Abstract

For the first time, we demonstrate the application of the time domain transmission line method (TLM) to accurate modeling of surface plasmon polariton (SPP) structures. The constructed TLM node allows for modeling of dispersive materials through simple time-difference equations. Using such node, an ultra-wide band excitation can be applied to obtain the response over the band of interest. Bérenger’s perfectly matched layer (PML) boundary condition can readily be implemented using the same node. We illustrate our TLM approach through the modeling of different challenging structures including SPPs filters and focusing structures.

© 2010 OSA

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2010 (2)

2009 (2)

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95(7), 071112 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

2008 (4)

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92(1), 013103 (2008).
[CrossRef]

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Topics in Quantum Mechanics 14(6), 1462–1472 (2008).
[CrossRef]

J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16(1), 413–425 (2008).
[CrossRef] [PubMed]

A. Hosseini, H. Nejati, and Y. Massoud, “Modeling and design methodology for metal-insulator-metal plasmonic Bragg reflectors,” Opt. Express 16(3), 1475–1480 (2008).
[CrossRef] [PubMed]

2007 (4)

B. Guo, Q. Gan, G. Song, J. Gao, and L. Chen, “Numerical study of a high-resolution far-field scanning optical microscope via a surface plasmon modulated light source,” J. Lightwave Technol. 25(3), 830–833 (2007).
[CrossRef]

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19(2), 91–93 (2007).
[CrossRef]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

H. Shi, C. Du, and X. Luo, “Focal length modulation based on a metallic slit surrounded with grooves in curved depths,” Appl. Phys. Lett. 91(9), 093111 (2007).
[CrossRef]

2006 (2)

2005 (4)

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

D. Pasalic and R. Vahldieck, “A Hybrid Drift-Diffusion-TLM Analysis of Traveling-Wave Photodetectors,” IEEE Trans. Microw. Theory Tech. 53(9), 2700–2706 (2005).
[CrossRef]

B. Wang and G. P. Wang, “Plasmon bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(1), 013107 (2005).
[CrossRef]

2004 (1)

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

2003 (2)

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

F. J. Garcı́a-Vidal, L. Martı́n-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

2001 (1)

O. Jacquin, F. Ndagijimana, A. Cachard, and P. Benech, “Application of the TLM technique to integrated optic component modelling,” Int. J. of Numer. Model: Electronic Networks Devices and Fields 14, 95–105 (2001).
[CrossRef]

1999 (2)

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material models in TLM—Part I: Materials with frequency-dependent properties,” IEEE Trans. Antenn. Propag. 47(10), 1528–1534 (1999).
[CrossRef]

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

1998 (1)

S. Le Maguer, N. Peňa, and M. Ney, “Matched absorbing medium techniques for full-wave TLM simulation of microwave and millimeter-wave components,” Ann. Telecommun. 53, 115–129 (1998).

1997 (1)

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Perfectly matched layer for transmission line modelling (TLM) method,” Electron. Lett. 33(9), 729–730 (1997).
[CrossRef]

1996 (2)

L. de Menezes and W. J. R. Hoefer, “Modeling of general constitutive relationships in SCN TLM,” IEEE Trans. Microw. Theory Tech. 44(6), 854–861 (1996).
[CrossRef]

K. Fung and S. Hui, “Improved TLM link model for reactive circuit components,” IEE Proc. Sci. Meas. Technol. 143(5), 341–344 (1996).
[CrossRef]

1995 (2)

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995).
[CrossRef]

C. Eswarappa and W. Hoefer, “Implementation of Berenger absorbing boundary conditions in TLM by interfacing FDTD perfectly matched layers,” Electron. Lett. 31(15), 1264 (1995).
[CrossRef]

1994 (1)

J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

1993 (1)

C. Christopoulos and J. Herring, “The application of transmission-line modeling (TLM) to electromagnetic compatibility problems,” IEEE Trans. Electromagnetic Compatibility 35(Part 2), 185–191 (1993).
[CrossRef]

1987 (1)

P. B. Johns, “A symmetrical condensed node for the TLM method,” IEEE Trans. Microw. Theory Tech. 35(4), 370–377 (1987).
[CrossRef]

1986 (1)

J. R. Brews, “Transmission line models for lossy waveguide interconnect in VLSI,” IEEE Trans. Electron. Dev. 33(9), 1356–1365 (1986).
[CrossRef]

1980 (1)

P. B. Johns and M. O’Brien, “Use of transmission-line modelling method to solve non-linear lumped networks,” Radio Electron. Eng. 50, 59–70 (1980).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1971 (1)

P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Electr. Eng. 118(9), 1203–1208 (1971).
[CrossRef]

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Barnes, W. L.

