Abstract

Planar optical waveguides consisting of thin dielectric films with metal cladding have been investigated theoretically and experimentally. A computer program was devised to provide the phase and attenuation constants and wavefunctions for TE and TM modes in symmetric and asymmetric guides. Approximate expressions suitable for slide-rule calculation were also derived. Numerical results and illustrations are given for films of photoresist with Al, Ag, and Au cladding. Direct measurements of the attenuation and phase constants at 0.633 μm of numerous experimental waveguides are in reasonable agreement with theory. Attenuations <1 dB/cm, which is sufficiently small for application in devices, were measured. Calculated wavefunctions illustrate the mismatch of modes at transitions between unclad and metal-clad waveguides. Experimentally, we find substantial losses at such abrupt junctions. They can be overcome by simple tapered transitions.

© 1974 Optical Society of America

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References

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  1. Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, Appl. Phys. Lett. 21, 291 (1972).
    [Crossref]
  2. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).
  3. D. F. Nelson, J. McKenna, J. Appl. Phys. 38, 4057 (1967).
    [Crossref]
  4. D. Marcuse, Bell Syst. Tech. J. 52, 63 (1973).
  5. J. J. Burke, Appl. Opt. 9, 2444 (1970).
    [Crossref] [PubMed]
  6. T. Takano, J. Hamasaki, IEEE J. Quantum Electron. QE-8, 206 (1972).
    [Crossref]
  7. T. E. Batchman, S. C. Rashleigh, IEEE J. Quantum Electron. QE-8, 848 (1972).
    [Crossref]
  8. A. Otto, W. Sohler, Opt. Commun. 3, 254 (1971).
    [Crossref]
  9. E. M. Garmire, H. Stoll, IEEE J. Quantum Electron. QE-8, 763 (1972).
    [Crossref]
  10. A. Reisinger, Appl. Opt. 12, 1015 (1973).
    [Crossref] [PubMed]
  11. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 516; R. H. Ritchie, Surface Science 34, 1 (1973).
    [Crossref]
  12. D. E. Gray, ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1963).
  13. E. A. Chandross, BTL; private communication.
  14. R. Ulrich, H. P. Weber, Appl. Opt. 11, 428 (1972).
    [Crossref] [PubMed]
  15. P. K. Tien, Appl. Opt. 10, 2395 (1971).
    [Crossref] [PubMed]
  16. H. P. Weber, F. A. Dunn, W. N. Leibolt, Appl. Opt. 12, 755 (1973).
    [Crossref] [PubMed]

1973 (3)

1972 (5)

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

R. Ulrich, H. P. Weber, Appl. Opt. 11, 428 (1972).
[Crossref] [PubMed]

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

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

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, Appl. Phys. Lett. 21, 291 (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)

1967 (1)

D. F. Nelson, J. McKenna, J. Appl. Phys. 38, 4057 (1967).
[Crossref]

Batchman, T. E.

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

Burke, J. J.

Chandross, E. A.

E. A. Chandross, BTL; private communication.

Chiba, K.

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

Dunn, F. A.

Furuya, K.

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

Garmire, E. M.

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

Hakuta, M.

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

Hamasaki, J.

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

Hasumi, R.

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

Leibolt, W. N.

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 52, 63 (1973).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

McKenna, J.

D. F. Nelson, J. McKenna, J. Appl. Phys. 38, 4057 (1967).
[Crossref]

Nelson, D. F.

D. F. Nelson, J. McKenna, J. Appl. Phys. 38, 4057 (1967).
[Crossref]

Otto, A.

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

Rashleigh, S. C.

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

Reisinger, A.

Sohler, W.

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

Stoll, H.

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

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 516; R. H. Ritchie, Surface Science 34, 1 (1973).
[Crossref]

Suematsu, Y.

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

Takano, T.

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

Tien, P. K.

Ulrich, R.

Weber, H. P.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

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

Bell Syst. Tech. J. (1)

D. Marcuse, Bell Syst. Tech. J. 52, 63 (1973).

IEEE J. Quantum Electron. (3)

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

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

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

J. Appl. Phys. (1)

D. F. Nelson, J. McKenna, J. Appl. Phys. 38, 4057 (1967).
[Crossref]

Opt. Commun. (1)

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

Other (4)

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 516; R. H. Ritchie, Surface Science 34, 1 (1973).
[Crossref]

D. E. Gray, ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1963).

E. A. Chandross, BTL; private communication.

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Figures (11)

Fig. 1
Fig. 1

(a) Cross section of a planar waveguide with K1 > K2 > K3, (b) air/polymer/glass (APG) guide, (c) air/polymer/metal (APM) guide, (d) metal/polymer/glass (MPG) guide, (e) metal/polymer/metal (MPM) guide.

Fig. 2
Fig. 2

(β/k) vs kd for APG guide.

Fig. 3
Fig. 3

Normalized wavefunction profiles (a) E y (x) for TE0,1 and (b) H y (x) for TM0,1 modes of the APG guide with kd = 10.

Fig. 4
Fig. 4

Complex propagation constants (a) (β′/k) and (b) (β″/k) vs kd for APAg guide.

Fig. 5
Fig. 5

Complex propagation constants (a) (β′/k) and (b) (β″/k) vs kd for APAl guide.

