Abstract

If the real part 1′ of the complex permittivity ^1 = 1′ − j∊1″ of the metal cladding of a dielectric optical waveguide is positive, well-guided modes can be supported by the dielectric film even if 1′ is greater than the permittivity of the dielectric film. The attenuation and phase characteristics and the field distributions of the guided modes are discussed for a number of guiding structures, and it is shown that far from cutoff most of the modes exhibit similar properties to those modes supported by the film when the metal cladding has a negative 1′. The low order TM modes exhibit different characteristics due to a coupling between them and the surface wave supported by the metal: dielectric interface. This guide has an additional interesting characteristic in that the phase velocities of the TE0 and TM0 modes can be made equal.

© 1976 Optical Society of America

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References

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  1. T. Takano, J. Hamasaki, IEEE J. Quantum Electron. QE-8, 206 (1972).
    [CrossRef]
  2. A. Otto, W. Sohler, Opt. Commun. 3, 254 (1971).
    [CrossRef]
  3. E. M. Garmire, H. Stoll, IEEE J. Quantum Electron. QE-8, 763 (1972).
    [CrossRef]
  4. T. E. Batchman, S. C. Rashleigh, IEEE J. Quantum Electron. QE-8, 848 (1972).
    [CrossRef]
  5. A. Reisinger, Appl. Opt. 12, 1015 (1973).
    [CrossRef] [PubMed]
  6. I. P. Kaminow, W. L. Mammel, H. P. Weber, Appl. Opt. 13, 396 (1974).
    [CrossRef] [PubMed]
  7. P. K. Tien, Appl. Opt. 10, 2395 (1971).
    [CrossRef] [PubMed]
  8. R. Ulrich, W. Prettl, Appl. Phys. 1, 55 (1973).
    [CrossRef]
  9. The modes become cutoff when the magnitude of the field in the cladding regions 1 or 3 ceases to decay exponentially away from the dielectric core.
  10. S. C. Rashleigh, “Planar Metal-clad Dielectric Waveguides,” PhD Dissertation, University of Queensland, Brisbane, Australia (1975).
  11. H. E. M. Barlow, A. C. Cullin, Proc. IEE 100, part 3, (68), 329 (1953).
  12. A. Otto, Z. Phys. 216, 398 (1968).
    [CrossRef]
  13. W. Steinmann, Phys. Status Solidi 28, 437 (1968).
    [CrossRef]
  14. A. Otto, Phys. Status Solidi 42, K37 (1970).
    [CrossRef]
  15. P. M. Van Den Berg, J. C. M. Borburgh, Appl. Phys. 3, 55 (1974).
    [CrossRef]
  16. D. E. Gray, Ed, American Institute of Physics Handbook (McGraw-Hill, New York, 1963), pp. 6.103–6.122.

1974 (2)

I. P. Kaminow, W. L. Mammel, H. P. Weber, Appl. Opt. 13, 396 (1974).
[CrossRef] [PubMed]

P. M. Van Den Berg, J. C. M. Borburgh, Appl. Phys. 3, 55 (1974).
[CrossRef]

1973 (2)

A. Reisinger, Appl. Opt. 12, 1015 (1973).
[CrossRef] [PubMed]

R. Ulrich, W. Prettl, Appl. Phys. 1, 55 (1973).
[CrossRef]

1972 (3)

T. Takano, J. Hamasaki, IEEE J. Quantum Electron. QE-8, 206 (1972).
[CrossRef]

E. M. Garmire, H. Stoll, IEEE J. Quantum Electron. QE-8, 763 (1972).
[CrossRef]

T. E. Batchman, S. C. Rashleigh, IEEE J. Quantum Electron. QE-8, 848 (1972).
[CrossRef]

1971 (2)

A. Otto, W. Sohler, Opt. Commun. 3, 254 (1971).
[CrossRef]

P. K. Tien, Appl. Opt. 10, 2395 (1971).
[CrossRef] [PubMed]

1970 (1)

A. Otto, Phys. Status Solidi 42, K37 (1970).
[CrossRef]

1968 (2)

A. Otto, Z. Phys. 216, 398 (1968).
[CrossRef]

W. Steinmann, Phys. Status Solidi 28, 437 (1968).
[CrossRef]

1953 (1)

H. E. M. Barlow, A. C. Cullin, Proc. IEE 100, part 3, (68), 329 (1953).

Barlow, H. E. M.

