Abstract

When a thin metallic region exists between the core and the cladding regions of a step-index optical fiber, hybrid surface plasma modes can be supported. For each azimuthal mode order two hybrid modes generally occur. Their disperison and attenuation characteristics are studied. The selective influence of the core radius on these is found to be strong only if the radius is small. As the radius increases the modes become degenerate with those of the pure TM polarization.

© 1993 Optical Society of America

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References

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  1. F. Abelès, “Surface plasmon (SEW) phenomena,” in Electromagnetic Surface Excitations, R. F. Wallis, G. I. Stegeman, eds. (Springer-Verlag, Berlin, 1986), pp. 8–20.
    [CrossRef]
  2. D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
    [CrossRef]
  3. Y. Yokota, M. Fukui, O. Tada, “Surface plasmon polaritons on n± type Si single crystal,” J. Phys. Soc. Jpn. 53, 2833–2836 (1984).
    [CrossRef]
  4. N. Tajima, M. Fukui, Y. Shintani, “In situ studies of oxidation of copper films by using ATR technique,” J. Phys. Soc. Jpn. 54, 4236–4240 (1985).
    [CrossRef]
  5. M. Fukui, K. Oda, “Studies on metal film growth through instantaneously observed attenuated total reflection spectra,” Appl. Surf. Sci. 33/34, 882–889 (1988).
    [CrossRef]
  6. Y. Nagano, K. Matsugi, M. Haraguchi, M. Fukui, “Optical response of semi-infinite and finite GaAs/Al0.3Ga0.7As superlattices,” J. Phys. Soc. Jpn. 58, 733–740 (1989).
    [CrossRef]
  7. M. T. Flanagan, R. H. Pantell, “Surface plasmon resonance and immuno sensors,” Electron. Lett. 20, 968–970 (1984).
    [CrossRef]
  8. C. Nylander, B. Liedberg, T. Lind, “Gas detection by means of surface plasmon resonance,” Sensors Actuators 3, 79–88 (1982/83).
    [CrossRef]
  9. E. Yeatman, E. A. Ash, “Surface plasmon microscopy,” Electron. Lett. 23, 1091–1092 (1987).
    [CrossRef]
  10. B. Rothenhausler, W. Knoll, “Surface plasmon microscopy,” Nature (London) 332, 615–617 (1988).
    [CrossRef]
  11. M. E. Caldwell, E. M. Yeatman, “Performance characteristics of surface plasmon liquid crystal light valve,” Electron. Lett. 27, 1471–1472 (1991).
    [CrossRef]
  12. S. J. Al-Bader, M. Imtaar, “Azimuthally uniform surface-plasma modes in thin metallic cylindrical shells,” IEEE J. Quantum Electron. QE-12, 525–533 (1992).
    [CrossRef]
  13. J. J. Burke, G. I. Stegeman, T. Tamir, “Surface polariton-like waves guided by lossy metal films,” Phys. Rev. 833, 5186–5201 (1986).
  14. R. Englman, R. Ruppin, “Optical lattice vibrations in finite ionic crystals,” J. Phys. C 1, 1515–1531 (1968).
    [CrossRef]
  15. J. C. Ashley, L. C. Emerson, “Dispersion relations for non-radiative surface plasmons on cylinders,” Surf. Sci. 41, 615–618 (1974).
    [CrossRef]
  16. G. C. Aers, A. D. Boardman, B. V. Paranjape, “Non-radiative surface plasmon-polariton modes of inhomogeneous metal circular cylinders,” J. Phys. F 10, 53–65 (1980).
    [CrossRef]
  17. C. A. Pfeiffer, E. N. Economou, K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
    [CrossRef]
  18. H. Khosravi, D. R. Tilley, R. Louden, “Surface polaritons in cylindrical optical fibers,” J. Opt. Soc. Am. A 8, 112–122 (1991).
    [CrossRef]

