Abstract

Coupling to optical waveguide modes was investigated by depositing two thin film layers on the hypotenuse of a rutile prism. Coupling efficiency was determined as a function of input beam angle for the three lowest order TE and TM modes. The coupling lineshape was found to agree with the predictions of a lossless, ray-optics analysis for all but the lowest order TM modes. This result is explained in terms of the relative effects of loss on the coupling efficiencies of the various modes.

© 1974 Optical Society of America

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References

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  1. P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
    [CrossRef]
  2. M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
    [CrossRef]
  3. P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1323 (1970).
    [CrossRef]
  4. R. Ulrich, J. Opt. Soc. Am. 60, 1337 (1970).
    [CrossRef]
  5. R. Ulrich, J. Opt. Soc. Am. 61, 1467 (1971).
    [CrossRef]
  6. J. E. Midwinter, IEEE J. Quantum Electron. QE-6, 583 (1970).
    [CrossRef]
  7. J. H. Harris, R. Shubert, IEEE Trans. Microwave Theory Tech. MTT-19, 269 (1971).
    [CrossRef]
  8. J. H. Harris, R. Shubert, J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
    [CrossRef]

1971 (2)

J. H. Harris, R. Shubert, IEEE Trans. Microwave Theory Tech. MTT-19, 269 (1971).
[CrossRef]

R. Ulrich, J. Opt. Soc. Am. 61, 1467 (1971).
[CrossRef]

1970 (5)

J. H. Harris, R. Shubert, J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
[CrossRef]

R. Ulrich, J. Opt. Soc. Am. 60, 1337 (1970).
[CrossRef]

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1323 (1970).
[CrossRef]

J. E. Midwinter, IEEE J. Quantum Electron. QE-6, 583 (1970).
[CrossRef]

1969 (1)

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Dakss, M. L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Harris, J. H.

J. H. Harris, R. Shubert, IEEE Trans. Microwave Theory Tech. MTT-19, 269 (1971).
[CrossRef]

J. H. Harris, R. Shubert, J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
[CrossRef]

Heidrich, P. F.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Kuhn, L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Martin, R. J.

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Midwinter, J. E.

J. E. Midwinter, IEEE J. Quantum Electron. QE-6, 583 (1970).
[CrossRef]

Polky, J. N.

Scott, B. A.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Shubert, R.

J. H. Harris, R. Shubert, IEEE Trans. Microwave Theory Tech. MTT-19, 269 (1971).
[CrossRef]

J. H. Harris, R. Shubert, J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
[CrossRef]

Tien, P. K.

P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1323 (1970).
[CrossRef]

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Ulrich, R.

R. Ulrich, J. Opt. Soc. Am. 61, 1467 (1971).
[CrossRef]

R. Ulrich, J. Opt. Soc. Am. 60, 1337 (1970).
[CrossRef]

P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1323 (1970).
[CrossRef]

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Appl. Phys. Lett. (2)

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. E. Midwinter, IEEE J. Quantum Electron. QE-6, 583 (1970).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. H. Harris, R. Shubert, IEEE Trans. Microwave Theory Tech. MTT-19, 269 (1971).
[CrossRef]

J. Opt. Soc. Am. (4)

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Figures (4)

Fig. 1
Fig. 1

Model for the prism–film coupler with plane-wave beam incident at angle θ3 from the z axis.

Fig. 2
Fig. 2

Experimental arrangement to measure angles at which laser beam L excites leaky modes in the prism–film coupled waveguide. Output power in a selected mode is detected using slit S and detector D.

Fig. 3
Fig. 3

Relative coupling efficiency vs input angle θ3 or effective index n for TE modes.

Fig. 4
Fig. 4

Relative coupling efficiency vs input angle θ3 or effective index n for TM modes.

Tables (3)

Tables Icon

Table I Comparison of Theoretical and Experimental Values of Effective Index n for n2 = 1.38, n1 = 2.324, W = 0.771 λ0, and S = 0.2 λ0 at λ0 = 6328 Å

Tables Icon

Table II Comparison of Calculated and Measured Linewidths at 50% Relative Efficiency

Tables Icon

Table III Reflection Coefficient Magnitude r and Sensitivity Function SF Line Center for Various Waveguide Modes

Equations (12)

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n = n 3 sin θ 3 .
2 k W ( n 1 2 n 2 ) 1 / 2 2 ξ 10 ( n ) 2 ξ 12 ( n ) 2 m π = 0 ,
ξ 10 ( n ) = tan 1 { ( q 1 / q 0 ) [ ( n 2 n 0 2 ) / ( n 1 2 n 2 ) ] 1 / 2 } ;
q l = { n l 2 for TM modes 1 for TM modes , l = 0,1,2,3.
R = r exp ( 2 i ξ 12 ( n ) ) = sinh [ k S ( n 2 n 2 2 ) 1 / 2 i ϕ ] sinh [ k S ( n 2 n 2 2 ) 1 / 2 + i ϕ + ] ,
ϕ ± = tan 1 [ q 1 q 2 ( n 2 n 2 2 n 1 2 n 2 ) 1 / 2 ] ± tan 1 [ q 3 q 2 ( n 2 n 2 2 n 3 2 n 2 ) 1 / 2 ] .
ξ 12 ( n ) tan 1 [ q 1 q 2 ( n 2 n 2 2 n 1 2 n 2 ) 1 / 2 ] ;
2 k W ( n 1 2 n 2 ) 1 / 2 2 ξ 10 ( n ) 2 ξ 12 ( n ) 2 m π = δ .
P 1 ( x = L ) / P 3 = ( 1 r 2 ) ( 1 r ) 2 η rel ,
η rel = { 1 + [ 4 r / ( 1 r ) 2 ] sin 2 ( δ / 2 ) } 1 .
F = [ r / ( 1 r ) 2 ] .
S F = ( F / r ) = [ ( 1 + r ) / ( 1 r ) 3 ] .

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