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

Benech, P.

O. Jacquin, F. Ndagijimana, A. Cachard, and P. Benech, “Application of the TLM technique to integrated optic component modelling,” Int. J. of Numer. Model: Electronic Networks Devices and Fields 14, 95–105 (2001).
[CrossRef]

Bérenger, J. P.

J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

Beurle, R. L.

P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Electr. Eng. 118(9), 1203–1208 (1971).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Brews, J. R.

J. R. Brews, “Transmission line models for lossy waveguide interconnect in VLSI,” IEEE Trans. Electron. Dev. 33(9), 1356–1365 (1986).
[CrossRef]

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Cachard, A.

O. Jacquin, F. Ndagijimana, A. Cachard, and P. Benech, “Application of the TLM technique to integrated optic component modelling,” Int. J. of Numer. Model: Electronic Networks Devices and Fields 14, 95–105 (2001).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95(7), 071112 (2009).
[CrossRef]

Chang, C. K.

Chen, L.

Chen, Y. C.

Choi, D.

Christopoulos, C.

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material models in TLM—Part I: Materials with frequency-dependent properties,” IEEE Trans. Antenn. Propag. 47(10), 1528–1534 (1999).
[CrossRef]

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Perfectly matched layer for transmission line modelling (TLM) method,” Electron. Lett. 33(9), 729–730 (1997).
[CrossRef]

C. Christopoulos and J. Herring, “The application of transmission-line modeling (TLM) to electromagnetic compatibility problems,” IEEE Trans. Electromagnetic Compatibility 35(Part 2), 185–191 (1993).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

de Menezes, L.

L. de Menezes and W. J. R. Hoefer, “Modeling of general constitutive relationships in SCN TLM,” IEEE Trans. Microw. Theory Tech. 44(6), 854–861 (1996).
[CrossRef]

Dereux, A.

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

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Dong, X.

Du, C.

H. Shi, C. Du, and X. Luo, “Focal length modulation based on a metallic slit surrounded with grooves in curved depths,” Appl. Phys. Lett. 91(9), 093111 (2007).
[CrossRef]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
[CrossRef] [PubMed]

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

F. J. Garcı́a-Vidal, L. Martı́n-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

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

Eswarappa, C.

C. Eswarappa and W. Hoefer, “Implementation of Berenger absorbing boundary conditions in TLM by interfacing FDTD perfectly matched layers,” Electron. Lett. 31(15), 1264 (1995).
[CrossRef]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95(7), 071112 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Topics in Quantum Mechanics 14(6), 1462–1472 (2008).
[CrossRef]

Forsberg, E.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19(2), 91–93 (2007).
[CrossRef]

Fung, K.

K. Fung and S. Hui, “Improved TLM link model for reactive circuit components,” IEE Proc. Sci. Meas. Technol. 143(5), 341–344 (1996).
[CrossRef]

Gan, Q.

Gao, H.

Gao, J.

Garci´a-Vidal, F. J.

F. J. Garcı́a-Vidal, L. Martı́n-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

Guo, B.

Han, Z.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19(2), 91–93 (2007).
[CrossRef]

Harris, R. D.

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995).
[CrossRef]

He, S.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19(2), 91–93 (2007).
[CrossRef]

Herring, J.

C. Christopoulos and J. Herring, “The application of transmission-line modeling (TLM) to electromagnetic compatibility problems,” IEEE Trans. Electromagnetic Compatibility 35(Part 2), 185–191 (1993).
[CrossRef]

Hoefer, W.

C. Eswarappa and W. Hoefer, “Implementation of Berenger absorbing boundary conditions in TLM by interfacing FDTD perfectly matched layers,” Electron. Lett. 31(15), 1264 (1995).
[CrossRef]

Hoefer, W. J. R.

