Abstract

In this work, we investigate the propagation of designer surface plasmons in planar perfect electric conductor structures that are subject to a parabolic graded-index distribution. A three-dimensional, fully vectorial finite-difference time-domain method was used to engineer a structure with a parabolic effective group index by modulating the dielectric constant of the structure’s square holes. Using this structure in our simulations, the lateral confinement of propagating designer surface plasmons is demonstrated. Focusing, collimation and waveguiding of designer plasmons in the lateral direction is realized by changing the width of the source beam. Our findings contribute to applications of designer surface plasmons that require energy concentration, diffusion, guiding, and beam aperture modification within planar perfect electric conductors.

© 2009 Optical Society of America

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    [CrossRef]

2008 (7)

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernndez-Domnguez, L. Martn-Moreno, and F. J. Garca-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2, 175–179 (2008). URL http://www.nature.com/nphoton/journal/v2/n3/abs/nphoton.2007.301.html.
[CrossRef]

W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16, 6216–6226 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-9-6216.
[CrossRef] [PubMed]

J. Gómez Rivas, “Terahertz: The art of confinement,” Nat. Photonics 2, 137–138 (2008). URL http://www.nature.com/nphoton/journal/v2/n3/abs/nphoton.2008.12.html.
[CrossRef]

L. Shen, X. Chen, Y. Zhong, and K. Agarwal, “Effect of absorption on terahertz surface plasmon polaritons propagating along periodically corrugated metal wires,” Phys. Rev. B 77, 075,408-1-7 (2008). URL http://link.aps.org/abstract/PRB/v77/e075408.
[CrossRef]

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-Bandwidth Slow-Light System Based on THz Plasmonic Graded Metallic Grating Structures,” Phys. Rev. Lett. 100, 256,803-1-3 (2008). URL http://link.aps.org/abstract/PRL/v100/e256803.
[CrossRef]

J. Shi, S.-C. Lin, and T. J. Huang, “Wide-band acoustic collimating by phononic crystal composites,” Appl. Phy. Lett. 92, 111,901-1-3 (2008). URL http://link.aip.org/link/?APPLAB/92/111901/1.
[CrossRef]

B. K Juluri, Y. B Zheng, D. Ahmed, L. Jensen, and T. J. Huang, “Effects of geometry and composition on charge-induced plasmonic shifts in gold nanoparticles,” J. Phys. Chem. C 112, 7309–7312 (2008). URL http://dx.doi.org/10.1021/jp077346h.
[CrossRef]

2007 (8)

Q. Gan, B. Guo, G. Song, L. Chen, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Plasmonic surface-wave splitter,” Appl. Phys. Lett. 90, 161,130-1-3 (2007). URL http://link.aip.org/link/?APL/90/161130/1.
[CrossRef]

F. Lopez-Tejeira, S. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, E. Devaux, T. Ebbesen, J. Krenn, I. Radko, S. Bozhevol-nyi, and M. Gonzalez, et al., “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007). URL http://www.nature.com/nphys/journal/v3/n5/abs/nphys584.html.
[CrossRef]

S. S. Oh, S.-G. Lee, J.-E. Kim, and H. Y. Park, “Self-collimation phenomena of surface waves in structured perfect electric conductors and metal surfaces,” Opt. Express 15, 1205–1210 (2007). URL http://www.opticsinfobase.org/abstract.cfm?uri=oe-15-3-1205.
[CrossRef] [PubMed]

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Bidirectional subwavelength slit splitter for THz surface plasmons,” Opt. Express 15, 18,050–18,055 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-26-18050.
[CrossRef]

Z. Ruan and M. Qiu, “Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface,” Appl. Phys. Lett. 90, 201,906-1-3 (2007). URL http://link.aip.org/link/?APPLAB/90/201906/1.
[CrossRef]

A. O. Pinchuk and G. C. Schatz, “Metamaterials with gradient negative index of refraction,” J. Opt. Soc. Am. A 24, A39–A44 (2007). URL http://www.opticsinfobase.org/abstract.cfm?URI=josaa-24-10-A39.
[CrossRef]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15, 1240–1253 (2007). URL http://www.opticsexpress.org/abstract.cfm?uri=oe-15-3-1240.
[CrossRef] [PubMed]

