Abstract

The excitation of the Uller–Zenneck surface wave in the optical regime was theoretically investigated for planar as well as periodically corrugated interfaces of two homogeneous, isotropic dielectric materials, with only one of the two being dissipative. A practical configuration involving the plane-wave illumination of a planar interface of the two partnering materials was found to be unsuitable for experimental confirmation of the existence of this surface wave. But, when the interface was periodically corrugated, the Uller–Zenneck wave was found to be excited over a wide range of angles of incidence. Air and crystalline silicon were identified as suitable partnering materials for experiments in the visible and ultraviolet spectral regimes.

© 2014 Optical Society of America

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References

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  1. J. Zenneck, “Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Lieterfläche und ihre Beziehung zur drahtlosen Telegraphie,” Ann. Phys. Lpz. 23, 846–866 (1907).
  2. K. Uller, “Beiträge zur Theorie der Elektromagnetischen Strahlung,” Ph.D. thesis (Universität Rostock, 1903), Chap. XIV.
  3. R. E. Collin, Field Theory of Guided Waves, 2nd ed. (Wiley, 1991).
  4. A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. Lpz. 28, 665–736 (1909).
  5. A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. Lpz. 81, 1135–1153 (1926).
  6. J. R. Wait, “The ancient and modern history of EM ground-wave propagation,” IEEE Antennas Propag. Mag. 40(5), 7–24 (1998).
    [CrossRef]
  7. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  8. J. Homola, ed., Surface Plasmon Resonance Based Sensors (Springer, 2006).
  9. T.-I. Jeon and D. Grischkowsky, “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113 (2006).
    [CrossRef]
  10. M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
    [CrossRef]
  11. V. I. Baĭbakov, V. N. Datsko, and Yu. V. Kistovich, “Experimental discovery of Zenneck’s surface electromagnetic waves,” Sov. Phys. Usp. 32, 378–379 (1989).
    [CrossRef]
  12. V. N. Datsko and A. A. Kopylov, “On surface electromagnetic waves,” Sov. Phys. Usp. 51, 101–102 (2008).
    [CrossRef]
  13. J. R. Wait, Electromagnetic Waves in Stratified Media, 2nd ed. (Pergamon, 1970).
  14. J. A. Polo, T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013).
  15. D. A. Hill and J. R. Wait, “Excitation of the Zenneck surface wave by a vertical aperture,” Radio Sci. 13, 969–977 (1978).
    [CrossRef]
  16. D. A. Hill and J. R. Wait, “On the excitation of the Zenneck surface wave over the ground at 10  MHz,” Ann. Télécommun. 35, 179–182 (1980).
  17. M. Faryad and A. Lakhtakia, “Grating-coupled excitation of multiple surface plasmon-polariton waves,” Phys. Rev. A 84, 033852 (2011).
    [CrossRef]
  18. J. Hendry, “Isolation of the Zenneck surface wave,” in Loughborough Antennas & Propagation Conference, Loughborough, UK, November8–9, 2010.
  19. D. P. Pulsifer, M. Faryad, A. Lakhtakia, A. S. Hall, and L. Liu, “Experimental excitation of the Dyakonov–Tamm wave in the grating-coupled configuration,” Opt. Lett. 39, 2125–2128 (2014).
    [CrossRef]
  20. Data on relative permittivity of crystalline silicon as a function of λ0 were downloaded from http://refractiveindex.info/legacy/?group=CRYSTALS&material=Si&option=Palik&wavelength=6.18 on May1, 2014.
  21. M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).
  22. A. S. Hall, M. Faryad, G. D. Barber, L. Liu, S. Erten, T. S. Mayer, A. Lakhtakia, and T. E. Mallouk, “Broadband light absorption with multiple surface plasmon polariton waves excited at the interface of a metallic grating and photonic crystal,” ACS Nano 7, 4995–5007 (2013).
    [CrossRef]
  23. L. Li, “Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity,” J. Opt. Soc. Am. A 10, 2581–2591 (1993).
    [CrossRef]
  24. M. G. Moharam, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]

2014 (1)

2013 (2)