H. E. M. Barlow, A. C. Cullin, Proc. IEE 100, part 3, (68), 329 (1953).

Batchman, T. E.

T. E. Batchman, S. C. Rashleigh, IEEE J. Quantum Electron. QE-8, 848 (1972).
[CrossRef]

Borburgh, J. C. M.

P. M. Van Den Berg, J. C. M. Borburgh, Appl. Phys. 3, 55 (1974).
[CrossRef]

Cullin, A. C.

H. E. M. Barlow, A. C. Cullin, Proc. IEE 100, part 3, (68), 329 (1953).

Garmire, E. M.

E. M. Garmire, H. Stoll, IEEE J. Quantum Electron. QE-8, 763 (1972).
[CrossRef]

Hamasaki, J.

T. Takano, J. Hamasaki, IEEE J. Quantum Electron. QE-8, 206 (1972).
[CrossRef]

Kaminow, I. P.

Mammel, W. L.

Otto, A.

A. Otto, W. Sohler, Opt. Commun. 3, 254 (1971).
[CrossRef]

A. Otto, Phys. Status Solidi 42, K37 (1970).
[CrossRef]

A. Otto, Z. Phys. 216, 398 (1968).
[CrossRef]

Prettl, W.

R. Ulrich, W. Prettl, Appl. Phys. 1, 55 (1973).
[CrossRef]

Rashleigh, S. C.

T. E. Batchman, S. C. Rashleigh, IEEE J. Quantum Electron. QE-8, 848 (1972).
[CrossRef]

S. C. Rashleigh, “Planar Metal-clad Dielectric Waveguides,” PhD Dissertation, University of Queensland, Brisbane, Australia (1975).

Reisinger, A.

Sohler, W.

A. Otto, W. Sohler, Opt. Commun. 3, 254 (1971).
[CrossRef]

Steinmann, W.

W. Steinmann, Phys. Status Solidi 28, 437 (1968).
[CrossRef]

Stoll, H.

E. M. Garmire, H. Stoll, IEEE J. Quantum Electron. QE-8, 763 (1972).
[CrossRef]

Takano, T.

T. Takano, J. Hamasaki, IEEE J. Quantum Electron. QE-8, 206 (1972).
[CrossRef]

Tien, P. K.

Ulrich, R.

R. Ulrich, W. Prettl, Appl. Phys. 1, 55 (1973).
[CrossRef]

Van Den Berg, P. M.

P. M. Van Den Berg, J. C. M. Borburgh, Appl. Phys. 3, 55 (1974).
[CrossRef]

Weber, H. P.

Appl. Opt. (3)

Appl. Phys. (2)

R. Ulrich, W. Prettl, Appl. Phys. 1, 55 (1973).
[CrossRef]

P. M. Van Den Berg, J. C. M. Borburgh, Appl. Phys. 3, 55 (1974).
[CrossRef]

IEEE J. Quantum Electron. (3)

T. Takano, J. Hamasaki, IEEE J. Quantum Electron. QE-8, 206 (1972).
[CrossRef]

E. M. Garmire, H. Stoll, IEEE J. Quantum Electron. QE-8, 763 (1972).
[CrossRef]

T. E. Batchman, S. C. Rashleigh, IEEE J. Quantum Electron. QE-8, 848 (1972).
[CrossRef]

Opt. Commun. (1)

A. Otto, W. Sohler, Opt. Commun. 3, 254 (1971).
[CrossRef]

Phys. Status Solidi (2)

W. Steinmann, Phys. Status Solidi 28, 437 (1968).
[CrossRef]

A. Otto, Phys. Status Solidi 42, K37 (1970).
[CrossRef]

Proc. IEE (1)

H. E. M. Barlow, A. C. Cullin, Proc. IEE 100, part 3, (68), 329 (1953).

Z. Phys. (1)

A. Otto, Z. Phys. 216, 398 (1968).
[CrossRef]

Other (3)

D. E. Gray, Ed, American Institute of Physics Handbook (McGraw-Hill, New York, 1963), pp. 6.103–6.122.

The modes become cutoff when the magnitude of the field in the cladding regions 1 or 3 ceases to decay exponentially away from the dielectric core.

