Abstract

We demonstrate the existence of electromagnetic surface modes and surface plasma waves in the interface of a one-dimensional photonic crystal and a metal. These modes can exist in the region in which bandgaps of the photonic crystal overlap and in the region below the plasma frequency of a metal in the frequency wave-vector space. An analytic dispersion relation to determine the existence of these electromagnetic surface modes is obtained, and it is shown that these modes can be excited and observed without prism or grating configurations even under normal incidence from vacuum.

© 2003 Optical Society of America

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References

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  1. P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977).
    [CrossRef]
  2. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  3. F. Ramos-Mendieta and P. Halevi, “Electromagnetic surface modes of a dielectric superlattice: the supercell method,” J. Opt. Soc. Am. B 14, 370–381 (1997).
    [CrossRef]
  4. F. Villa, J. A. Gaspar-Armenta, and F. Ramos-Mendieta, “One-dimensional photonic crystals: equivalent systems to single layers with a classical oscillator like dielectric function,” Opt. Commun. 216, 361–367 (2003).
    [CrossRef]
  5. F. Villa, L. E. Regalado, F. Ramos-Mendieta, J. Gaspar-Armenta, and T. López-Rı´os, “Photonic crystal sensor based on surface waves for thin film characterization,” Opt. Lett. 27, 646–648 (2002).
    [CrossRef]
  6. W. M. Robertson and M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
    [CrossRef]
  7. W. M. Robertson, “Experimental measurement of the effect of termination on surface electromagnetic waves in one-dimensional photonic bandgap arrays,” J. Lightwave Technol. 17, 2013–2017 (1999).
    [CrossRef]
  8. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, New York, 1986).
  9. E. N. Economu, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
    [CrossRef]
  10. H. Raether, Excitation of Plasmons and Interband Transitions by Electrons (Springer-Verlag, New York, 1980).
  11. P. Halevi, “Polaritons at interface between two dielectric media,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 249–304.
  12. H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, New York, 1989).
  13. C. J. Van der Laan and H. J. Franquena, “Equivalent layers: another way to look at them,” Appl. Opt. 34, 681–687 (1995).
    [CrossRef] [PubMed]
  14. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

2003

F. Villa, J. A. Gaspar-Armenta, and F. Ramos-Mendieta, “One-dimensional photonic crystals: equivalent systems to single layers with a classical oscillator like dielectric function,” Opt. Commun. 216, 361–367 (2003).
[CrossRef]

2002

1999

W. M. Robertson and M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
[CrossRef]

W. M. Robertson, “Experimental measurement of the effect of termination on surface electromagnetic waves in one-dimensional photonic bandgap arrays,” J. Lightwave Technol. 17, 2013–2017 (1999).
[CrossRef]

1997

1995

1977

1969

E. N. Economu, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Economu, E. N.

E. N. Economu, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Franquena, H. J.

Gaspar-Armenta, J.

Gaspar-Armenta, J. A.

F. Villa, J. A. Gaspar-Armenta, and F. Ramos-Mendieta, “One-dimensional photonic crystals: equivalent systems to single layers with a classical oscillator like dielectric function,” Opt. Commun. 216, 361–367 (2003).
[CrossRef]

Halevi, P.

Hong, C.-S.

López-Ri´os, T.

May, M. S.

W. M. Robertson and M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
[CrossRef]

Ramos-Mendieta, F.

Regalado, L. E.

Robertson, W. M.

W. M. Robertson and M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
[CrossRef]

W. M. Robertson, “Experimental measurement of the effect of termination on surface electromagnetic waves in one-dimensional photonic bandgap arrays,” J. Lightwave Technol. 17, 2013–2017 (1999).
[CrossRef]

Van der Laan, C. J.

Villa, F.

F. Villa, J. A. Gaspar-Armenta, and F. Ramos-Mendieta, “One-dimensional photonic crystals: equivalent systems to single layers with a classical oscillator like dielectric function,” Opt. Commun. 216, 361–367 (2003).
[CrossRef]

F. Villa, L. E. Regalado, F. Ramos-Mendieta, J. Gaspar-Armenta, and T. López-Rı´os, “Photonic crystal sensor based on surface waves for thin film characterization,” Opt. Lett. 27, 646–648 (2002).
[CrossRef]

Yariv, A.

Yeh, P.

Appl. Opt.

Appl. Phys. Lett.

W. M. Robertson and M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Opt. Commun.

F. Villa, J. A. Gaspar-Armenta, and F. Ramos-Mendieta, “One-dimensional photonic crystals: equivalent systems to single layers with a classical oscillator like dielectric function,” Opt. Commun. 216, 361–367 (2003).
[CrossRef]

Opt. Lett.

Phys. Rev.

E. N. Economu, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Other

H. Raether, Excitation of Plasmons and Interband Transitions by Electrons (Springer-Verlag, New York, 1980).

P. Halevi, “Polaritons at interface between two dielectric media,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 249–304.

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, New York, 1989).