A. S. Hall, M. Faryad, G. D. Barber, L. Liu, S. Erten, T. S. Mayer, A. Lakhtakia, and T. E. Mallouk, “Broadband light absorption with multiple surface plasmon polariton waves excited at the interface of a metallic grating and photonic crystal,” ACS Nano 7, 4995–5007 (2013).
[CrossRef]

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

2011 (1)

M. Faryad and A. Lakhtakia, “Grating-coupled excitation of multiple surface plasmon-polariton waves,” Phys. Rev. A 84, 033852 (2011).
[CrossRef]

2008 (1)

V. N. Datsko and A. A. Kopylov, “On surface electromagnetic waves,” Sov. Phys. Usp. 51, 101–102 (2008).
[CrossRef]

2006 (1)

T.-I. Jeon and D. Grischkowsky, “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113 (2006).
[CrossRef]

1998 (1)

J. R. Wait, “The ancient and modern history of EM ground-wave propagation,” IEEE Antennas Propag. Mag. 40(5), 7–24 (1998).
[CrossRef]

1995 (1)

1993 (1)

1989 (1)

V. I. Baĭbakov, V. N. Datsko, and Yu. V. Kistovich, “Experimental discovery of Zenneck’s surface electromagnetic waves,” Sov. Phys. Usp. 32, 378–379 (1989).
[CrossRef]

1980 (1)

D. A. Hill and J. R. Wait, “On the excitation of the Zenneck surface wave over the ground at 10  MHz,” Ann. Télécommun. 35, 179–182 (1980).

1978 (1)

D. A. Hill and J. R. Wait, “Excitation of the Zenneck surface wave by a vertical aperture,” Radio Sci. 13, 969–977 (1978).
[CrossRef]

1926 (1)

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. Lpz. 81, 1135–1153 (1926).

1909 (1)

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. Lpz. 28, 665–736 (1909).

1907 (1)

J. Zenneck, “Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Lieterfläche und ihre Beziehung zur drahtlosen Telegraphie,” Ann. Phys. Lpz. 23, 846–866 (1907).

Baibakov, V. I.

V. I. Baĭbakov, V. N. Datsko, and Yu. V. Kistovich, “Experimental discovery of Zenneck’s surface electromagnetic waves,” Sov. Phys. Usp. 32, 378–379 (1989).
[CrossRef]

Barber, G. D.

A. S. Hall, M. Faryad, G. D. Barber, L. Liu, S. Erten, T. S. Mayer, A. Lakhtakia, and T. E. Mallouk, “Broadband light absorption with multiple surface plasmon polariton waves excited at the interface of a metallic grating and photonic crystal,” ACS Nano 7, 4995–5007 (2013).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves, 2nd ed. (Wiley, 1991).

Datsko, V. N.

V. N. Datsko and A. A. Kopylov, “On surface electromagnetic waves,” Sov. Phys. Usp. 51, 101–102 (2008).
[CrossRef]

V. I. Baĭbakov, V. N. Datsko, and Yu. V. Kistovich, “Experimental discovery of Zenneck’s surface electromagnetic waves,” Sov. Phys. Usp. 32, 378–379 (1989).
[CrossRef]

Delagnes, J. C.

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

Dominec, F.

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

Erten, S.

A. S. Hall, M. Faryad, G. D. Barber, L. Liu, S. Erten, T. S. Mayer, A. Lakhtakia, and T. E. Mallouk, “Broadband light absorption with multiple surface plasmon polariton waves excited at the interface of a metallic grating and photonic crystal,” ACS Nano 7, 4995–5007 (2013).
[CrossRef]

Faryad, M.

D. P. Pulsifer, M. Faryad, A. Lakhtakia, A. S. Hall, and L. Liu, “Experimental excitation of the Dyakonov–Tamm wave in the grating-coupled configuration,” Opt. Lett. 39, 2125–2128 (2014).
[CrossRef]

A. S. Hall, M. Faryad, G. D. Barber, L. Liu, S. Erten, T. S. Mayer, A. Lakhtakia, and T. E. Mallouk, “Broadband light absorption with multiple surface plasmon polariton waves excited at the interface of a metallic grating and photonic crystal,” ACS Nano 7, 4995–5007 (2013).
[CrossRef]

M. Faryad and A. Lakhtakia, “Grating-coupled excitation of multiple surface plasmon-polariton waves,” Phys. Rev. A 84, 033852 (2011).
[CrossRef]

Graham, C.