1992

S. J. Al-Bader, M. Imtaar, “Azimuthally uniform surface-plasma modes in thin metallic cylindrical shells,” IEEE J. Quantum Electron. QE-12, 525–533 (1992).
[CrossRef]

1991

M. E. Caldwell, E. M. Yeatman, “Performance characteristics of surface plasmon liquid crystal light valve,” Electron. Lett. 27, 1471–1472 (1991).
[CrossRef]

H. Khosravi, D. R. Tilley, R. Louden, “Surface polaritons in cylindrical optical fibers,” J. Opt. Soc. Am. A 8, 112–122 (1991).
[CrossRef]

1989

Y. Nagano, K. Matsugi, M. Haraguchi, M. Fukui, “Optical response of semi-infinite and finite GaAs/Al0.3Ga0.7As superlattices,” J. Phys. Soc. Jpn. 58, 733–740 (1989).
[CrossRef]

1988

B. Rothenhausler, W. Knoll, “Surface plasmon microscopy,” Nature (London) 332, 615–617 (1988).
[CrossRef]

M. Fukui, K. Oda, “Studies on metal film growth through instantaneously observed attenuated total reflection spectra,” Appl. Surf. Sci. 33/34, 882–889 (1988).
[CrossRef]

1987

E. Yeatman, E. A. Ash, “Surface plasmon microscopy,” Electron. Lett. 23, 1091–1092 (1987).
[CrossRef]

1986

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface polariton-like waves guided by lossy metal films,” Phys. Rev. 833, 5186–5201 (1986).

1985

N. Tajima, M. Fukui, Y. Shintani, “In situ studies of oxidation of copper films by using ATR technique,” J. Phys. Soc. Jpn. 54, 4236–4240 (1985).
[CrossRef]

1984

Y. Yokota, M. Fukui, O. Tada, “Surface plasmon polaritons on n± type Si single crystal,” J. Phys. Soc. Jpn. 53, 2833–2836 (1984).
[CrossRef]

M. T. Flanagan, R. H. Pantell, “Surface plasmon resonance and immuno sensors,” Electron. Lett. 20, 968–970 (1984).
[CrossRef]

1981

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
[CrossRef]

1980

G. C. Aers, A. D. Boardman, B. V. Paranjape, “Non-radiative surface plasmon-polariton modes of inhomogeneous metal circular cylinders,” J. Phys. F 10, 53–65 (1980).
[CrossRef]

1974

C. A. Pfeiffer, E. N. Economou, K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

J. C. Ashley, L. C. Emerson, “Dispersion relations for non-radiative surface plasmons on cylinders,” Surf. Sci. 41, 615–618 (1974).
[CrossRef]

1968

R. Englman, R. Ruppin, “Optical lattice vibrations in finite ionic crystals,” J. Phys. C 1, 1515–1531 (1968).
[CrossRef]

Abelès, F.

F. Abelès, “Surface plasmon (SEW) phenomena,” in Electromagnetic Surface Excitations, R. F. Wallis, G. I. Stegeman, eds. (Springer-Verlag, Berlin, 1986), pp. 8–20.
[CrossRef]

Aers, G. C.

G. C. Aers, A. D. Boardman, B. V. Paranjape, “Non-radiative surface plasmon-polariton modes of inhomogeneous metal circular cylinders,” J. Phys. F 10, 53–65 (1980).
[CrossRef]

Al-Bader, S. J.

S. J. Al-Bader, M. Imtaar, “Azimuthally uniform surface-plasma modes in thin metallic cylindrical shells,” IEEE J. Quantum Electron. QE-12, 525–533 (1992).
[CrossRef]

Ash, E. A.

E. Yeatman, E. A. Ash, “Surface plasmon microscopy,” Electron. Lett. 23, 1091–1092 (1987).
[CrossRef]

Ashley, J. C.

