Abstract

Attenuation characteristics of a metal-clad four-layer thin-film optical waveguide are presented. Guided-wave losses are calculated as functions of isolation-layer thickness, type of metal, and isolation-layer refractive index. The TM polarized waves were found to exhibit an absorption peak as a function of isolation thickness. This peak is interpreted as resonant coupling to a lossy surface-plasma wave.

© 1974 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. N. Polky and J. H. Harris, Appl. Phys. Lett. 21, 307 (1971); D. P. Gia Russo and J. H. Harris, Appl. Opt. 10, 2786L (1971); W. S. C. Chang and K. W. Loh, IEEE J. Quantum Electron. 8, 463 (1972).
    [Crossref]
  2. American Institute of Physics Handbook, edited by D. E. Gray (McGraw–Hill, New York, 1963), Ch. 6g.
  3. T. Takano and J. Hamasaki, IEEE J. Quantum Electron. 8, 206 (1972).
    [Crossref]
  4. E. Garmire and H. Stoll, IEEE J. Quantum Electron. 8, 763 (1972).
    [Crossref]
  5. T. E. Batchman and S. C. Rashleigh, IEEE J. Quantum Electron. 8, 848 (1972).
    [Crossref]
  6. Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, and R. Hasumi, Appl. Phys. Lett. 21, 291 (1972).
    [Crossref]
  7. J. Zenneck, Ann. Phys. (Paris) 23, 846 (1907); A. Otto, Z. Phys. 216, 398 (1968).
    [Crossref]
  8. R. Shubert and J. Harris, J. Opt. Soc. Am. 61, 154 (1971).
    [Crossref]
  9. System/360 Scientific Subroutine Package (International Business Machines Corp., White Plains, N.Y., 1968), p. 217.
  10. A. Reisinger, Appl. Opt. 12, 1015 (1973).
    [Crossref] [PubMed]
  11. R. F. Harrington, Time Harmonic Electromagnetic Fields (McGraw–Hill, New York, 1961), p. 129.

1973 (1)

1972 (4)

T. Takano and J. Hamasaki, IEEE J. Quantum Electron. 8, 206 (1972).
[Crossref]

E. Garmire and H. Stoll, IEEE J. Quantum Electron. 8, 763 (1972).
[Crossref]

T. E. Batchman and S. C. Rashleigh, IEEE J. Quantum Electron. 8, 848 (1972).
[Crossref]

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, and R. Hasumi, Appl. Phys. Lett. 21, 291 (1972).
[Crossref]

1971 (2)

R. Shubert and J. Harris, J. Opt. Soc. Am. 61, 154 (1971).
[Crossref]

J. N. Polky and J. H. Harris, Appl. Phys. Lett. 21, 307 (1971); D. P. Gia Russo and J. H. Harris, Appl. Opt. 10, 2786L (1971); W. S. C. Chang and K. W. Loh, IEEE J. Quantum Electron. 8, 463 (1972).
[Crossref]

1907 (1)

J. Zenneck, Ann. Phys. (Paris) 23, 846 (1907); A. Otto, Z. Phys. 216, 398 (1968).
[Crossref]

Batchman, T. E.

T. E. Batchman and S. C. Rashleigh, IEEE J. Quantum Electron. 8, 848 (1972).
[Crossref]

Chiba, K.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, and R. Hasumi, Appl. Phys. Lett. 21, 291 (1972).
[Crossref]

Furuya, K.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, and R. Hasumi, Appl. Phys. Lett. 21, 291 (1972).
[Crossref]

Garmire, E.

E. Garmire and H. Stoll, IEEE J. Quantum Electron. 8, 763 (1972).
[Crossref]

Hakuta, M.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, and R. Hasumi, Appl. Phys. Lett. 21, 291 (1972).
[Crossref]

Hamasaki, J.

T. Takano and J. Hamasaki, IEEE J. Quantum Electron. 8, 206 (1972).
[Crossref]

Harrington, R. F.

R. F. Harrington, Time Harmonic Electromagnetic Fields (McGraw–Hill, New York, 1961), p. 129.

Harris, J.

Harris, J. H.

J. N. Polky and J. H. Harris, Appl. Phys. Lett. 21, 307 (1971); D. P. Gia Russo and J. H. Harris, Appl. Opt. 10, 2786L (1971); W. S. C. Chang and K. W. Loh, IEEE J. Quantum Electron. 8, 463 (1972).
[Crossref]

Hasumi, R.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, and R. Hasumi, Appl. Phys. Lett. 21, 291 (1972).
[Crossref]

Polky, J. N.

J. N. Polky and J. H. Harris, Appl. Phys. Lett. 21, 307 (1971); D. P. Gia Russo and J. H. Harris, Appl. Opt. 10, 2786L (1971); W. S. C. Chang and K. W. Loh, IEEE J. Quantum Electron. 8, 463 (1972).
[Crossref]

Rashleigh, S. C.

