) Chap. 9: periodic structures.

P. J. B. Clarricoats, “Backward waves in waveguides containing dielectrics,” Proc. IEE 108, 496–501 (1961).

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Figures (5)

Fig. 1
Fig. 1

Dispersion curve of the circular Clarricoats-Waldron guide shown in the inset. The region of negative effective index is shown in red.

Fig. 2
Fig. 2

Electric and magnetic field distribution of the fundamental backward mode in a circular Clarricoats-Waldron guide with dielectric contrast 30, operating a 1THz.

Fig. 3
Fig. 3

(left panel) Normalized Poynting vector distribution over a cross section of a Clarricoats-Waldron guide with dielectric contrast 30, operating at 1THz. The regions of positive power flow are indicated in red, while the regions of negative power flow are indicated in blue. (right panel) the magnetic field is shown along with the regions of positive and negative flow. The dielectric interface is shown in gray.

Fig. 4
Fig. 4

(a) Numerical simulation of power flow and field distribution in a Clarricoats-Waldron rectangular waveguide of dimensions 80μm x 40μm, loaded with a Germanium rod of dimensions 53μm x 26.5μm, operating at 1THz . (b) Dispersion relation.

Fig. 5
Fig. 5

Power flow and electric field distribution in a single element and in a 2D Clarricoats-Waldron array.

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