M. Johnston, “Plasmonics: Superfocusing of terahertz waves,” Nat. Photonics 1, 14–15 (2007). URL http://www.nature.com/nphoton/journal/v1/n1/full/nphoton.2006.60.html.
[CrossRef]

2006 (7)

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006). URL http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-20-2972.
[CrossRef] [PubMed]

F. S. Roux and I. De Leon, “Planar photonic crystal gradient index lens, simulated with a finite difference time domain method,” Phys. Rev. B 74, 113,103-1-4 (2006). URL http://link.aps.org/abstract/PRB/v74/e113103.
[CrossRef]

Z. Ruan and M. Qiu, “Negative refraction and sub-wavelength imaging through surface waves on structured perfect conductor surfaces,” Opt. Express 14, 6172–6177 (2006). URL http://www.opticsexpress.org/abstract.cfm?uri=oe-14-13-6172.
[CrossRef] [PubMed]

S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251,120-1-4 (2006). URL http://link.aip.org/link/?APL/88/251120/1.
[CrossRef]

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz Surface Plasmon-Polariton Propagation and Focusing on Periodically Corrugated Metal Wires,” Phys. Rev. Lett. 97, 176,805-1-4 (2006). URL http://link.aps.org/abstract/PRL/v97/e176805.
[CrossRef]

Y. Chen, Z. Song, Y. Li, M. Hu, Q. Xing, Z. Zhang, L. Chai, and C.-Y. Wang, “Effective surface plasmon polaritons on the metal wire with arrays of subwavelength grooves,” Opt. Express 14, 13,021-13,029 (2006). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-13021.

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide Arrays as Plasmonic Metamaterials: Transmission below Cutoff,” Phys. Rev. Lett. 96, 073,904-1-5 (2006). URL http://link.aps.org/abstract/PRL/v96/e073904.
[CrossRef]

2005 (6)

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7, S97–S101 (2005). URL http://www.iop.org/EJ/abstract/1464-4258/7/2/013/.
[CrossRef]

F. J. G. de Abajo and J. J. Sáenz, “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces,” Phys. Rev. Lett. 95, 233,901-1-4 (2005). URL http://link.aps.org/abstract/PRL/v95/e233901.

M. Qiu, “Photonic band structures for surface waves on structured metal surfaces,” Opt. Express 13, 7583–7588 (2005). URL http://www.opticsexpress.org/abstract.cfm?uri=oe-13-19-7583.
[CrossRef] [PubMed]

A. Hibbins, B. Evans, and J. Sambles, “Experimental Verification of Designer Surface Plasmons,” Science 308, 670–672 (2005). URL http://www.sciencemag.org/cgi/content/abstract/308/5722/670.
[CrossRef] [PubMed]

F. Miyamaru and M. Hangyo, “Strong enhancement of terahertz transmission for a three-layer heterostructure of metal hole arrays,” Phys. Rev. B 72, 035,429-1-5 (2005). URL http://link.aps.org/abstract/PRB/v72/e035429.
[CrossRef]

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86, 181,108-1-3 (2005). URL http://link.aip.org/link/?APL/86/181108/1.
[CrossRef]

2004 (3)

J. Saxler, J. Gómez Rivas, C. Janke, H. Pellemans, P. Bolívar, and H. Kurz, “Time-domain measurements of surface plasmon polaritons in the terahertz frequency range,” Phys. Rev. B 69, 155,427-1-4 (2004). URL http://link.aps.org/abstract/PRB/v69/e155427.
[CrossRef]

H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12, 1004–1010 (2004). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-6-1004.
[CrossRef] [PubMed]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305, 847–848 (2004). URL http://www.sciencemag.org/cgi/content/abstract/305/5685/847.
[CrossRef] [PubMed]

2003 (2)

J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through sub-wavelength holes,” Phys. Rev. B 68, 201,306-1-4 (2003). URL http://link.aps.org/abstract/PRB/v68/e201306.
[CrossRef]

D. Wu, N. Fang, C. Sun, X. Zhang, W. Padilla, D. Basov, D. Smith, and S. Schultz, “Terahertz plasmonic high pass filter,” Appl. Phys. Lett. 83, 201–203 (2003). URL http://link.aip.org/link/?APPLAB/83/201/1.
[CrossRef]

