Abstract

We present studies on the propagation of plasmon waves in metallic multimode waveguides surrounded by a dielectric medium. The permittivity of the metal was determined by a Drude model. The propagation was simulated by the method of lines. The propagating field exhibited the well-known self-imaging phenomenon known as the Talbot effect. The metallic waveguides are lossy. The influence of various parameters on the losses was examined. By a suitable choice of parameters, propagation distances of several Talbot periods are possible. Our investigation also includes simulations for the propagation of eigenmodes of the waveguides and results for the calculation of the effective index.

© 2010 Optical Society of America

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  2. J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
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  16. S. F. Helfert, B. Huneke, and J. Jahns, “Self-imaging effect in multimode waveguides with longitudinal periodicity,” J. Eur. Opt. Soc. 4, 09031 (2009).
    [CrossRef]
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    [CrossRef]
  18. R. Pregla and S. F. Helfert, “Modeling of microwave devices with the method of lines,” in Recent Research Developments in Microwave Theory and Techniques, B. Beker and Y. Chen, eds. (Research Signpost, 2002), pp. 145-196.
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    [CrossRef]
  20. M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).
  21. O. Conradi, S. Helfert, and R. Pregla, “Modification of the finite difference scheme for efficient analysis of thin lossy metal layers in optical devices,” Opt. Quantum Electron. 30, 369-373 (1998).
    [CrossRef]
  22. J. Gerdes, “Bidirectional eigenmode propagation analysis of optical waveguides based on method of lines,” Electron. Lett. 30, 550-551 (1994).
    [CrossRef]
  23. S. F. Helfert, A. Barcz, and R. Pregla, “Three-dimensional vectorial analysis of waveguide structures with the method of lines,” Opt. Quantum Electron. 35, 381-394 (2003).
    [CrossRef]
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  26. 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).
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2009 (1)

S. F. Helfert, B. Huneke, and J. Jahns, “Self-imaging effect in multimode waveguides with longitudinal periodicity,” J. Eur. Opt. Soc. 4, 09031 (2009).
[CrossRef]

2007 (2)

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

M. R. Dennis, N. I. Zheludev, and F. J. G. de Abajo, “The plasmon Talbot effect,” Opt. Express 15, 9692-9700 (2007).
[CrossRef]

2006 (1)

Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88, 171108 (2006).
[CrossRef]

2005 (1)

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano. Lett. 5, 1726-1729 (2005).

2003 (1)

S. F. Helfert, A. Barcz, and R. Pregla, “Three-dimensional vectorial analysis of waveguide structures with the method of lines,” Opt. Quantum Electron. 35, 381-394 (2003).
[CrossRef]

2002 (1)

S. F. Helfert and R. Pregla, “The method of lines: a versatile tool for the analysis of waveguide structures,” Electromagnetics 22, 615-637 (2002),
[CrossRef]

2001 (2)

J. Jahns, E. ElJoudi, D. Hagedorn, and S. Kinne, “Talbot interferometer as a time filter,” Optik (Jena) 112, 295-298 (2001).
[CrossRef]

O. Conradi, S. Helfert, and R. Pregla, “Comprehensive modeling of vertical-cavity laser-diodes by the method of lines,” IEEE J. Quantum Electron. 37, 928-935 (2001).
[CrossRef]

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).

1999 (1)

J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
[CrossRef]

1998 (2)

1995 (2)

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B 29, 261-267(1995).

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615-627(1995).
[CrossRef]

1994 (1)

J. Gerdes, “Bidirectional eigenmode propagation analysis of optical waveguides based on method of lines,” Electron. Lett. 30, 550-551 (1994).
[CrossRef]

1986 (1)

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).

1975 (1)

R. Ulrich and G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett. 27, 337-339(1975).
[CrossRef]

1973 (1)

1971 (1)

A. W. Lohmann and D. A. Silva, “An interferometer based on the talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

1836 (1)

H. F. Talbot, “Facts relating to optical science, No. IV,” Philos. Mag. 9, 401-407 (1836).

Ankele, G.

R. Ulrich and G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett. 27, 337-339(1975).
[CrossRef]

Baida, F. I.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Barcz, A.

S. F. Helfert, A. Barcz, and R. Pregla, “Three-dimensional vectorial analysis of waveguide structures with the method of lines,” Opt. Quantum Electron. 35, 381-394 (2003).
[CrossRef]

Berini, P.