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

Grann, E. B.

Grischkowsky, D.

T.-I. Jeon and D. Grischkowsky, “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113 (2006).
[CrossRef]

Hall, A. S.

D. P. Pulsifer, M. Faryad, A. Lakhtakia, A. S. Hall, and L. Liu, “Experimental excitation of the Dyakonov–Tamm wave in the grating-coupled configuration,” Opt. Lett. 39, 2125–2128 (2014).
[CrossRef]

A. S. Hall, M. Faryad, G. D. Barber, L. Liu, S. Erten, T. S. Mayer, A. Lakhtakia, and T. E. Mallouk, “Broadband light absorption with multiple surface plasmon polariton waves excited at the interface of a metallic grating and photonic crystal,” ACS Nano 7, 4995–5007 (2013).
[CrossRef]

Hendry, J.

J. Hendry, “Isolation of the Zenneck surface wave,” in Loughborough Antennas & Propagation Conference, Loughborough, UK, November8–9, 2010.

Hill, D. A.

D. A. Hill and J. R. Wait, “On the excitation of the Zenneck surface wave over the ground at 10  MHz,” Ann. Télécommun. 35, 179–182 (1980).

D. A. Hill and J. R. Wait, “Excitation of the Zenneck surface wave by a vertical aperture,” Radio Sci. 13, 969–977 (1978).
[CrossRef]

Jeon, T.-I.

T.-I. Jeon and D. Grischkowsky, “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113 (2006).
[CrossRef]

Kistovich, Yu. V.

V. I. Baĭbakov, V. N. Datsko, and Yu. V. Kistovich, “Experimental discovery of Zenneck’s surface electromagnetic waves,” Sov. Phys. Usp. 32, 378–379 (1989).
[CrossRef]

Kopylov, A. A.

V. N. Datsko and A. A. Kopylov, “On surface electromagnetic waves,” Sov. Phys. Usp. 51, 101–102 (2008).
[CrossRef]

Kužel, P.

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

Lakhtakia, A.

D. P. Pulsifer, M. Faryad, A. Lakhtakia, A. S. Hall, and L. Liu, “Experimental excitation of the Dyakonov–Tamm wave in the grating-coupled configuration,” Opt. Lett. 39, 2125–2128 (2014).
[CrossRef]

A. S. Hall, M. Faryad, G. D. Barber, L. Liu, S. Erten, T. S. Mayer, A. Lakhtakia, and T. E. Mallouk, “Broadband light absorption with multiple surface plasmon polariton waves excited at the interface of a metallic grating and photonic crystal,” ACS Nano 7, 4995–5007 (2013).
[CrossRef]

M. Faryad and A. Lakhtakia, “Grating-coupled excitation of multiple surface plasmon-polariton waves,” Phys. Rev. A 84, 033852 (2011).
[CrossRef]

J. A. Polo, T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013).

Li, L.

Liu, L.

D. P. Pulsifer, M. Faryad, A. Lakhtakia, A. S. Hall, and L. Liu, “Experimental excitation of the Dyakonov–Tamm wave in the grating-coupled configuration,” Opt. Lett. 39, 2125–2128 (2014).
[CrossRef]

A. S. Hall, M. Faryad, G. D. Barber, L. Liu, S. Erten, T. S. Mayer, A. Lakhtakia, and T. E. Mallouk, “Broadband light absorption with multiple surface plasmon polariton waves excited at the interface of a metallic grating and photonic crystal,” ACS Nano 7, 4995–5007 (2013).
[CrossRef]

Mackay, T. G.

J. A. Polo, T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013).

Maier, S. A.

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

Mallouk, T. E.

A. S. Hall, M. Faryad, G. D. Barber, L. Liu, S. Erten, T. S. Mayer, A. Lakhtakia, and T. E. Mallouk, “Broadband light absorption with multiple surface plasmon polariton waves excited at the interface of a metallic grating and photonic crystal,” ACS Nano 7, 4995–5007 (2013).
[CrossRef]

Mayer, T. S.