J. C. Ashley, L. C. Emerson, “Dispersion relations for non-radiative surface plasmons on cylinders,” Surf. Sci. 41, 615–618 (1974).
[CrossRef]

Boardman, A. D.

G. C. Aers, A. D. Boardman, B. V. Paranjape, “Non-radiative surface plasmon-polariton modes of inhomogeneous metal circular cylinders,” J. Phys. F 10, 53–65 (1980).
[CrossRef]

Burke, J. J.

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface polariton-like waves guided by lossy metal films,” Phys. Rev. 833, 5186–5201 (1986).

Caldwell, M. E.

M. E. Caldwell, E. M. Yeatman, “Performance characteristics of surface plasmon liquid crystal light valve,” Electron. Lett. 27, 1471–1472 (1991).
[CrossRef]

Economou, E. N.

C. A. Pfeiffer, E. N. Economou, K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

Emerson, L. C.

J. C. Ashley, L. C. Emerson, “Dispersion relations for non-radiative surface plasmons on cylinders,” Surf. Sci. 41, 615–618 (1974).
[CrossRef]

Englman, R.

R. Englman, R. Ruppin, “Optical lattice vibrations in finite ionic crystals,” J. Phys. C 1, 1515–1531 (1968).
[CrossRef]

Flanagan, M. T.

M. T. Flanagan, R. H. Pantell, “Surface plasmon resonance and immuno sensors,” Electron. Lett. 20, 968–970 (1984).
[CrossRef]

Fukui, M.

Y. Nagano, K. Matsugi, M. Haraguchi, M. Fukui, “Optical response of semi-infinite and finite GaAs/Al0.3Ga0.7As superlattices,” J. Phys. Soc. Jpn. 58, 733–740 (1989).
[CrossRef]

M. Fukui, K. Oda, “Studies on metal film growth through instantaneously observed attenuated total reflection spectra,” Appl. Surf. Sci. 33/34, 882–889 (1988).
[CrossRef]

N. Tajima, M. Fukui, Y. Shintani, “In situ studies of oxidation of copper films by using ATR technique,” J. Phys. Soc. Jpn. 54, 4236–4240 (1985).
[CrossRef]

Y. Yokota, M. Fukui, O. Tada, “Surface plasmon polaritons on n± type Si single crystal,” J. Phys. Soc. Jpn. 53, 2833–2836 (1984).
[CrossRef]

Haraguchi, M.

Y. Nagano, K. Matsugi, M. Haraguchi, M. Fukui, “Optical response of semi-infinite and finite GaAs/Al0.3Ga0.7As superlattices,” J. Phys. Soc. Jpn. 58, 733–740 (1989).
[CrossRef]

Imtaar, M.

S. J. Al-Bader, M. Imtaar, “Azimuthally uniform surface-plasma modes in thin metallic cylindrical shells,” IEEE J. Quantum Electron. QE-12, 525–533 (1992).
[CrossRef]

Khosravi, H.

Knoll, W.

B. Rothenhausler, W. Knoll, “Surface plasmon microscopy,” Nature (London) 332, 615–617 (1988).
[CrossRef]

Liedberg, B.

C. Nylander, B. Liedberg, T. Lind, “Gas detection by means of surface plasmon resonance,” Sensors Actuators 3, 79–88 (1982/83).
[CrossRef]

Lind, T.

C. Nylander, B. Liedberg, T. Lind, “Gas detection by means of surface plasmon resonance,” Sensors Actuators 3, 79–88 (1982/83).
[CrossRef]

Louden, R.

Matsugi, K.

Y. Nagano, K. Matsugi, M. Haraguchi, M. Fukui, “Optical response of semi-infinite and finite GaAs/Al0.3Ga0.7As superlattices,” J. Phys. Soc. Jpn. 58, 733–740 (1989).
[CrossRef]

Nagano, Y.