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).

Besbes, M.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Bienstman, P.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Bryngdahl, O.

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).

Conradi, O.

O. Conradi, S. Helfert, and R. Pregla, “Comprehensive modeling of vertical-cavity laser-diodes by the method of lines,” IEEE J. Quantum Electron. 37, 928-935 (2001).
[CrossRef]

H. J. W. M. Hoekstra, P. V. Lambeck, G. J. M. Krijnen, J. Čtyroký, M. D. Minicis, C. Sibilia, O. Conradi, S. Helfert, and R. Pregla, “A cost 240 benchmark test for beam propagation methods applied to an electrooptical modulator based on surface plasmons,” J. Lightwave Technol. 16, 1921-1927(1998).
[CrossRef]

O. Conradi, S. Helfert, and R. Pregla, “Modification of the finite difference scheme for efficient analysis of thin lossy metal layers in optical devices,” Opt. Quantum Electron. 30, 369-373 (1998).
[CrossRef]

Ctyroky, J.

J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
[CrossRef]

Ctyroký, J.

de Abajo, F. J. G.

Dennis, M. R.

ElJoudi, E.

J. Jahns, E. ElJoudi, D. Hagedorn, and S. Kinne, “Talbot interferometer as a time filter,” Optik (Jena) 112, 295-298 (2001).
[CrossRef]

Gerdes, J.

J. Gerdes, “Bidirectional eigenmode propagation analysis of optical waveguides based on method of lines,” Electron. Lett. 30, 550-551 (1994).
[CrossRef]

Granet, G.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Guizal, B.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Hagedorn, D.

J. Jahns, E. ElJoudi, D. Hagedorn, and S. Kinne, “Talbot interferometer as a time filter,” Optik (Jena) 112, 295-298 (2001).
[CrossRef]

Harris, R.

J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
[CrossRef]

Harris, R. D.

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B 29, 261-267(1995).

Helfert, S.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

O. Conradi, S. Helfert, and R. Pregla, “Comprehensive modeling of vertical-cavity laser-diodes by the method of lines,” IEEE J. Quantum Electron. 37, 928-935 (2001).
[CrossRef]

H. J. W. M. Hoekstra, P. V. Lambeck, G. J. M. Krijnen, J. Čtyroký, M. D. Minicis, C. Sibilia, O. Conradi, S. Helfert, and R. Pregla, “A cost 240 benchmark test for beam propagation methods applied to an electrooptical modulator based on surface plasmons,” J. Lightwave Technol. 16, 1921-1927(1998).
[CrossRef]

O. Conradi, S. Helfert, and R. Pregla, “Modification of the finite difference scheme for efficient analysis of thin lossy metal layers in optical devices,” Opt. Quantum Electron. 30, 369-373 (1998).
[CrossRef]

Helfert, S. F.

S. F. Helfert, B. Huneke, and J. Jahns, “Self-imaging effect in multimode waveguides with longitudinal periodicity,” J. Eur. Opt. Soc. 4, 09031 (2009).
[CrossRef]

S. F. Helfert, A. Barcz, and R. Pregla, “Three-dimensional vectorial analysis of waveguide structures with the method of lines,” Opt. Quantum Electron. 35, 381-394 (2003).
[CrossRef]

S. F. Helfert and R. Pregla, “The method of lines: a versatile tool for the analysis of waveguide structures,” Electromagnetics 22, 615-637 (2002),
[CrossRef]

R. Pregla and S. F. Helfert, “Modeling of microwave devices with the method of lines,” in Recent Research Developments in Microwave Theory and Techniques, B. Beker and Y. Chen, eds. (Research Signpost, 2002), pp. 145-196.

Hoekstra, H.

J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
[CrossRef]

Hoekstra, H. J. W. M.

Homola, J.

J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
[CrossRef]

Hugonin, J.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Huneke, B.

S. F. Helfert, B. Huneke, and J. Jahns, “Self-imaging effect in multimode waveguides with longitudinal periodicity,” J. Eur. Opt. Soc. 4, 09031 (2009).
[CrossRef]

Jahns, J.