2001 (1)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). URL http://link.aps.org/abstract/PRL/v86/p1114.
[CrossRef] [PubMed]

2000 (1)

P. Berini, “Plasmon polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000). URL http://link.aps.org/doi/10.1103/PhysRevB.61.10484.
[CrossRef]

1999 (1)

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Grating-coupled surface plasmons at microwave frequencies,” J. Appl. Phys. 86, 1791–1795 (1999). URL http://link.aip.org/link/?JAPIAU/86/1791/1.
[CrossRef]

1998 (1)

T. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). URL http://www.nature.com/nature/journal/v391/n6668/abs/391667a0.html.
[CrossRef]

1997 (1)

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107, 6756–6769 (1997). URL http://link.aip.org/link/?JCPSA6/107/6756/1.
[CrossRef]

1980 (1)

Agarwal, K.

L. Shen, X. Chen, Y. Zhong, and K. Agarwal, “Effect of absorption on terahertz surface plasmon polaritons propagating along periodically corrugated metal wires,” Phys. Rev. B 77, 075,408-1-7 (2008). URL http://link.aps.org/abstract/PRB/v77/e075408.
[CrossRef]

Agrawal, A.

Ahmed, D.

B. K Juluri, Y. B Zheng, D. Ahmed, L. Jensen, and T. J. Huang, “Effects of geometry and composition on charge-induced plasmonic shifts in gold nanoparticles,” J. Phys. Chem. C 112, 7309–7312 (2008). URL http://dx.doi.org/10.1021/jp077346h.
[CrossRef]

Andrews, S. R.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernndez-Domnguez, L. Martn-Moreno, and F. J. Garca-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2, 175–179 (2008). URL http://www.nature.com/nphoton/journal/v2/n3/abs/nphoton.2007.301.html.
[CrossRef]

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz Surface Plasmon-Polariton Propagation and Focusing on Periodically Corrugated Metal Wires,” Phys. Rev. Lett. 97, 176,805-1-4 (2006). URL http://link.aps.org/abstract/PRL/v97/e176805.
[CrossRef]

S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251,120-1-4 (2006). URL http://link.aip.org/link/?APL/88/251120/1.
[CrossRef]

Bao, C.

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C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernndez-Domnguez, L. Martn-Moreno, and F. J. Garca-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2, 175–179 (2008). URL http://www.nature.com/nphoton/journal/v2/n3/abs/nphoton.2007.301.html.
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Miyamaru, F.

F. Miyamaru and M. Hangyo, “Strong enhancement of terahertz transmission for a three-layer heterostructure of metal hole arrays,” Phys. Rev. B 72, 035,429-1-5 (2005). URL http://link.aps.org/abstract/PRB/v72/e035429.
[CrossRef]

Moore, D. T.

Nahata, A.

Nomura, W.

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86, 181,108-1-3 (2005). URL http://link.aip.org/link/?APL/86/181108/1.
[CrossRef]

Oh, S. S.

Ohtsu, M.

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86, 181,108-1-3 (2005). URL http://link.aip.org/link/?APL/86/181108/1.
[CrossRef]

Padilla, W.

D. Wu, N. Fang, C. Sun, X. Zhang, W. Padilla, D. Basov, D. Smith, and S. Schultz, “Terahertz plasmonic high pass filter,” Appl. Phys. Lett. 83, 201–203 (2003). URL http://link.aip.org/link/?APPLAB/83/201/1.
[CrossRef]

Park, H. Y.

Pellemans, H.

J. Saxler, J. Gómez Rivas, C. Janke, H. Pellemans, P. Bolívar, and H. Kurz, “Time-domain measurements of surface plasmon polaritons in the terahertz frequency range,” Phys. Rev. B 69, 155,427-1-4 (2004). URL http://link.aps.org/abstract/PRB/v69/e155427.
[CrossRef]

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). URL http://link.aps.org/abstract/PRL/v86/p1114.
[CrossRef] [PubMed]

Pendry, J. B.

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7, S97–S101 (2005). URL http://www.iop.org/EJ/abstract/1464-4258/7/2/013/.
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305, 847–848 (2004). URL http://www.sciencemag.org/cgi/content/abstract/305/5685/847.
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). URL http://link.aps.org/abstract/PRL/v86/p1114.
[CrossRef] [PubMed]

Perez, M. V.