Y. Nagano, K. Matsugi, M. Haraguchi, M. Fukui, “Optical response of semi-infinite and finite GaAs/Al0.3Ga0.7As superlattices,” J. Phys. Soc. Jpn. 58, 733–740 (1989).
[CrossRef]

Ngai, K. L.

C. A. Pfeiffer, E. N. Economou, K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

Nylander, C.

C. Nylander, B. Liedberg, T. Lind, “Gas detection by means of surface plasmon resonance,” Sensors Actuators 3, 79–88 (1982/83).
[CrossRef]

Oda, K.

M. Fukui, K. Oda, “Studies on metal film growth through instantaneously observed attenuated total reflection spectra,” Appl. Surf. Sci. 33/34, 882–889 (1988).
[CrossRef]

Pantell, R. H.

M. T. Flanagan, R. H. Pantell, “Surface plasmon resonance and immuno sensors,” Electron. Lett. 20, 968–970 (1984).
[CrossRef]

Paranjape, B. V.

G. C. Aers, A. D. Boardman, B. V. Paranjape, “Non-radiative surface plasmon-polariton modes of inhomogeneous metal circular cylinders,” J. Phys. F 10, 53–65 (1980).
[CrossRef]

Pfeiffer, C. A.

C. A. Pfeiffer, E. N. Economou, K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

Rothenhausler, B.

B. Rothenhausler, W. Knoll, “Surface plasmon microscopy,” Nature (London) 332, 615–617 (1988).
[CrossRef]

Ruppin, R.

R. Englman, R. Ruppin, “Optical lattice vibrations in finite ionic crystals,” J. Phys. C 1, 1515–1531 (1968).
[CrossRef]

Sarid, D.

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
[CrossRef]

Shintani, Y.

N. Tajima, M. Fukui, Y. Shintani, “In situ studies of oxidation of copper films by using ATR technique,” J. Phys. Soc. Jpn. 54, 4236–4240 (1985).
[CrossRef]

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface polariton-like waves guided by lossy metal films,” Phys. Rev. 833, 5186–5201 (1986).

Tada, O.

Y. Yokota, M. Fukui, O. Tada, “Surface plasmon polaritons on n± type Si single crystal,” J. Phys. Soc. Jpn. 53, 2833–2836 (1984).
[CrossRef]

Tajima, N.

N. Tajima, M. Fukui, Y. Shintani, “In situ studies of oxidation of copper films by using ATR technique,” J. Phys. Soc. Jpn. 54, 4236–4240 (1985).
[CrossRef]

Tamir, T.

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface polariton-like waves guided by lossy metal films,” Phys. Rev. 833, 5186–5201 (1986).

Tilley, D. R.

Yeatman, E.

E. Yeatman, E. A. Ash, “Surface plasmon microscopy,” Electron. Lett. 23, 1091–1092 (1987).
[CrossRef]

Yeatman, E. M.

M. E. Caldwell, E. M. Yeatman, “Performance characteristics of surface plasmon liquid crystal light valve,” Electron. Lett. 27, 1471–1472 (1991).
[CrossRef]

Yokota, Y.

Y. Yokota, M. Fukui, O. Tada, “Surface plasmon polaritons on n± type Si single crystal,” J. Phys. Soc. Jpn. 53, 2833–2836 (1984).
[CrossRef]

Appl. Surf. Sci.

M. Fukui, K. Oda, “Studies on metal film growth through instantaneously observed attenuated total reflection spectra,” Appl. Surf. Sci. 33/34, 882–889 (1988).
[CrossRef]

Electron. Lett.

M. T. Flanagan, R. H. Pantell, “Surface plasmon resonance and immuno sensors,” Electron. Lett. 20, 968–970 (1984).
[CrossRef]

E. Yeatman, E. A. Ash, “Surface plasmon microscopy,” Electron. Lett. 23, 1091–1092 (1987).
[CrossRef]

M. E. Caldwell, E. M. Yeatman, “Performance characteristics of surface plasmon liquid crystal light valve,” Electron. Lett. 27, 1471–1472 (1991).
[CrossRef]

IEEE J. Quantum Electron.