T. E. Batchman and S. C. Rashleigh, IEEE J. Quantum Electron. 8, 848 (1972).
[Crossref]

Reisinger, A.

Shubert, R.

Stoll, H.

E. Garmire and H. Stoll, IEEE J. Quantum Electron. 8, 763 (1972).
[Crossref]

Suematsu, Y.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, and R. Hasumi, Appl. Phys. Lett. 21, 291 (1972).
[Crossref]

Takano, T.

T. Takano and J. Hamasaki, IEEE J. Quantum Electron. 8, 206 (1972).
[Crossref]

Zenneck, J.

J. Zenneck, Ann. Phys. (Paris) 23, 846 (1907); A. Otto, Z. Phys. 216, 398 (1968).
[Crossref]

Ann. Phys. (Paris) (1)

J. Zenneck, Ann. Phys. (Paris) 23, 846 (1907); A. Otto, Z. Phys. 216, 398 (1968).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

J. N. Polky and J. H. Harris, Appl. Phys. Lett. 21, 307 (1971); D. P. Gia Russo and J. H. Harris, Appl. Opt. 10, 2786L (1971); W. S. C. Chang and K. W. Loh, IEEE J. Quantum Electron. 8, 463 (1972).
[Crossref]

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, and R. Hasumi, Appl. Phys. Lett. 21, 291 (1972).
[Crossref]

IEEE J. Quantum Electron. (3)

T. Takano and J. Hamasaki, IEEE J. Quantum Electron. 8, 206 (1972).
[Crossref]

E. Garmire and H. Stoll, IEEE J. Quantum Electron. 8, 763 (1972).
[Crossref]

T. E. Batchman and S. C. Rashleigh, IEEE J. Quantum Electron. 8, 848 (1972).
[Crossref]

J. Opt. Soc. Am. (1)

Other (3)

System/360 Scientific Subroutine Package (International Business Machines Corp., White Plains, N.Y., 1968), p. 217.

R. F. Harrington, Time Harmonic Electromagnetic Fields (McGraw–Hill, New York, 1961), p. 129.

American Institute of Physics Handbook, edited by D. E. Gray (McGraw–Hill, New York, 1963), Ch. 6g.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

(a) Three-layer planar dielectric waveguiding structure. (b) Two-layer lossy waveguide structure, with the metal considered as a high-loss dielectric.

Fig. 2
Fig. 2

Four-layer waveguide structure. The form of the potential in each region is shown (see Appendix A). Optical energy in most cases is concentrated in layer 2.

Fig. 3
Fig. 3

Wave attenuation vs isolation-layer thickness, t3. Values for both TE and TM are included. The solid line is based on an exact solution, the dashed line is a first-order solution. Four-layer waveguide with a sodium fluoride isolation layer and a gold electrode.

Fig. 4
Fig. 4

TM-wave attenuation vs isolation-layer thickness for different metals. The curves are for gold and aluminum electrodes, with all other parameters constant.

Fig. 5
Fig. 5

Wave attenuation vs isolation-layer thickness for three different isolation materials. In each case, the electrode is gold.

Fig. 6
Fig. 6

Distribution of |Hy| in a four-layer waveguide for TM waves. Three values of t3 are considered. Guiding-layer boundaries are shown as dashed lines and the metal–isolation-layer interface is at the sharp peak of |Hy| for each curve.

Fig. 7
Fig. 7

|Ey| for a TE wave on the same structure as Fig. 6 with t3 = 0.14 μm. Results for t3 = 0.06 μm, 0.1 μm, are essentially the same, and are not shown.

Fig. 8
Fig. 8

Real part of nw plotted vs t3 for TM waves on a four-layer structure with t2 = 1.4 μm and t2 = ∞. The absorption peak is superimposed on this plot as a dashed line with no relation to the ordinate scale.

Tables (1)

Tables Icon

Table I The complex guided-wave refractive index nw of the structure in Fig. 1(b) for various metal–dielectric combinations. These values were calculated by use of Eq. (2). The attenuation in dB/cm is 8.7 × 105 times Im(nw). All values are for λ0 = 0.6328 μm.