L. de Menezes and W. J. R. Hoefer, “Modeling of general constitutive relationships in SCN TLM,” IEEE Trans. Microw. Theory Tech. 44(6), 854–861 (1996).
[CrossRef]

Homola, J.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

Hosseini, A.

Hui, S.

K. Fung and S. Hui, “Improved TLM link model for reactive circuit components,” IEE Proc. Sci. Meas. Technol. 143(5), 341–344 (1996).
[CrossRef]

Jacquin, O.

O. Jacquin, F. Ndagijimana, A. Cachard, and P. Benech, “Application of the TLM technique to integrated optic component modelling,” Int. J. of Numer. Model: Electronic Networks Devices and Fields 14, 95–105 (2001).
[CrossRef]

Johns, P. B.

P. B. Johns, “A symmetrical condensed node for the TLM method,” IEEE Trans. Microw. Theory Tech. 35(4), 370–377 (1987).
[CrossRef]

P. B. Johns and M. O’Brien, “Use of transmission-line modelling method to solve non-linear lumped networks,” Radio Electron. Eng. 50, 59–70 (1980).
[CrossRef]

P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Electr. Eng. 118(9), 1203–1208 (1971).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Jung, J.

Kim, H.

B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010).
[CrossRef]

J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16(1), 413–425 (2008).
[CrossRef] [PubMed]

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92(1), 013103 (2008).
[CrossRef]

Kim, H. K.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

Kim, S.

B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010).
[CrossRef]

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92(1), 013103 (2008).
[CrossRef]

Kocabas, S. E.

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Topics in Quantum Mechanics 14(6), 1462–1472 (2008).
[CrossRef]

Kuan, C. H.

Le Maguer, S.

S. Le Maguer, N. Peňa, and M. Ney, “Matched absorbing medium techniques for full-wave TLM simulation of microwave and millimeter-wave components,” Ann. Telecommun. 53, 115–129 (1998).

Lee, B.

D. Choi, Y. Lim, S. Roh, I. M. Lee, J. Jung, and B. Lee, “Optical beam focusing with a metal slit array arranged along a semicircular surface and its optimization with a genetic algorithm,” Appl. Opt. 49(7), A30–A35 (2010).
[CrossRef] [PubMed]

B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010).
[CrossRef]

J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16(1), 413–425 (2008).
[CrossRef] [PubMed]

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92(1), 013103 (2008).
[CrossRef]

Lee, C. K.

Lee, I. M.

Lezec, H. J.

F. J. Garcı́a-Vidal, L. Martı́n-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

Lim, Y.

B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010).
[CrossRef]

D. Choi, Y. Lim, S. Roh, I. M. Lee, J. Jung, and B. Lee, “Optical beam focusing with a metal slit array arranged along a semicircular surface and its optimization with a genetic algorithm,” Appl. Opt. 49(7), A30–A35 (2010).
[CrossRef] [PubMed]

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92(1), 013103 (2008).
[CrossRef]

Lin, D. Z.

Lin, M. W.

Liu, J. M.

Luo, X.

H. Shi, C. Du, and X. Luo, “Focal length modulation based on a metallic slit surrounded with grooves in curved depths,” Appl. Phys. Lett. 91(9), 093111 (2007).
[CrossRef]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
[CrossRef] [PubMed]

Marti´n-Moreno, L.

F. J. Garcı́a-Vidal, L. Martı́n-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

Massoud, Y.

Miller, D. A. B.

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Topics in Quantum Mechanics 14(6), 1462–1472 (2008).
[CrossRef]

Ndagijimana, F.

O. Jacquin, F. Ndagijimana, A. Cachard, and P. Benech, “Application of the TLM technique to integrated optic component modelling,” Int. J. of Numer. Model: Electronic Networks Devices and Fields 14, 95–105 (2001).
[CrossRef]

Nejati, H.

Ney, M.

S. Le Maguer, N. Peňa, and M. Ney, “Matched absorbing medium techniques for full-wave TLM simulation of microwave and millimeter-wave components,” Ann. Telecommun. 53, 115–129 (1998).

O’Brien, M.