C. Gómez-Reino, M. V. Perez, and C. Bao, Gradient-index Optics: Fundamentals and Applications (Springer, 2002).

Pinchuk, A. O.

Qiu, M.

Radko, I.

F. Lopez-Tejeira, S. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, E. Devaux, T. Ebbesen, J. Krenn, I. Radko, S. Bozhevol-nyi, and M. Gonzalez, et al., “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007). URL http://www.nature.com/nphys/journal/v3/n5/abs/nphys584.html.
[CrossRef]

Rodrigo, S.

F. Lopez-Tejeira, S. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, E. Devaux, T. Ebbesen, J. Krenn, I. Radko, S. Bozhevol-nyi, and M. Gonzalez, et al., “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007). URL http://www.nature.com/nphys/journal/v3/n5/abs/nphys584.html.
[CrossRef]

Rodriguez, A.

Roundy, D.

Roux, F. S.

F. S. Roux and I. De Leon, “Planar photonic crystal gradient index lens, simulated with a finite difference time domain method,” Phys. Rev. B 74, 113,103-1-4 (2006). URL http://link.aps.org/abstract/PRB/v74/e113103.
[CrossRef]

Ruan, Z.

Z. Ruan and M. Qiu, “Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface,” Appl. Phys. Lett. 90, 201,906-1-3 (2007). URL http://link.aip.org/link/?APPLAB/90/201906/1.
[CrossRef]

Z. Ruan and M. Qiu, “Negative refraction and sub-wavelength imaging through surface waves on structured perfect conductor surfaces,” Opt. Express 14, 6172–6177 (2006). URL http://www.opticsexpress.org/abstract.cfm?uri=oe-14-13-6172.
[CrossRef] [PubMed]

Sáenz, J. J.

F. J. G. de Abajo and J. J. Sáenz, “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces,” Phys. Rev. Lett. 95, 233,901-1-4 (2005). URL http://link.aps.org/abstract/PRL/v95/e233901.

Sambles, J.

A. Hibbins, B. Evans, and J. Sambles, “Experimental Verification of Designer Surface Plasmons,” Science 308, 670–672 (2005). URL http://www.sciencemag.org/cgi/content/abstract/308/5722/670.
[CrossRef] [PubMed]

Sambles, J. R.

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide Arrays as Plasmonic Metamaterials: Transmission below Cutoff,” Phys. Rev. Lett. 96, 073,904-1-5 (2006). URL http://link.aps.org/abstract/PRL/v96/e073904.
[CrossRef]

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Grating-coupled surface plasmons at microwave frequencies,” J. Appl. Phys. 86, 1791–1795 (1999). URL http://link.aip.org/link/?JAPIAU/86/1791/1.
[CrossRef]

Saxler, J.

J. Saxler, J. Gómez Rivas, C. Janke, H. Pellemans, P. Bolívar, and H. Kurz, “Time-domain measurements of surface plasmon polaritons in the terahertz frequency range,” Phys. Rev. B 69, 155,427-1-4 (2004). URL http://link.aps.org/abstract/PRB/v69/e155427.
[CrossRef]

Schatz, G. C.

Schotsch, C.

J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through sub-wavelength holes,” Phys. Rev. B 68, 201,306-1-4 (2003). URL http://link.aps.org/abstract/PRB/v68/e201306.
[CrossRef]

Schultz, S.

D. Wu, N. Fang, C. Sun, X. Zhang, W. Padilla, D. Basov, D. Smith, and S. Schultz, “Terahertz plasmonic high pass filter,” Appl. Phys. Lett. 83, 201–203 (2003). URL http://link.aip.org/link/?APPLAB/83/201/1.
[CrossRef]

Shen, L.

L. Shen, X. Chen, Y. Zhong, and K. Agarwal, “Effect of absorption on terahertz surface plasmon polaritons propagating along periodically corrugated metal wires,” Phys. Rev. B 77, 075,408-1-7 (2008). URL http://link.aps.org/abstract/PRB/v77/e075408.
[CrossRef]

Shi, J.