S. J. Al-Bader, M. Imtaar, “Azimuthally uniform surface-plasma modes in thin metallic cylindrical shells,” IEEE J. Quantum Electron. QE-12, 525–533 (1992).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. C

R. Englman, R. Ruppin, “Optical lattice vibrations in finite ionic crystals,” J. Phys. C 1, 1515–1531 (1968).
[CrossRef]

J. Phys. F

G. C. Aers, A. D. Boardman, B. V. Paranjape, “Non-radiative surface plasmon-polariton modes of inhomogeneous metal circular cylinders,” J. Phys. F 10, 53–65 (1980).
[CrossRef]

J. Phys. Soc. Jpn.

Y. Nagano, K. Matsugi, M. Haraguchi, M. Fukui, “Optical response of semi-infinite and finite GaAs/Al0.3Ga0.7As superlattices,” J. Phys. Soc. Jpn. 58, 733–740 (1989).
[CrossRef]

Y. Yokota, M. Fukui, O. Tada, “Surface plasmon polaritons on n± type Si single crystal,” J. Phys. Soc. Jpn. 53, 2833–2836 (1984).
[CrossRef]

N. Tajima, M. Fukui, Y. Shintani, “In situ studies of oxidation of copper films by using ATR technique,” J. Phys. Soc. Jpn. 54, 4236–4240 (1985).
[CrossRef]

Nature (London)

B. Rothenhausler, W. Knoll, “Surface plasmon microscopy,” Nature (London) 332, 615–617 (1988).
[CrossRef]

Phys. Rev.

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface polariton-like waves guided by lossy metal films,” Phys. Rev. 833, 5186–5201 (1986).

Phys. Rev. B

C. A. Pfeiffer, E. N. Economou, K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

Phys. Rev. Lett.

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
[CrossRef]

Sensors Actuators

C. Nylander, B. Liedberg, T. Lind, “Gas detection by means of surface plasmon resonance,” Sensors Actuators 3, 79–88 (1982/83).
[CrossRef]

Surf. Sci.

J. C. Ashley, L. C. Emerson, “Dispersion relations for non-radiative surface plasmons on cylinders,” Surf. Sci. 41, 615–618 (1974).
[CrossRef]

Other

F. Abelès, “Surface plasmon (SEW) phenomena,” in Electromagnetic Surface Excitations, R. F. Wallis, G. I. Stegeman, eds. (Springer-Verlag, Berlin, 1986), pp. 8–20.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a) Dispersion of the first seven hybrid modes, showing the evolution of the HEn1 modes into the lower branch surface modes. The core radius k0a = 30. (b) Dispersion of the three guided modes in (a). The modes remain guided for increased core radius.

Fig. 2
Fig. 2

(a) Dispersion of upper and lower branch modes for k0a = 5. Upper branch curves for n = 1, 2, 3 occur progressively away from the n = 0 curve, toward the n = 4 curve. Upper branch, antisymmetric modes are represented by solid curves and lower branch, symmetric modes by dashed curves. The dashed–dotted line represents the core refractive index of 1.515. (b) Attenuation of the upper and lower branch modes of (a). Curves for n = 1, 2, 3 are those between the curves n = 0 and n = 4.

Fig. 3
Fig. 3

(a) Dispersion of upper, antisymmetric (solid curves) and lower, symmetric (dashed curves) branch modes for k0a = 20. (b) Attenuation of the modes of (a).

Fig. 4
Fig. 4

(a) Dispersion of upper, antisymmetric (solid curves) and lower, symmetric (dashed curves) branch modes for k0a = 100. (b) Attenuation of the modes of (a).