P. B. Johns and M. O’Brien, “Use of transmission-line modelling method to solve non-linear lumped networks,” Radio Electron. Eng. 50, 59–70 (1980).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Park, J.

J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16(1), 413–425 (2008).
[CrossRef] [PubMed]

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92(1), 013103 (2008).
[CrossRef]

Pasalic, D.

D. Pasalic and R. Vahldieck, “A Hybrid Drift-Diffusion-TLM Analysis of Traveling-Wave Photodetectors,” IEEE Trans. Microw. Theory Tech. 53(9), 2700–2706 (2005).
[CrossRef]

Paul, J.

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material models in TLM—Part I: Materials with frequency-dependent properties,” IEEE Trans. Antenn. Propag. 47(10), 1528–1534 (1999).
[CrossRef]

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Perfectly matched layer for transmission line modelling (TLM) method,” Electron. Lett. 33(9), 729–730 (1997).
[CrossRef]

Pena, N.

S. Le Maguer, N. Peňa, and M. Ney, “Matched absorbing medium techniques for full-wave TLM simulation of microwave and millimeter-wave components,” Ann. Telecommun. 53, 115–129 (1998).

Roh, S.

Shi, H.

H. Shi, C. Du, and X. Luo, “Focal length modulation based on a metallic slit surrounded with grooves in curved depths,” Appl. Phys. Lett. 91(9), 093111 (2007).
[CrossRef]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
[CrossRef] [PubMed]

Song, G.

Sun, Z.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

Thomas, D. W. P.

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material models in TLM—Part I: Materials with frequency-dependent properties,” IEEE Trans. Antenn. Propag. 47(10), 1528–1534 (1999).
[CrossRef]

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Perfectly matched layer for transmission line modelling (TLM) method,” Electron. Lett. 33(9), 729–730 (1997).
[CrossRef]

Vahldieck, R.

D. Pasalic and R. Vahldieck, “A Hybrid Drift-Diffusion-TLM Analysis of Traveling-Wave Photodetectors,” IEEE Trans. Microw. Theory Tech. 53(9), 2700–2706 (2005).
[CrossRef]

Veronis, G.

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Topics in Quantum Mechanics 14(6), 1462–1472 (2008).
[CrossRef]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95(7), 071112 (2009).
[CrossRef]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Wang, B.

B. Wang and G. P. Wang, “Plasmon bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(1), 013107 (2005).
[CrossRef]

Wang, C.

Wang, G. P.

B. Wang and G. P. Wang, “Plasmon bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(1), 013107 (2005).
[CrossRef]

White, J. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Wilkinson, J. S.

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995).
[CrossRef]

Yang, D. L.

Yee, S. S.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

Yeh, C. S.

Yeh, J. T.

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95(7), 071112 (2009).
[CrossRef]

Ann. Telecommun. (1)

S. Le Maguer, N. Peňa, and M. Ney, “Matched absorbing medium techniques for full-wave TLM simulation of microwave and millimeter-wave components,” Ann. Telecommun. 53, 115–129 (1998).

Appl. Opt. (1)

Appl. Phys. Lett. (6)

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95(7), 071112 (2009).
[CrossRef]

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92(1), 013103 (2008).
[CrossRef]

B. Wang and G. P. Wang, “Plasmon bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(1), 013107 (2005).
[CrossRef]

F. J. Garcı́a-Vidal, L. Martı́n-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

H. Shi, C. Du, and X. Luo, “Focal length modulation based on a metallic slit surrounded with grooves in curved depths,” Appl. Phys. Lett. 91(9), 093111 (2007).
[CrossRef]

Electron. Lett. (2)

C. Eswarappa and W. Hoefer, “Implementation of Berenger absorbing boundary conditions in TLM by interfacing FDTD perfectly matched layers,” Electron. Lett. 31(15), 1264 (1995).
[CrossRef]

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Perfectly matched layer for transmission line modelling (TLM) method,” Electron. Lett. 33(9), 729–730 (1997).
[CrossRef]

IEE Proc. Sci. Meas. Technol. (1)

K. Fung and S. Hui, “Improved TLM link model for reactive circuit components,” IEE Proc. Sci. Meas. Technol. 143(5), 341–344 (1996).
[CrossRef]