J. Shi, S.-C. Lin, and T. J. Huang, “Wide-band acoustic collimating by phononic crystal composites,” Appl. Phy. Lett. 92, 111,901-1-3 (2008). URL http://link.aip.org/link/?APPLAB/92/111901/1.
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Smith, D.

D. Wu, N. Fang, C. Sun, X. Zhang, W. Padilla, D. Basov, D. Smith, and S. Schultz, “Terahertz plasmonic high pass filter,” Appl. Phys. Lett. 83, 201–203 (2003). URL http://link.aip.org/link/?APPLAB/83/201/1.
[CrossRef]

Song, G.

Q. Gan, B. Guo, G. Song, L. Chen, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Plasmonic surface-wave splitter,” Appl. Phys. Lett. 90, 161,130-1-3 (2007). URL http://link.aip.org/link/?APL/90/161130/1.
[CrossRef]

Song, Z.

Y. Chen, Z. Song, Y. Li, M. Hu, Q. Xing, Z. Zhang, L. Chai, and C.-Y. Wang, “Effective surface plasmon polaritons on the metal wire with arrays of subwavelength grooves,” Opt. Express 14, 13,021-13,029 (2006). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-13021.

Stellman, P.

P. Stellman, K. Tian, and G. Barbastathis, “Design of Gradient Index (GRIN) Lens using Photonic Non-Crystals,” in Conference on Lasers and Electro-Optics, p. 1 (2007). URL http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=4453288.

Sun, C.

D. Wu, N. Fang, C. Sun, X. Zhang, W. Padilla, D. Basov, D. Smith, and S. Schultz, “Terahertz plasmonic high pass filter,” Appl. Phys. Lett. 83, 201–203 (2003). URL http://link.aip.org/link/?APPLAB/83/201/1.
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Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, 2000).

Taylor, H. S.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107, 6756–6769 (1997). URL http://link.aip.org/link/?JCPSA6/107/6756/1.
[CrossRef]

Thio, T.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). URL http://link.aps.org/abstract/PRL/v86/p1114.
[CrossRef] [PubMed]

T. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). URL http://www.nature.com/nature/journal/v391/n6668/abs/391667a0.html.
[CrossRef]

Tian, K.

P. Stellman, K. Tian, and G. Barbastathis, “Design of Gradient Index (GRIN) Lens using Photonic Non-Crystals,” in Conference on Lasers and Electro-Optics, p. 1 (2007). URL http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=4453288.

Wang, C.-Y.

Y. Chen, Z. Song, Y. Li, M. Hu, Q. Xing, Z. Zhang, L. Chai, and C.-Y. Wang, “Effective surface plasmon polaritons on the metal wire with arrays of subwavelength grooves,” Opt. Express 14, 13,021-13,029 (2006). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-13021.

Williams, C. R.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernndez-Domnguez, L. Martn-Moreno, and F. J. Garca-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2, 175–179 (2008). URL http://www.nature.com/nphoton/journal/v2/n3/abs/nphoton.2007.301.html.
[CrossRef]

Wolff, P.

T. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). URL http://www.nature.com/nature/journal/v391/n6668/abs/391667a0.html.
[CrossRef]

Wu, D.

D. Wu, N. Fang, C. Sun, X. Zhang, W. Padilla, D. Basov, D. Smith, and S. Schultz, “Terahertz plasmonic high pass filter,” Appl. Phys. Lett. 83, 201–203 (2003). URL http://link.aip.org/link/?APPLAB/83/201/1.
[CrossRef]

Xing, Q.

Y. Chen, Z. Song, Y. Li, M. Hu, Q. Xing, Z. Zhang, L. Chai, and C.-Y. Wang, “Effective surface plasmon polaritons on the metal wire with arrays of subwavelength grooves,” Opt. Express 14, 13,021-13,029 (2006). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-13021.

Yatsui, T.

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86, 181,108-1-3 (2005). URL http://link.aip.org/link/?APL/86/181108/1.
[CrossRef]

Zhang, X.

D. Wu, N. Fang, C. Sun, X. Zhang, W. Padilla, D. Basov, D. Smith, and S. Schultz, “Terahertz plasmonic high pass filter,” Appl. Phys. Lett. 83, 201–203 (2003). URL http://link.aip.org/link/?APPLAB/83/201/1.
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Zhang, Z.