S. F. Helfert, B. Huneke, and J. Jahns, “Self-imaging effect in multimode waveguides with longitudinal periodicity,” J. Eur. Opt. Soc. 4, 09031 (2009).
[CrossRef]

J. Jahns, E. ElJoudi, D. Hagedorn, and S. Kinne, “Talbot interferometer as a time filter,” Optik (Jena) 112, 295-298 (2001).
[CrossRef]

Janssen, O.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Kinne, S.

J. Jahns, E. ElJoudi, D. Hagedorn, and S. Kinne, “Talbot interferometer as a time filter,” Optik (Jena) 112, 295-298 (2001).
[CrossRef]

Krijnen, G. J. M.

Labeke, D. V.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Lalanne, P.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Lambeck, P.

J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
[CrossRef]

Lambeck, P. V.

Lee, H.

Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88, 171108 (2006).
[CrossRef]

Liu, Z.

Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88, 171108 (2006).
[CrossRef]

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano. Lett. 5, 1726-1729 (2005).

Lohmann, A. W.

A. W. Lohmann and D. A. Silva, “An interferometer based on the talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

Lyndin, N.

J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
[CrossRef]

Minicis, M. D.

Moreau, A.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Musa, S.

J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
[CrossRef]

Nugrowati, A.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Pascher, W.

R. Pregla and W. Pascher, “The method of lines,” in Numerical Techniques for Microwave and Millimeter Wave Passive Structures, T. Itoh, ed. (Wiley, 1989), pp. 381-446.

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615-627(1995).
[CrossRef]

Pereira, S.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Pikus, Y.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano. Lett. 5, 1726-1729 (2005).

Pregla, R.

S. F. Helfert, A. Barcz, and R. Pregla, “Three-dimensional vectorial analysis of waveguide structures with the method of lines,” Opt. Quantum Electron. 35, 381-394 (2003).
[CrossRef]

S. F. Helfert and R. Pregla, “The method of lines: a versatile tool for the analysis of waveguide structures,” Electromagnetics 22, 615-637 (2002),
[CrossRef]

O. Conradi, S. Helfert, and R. Pregla, “Comprehensive modeling of vertical-cavity laser-diodes by the method of lines,” IEEE J. Quantum Electron. 37, 928-935 (2001).
[CrossRef]

H. J. W. M. Hoekstra, P. V. Lambeck, G. J. M. Krijnen, J. Čtyroký, M. D. Minicis, C. Sibilia, O. Conradi, S. Helfert, and R. Pregla, “A cost 240 benchmark test for beam propagation methods applied to an electrooptical modulator based on surface plasmons,” J. Lightwave Technol. 16, 1921-1927(1998).
[CrossRef]

O. Conradi, S. Helfert, and R. Pregla, “Modification of the finite difference scheme for efficient analysis of thin lossy metal layers in optical devices,” Opt. Quantum Electron. 30, 369-373 (1998).
[CrossRef]

R. Pregla and W. Pascher, “The method of lines,” in Numerical Techniques for Microwave and Millimeter Wave Passive Structures, T. Itoh, ed. (Wiley, 1989), pp. 381-446.

R. Pregla and S. F. Helfert, “Modeling of microwave devices with the method of lines,” in Recent Research Developments in Microwave Theory and Techniques, B. Beker and Y. Chen, eds. (Research Signpost, 2002), pp. 145-196.

R. Pregla, “MoL-BPM method of lines based beam propagation method,” in Methods for Modeling and Simulation of Guided-Wave Optoelectronic Devices (PIER 11), W. P. Huang, ed. (EMW Publishing, 1995), pp. 51-102.

R. Pregla, Analysis of Electromagnetic Fields and Waves: the Method of Lines (Wiley, 2008).

R. Pregla, “Novel FD-BPM for optical waveguide structures with isotropic or anisotropic material,” in Proceedings of the European Conference on Integrated Optics and Technical Exhibit (European Optical Society, 1999), pp. 55-58.

Raether, H.

H. Raether, Surface Plasmons, Vol. 111 of Springer Tracts in Modern Physics (Springer-Verlag, 1988).

Seideman, T.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Sibilia, C.

Silva, D. A.

A. W. Lohmann and D. A. Silva, “An interferometer based on the talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615-627(1995).
[CrossRef]

Srituravanich, W.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano. Lett. 5, 1726-1729 (2005).

Steele, J. M.

Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88, 171108 (2006).
[CrossRef]

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano. Lett. 5, 1726-1729 (2005).