Fig. 5
Fig. 5

(a) Dispersion (solid curves) and attenuation (dashed curves) of upper, antisymmetric branch modes for k0t = 0.1. (b) Dispersion (solid curves) and attenuation (dashed curves) of guided lower, symmetric branch modes for k0t = 0.1.

Fig. 6
Fig. 6

(a) Dispersion (solid curves) and attenuation (dashed curves) of upper, antisymmetric branch modes for k0t = 0.5. (b) Dispersion (solid curves) and attenuation (dashed curves) of lower, symmetric branch modes for k0t = 0.5.

Fig. 7
Fig. 7

Profile of Hϕ. The solid curve shows the imaginary part, and the dashed curve shows the real part of the profile. The magnitudes shown on the scale correspond to Ez = 1 at r = a. The mode index nθ = 1.506444 + i0.003663.

Equations (29)

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

2 E + k 2 E = 0 ,
2 H + k 2 H = 0 ,
[ E z H z E ϕ H ϕ ] = [ a 1 0 0 0 0 0 a 1 0 b 1 0 d 1 0 e 1 0 b 1 0 ] [ A 1 0 B 1 0 ] = M 1 [ A 1 0 B 1 0 ]
a 1 = I n ( p 1 r ) ,
b 1 = β n I n ( p 1 r ) p 1 2 r ,
d 1 = i ω μ I n ( p 1 r ) p 1 ,
e 1 = - i ω 1 I n ( p 1 r ) p 1 .
[ E z H z E ϕ H ϕ ] = [ a 2 a 2 0 0 0 0 a 2 a 2 b 2 b 2 d 2 d 2 e 2 e 2 f 2 f 2 ] [ A 2 A 2 B 2 B 2 ] = M 2 [ A 2 A 2 B 2 B 2 ] ,
a 2 = I n ( p 2 r ) ,
a 2 = K n ( p 2 r ) ,
b 2 = β n I n ( p 2 r ) p 2 2 r ,
b 2 = β n K n ( p 2 r ) p 2 2 r ,
d 2 = i ω μ I n ( p 2 r ) p 2 ,
d 2 = i ω μ K n ( p 2 r ) p 2 ,
e 2 = - i ω 2 I n ( p 2 r ) p 2 ,
e 2 = - i ω 2 K n ( p 2 r ) p 2 ,
f 2 = β n I n ( p 2 r ) p 2 2 r ,
f 2 = β n K n ( p 2 r ) p 2 2 r .
[ E z H z E ϕ H ϕ ] = [ a 3 0 0 0 0 0 a 3 0 b 3 0 d 3 0 e 3 0 b 3 0 ] [ A 3 0 B 3 0 ] = M 3 [ A 3 0 B 3 0 ] ,
a 3 = K n ( p 3 r ) ,
b 3 = - β n K n ( p 3 r ) p 3 2 r ,
d 3 = - i ω μ K n ( p 3 r ) p 3 ,
e 3 = i ω 3 K n ( p 3 r ) p 3 ,
p t 2 = k 0 2 ( 0 - t ) ,
M 1 ( r = a ) [ A 1 0 B 1 0 ] = M 2 ( r = a ) [ A 2 A 2 B 2 B 2 ] ,
M 2 ( r = a + t ) [ A 2 A 2 B 2 B 2 ] = M 3 ( r = a + t ) [ A 3 0 B 3 0 ] ,
M 1 ( r = a ) [ A 1 0 B 1 0 ] = M 2 ( r = a ) [ M 2 ( r = a + t ) ] - 1 M 3 ( r = a + t ) [ A 3 0 B 3 0 ] ,
[ a 1 0 - M 11 - M 13 0 a 1 - M 21 - M 23 b 1 d 1 - M 31 - M 33 e 1 f 1 - M 41 - M 43 ] [ A 1 B 1 A 3 B 3 ] = 0 ,
M = M 2 ( r = a ) [ M 2 ( r = a + t ) ] - 1 - M 3 ( r = a + t ) .

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