Y. Chen, Z. Song, Y. Li, M. Hu, Q. Xing, Z. Zhang, L. Chai, and C.-Y. Wang, “Effective surface plasmon polaritons on the metal wire with arrays of subwavelength grooves,” Opt. Express 14, 13,021-13,029 (2006). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-13021.

Zheng, Y. B

B. K Juluri, Y. B Zheng, D. Ahmed, L. Jensen, and T. J. Huang, “Effects of geometry and composition on charge-induced plasmonic shifts in gold nanoparticles,” J. Phys. Chem. C 112, 7309–7312 (2008). URL http://dx.doi.org/10.1021/jp077346h.
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Zhong, Y.

L. Shen, X. Chen, Y. Zhong, and K. Agarwal, “Effect of absorption on terahertz surface plasmon polaritons propagating along periodically corrugated metal wires,” Phys. Rev. B 77, 075,408-1-7 (2008). URL http://link.aps.org/abstract/PRB/v77/e075408.
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Zhu, W.

Appl. Opt. (1)

Appl. Phy. Lett. (1)

J. Shi, S.-C. Lin, and T. J. Huang, “Wide-band acoustic collimating by phononic crystal composites,” Appl. Phy. Lett. 92, 111,901-1-3 (2008). URL http://link.aip.org/link/?APPLAB/92/111901/1.
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Appl. Phys. Lett. (5)

S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251,120-1-4 (2006). URL http://link.aip.org/link/?APL/88/251120/1.
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Z. Ruan and M. Qiu, “Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface,” Appl. Phys. Lett. 90, 201,906-1-3 (2007). URL http://link.aip.org/link/?APPLAB/90/201906/1.
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D. Wu, N. Fang, C. Sun, X. Zhang, W. Padilla, D. Basov, D. Smith, and S. Schultz, “Terahertz plasmonic high pass filter,” Appl. Phys. Lett. 83, 201–203 (2003). URL http://link.aip.org/link/?APPLAB/83/201/1.
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W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86, 181,108-1-3 (2005). URL http://link.aip.org/link/?APL/86/181108/1.
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Q. Gan, B. Guo, G. Song, L. Chen, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Plasmonic surface-wave splitter,” Appl. Phys. Lett. 90, 161,130-1-3 (2007). URL http://link.aip.org/link/?APL/90/161130/1.
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J. Appl. Phys. (1)

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Grating-coupled surface plasmons at microwave frequencies,” J. Appl. Phys. 86, 1791–1795 (1999). URL http://link.aip.org/link/?JAPIAU/86/1791/1.
[CrossRef]

J. Chem. Phys. (1)

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107, 6756–6769 (1997). URL http://link.aip.org/link/?JCPSA6/107/6756/1.
[CrossRef]

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

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7, S97–S101 (2005). URL http://www.iop.org/EJ/abstract/1464-4258/7/2/013/.
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J. Opt. Soc. Am. A (1)

J. Phys. Chem. C (1)

B. K Juluri, Y. B Zheng, D. Ahmed, L. Jensen, and T. J. Huang, “Effects of geometry and composition on charge-induced plasmonic shifts in gold nanoparticles,” J. Phys. Chem. C 112, 7309–7312 (2008). URL http://dx.doi.org/10.1021/jp077346h.
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Nat. Photonics (3)

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernndez-Domnguez, L. Martn-Moreno, and F. J. Garca-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2, 175–179 (2008). URL http://www.nature.com/nphoton/journal/v2/n3/abs/nphoton.2007.301.html.
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M. Johnston, “Plasmonics: Superfocusing of terahertz waves,” Nat. Photonics 1, 14–15 (2007). URL http://www.nature.com/nphoton/journal/v1/n1/full/nphoton.2006.60.html.
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J. Gómez Rivas, “Terahertz: The art of confinement,” Nat. Photonics 2, 137–138 (2008). URL http://www.nature.com/nphoton/journal/v2/n3/abs/nphoton.2008.12.html.
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Nat. Phys. (1)

F. Lopez-Tejeira, S. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, E. Devaux, T. Ebbesen, J. Krenn, I. Radko, S. Bozhevol-nyi, and M. Gonzalez, et al., “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007). URL http://www.nature.com/nphys/journal/v3/n5/abs/nphys584.html.
[CrossRef]