IEEE J. Sel. Topics in Quantum Mechanics (1)

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Topics in Quantum Mechanics 14(6), 1462–1472 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19(2), 91–93 (2007).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material models in TLM—Part I: Materials with frequency-dependent properties,” IEEE Trans. Antenn. Propag. 47(10), 1528–1534 (1999).
[CrossRef]

IEEE Trans. Electromagnetic Compatibility (1)

C. Christopoulos and J. Herring, “The application of transmission-line modeling (TLM) to electromagnetic compatibility problems,” IEEE Trans. Electromagnetic Compatibility 35(Part 2), 185–191 (1993).
[CrossRef]

IEEE Trans. Electron. Dev. (1)

J. R. Brews, “Transmission line models for lossy waveguide interconnect in VLSI,” IEEE Trans. Electron. Dev. 33(9), 1356–1365 (1986).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (3)

D. Pasalic and R. Vahldieck, “A Hybrid Drift-Diffusion-TLM Analysis of Traveling-Wave Photodetectors,” IEEE Trans. Microw. Theory Tech. 53(9), 2700–2706 (2005).
[CrossRef]

P. B. Johns, “A symmetrical condensed node for the TLM method,” IEEE Trans. Microw. Theory Tech. 35(4), 370–377 (1987).
[CrossRef]

L. de Menezes and W. J. R. Hoefer, “Modeling of general constitutive relationships in SCN TLM,” IEEE Trans. Microw. Theory Tech. 44(6), 854–861 (1996).
[CrossRef]

Int. J. of Numer. Model: Electronic Networks Devices and Fields (1)

O. Jacquin, F. Ndagijimana, A. Cachard, and P. Benech, “Application of the TLM technique to integrated optic component modelling,” Int. J. of Numer. Model: Electronic Networks Devices and Fields 14, 95–105 (2001).
[CrossRef]

J. Comput. Phys. (1)

J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

J. Lightwave Technol. (1)

Nano Lett. (1)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Nature (2)

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

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

Opt. Express (4)

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Proc. Inst. Electr. Eng. (1)

P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Electr. Eng. 118(9), 1203–1208 (1971).
[CrossRef]

Prog. Quantum Electron. (1)

B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010).
[CrossRef]

Radio Electron. Eng. (1)

P. B. Johns and M. O’Brien, “Use of transmission-line modelling method to solve non-linear lumped networks,” Radio Electron. Eng. 50, 59–70 (1980).
[CrossRef]

Science (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Sens. Actuators B Chem. (2)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995).
[CrossRef]

Other (10)

A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition, 3rd ed. (Artech House Publishers, 2005).

L. Vietzorreck, F. Coccetti, V. Chtchekatourov, and P. Russer, “Modeling of MEMS capacitive switches by TLM,” in 2000 IEEE MTT-S International Microwave Symposium Digest, (2000), pp. 1221–1224.

S. Hui, K. FUNG, and C. Christopoulos, “Decoupled simulation of multistage power electronics systems using transmission-line links”. Power electronics specialist conference, (Toledo, Spain, 1992), pp. 1324–1330.

C. Christopoulos, The Transmission-Line Modeling Method: TLM, (Wiley-IEEE Press, 1995).

D. D. Cogan, Transmission line matrix (TLM) techniques for diffusion applications, (CRC Press, 1998).

L. de Menezes, and W. J. R. Hoefer, “Modeling frequency dependent dielectrics in TLM,” in IEEE Antennas Propagat.-S Symp. Dig., (1994), pp. 1140–1143.

L. de Menezes, and W. J. R. Hoefer, “Modeling nonlinear dispersive media in 2-D-TLM,” in 24th European Microwave Conference Proc., (1994), pp. 1739–1744.

S. A. Maier, Plasmonics: Fundamentals and Applications, (Springer, 2007).

C. Sönnichsen, Plasmons in metal nanostructures, Ph.D. dissertation, Ludwig-Maximilians-Universtät München, (München, 2001).

E. D. Palik, Handbook of optical constants of solids. (Academic Press, 1998).

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Figures (25)

Fig. 1
Fig. 1

The space representation in TLM by the Symmetrical Condensed Node.