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).

Sukharev, M.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Sun, C.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano. Lett. 5, 1726-1729 (2005).

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science, No. IV,” Philos. Mag. 9, 401-407 (1836).

Tamir, T.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).

Ulrich, R.

R. Ulrich and G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett. 27, 337-339(1975).
[CrossRef]

Urbach, H.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Usievich, B.

J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
[CrossRef]

van de Nes, A.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

van Haver, S.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Wilkinson, J.

J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
[CrossRef]

Wilkinson, J. S.

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B 29, 261-267(1995).

Xu, M.

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Zhang, X.

Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88, 171108 (2006).
[CrossRef]

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano. Lett. 5, 1726-1729 (2005).

Zheludev, N. I.

Appl. Phys. Lett. (2)

Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88, 171108 (2006).
[CrossRef]

R. Ulrich and G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett. 27, 337-339(1975).
[CrossRef]

Electromagnetics (1)

S. F. Helfert and R. Pregla, “The method of lines: a versatile tool for the analysis of waveguide structures,” Electromagnetics 22, 615-637 (2002),
[CrossRef]

Electron. Lett. (1)

J. Gerdes, “Bidirectional eigenmode propagation analysis of optical waveguides based on method of lines,” Electron. Lett. 30, 550-551 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

O. Conradi, S. Helfert, and R. Pregla, “Comprehensive modeling of vertical-cavity laser-diodes by the method of lines,” IEEE J. Quantum Electron. 37, 928-935 (2001).
[CrossRef]

J. Eur. Opt. Soc. (2)

S. F. Helfert, B. Huneke, and J. Jahns, “Self-imaging effect in multimode waveguides with longitudinal periodicity,” J. Eur. Opt. Soc. 4, 09031 (2009).
[CrossRef]

M. Besbes, J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, , B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (1)

Nano. Lett. (1)

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano. Lett. 5, 1726-1729 (2005).

Opt. Commun. (1)

A. W. Lohmann and D. A. Silva, “An interferometer based on the talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

Opt. Express (1)

Opt. Quantum Electron. (2)

O. Conradi, S. Helfert, and R. Pregla, “Modification of the finite difference scheme for efficient analysis of thin lossy metal layers in optical devices,” Opt. Quantum Electron. 30, 369-373 (1998).
[CrossRef]

S. F. Helfert, A. Barcz, and R. Pregla, “Three-dimensional vectorial analysis of waveguide structures with the method of lines,” Opt. Quantum Electron. 35, 381-394 (2003).
[CrossRef]

Optik (Jena) (1)

J. Jahns, E. ElJoudi, D. Hagedorn, and S. Kinne, “Talbot interferometer as a time filter,” Optik (Jena) 112, 295-298 (2001).
[CrossRef]

Philos. Mag. (1)

H. F. Talbot, “Facts relating to optical science, No. IV,” Philos. Mag. 9, 401-407 (1836).

Phys. Rev. B (2)

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).

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).

Sens. Actuators B (2)

J. Ctyroky, J. Homola, P. Lambeck, S. Musa, H. Hoekstra, R. Harris, J. Wilkinson, B. Usievich, and N. Lyndin, “Theory and modelling of optical waveguide sensors utilising 20 surface plasmon resonance,” Sens. Actuators B 54, 66-73(1999).
[CrossRef]

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B 29, 261-267(1995).

Other (6)

H. Raether, Surface Plasmons, Vol. 111 of Springer Tracts in Modern Physics (Springer-Verlag, 1988).

R. Pregla and W. Pascher, “The method of lines,” in Numerical Techniques for Microwave and Millimeter Wave Passive Structures, T. Itoh, ed. (Wiley, 1989), pp. 381-446.

R. Pregla, Analysis of Electromagnetic Fields and Waves: the Method of Lines (Wiley, 2008).

R. Pregla, “Novel FD-BPM for optical waveguide structures with isotropic or anisotropic material,” in Proceedings of the European Conference on Integrated Optics and Technical Exhibit (European Optical Society, 1999), pp. 55-58.

R. Pregla, “MoL-BPM method of lines based beam propagation method,” in Methods for Modeling and Simulation of Guided-Wave Optoelectronic Devices (PIER 11), W. P. Huang, ed. (EMW Publishing, 1995), pp. 51-102.