Nature (1)

T. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). URL http://www.nature.com/nature/journal/v391/n6668/abs/391667a0.html.
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Opt. Express (8)

W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16, 6216–6226 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-9-6216.
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H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12, 1004–1010 (2004). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-6-1004.
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M. Qiu, “Photonic band structures for surface waves on structured metal surfaces,” Opt. Express 13, 7583–7588 (2005). URL http://www.opticsexpress.org/abstract.cfm?uri=oe-13-19-7583.
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Y. Chen, Z. Song, Y. Li, M. Hu, Q. Xing, Z. Zhang, L. Chai, and C.-Y. Wang, “Effective surface plasmon polaritons on the metal wire with arrays of subwavelength grooves,” Opt. Express 14, 13,021-13,029 (2006). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-13021.

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15, 1240–1253 (2007). URL http://www.opticsexpress.org/abstract.cfm?uri=oe-15-3-1240.
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Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Bidirectional subwavelength slit splitter for THz surface plasmons,” Opt. Express 15, 18,050–18,055 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-26-18050.
[CrossRef]

Z. Ruan and M. Qiu, “Negative refraction and sub-wavelength imaging through surface waves on structured perfect conductor surfaces,” Opt. Express 14, 6172–6177 (2006). URL http://www.opticsexpress.org/abstract.cfm?uri=oe-14-13-6172.
[CrossRef] [PubMed]

S. S. Oh, S.-G. Lee, J.-E. Kim, and H. Y. Park, “Self-collimation phenomena of surface waves in structured perfect electric conductors and metal surfaces,” Opt. Express 15, 1205–1210 (2007). URL http://www.opticsinfobase.org/abstract.cfm?uri=oe-15-3-1205.
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Opt. Lett. (1)

Phys. Rev. B (6)

J. Saxler, J. Gómez Rivas, C. Janke, H. Pellemans, P. Bolívar, and H. Kurz, “Time-domain measurements of surface plasmon polaritons in the terahertz frequency range,” Phys. Rev. B 69, 155,427-1-4 (2004). URL http://link.aps.org/abstract/PRB/v69/e155427.
[CrossRef]

F. S. Roux and I. De Leon, “Planar photonic crystal gradient index lens, simulated with a finite difference time domain method,” Phys. Rev. B 74, 113,103-1-4 (2006). URL http://link.aps.org/abstract/PRB/v74/e113103.
[CrossRef]

L. Shen, X. Chen, Y. Zhong, and K. Agarwal, “Effect of absorption on terahertz surface plasmon polaritons propagating along periodically corrugated metal wires,” Phys. Rev. B 77, 075,408-1-7 (2008). URL http://link.aps.org/abstract/PRB/v77/e075408.
[CrossRef]

F. Miyamaru and M. Hangyo, “Strong enhancement of terahertz transmission for a three-layer heterostructure of metal hole arrays,” Phys. Rev. B 72, 035,429-1-5 (2005). URL http://link.aps.org/abstract/PRB/v72/e035429.
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J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through sub-wavelength holes,” Phys. Rev. B 68, 201,306-1-4 (2003). URL http://link.aps.org/abstract/PRB/v68/e201306.
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P. Berini, “Plasmon polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000). URL http://link.aps.org/doi/10.1103/PhysRevB.61.10484.
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Phys. Rev. Lett. (5)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). URL http://link.aps.org/abstract/PRL/v86/p1114.
[CrossRef] [PubMed]

F. J. G. de Abajo and J. J. Sáenz, “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces,” Phys. Rev. Lett. 95, 233,901-1-4 (2005). URL http://link.aps.org/abstract/PRL/v95/e233901.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz Surface Plasmon-Polariton Propagation and Focusing on Periodically Corrugated Metal Wires,” Phys. Rev. Lett. 97, 176,805-1-4 (2006). URL http://link.aps.org/abstract/PRL/v97/e176805.
[CrossRef]

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide Arrays as Plasmonic Metamaterials: Transmission below Cutoff,” Phys. Rev. Lett. 96, 073,904-1-5 (2006). URL http://link.aps.org/abstract/PRL/v96/e073904.
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Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-Bandwidth Slow-Light System Based on THz Plasmonic Graded Metallic Grating Structures,” Phys. Rev. Lett. 100, 256,803-1-3 (2008). URL http://link.aps.org/abstract/PRL/v100/e256803.
[CrossRef]