S. C. Rashleigh, “Planar Metal-clad Dielectric Waveguides,” PhD Dissertation, University of Queensland, Brisbane, Australia (1975).

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Figures (13)

Fig. 1
Fig. 1

Geometry of the asymmetrical metal-clad waveguide. Propagation is in the z direction.

Fig. 2
Fig. 2

Real and imaginary parts of the wave function profile in the transverse direction for the surface wave supported by the (a) silver: dielectric and (b) germanium: dielectric interfaces. Refractive index of the dielectric is n = 1.615.

Fig. 3
Fig. 3

Attenuation coefficient vs core thickness for the chromium-clad waveguide for the case when 1′ < n22. Two values of n3 are shown.

Fig. 4
Fig. 4

Mode index vs core thickness for the chromium-clad waveguide for the case when 1′ < n22. Two values of n3 are shown.

Fig. 5
Fig. 5

Real and imaginary parts of the wave function profiles in the transverse direction for the TE0 and TE1 modes of the chromium-clad waveguide when 1′ < n22.

Fig. 6
Fig. 6

Real and imaginary parts of the wave function profiles in the transverse direction for the low order TM modes of the chromium-clad waveguide when 1′ < n22.

Fig. 7
Fig. 7

Attenuation coefficient vs core thickness for the germanium-clad waveguide for the case when 1′ > n22. The TM0 mode exists for vanishing t2, and the TMSW mode becomes cutoff for a nonzero t2.

Fig. 8
Fig. 8

Mode index vs core thickness for the germanium-clad waveguide for the case when 1′ > n22. The TM0 and TM1 curves are seen to cross over the TE0 and TE1 curves, respectively.

Fig. 9
Fig. 9

Real and imaginary parts of the wave function profiles in transverse direction for the TE0 and TE1 modes of the germanium-clad waveguide when 1′ > n22.

Fig. 10
Fig. 10

Real and imaginary parts of the wave function profiles in the transverse direction for the TM0 mode of the germanium clad-waveguide when 1′ > n22. Three values of t2 are shown.

Fig. 11
Fig. 11

Real part of the wave function profile in the transverse direction for the TMSW, TM1, and TM3 modes of the germanium-clad waveguide when 1′ > n22. Two values of t2, (a) t2 = 1.0 μm and (b) t2 = 5.0 μm, are shown.

Fig. 12
Fig. 12

Attenuation coefficient vs core thickness for the germanium-clad waveguide for the case when 1′ > n22 and n3 = 1.56. The absence of the TM1 mode is noticeable.

Fig. 13
Fig. 13

Mode index vs core thickness for the germanium-clad waveguide for the case when 1′ > n22 and n3 = 1.56. The TE modes become cutoff at β/k0 = n3, and only the curves for the TE0 and TM0 modes cross.

Tables (1)

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Table I Complex Relative Permittivities ^ 1 of Ag, Al, Ch, and Ge for λ0 = 0.6328 μma

Equations (3)

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ϕ 1 exp ( p x 1 x ) ,
p x 1 = [ ( β - j α ) 2 - ( 1 - j 1 ) k 0 2 ] 1 / 2 = [ ( β 2 - α 2 - 1 k 0 2 ) + j ( 1 k 0 2 - 2 α β ) ] 1 / 2 ,
p x 3 = [ ( β 2 - α 2 - n 3 2 k 0 2 ) - j 2 α β ] 1 / 2 .

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