Abstract

The coupling between negative and positive index medium waveguides is investigated theoretically in this paper. A coupled mode theory is developed for such a waveguide system and its validity is verified. Interesting phenomena in the coupled waveguides are demonstrated, which occur in the case when the negative index medium waveguide in isolation guides its mode backward. A new type of coupled mode solution that varies exponentially with the coupling length is found in the special case when the propagation constants of two individual waveguides are nearly the same. A coupler operating in this case is insensitive to the coupling length, and its coupling efficiency can reach 100% as long as the coupling length is long enough. However, when the propagation constants of the two individual waveguides differ greatly, the coupled mode solution is still a periodic function of the coupling length, but the coupled power is output backward. In addition, the modes in the composite waveguide system are also studied using the coupled mode theory, and their fundamental properties are revealed.

© 2008 IEEE

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2007 (1)

2006 (2)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).

J. Zhou, L. Zhang, G. Tuttle, T. Koschnny, C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B 73, 041101 (2006).

2005 (3)

2004 (4)

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, J. A. Kong, "Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns," Appl. Phys. Lett. 84, 1537-1539 (2004).

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, J. A. Kong, "Left-handed material composed of only S-shaped resonators," Phys. Rev. E 70, 057605 (2004).

A. F. Starr, P. M. Rye, D. R. Smith, S. Nemat-Nasser, "Fabrication and characterization of a negative-index composite metamaterial," Phys. Rev. B 70, 113102 (2004).

A. Alu, N. Engheta, "Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers," IEEE Trans. Microwave Theory Tech. 52, 199-210 (2004).

2003 (4)

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, J. A. Kong, "Guided modes with imaginary, transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).

A. C. Peacock, N. G. R. Broderick, "Guided modes in channel waveguides with a negative index of refraction," Opt. Exp. 11, 2502-2510 (2003).

K. Halterman, J. M. Elson, P. L. Overfelt, "Characteristics of bound modes in coupled dielectric waveguides containing negative index media," Opt. Exp. 11, 521-524 (2003).

2001 (1)

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental verification of a negative index of refraction," Science 242, 77-79 (2001).

2000 (2)

D. R. Smith, N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2433-2436 (2000).

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).

1989 (1)

1987 (2)

W. Streifer, M. Osinski, A. Hardy, "Reformulation of the coupledmode theory of multiwaveguide systems," J. Lightw. Technol. 5, 1-4 (1987).

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," J. Lightw. Technol. 5, 16-23 (1987).

1986 (1)

A. W. Snyder, A. Ankiewicz, "Fibre couplers composed of unequal cores," Electron. Lett. 22, 1237-1238 (1986).

1985 (1)

A. Hardy, W. Streifer, "Coupled mode theory of parallel waveguides," J. Lightw. Technol. 3, 1135-1146 (1985).

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of $\epsilon$ and $\mu$," Sov. Phys. Usp. 10, 509-514 (1968).

Appl. Phys. Lett. (1)

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, J. A. Kong, "Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns," Appl. Phys. Lett. 84, 1537-1539 (2004).

Electron. Lett. (1)

A. W. Snyder, A. Ankiewicz, "Fibre couplers composed of unequal cores," Electron. Lett. 22, 1237-1238 (1986).

IEEE Trans. Microwave Theory Tech. (1)

A. Alu, N. Engheta, "Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers," IEEE Trans. Microwave Theory Tech. 52, 199-210 (2004).

J. Appl. Phys. (1)

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, J. A. Kong, "Guided modes with imaginary, transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).

J. Lightw. Technol. (3)

A. Hardy, W. Streifer, "Coupled mode theory of parallel waveguides," J. Lightw. Technol. 3, 1135-1146 (1985).

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," J. Lightw. Technol. 5, 16-23 (1987).

W. Streifer, M. Osinski, A. Hardy, "Reformulation of the coupledmode theory of multiwaveguide systems," J. Lightw. Technol. 5, 1-4 (1987).

Opt. Exp. (1)

K. Halterman, J. M. Elson, P. L. Overfelt, "Characteristics of bound modes in coupled dielectric waveguides containing negative index media," Opt. Exp. 11, 521-524 (2003).

Opt. Exp. (1)

A. C. Peacock, N. G. R. Broderick, "Guided modes in channel waveguides with a negative index of refraction," Opt. Exp. 11, 2502-2510 (2003).

Opt. Lett. (4)

Phys. Rev. B (1)

J. Zhou, L. Zhang, G. Tuttle, T. Koschnny, C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B 73, 041101 (2006).

Phys. Rev. B (1)

A. F. Starr, P. M. Rye, D. R. Smith, S. Nemat-Nasser, "Fabrication and characterization of a negative-index composite metamaterial," Phys. Rev. B 70, 113102 (2004).

Phys. Rev. E (2)

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, J. A. Kong, "Left-handed material composed of only S-shaped resonators," Phys. Rev. E 70, 057605 (2004).

Phys. Rev. Lett. (3)

D. R. Smith, N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2433-2436 (2000).

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).

Science (2)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental verification of a negative index of refraction," Science 242, 77-79 (2001).

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of $\epsilon$ and $\mu$," Sov. Phys. Usp. 10, 509-514 (1968).

Other (1)

A. Alu, N. Engheta, "Anomalous mode coupling in guided-wave structures containing metamaterials with negative permittivity and permeability," Proc. IEEE Nanotechnology (2002) pp. 233-234.

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