A. S. Hall, M. Faryad, G. D. Barber, L. Liu, S. Erten, T. S. Mayer, A. Lakhtakia, and T. E. Mallouk, “Broadband light absorption with multiple surface plasmon polariton waves excited at the interface of a metallic grating and photonic crystal,” ACS Nano 7, 4995–5007 (2013).
[CrossRef]

Mitrofanov, O.

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

Moharam, M. G.

Mounaix, P.

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

Natrella, M.

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

Navarro-Cía, M.

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

Polo, J. A.

J. A. Polo, T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013).

Pommet, D. A.

Pulsifer, D. P.

Renaud, C. C.

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

Seeds, A. J.

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. Lpz. 81, 1135–1153 (1926).

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. Lpz. 28, 665–736 (1909).

Uller, K.

K. Uller, “Beiträge zur Theorie der Elektromagnetischen Strahlung,” Ph.D. thesis (Universität Rostock, 1903), Chap. XIV.

Wait, J. R.

J. R. Wait, “The ancient and modern history of EM ground-wave propagation,” IEEE Antennas Propag. Mag. 40(5), 7–24 (1998).
[CrossRef]

D. A. Hill and J. R. Wait, “On the excitation of the Zenneck surface wave over the ground at 10  MHz,” Ann. Télécommun. 35, 179–182 (1980).

D. A. Hill and J. R. Wait, “Excitation of the Zenneck surface wave by a vertical aperture,” Radio Sci. 13, 969–977 (1978).
[CrossRef]

J. R. Wait, Electromagnetic Waves in Stratified Media, 2nd ed. (Pergamon, 1970).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).

Zenneck, J.

J. Zenneck, “Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Lieterfläche und ihre Beziehung zur drahtlosen Telegraphie,” Ann. Phys. Lpz. 23, 846–866 (1907).

ACS Nano (1)

A. S. Hall, M. Faryad, G. D. Barber, L. Liu, S. Erten, T. S. Mayer, A. Lakhtakia, and T. E. Mallouk, “Broadband light absorption with multiple surface plasmon polariton waves excited at the interface of a metallic grating and photonic crystal,” ACS Nano 7, 4995–5007 (2013).
[CrossRef]

Ann. Phys. Lpz. (3)

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. Lpz. 28, 665–736 (1909).

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. Lpz. 81, 1135–1153 (1926).

J. Zenneck, “Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Lieterfläche und ihre Beziehung zur drahtlosen Telegraphie,” Ann. Phys. Lpz. 23, 846–866 (1907).

Ann. Télécommun. (1)

D. A. Hill and J. R. Wait, “On the excitation of the Zenneck surface wave over the ground at 10  MHz,” Ann. Télécommun. 35, 179–182 (1980).

Appl. Phys. Lett. (2)

T.-I. Jeon and D. Grischkowsky, “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113 (2006).
[CrossRef]

M. Navarro-Cía, M. Natrella, F. Dominec, J. C. Delagnes, P. Kužel, P. Mounaix, C. Graham, C. C. Renaud, A. J. Seeds, and O. Mitrofanov, “Terahertz imaging of sub-wavelength particles with Zenneck surface waves,” Appl. Phys. Lett. 103, 221103 (2013).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

J. R. Wait, “The ancient and modern history of EM ground-wave propagation,” IEEE Antennas Propag. Mag. 40(5), 7–24 (1998).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Phys. Rev. A (1)

M. Faryad and A. Lakhtakia, “Grating-coupled excitation of multiple surface plasmon-polariton waves,” Phys. Rev. A 84, 033852 (2011).
[CrossRef]

Radio Sci. (1)

D. A. Hill and J. R. Wait, “Excitation of the Zenneck surface wave by a vertical aperture,” Radio Sci. 13, 969–977 (1978).
[CrossRef]

Sov. Phys. Usp. (2)

V. I. Baĭbakov, V. N. Datsko, and Yu. V. Kistovich, “Experimental discovery of Zenneck’s surface electromagnetic waves,” Sov. Phys. Usp. 32, 378–379 (1989).
[CrossRef]

V. N. Datsko and A. A. Kopylov, “On surface electromagnetic waves,” Sov. Phys. Usp. 51, 101–102 (2008).
[CrossRef]

Other (9)

J. R. Wait, Electromagnetic Waves in Stratified Media, 2nd ed. (Pergamon, 1970).

J. A. Polo, T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013).

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

J. Homola, ed., Surface Plasmon Resonance Based Sensors (Springer, 2006).

J. Hendry, “Isolation of the Zenneck surface wave,” in Loughborough Antennas & Propagation Conference, Loughborough, UK, November8–9, 2010.