Fig. 6
Fig. 6

Complex propagation constants (a) (β′/k) and (b) (β″/k) vs kd for AgPG guide.

Fig. 7
Fig. 7

Normalized complex wavefunction profiles (a) Re E y (x) and (b) for ImE y (x) for TE, and (c) Re H y (x) and (d) Im H y (x) for TM modes of the APAg guide with kd = 10.

Fig. 8
Fig. 8

Complex propagation constants (a) (β′/k) and (b) (β″/k) vs kd for AgPAg guide.

Fig. 9
Fig. 9

Normalized complex wavefunction profiles (a) Re H y , and (b) Im H y for TM0,1 modes of the AgPAg guide with kd = 10.

Fig. 10
Fig. 10

Typical sliding prism attenuation measurement trace.

Fig. 11
Fig. 11

Taper transitions between unclad and metal-clad waveguides consisting of air (A), polymer (P), glass (G), metal (M), and transition dielectric (T) regions.

Tables (1)

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Table I Comparison of Measured and Calculated Parameters

Equations (40)

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K j = K j - i K j , j = 1 , 2 , 3 ,
K 1 > K 2 K 3 .
n j 2 = K j ,             K j = ( n j 2 - n j 2 ) ,             K j = 2 n j n j .
E y = A e - γ x ,             for 0 < x < ,
E y = A [ cos κ x - ( γ / κ ) sin κ x ] ,             for - d < x < 0 ,
E y = A [ cos κ d + ( γ / κ ) sin κ d ] × exp [ θ ( x + d ) ] ,             for - < x < - d ,
H x = - ( i / ω μ 0 ) ( E y / z ) ,
H z = ( i / ω μ 0 ) ( E y / x ) ,
k = ( ω / c ) = ( 2 π / λ )
γ 2 = β 2 - K 2 k 2 ,
θ 2 = β 2 - K 3 k 2 ,
κ 2 = K 1 k 2 - β 2 ,
tan κ d = κ ( γ + θ ) / ( κ 2 - γ θ ) ,
P = ½ Re ( β * ω μ 0 - E y 2 d x ) ,
H y = D e - γ x ,             0 < x < ,
H y = D [ cos κ x - ( K 1 / K 2 ) ( γ / κ ) sin κ x ] ,             - d < x < 0 ,
H y = D [ cos κ d + ( K 1 / K 2 ) ( γ / κ ) sin κ d ] × exp [ θ ( x + d ) ] ,             - < x < - d ,
E x = ( i / K j ω 0 ) ( H y / z ) ,
E z = - ( i / K j ω 0 ) ( H y / x ) ,
tan κ d = K 1 κ ( K 3 γ + K 2 θ ) / ( K 2 K 3 κ 2 - K 1 2 γ θ )
P = ½ Re ( β ω 0 - K j - 1 H y 2 d x ) .
k d = ( K 1 - B ) - 1 / 2 { arctan f [ ( B - K 2 ) / ( K 1 - B ) ] 1 / 2 + arctan g [ ( B - K 3 ) / ( K 1 - B ) ] 1 / 2 + ν π } ,
B = ( β / k ) 2
f = g = 1 ,             for TE modes ,
f = K 1 / K 2 ,             g = K 1 / K 3 ,             for TM modes .
arctan [ ( u + v ) / ( 1 - u v ) ] = arctan u + arctan v
k d = ( K 1 - K 2 ) - 1 / 2 { arctan g [ ( K 2 - K 3 ) / ( K 1 - K 2 ) ] 1 / 2 + ν π } .
K 2 B K 1 .
arctan u = ( π / 2 ) - arctan ( u - 1 )
k d = ( K 1 - B ) - 1 / 2 { ( ν + 1 ) π - arctan f - 1 [ ( K 1 - B ) / ( B - K 2 ) ] 1 / 2 - arctan g - 1 [ ( K 1 - B ) / ( B - K 3 ) ] 1 / 2 }
( β / k ) = K 1 1 / 2 ( 1 + 1 2 K 1 [ ( ν + 1 ) π / k d ] 2 { 1 - ( 2 / k d ) Re [ ( K 1 - K 2 ) - 1 / 2 f - 1 + ( K 1 - K 3 ) - 1 / 2 g - 1 ] } ) ,
( β / k ) = - K 1 - 1 / 2 ( ν + 1 ) 2 π 2 ( k d ) - 3 Im [ ( K 1 - K 2 ) - 1 / 2 f - 1 + ( K 1 - K 3 ) - 1 / 2 g - 1 ] .
K 3 = - K ¯ 3
k d = ( B - K 1 ) - 1 / 2 { arctanh ( K 1 / K ¯ 3 ) [ ( B + K ¯ 3 ) / ( B - K 1 ) ] 1 / 2 - arctanh ( K 1 / K 2 ) × [ ( B - K 2 ) / ( B - K 1 ) ] 1 / 2 - i ν π }
B = K 1 K 3 / ( K 1 + K 3 ) .
( β / k ) = [ K 1 K 3 / ( K 1 + K 3 ) ] 1 / 2
( β / β ) = K 1 K 3 / 2 K 3 ( K 1 + K 3 ) .
B = K 2 K 3 / ( K 2 + K 3 ) .
2 arctanh u - i π = 2 arctanh ( u - 1 )
B [ 2 K 1 / ( k d K 3 ) ] 2 .

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