Abstract

A natural framework for evaluating prism-coupler performance is provided by a recently developed geometrical construction in which refraction through a prism for an arbitrary angle of incidence is represented by an ellipse. The useful operating range of a prism coupler is represented by the portion of the representational ellipse that appears within a window determined by the mode propagation conditions of a thin-film–substrate system.

© 1983 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. P. K. Tien. Appl. Opt. 10, 2395 (1971).
    [CrossRef] [PubMed]
  3. R. Ulrich, R. Torge. Appl. Opt. 12, 2901 (1973).
    [CrossRef] [PubMed]
  4. D. K. Paul, Soc. Photo-Opt. Instrum. Eng. 342, 100 (1982).
  5. A. Feldman, Am. J. Phys. (to be published Oct.1983).
  6. R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), pp. 470–477.
  7. J. R. Carruthers, I. P. Kaminow, L. W. Stulz, Appl. Opt. 13, 2333 (1974).
    [CrossRef] [PubMed]

1982 (1)

D. K. Paul, Soc. Photo-Opt. Instrum. Eng. 342, 100 (1982).

1974 (1)

1973 (1)

1971 (1)

1969 (1)

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

Carruthers, J. R.

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), pp. 470–477.

Feldman, A.

A. Feldman, Am. J. Phys. (to be published Oct.1983).

Kaminow, I. P.

Martin, R. J.

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

Paul, D. K.

D. K. Paul, Soc. Photo-Opt. Instrum. Eng. 342, 100 (1982).

Stulz, L. W.

Tien, P. K.

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

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

Torge, R.

Ulrich, R.

R. Ulrich, R. Torge. Appl. Opt. 12, 2901 (1973).
[CrossRef] [PubMed]

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

Appl. Opt. (3)

Appl. Phys. Lett. (1)

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

Soc. Photo-Opt. Instrum. Eng. (1)

D. K. Paul, Soc. Photo-Opt. Instrum. Eng. 342, 100 (1982).

Other (2)

A. Feldman, Am. J. Phys. (to be published Oct.1983).

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), pp. 470–477.

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Figures (5)

Fig. 1
Fig. 1

Prism-coupler–thin-film system.

Fig. 2
Fig. 2

Representational ellipse of a prism-coupler–thin-film system.

Fig. 3
Fig. 3

Representational ellipses and mode-coupling window for three prism couplers on a thin-film–substrate combination. The prism index is the only varied parameter. The parameters used are nf = 1.77, ns = 1.46, A = 45°, and np = 1.95, 2.18, 2.6. Within the window are two vertical lines; the left line denotes an incident ray normal to the film surface; the right line denotes an incident ray parallel to the film surface.

Fig. 4
Fig. 4

Representational ellipses for prisms with a fixed refractive index but with different prism angles. The parameters used are nf = 1.77, ns = 1.46, np = 1.95, and A = 35, 45, 55°. The mode-coupling windows are interpreted in the manner as in Fig. 3.

Fig. 5
Fig. 5

Representational ellipse and mode-coupling window for the case in which all allowable modes cannot necessarily be accessed by an external incident wave: nf = 2.6; ns = 1.46; np = 1.95; and A = 45°.

Equations (5)

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α = ( A / 2 ) δ ,
β = ( A / 2 ) + δ .
sin θ i = n p sin [ ( A / 2 ) δ ] ,
n eff = n p sin [ ( A / 2 ) + δ ] ,
( n eff sin θ i ) 2 [ 2 n p sin ( A / 2 ) ] 2 + ( n eff + sin θ i ) 2 [ 2 n p cos ( A / 2 ) ] 2 = 1 .

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