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, New York, 1986).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

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Figures (9)

Fig. 1
Fig. 1

Configuration of a symmetric 1-D PC embedded in dielectric media.

Fig. 2
Fig. 2

Band structure for the TE polarization of an infinite periodic system. The light line for vacuum is represented by a dot–dot–dash line. Surface metal–PC modes are indicated by dotted lines. The region of damped propagating waves in the metal is indicated as delimited by the mesh-shaded region. Under normal incidence the limit of this region corresponds to the plasma frequency ωp of the metal. The inset shows the squared magnitude of the electric field for the surface mode indicated by a triangle in the same figure.

Fig. 3
Fig. 3

Band structure for the TM polarization of the same infinite crystal as in Fig. 2. The light line for vacuum is represented by a dot–dot–dash line. Surface metal–PC modes are represented by dotted lines. The region of damped propagating waves in the metal is indicated by a mesh shaded region. Under normal incidence the limit of this region corresponds to plasma frequency ωp of the metal. Surface plasma modes that exist in the metal–PC interface are indicated by a dashed line that is below the light line of material with the highest refractive index (dot–dash line). The inset shows the squared magnitude of the magnetic field for the surface plasma mode indicated by a diamond in the same figure.

Fig. 4
Fig. 4

Real and imaginary parts of optical admittance of the metal ηm (dash–dot–dot and dashed lines, respectively) and the 1DPC ηe (solid line). The plasma frequency is indicated by the vertical dot–dash line. Beyond that frequency in the graph the real part of the admittance of the metal (silver) becomes nonnegligible for this material. In this graph all the admittances were normalized dividing by the admittance of vacuum y.

Fig. 5
Fig. 5

Reflectance versus reduced frequency to illustrate the 1DPC–metal surface mode indicated by a triangle in Fig. 3. We considered the system air–metal–1DPC under normal incidence with a photonic crystal of 19 symmetric periods and a metallic layer with a physical thickness of 50 nm.

Fig. 6
Fig. 6

Band structure for the TM polarization of an infinite crystal constructed with the same period of the example given in Figs. 2 and 3 but with the sequence of layers qpq. The light line for vacuum is represented by a dot–dot–dash line. Surface metal–PC modes are represented by dotted lines. As before, the region of damped propagating waves in the metal is indicated as delimited by the mesh-shaded region. Under normal incidence the limit of this region corresponds to the plasma frequency ωp of the metal. Surface plasma modes that exist in the metal–PC interface are indicated by a dashed line that is below the light line of material with the highest refractive index (dot–dash line).

Fig. 7
Fig. 7

Real and imaginary parts of optical admittance of the metal ηm (dash–dot–dot and dashed lines, respectively) and the 1DPC1 ηe (solid line) for the example given in Fig. 6. In this graph we considered normal incidence β̅=0. We normalized admittances by dividing by the admittance of vacuum y.

Fig. 8
Fig. 8

Real and imaginary parts of optical admittance of the metal ηm (dash–dot–dot and dashed lines, respectively) and the 1DPC1 ηe (solid line) for the example given in Fig. 6. In this graph we considered β¯=0.8. We normalized admittances by dividing by the admittance of vacuum y.

Fig. 9
Fig. 9

Reflectance versus angle of incidence to illustrate the surface modes indicated by a sphere (PC–metal mode) and a diamond (SPW) in Fig. 6. We considered the system prism–metal–1DPC with a PC of 19 periods and a metallic layer with a physical thickness of 50 nm. The reduced frequency in this case was ω¯=0.4, which corresponds to a wavelength of λ0=562.5 nm for this system. The refractive index of the prism considered to excite the modes was n0=3.0.

Equations (18)

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m(ηj, δj)=cos(δj)iηjsin(δj)iηjsin(δj)cos(δj).
δj=2πΛ k¯zjdj
ηj=yk¯zj/ω¯TEpolarizationynj2ω¯/k¯zjTMpolarization
k¯zj=(nj2ω¯2-β¯2)1/2
M(ηe, δe)=cos(δe)iηesin(δe)iηesin(δe)cos(δe),
M11=cos(2δp)cos(δq)-ρ+sin(2δp)sin(δq),
M22=M11,
M21=iηp[sin(2δp)cos(δq)+ρ+cos(2δp)sin(δq)-ρ-sin(δq)],
M12=iηp [sin(2δp)cos(δq)+ρ+cos(2δp)sin(δq)+ρ-sin(δq)],
ρ+=12ηpηq+ηqηp,
ρ-=12ηpηq-ηqηp.
cos(δe)=cos(2δp)cos(δq)-ρ+sin(2δp)sin(δq),
ηe=ηpsin(δe) [sin(2δp)cos(δq)+ρ+cos(2δp)sin(δq)-ρ-sin(δq)].
η0+ηe+iη0ηeηm+ηmtan(δm)=0.
ηm=-η0,
ηm=-ηe.
η0+ηm+iη0ηmηe+ηetan(σδe)=0.
ηe=-η0.

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