Science (2)

A. Hibbins, B. Evans, and J. Sambles, “Experimental Verification of Designer Surface Plasmons,” Science 308, 670–672 (2005). URL http://www.sciencemag.org/cgi/content/abstract/308/5722/670.
[CrossRef] [PubMed]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305, 847–848 (2004). URL http://www.sciencemag.org/cgi/content/abstract/305/5685/847.
[CrossRef] [PubMed]

Other (3)

C. Gómez-Reino, M. V. Perez, and C. Bao, Gradient-index Optics: Fundamentals and Applications (Springer, 2002).

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, 2000).

P. Stellman, K. Tian, and G. Barbastathis, “Design of Gradient Index (GRIN) Lens using Photonic Non-Crystals,” in Conference on Lasers and Electro-Optics, p. 1 (2007). URL http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=4453288.

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Figures (7)

Fig. 1.
Fig. 1.

(a) Principle of a gradient index based lens. A parabolic gradient (green line) of the group index (N) along the transverse direction of the propagation (Y-axis) enables the focusing or collimation of incoming beam (red arrows). A PEC structure with periodic array of square holes with varying (b) size of square holes and (c) dielectric constant, along the transverse direction of propagation (Y-axis) enables the focusing or collimation of DSPs (red arrows).

Fig. 2.
Fig. 2.

Dispersion relations calculated using Eq. 1 for a PEC structure filled with (a) different εh and fixed a= 0.85d, h=1d (b) different a and fixed εh =2, h=1d and (c) different h with fixed a= 0.85d, εh =2.

Fig. 3.
Fig. 3.

(a) Dispersion relations calculated using FDTD for a PEC structure filled with different εh . Inset shows the unit cell. (b) Variation of Ng with εh at an operating frequency of 0.3742 normalized units obtained from FDTD (dotted line) and a best fit to the data (solid line).

Fig. 4.
Fig. 4.

FDTD model of graded PEC structure (a) X-Y view, (b) X-Z view, (c) Y-Z view, and (d) parabolic change of the Ng (line) and distribution of εh (dots) along the transverse direction of propagation (Y-axis) of DSPs. Perfect matching layers (PML) are employed at the boundaries of the simulation domain.

Fig. 5.
Fig. 5.

Propagation of DSPs excited by Gaussian beams with w = 5d, snapshot of Ez field in a) 0.1d above X-Y plane b) X-Z plane, c) Y-Z plane at X=-40d (source), d) Y-Z plane at X=0d (midway) and e) comparison of the magnitude of Ez at X=0d (solid line) and X=-40d (dotted line).

Fig. 6.
Fig. 6.

Propagation of DSPs excited by Gaussian beams with w = 2d, snapshot of Ez field in a) 0.1d above X-Y plane b) X-Z plane, c) Y-Z plane at X=-40d (source), d) Y-Z plane at X=0d (midway) and e) comparison of the magnitude of Ez at X=0d (solid line) and X=-40d (dotted line).

Fig. 7.
Fig. 7.

Propagation of DSPs excited by Gaussian beams with w = 3.5d, snapshot of Ez field in a) 0.1d above X-Y plane b) X-Z plane, c) Y-Z plane at X=-40d (source), d) Y-Z plane at X=0d (midway) and e) comparison of the magnitude of Ez at X=0d (solid line) and X=-40d (dotted line).

Equations (4)

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k x 2 k o 2 k o = S 2 k o π 2 / a 2 ε h k o 2 ( 1 e 2 q z h 1 + e 2 q z h ) ,
N g = c / d k x = ω c k x [ 1 + 2 A ω 2 ( ω pl 2 ω 2 ) + A ω 4 ( ω pl 2 ω 2 ) 2 4 A ε h h ω 4 c ( ω pl 2 ω 2 ) 3 / 2 ( e 2 h q z 1 e 4 h q z ) ] ,
A = 64 a 4 π 4 d 4 ε h ( 1 e 2 q z h 1 + e 2 q z h ) 2 .
N g 2 ( Y ) = N o 2 [ 1 ( αY ) 2 ]

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