R. Pregla and S. F. Helfert, “Modeling of microwave devices with the method of lines,” in Recent Research Developments in Microwave Theory and Techniques, B. Beker and Y. Chen, eds. (Research Signpost, 2002), pp. 145-196.

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Figures (11)

Fig. 1
Fig. 1

(a) Dielectric multimode waveguide structure and (b) normalized propagation constants of the eigenmodes for w = 20 μm , wavelength λ = 1.5 μm , n co = 1.52 , and n cl = 1.45 . This waveguide was studied in [16]; the Talbot distance was determined as z T = 3600 μm .

Fig. 2
Fig. 2

(a) Examined metallic waveguide structure and (b) frequency dependency of ϵ m (permittivity of metal).

Fig. 3
Fig. 3

Magnetic field distribution ( H x ) of the eigenmodes in a dielectric (left) and a metallic waveguide (right).

Fig. 4
Fig. 4

Magnetic field distribution ( H x ) in the center of a dielectric waveguide (top) and at the metal–dielectric surface (bottom).

Fig. 5
Fig. 5

Normalized propagation constants of the first even and odd modes in the plasmonic waveguide: top, loss factor; bottom, phase factor; wavelength λ = 600 nm .

Fig. 6
Fig. 6

Effective index of the plasmon modes in a 2-D waveguide.

Fig. 7
Fig. 7

Effective index of the first odd mode in a metallic waveguide (Fig. 2) as a function of the wavelength with the permittivity of the surrounding material as the parameter: height, t = 0.1 μm and width, w = 2 μm .

Fig. 8
Fig. 8

Field distribution of the H x component at the interface between the dielectric and the silver layer for λ 0 = 0.6 μm ; the imaginary part of ϵ m was neglected.

Fig. 9
Fig. 9

Field distribution of the H x component at the interface between the dielectric and the silver layer at λ 0 = 0.6 μm ; the influence of I ( ϵ m ) is considered.

Fig. 10
Fig. 10

Field distribution of the H x component at the interface between the dielectric and the silver layer at λ 0 = 0.9 μm ; the influence of I ( ϵ m ) is considered.

Fig. 11
Fig. 11

Field distribution of the H x component at the interface between the dielectric and the silver layer: (a) even excitation and ( b) odd excitation; parameters: λ 0 = 0.6 μm and t = 0.06 μm .

Tables (1)

Tables Icon

Table 1 Self-Imaging Distances L si Determined from the Field Distribution in Comparison with Eq. (17)

Equations (19)

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u ( x , z ) = u ( x , z + z T ) e j ϕ ,
2 z ¯ 2 H t Q H H t = 0 with     H t = ( H ˜ y H ˜ x ) .
2 z ¯ 2 H ^ Q ^ H H ^ = 0.
Q ^ H = T ^ H 1 Γ 2 T ^ H .
H ¯ ^ = T ^ H H ^
H ¯ ^ ( z ) = e Γ z ¯ H ¯ ^ f ( 0 ) + e Γ z ¯ H ¯ ^ b ( 0 ) .
Γ k = α ¯ k + j β ¯ k .
n eff = β ¯ j α ¯ = j Γ .
d d z ¯ E ^ = j R ^ H H ^ ( z ) .
E ^ ( z ) = T ^ E ( H ¯ ^ f ( z ) H ¯ ^ b ( z ) )
ϵ m = ϵ ω p 2 ω 2 j γ ω .
tanh ( k 0 t 2 n eff 2 ϵ m ) = ϵ m ϵ d n eff 2 ϵ d n eff 2 ϵ m ( even ) ,
coth ( k 0 t 2 n eff 2 ϵ m ) = ϵ m ϵ d n eff 2 ϵ d n eff 2 ϵ m ( odd ) .
n eff = ϵ d ϵ m ϵ d + ϵ m .
n eff ϵ d ( 1 ϵ d 2 ϵ m ) .
n eff = ϵ d + ϵ d 3 / 2 ϵ m | ϵ re | 2 + | ϵ im | 2 j ϵ d 3 / 2 1 2 | ϵ im | | ϵ re | 2 + | ϵ im | .
L si = 3 4 L π = 3 8 λ 0 Δ β ¯ .
loss 1 = 1 | H ( z = L si ) | / | H ( z = 0 ) | .
loss 2 = 1 exp { α ¯ k 0 L si } .

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