Equations (30)

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

tan - 1 K 1 i K 2 + tan - 1 K 3 i K 2 - U 2 t 2 = m π ,             m = 0 , 1 , 2 ,
K n = { U n - TE , U n / n - TM ,             n = 1 , 2 , 3
U n = 2 π λ 0 ( n n 2 - n w 2 ) 1 2 ,
n w = [ n 1 2 ( n 2 4 - n 2 2 n 1 2 ) ( n 2 4 - n 1 4 ) ] 1 2
tan - 1 K 1 i K 2 + tan - 1 [ K 3 K 2 tan ( tan - 1 ( K 4 i K 3 ) - U 3 t 3 ) ] - U 2 t 2 = m π ,             m = 0 , 1 , 2 ,
t 2 = { tan - 1 K 1 i K 2 + tan - 1 [ K 3 K 2 tan ( tan - 1 ( K 4 i K 2 ) - U 3 t 3 ) ] - m π } / U 2 ,
D 1 , 4 ( k 0 + Δ k ) = D 1 , 4 | k = k 0 + Δ k 1 ! D 1 , 4 k | k = k 0 + ( Δ k ) 2 2 ! 2 D 1 , 4 2 k | k = k 0 + ,
( Δ k ) n ( n ) D 1 , 4 k ( n ) | k = k 0 Δ k D 1 , 4 k | k = k 0             ( n = 2 , 3 , )
k w k 0 - D 1 , 4 D 1 , 4 / k | k = k 0 .
k w [ k 0 - D 1 , 4 D 1 , 4 / k | k = k 0 ] - D 1 , 4 D 1 , 4 / k | k = k w .
E = - × F + i w A - 1 i ω ( · A ) ,
H = × A + i w F - 1 i ω μ ( · F ) .
ψ 1 = A 1 e - i U 1 z , ψ 2 = A 2 cos ( U 2 z + ϕ 2 ) , ψ n - 1 = A n - 1 cos ( U n - 1 z + ϕ n - 1 ) , ψ n = A n e i U n z ,
1 n i 2 ψ i ( z i ) z = 1 n i + 1 2 ψ i + 1 ( z i ) z             and             ψ i ( z i ) = ψ i + 1 ( z i ) ,             i = 1 , 2 , , n - 1.
A n = A n - 1 cos ( U n - 1 z n - 1 + ϕ n ) e i U n z n - 1 ,
ϕ n - 1 + U n - 1 z n - 1 - tan - 1 K n i K n - 1 - m π = 0 ,             m = 0 , 1 , 2 ,
A i + 1 = A i cos ( U i z i + ϕ i ) cos ( U i + 1 z i + ϕ i + 1 ) ,
ϕ i + 1 = - U i + 1 z i + tan - 1 [ K i K i + 1 tan ( U i z i + ϕ i ) ] ,
A 2 = A 1 cos ϕ 2 ,
ϕ 2 = - tan - 1 ( K 1 i K 2 ) ,
K i = U i / n i 2 .
ψ 3 = A 1 i K 2 ( K 1 2 - K 2 2 ) 1 2 cos ( U 2 z 2 + tan - 1 K 1 i K 2 ) e i U 3 ( z - z 2 ) .
D 1 , 4 = e i U 4 z 3 [ ( K 3 + K 3 ) e - i U 3 z 3 D 1 , 3 + ( K 3 - K 4 ) e - i U 3 z 3 D 1 , 3 ] .
A sin α - B cos α = ( A 2 + B 2 ) 1 2 sin ( α - tan - 1 B A ) , A sin α + B cos α = ( A 2 + B 2 ) 1 2 cos ( α - tan - 1 A B ) ,
D 1 , 4 = 2 i e i U 4 z 3 ( K 3 2 - K 3 2 ) 1 2 ( K 1 2 - K 2 2 ) 1 2 × ( K 2 2 cos 2 ϕ + K 3 2 sin 2 ϕ ) 1 2 sin { U 2 t 2 - tan - 1 K 1 i K 2 + tan - 1 [ K 3 K 2 tan ( U 3 t 3 - tan - 1 K 4 i K 3 ) ] } ,
ϕ = U 3 t 3 - tan - 1 K 4 i K 3 .
D 1 , 4 k = - i z 3 k U 4 D 1 , 4 + e i U 4 z 3 × e - i U 4 z 3 ( K 3 + K 4 ) [ D 1 , 3 k - D 1 , 3 k ( 1 K 3 K 4 - i z 3 U 3 ) ] + e i U 4 z 3 e i U 3 z 3 ( K 3 - K 4 ) [ D 1 , 3 k + D 1 , 3 ( 1 K 3 K 4 - i z 3 U 3 ) ] ,
z 3 = t 2 + t 3 .
D 1 , 3 k = - i t 2 k U 3 D 1 , 3 + e i U 3 t 2 e - i U 2 t 2 k [ ( K 1 + K 2 ) × ( K 2 + K 3 ) ( i t 2 U 2 ) - ( 1 K 1 + 1 K 2 ) ( 1 K 2 - 1 K 3 ) ] + e i U 3 t 2 e i U 2 t 2 k [ ( K 1 - K 2 ) ( K 2 - K 3 ) × ( - i t 2 U 2 ) + ( 1 K 2 - 1 K 1 ) ( 1 K 3 - 1 K 2 ) ] .
D 1 , 3 = ( K 1 + K 2 ) ( K 2 + K 3 ) e - i U 2 t 2 + ( K 1 - K 2 ) ( K 2 - K 3 ) e i U 3 t 2