Fig. 2
Fig. 2

The TLM connection process.

Fig. 3
Fig. 3

The transmitted time domain signal in a slab waveguide is compared for the two types of boundaries; PML boundary and line matching boundary.

Fig. 4
Fig. 4

The transmitted Frequency domain signal in a slab waveguide is compared for the two types of boundaries; PML boundary and line matching boundary.

Fig. 5
Fig. 5

The geometry of the SPP-WBG.

Fig. 6
Fig. 6

The transmission response of the plasmonic Bragg grating whose operation wavelength is at 1.55 μm.

Fig. 7
Fig. 7

The magnetic field distribution inside the plasmonic Bragg grating for an incident wavelength of 1000.0 nm.

Fig. 8
Fig. 8

The magnetic field distribution inside the plasmonic Bragg grating for an incident wavelength of 1550.0 nm.

Fig. 9
Fig. 9

The impulse response of the plasmonic Bragg grating for different grating thicknesses.

Fig. 10
Fig. 10

The schematic of SPP beam focusing using aperture dielectric grating.

Fig. 11
Fig. 11

The magnetic field distribution of the focused beam from subwavelength metallic slit in the presence of an aperture dielectric grating at an incidence wavelength of 532.0 nm.

Fig. 12
Fig. 12

The transverse intensity profile around the spot of the focused beam for the subwavelength metallic slit at an incidence wavelength of 532.0 nm.

Fig. 13
Fig. 13

The longitudinal intensity distribution for the subwavelength metallic slit surrounded by a chirped dielectric grating at a selected set of wavelengths.

Fig. 14
Fig. 14

The spectral distribution of the focal length for the lens structure of subwavelength metallic slit with chirped dielectric grating.

Fig. 15
Fig. 15

The schematic of the focusing structure with metallic grooves.

Fig. 16
Fig. 16

The magnetic field distribution for the subwavelength slit without the grooves.

Fig. 17
Fig. 17

The magnetic field distribution for the focusing structure with the grooves included.

Fig. 18
Fig. 18

The transverse intensity profile around the focusing spot for the subwavelength slit with metallic surface grooves.

Fig. 19
Fig. 19

The longitudinal intensity distribution for the subwavelength slit with metallic surface grooves at a selected set of wavelengths.

Fig. 20
Fig. 20

The spectral distribution of the focal length for the subwavelength slit with metallic surface grooves.

Fig. 21
Fig. 21

The schematic of the planar slit array.

Fig. 22
Fig. 22

The magnetic field distribution for the planar slit array.

Fig. 23
Fig. 23

The transverse intensity profile around the focal spot for the slit array.

Fig. 24
Fig. 24

The longitudinal intensity distribution for the planar slit array at a selected set of wavelengths.

Fig. 25
Fig. 25

The spectral distribution of the focal length of the planar slit array.

Equations (18)

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

V i = [ V 0 i V 1 i . . . V 11 i ] T
V r = [ V 0 r V 1 r . . . V 11 r ] T
F = [ V x V y V z i x i y i z ] T
F e x = [ V x e x V y e x V z e x i x e x i y e x i z e x ] T
F e x = R e x V i 1 2 V f
F = T F e x
T = [ t e x t e y 0 t e z t m x 0 t m y t m z ]
t e x = 2 ( 4 + g e x + 2 s ¯ χ e x )
t m x = 2 ( 4 + r m x + 2 s ¯ χ m x )
s ¯ 2 1 z 1 1 + z 1
V r = R F P V i
χ e = χ ω p 2 ω ( ω + i γ )
σ e ( s ) = σ 0 1 + s τ c
g e ( z ) = g e c ( 1 β 0 ) 1 z 1 β 0
( 1 + z 1 ) g e ( z ) = g e 0 + z 1 g e 1 ( z )
V x V x e x = 2 ( 1 + z 1 ) 4 + g e 0 + 4 χ + z 1 ( 4 4 χ ) + z 1 g e 1 ( z )
V x = V x y + V x z , V y = V y x + V y z , V z = V z x + V z y
i x = i x y + i x z , i y = i y x + i y z , i z = i z x + i z y

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