Data on relative permittivity of crystalline silicon as a function of λ0 were downloaded from http://refractiveindex.info/legacy/?group=CRYSTALS&material=Si&option=Palik&wavelength=6.18 on May1, 2014.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).

K. Uller, “Beiträge zur Theorie der Elektromagnetischen Strahlung,” Ph.D. thesis (Universität Rostock, 1903), Chap. XIV.

R. E. Collin, Field Theory of Guided Waves, 2nd ed. (Wiley, 1991).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of the canonical boundary-value problem. The Uller–Zenneck wave is guided by the interface z=0. (b) Excitation of the Uller–Zenneck wave by a plane wave that is obliquely incident at the interface z=0, when the dissipative partnering material has a large but finite thickness. (c) Schematic of the grating-coupled configuration. Same as (b), but the guiding interface is periodically corrugated. The specular components of the reflected and transmitted fields are labeled as 0, whereas their nonspecular components are labeled by nonzero integers.

Fig. 2.
Fig. 2.

Real and imaginary parts of the relative permittivity εs of crystalline silicon as functions of λ0 [20].

Fig. 3.
Fig. 3.

Canonical boundary-value problem. (a) Spectrum of Re(q)/k0nd for the surface wave guided by the planar interface of air and crystalline silicon. (b) Spectra of Δprop, Δd, and Δs. The surface wave is an SPP wave for λ0<293nm and an Uller–Zenneck wave for λ0294nm.

Fig. 4.
Fig. 4.

Practical configuration with a planar guiding interface. (a) Spectrum of θC=sin1[Re(q)/k0nd] when the excitation of the Uller–Zenneck wave is predicted by the solution of the canonical boundary-value problem. (b) Absorptance Ap, (c) reflectance Rp, and (d) transmittance Tp as functions of λ0 and θ when Lm=250nm.

Fig. 5.
Fig. 5.

Practical configuration with periodically corrugated guiding interface. (a) Spectra of θnC=sin1{[Re(q)2πn/L]/k0nd} when the excitation of the Uller–Zenneck wave is predicted by the solution of the canonical boundary-value problem. (b) Absorptance Ap, (c) specular reflectance Rp(0), and (d) total transmittance Tp as functions of λ0 and θ when L=350nm, Lg=35nm, ζ=0.5, and Lm=1000nm.

Equations (15)

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

E(r)=ap(αdu^x+qu^zk0nd)exp[i(qxαdz)],z<0,
E(r)=bp(αsu^x+qu^zk0ns)exp[i(qx+αsz)],z>0,
q=k0εdεsεd+εs,
αd=k0εdεd+εs,αs=k0εsεd+εs.
E(r)=(u^xcosθ+u^zsinθ)exp[ik0nd(xsinθ+zcosθ)]+rp(u^xcosθ+u^zsinθ)exp[ik0nd(xsinθzcosθ)],z<0,
E(r)=tp(u^xcosθ+u^zsinθ)exp{ik0nd[xsinθ+(zLm)cosθ]},z>Lm,
E(r)=(u^xcosθ+u^zsinθ)exp[ik0nd(xsinθ+zcosθ)]+n=NtNtrp(n)pnexp[i(κ(n)xα(n)z)],z0.
κ(n)=k0ndsinθ+2πn/L,
α(n)={+k02εd(κ(n))2,k02εd(κ(n))2,+i(κ(n))2k02εd,k02εd<(κ(n))2,
pn±=α(n)u^x+κ(n)u^zk0nd.
E(r)=n=NtNttp(n)pn+exp{i[κ(n)x+α(n)(zLt)]},z>Lt,
Rp(n)=|rp(n)|2Re(α(n))α(0),Tp(n)=|tp(n)|2Re(α(n))α(0),
Rp=n=NtNtRp(n),Tp=n=NtNtTp(n),
Ap=1(Rp+Tp).
θnC=sin1{Re(q)2πn/Lk0nd}

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