Abstract

We consider thin film light guides consisting of a transparent film of high refractive index deposited on a substrate of lower index. The propagation of light in such a two-dimensional transmission medium can be described within the limits of geometrical optics by an effective index of refraction N. Its value depends on the film thickness. Therefore, a light beam in the thin film guide is refracted or totally reflected at a step of film thickness. We discuss these phenomena (Snell’s law) and demonstrate them experimentally, using ZnS films on glass as guides. As applications, we show a thin film prism and thin film lenses for guided light beams. By properly choosing the film thicknesses at both sides of the step, one can obtain an unusually large positive or negative wavelength dispersion of the refraction or, if desired, achromatic refraction.

© 1971 Optical Society of America

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References

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  1. E. S. Miller, Bell Syst. Tech. J. 48, 2059 (1969).
  2. R. Shubert, J. H. Harris, IEEE Trans. Microwave Theory Techn. MTT-16, 1048(1968).
    [CrossRef]
  3. P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969); P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
    [CrossRef]
  4. R. Ulrich, J. Opt. Soc. Am. 60, 1337 (1970).
    [CrossRef]
  5. L. Kuhn, M. L. Dakks, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
    [CrossRef]
  6. M. L. Dakks, L. Kuhn, B. A. Scott, P. F. Heidrich, Appl. Phys. Lett. 16, 523 (1970); H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970); J. H. Harris, R. Shubert, N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
    [CrossRef]
  7. D. Marcuse, Bell Syst. Tech. J. 49, 273, 919 (1970).
  8. In Ref. 2, Eqs. (20)–(22), the effective index is defined erroneously as the reciprocal of Eq. (2) here.
  9. J. Kane, H. Osterberg, J. Opt. Soc. Am. 54, 347 (1964); E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).
    [CrossRef]
  10. J. E. Goell, R. D. Standley, Bell Syst. Tech. J. 48, 3445 (1969).
  11. D. H. Hensler, J. D. Cuthbert, P. K. Tien, R. J. Martin, Appl. Opt. 10, 1037 (1971).
    [CrossRef] [PubMed]
  12. R. Ulrich, H. P. Weber, BTL; to be published.
  13. P. K. Tien, R. J. Martin, Appl. Phys. Lett. 18, 398 (1971).
    [CrossRef]
  14. D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).
  15. E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969).
  16. R. Shubert, J. H. Harris, J. Opt. Soc. Am. 61, 154 (1971).
    [CrossRef]
  17. M. Born, E. Wolf, Principles of Optics (New YorkPergamon, 1965).

1971 (3)

1970 (4)

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

L. Kuhn, M. L. Dakks, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
[CrossRef]

M. L. Dakks, L. Kuhn, B. A. Scott, P. F. Heidrich, Appl. Phys. Lett. 16, 523 (1970); H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970); J. H. Harris, R. Shubert, N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
[CrossRef]

D. Marcuse, Bell Syst. Tech. J. 49, 273, 919 (1970).

1969 (5)

E. S. Miller, Bell Syst. Tech. J. 48, 2059 (1969).

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969); P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
[CrossRef]

J. E. Goell, R. D. Standley, Bell Syst. Tech. J. 48, 3445 (1969).

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969).

1968 (1)

R. Shubert, J. H. Harris, IEEE Trans. Microwave Theory Techn. MTT-16, 1048(1968).
[CrossRef]

1964 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (New YorkPergamon, 1965).

Cuthbert, J. D.

Dakks, M. L.

L. Kuhn, M. L. Dakks, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
[CrossRef]

M. L. Dakks, L. Kuhn, B. A. Scott, P. F. Heidrich, Appl. Phys. Lett. 16, 523 (1970); H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970); J. H. Harris, R. Shubert, N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
[CrossRef]

Goell, J. E.

J. E. Goell, R. D. Standley, Bell Syst. Tech. J. 48, 3445 (1969).

Harris, J. H.

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

R. Shubert, J. H. Harris, IEEE Trans. Microwave Theory Techn. MTT-16, 1048(1968).
[CrossRef]

Heidrich, P. F.

L. Kuhn, M. L. Dakks, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
[CrossRef]

M. L. Dakks, L. Kuhn, B. A. Scott, P. F. Heidrich, Appl. Phys. Lett. 16, 523 (1970); H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970); J. H. Harris, R. Shubert, N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
[CrossRef]

Hensler, D. H.

Kane, J.

Kuhn, L.

M. L. Dakks, L. Kuhn, B. A. Scott, P. F. Heidrich, Appl. Phys. Lett. 16, 523 (1970); H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970); J. H. Harris, R. Shubert, N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
[CrossRef]

L. Kuhn, M. L. Dakks, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969).

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 49, 273, 919 (1970).

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).

Martin, R. J.

P. K. Tien, R. J. Martin, Appl. Phys. Lett. 18, 398 (1971).
[CrossRef]

D. H. Hensler, J. D. Cuthbert, P. K. Tien, R. J. Martin, Appl. Opt. 10, 1037 (1971).
[CrossRef] [PubMed]

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969); P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
[CrossRef]

Miller, E. S.

E. S. Miller, Bell Syst. Tech. J. 48, 2059 (1969).

Osterberg, H.

Scott, B. A.

M. L. Dakks, L. Kuhn, B. A. Scott, P. F. Heidrich, Appl. Phys. Lett. 16, 523 (1970); H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970); J. H. Harris, R. Shubert, N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
[CrossRef]

L. Kuhn, M. L. Dakks, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
[CrossRef]

Shubert, R.

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

R. Shubert, J. H. Harris, IEEE Trans. Microwave Theory Techn. MTT-16, 1048(1968).
[CrossRef]

Standley, R. D.

J. E. Goell, R. D. Standley, Bell Syst. Tech. J. 48, 3445 (1969).

Tien, P. K.

D. H. Hensler, J. D. Cuthbert, P. K. Tien, R. J. Martin, Appl. Opt. 10, 1037 (1971).
[CrossRef] [PubMed]

P. K. Tien, R. J. Martin, Appl. Phys. Lett. 18, 398 (1971).
[CrossRef]

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969); P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
[CrossRef]

Ulrich, R.

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

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969); P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
[CrossRef]

R. Ulrich, H. P. Weber, BTL; to be published.

Weber, H. P.

R. Ulrich, H. P. Weber, BTL; to be published.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (New YorkPergamon, 1965).

Appl. Opt. (1)

Appl. Phys. Lett. (4)

P. K. Tien, R. J. Martin, Appl. Phys. Lett. 18, 398 (1971).
[CrossRef]

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969); P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
[CrossRef]

L. Kuhn, M. L. Dakks, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
[CrossRef]

M. L. Dakks, L. Kuhn, B. A. Scott, P. F. Heidrich, Appl. Phys. Lett. 16, 523 (1970); H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970); J. H. Harris, R. Shubert, N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
[CrossRef]

Bell Syst. Tech. J. (5)

D. Marcuse, Bell Syst. Tech. J. 49, 273, 919 (1970).

E. S. Miller, Bell Syst. Tech. J. 48, 2059 (1969).

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969).

J. E. Goell, R. D. Standley, Bell Syst. Tech. J. 48, 3445 (1969).

IEEE Trans. Microwave Theory Techn. (1)

R. Shubert, J. H. Harris, IEEE Trans. Microwave Theory Techn. MTT-16, 1048(1968).
[CrossRef]

J. Opt. Soc. Am. (3)

Other (3)

M. Born, E. Wolf, Principles of Optics (New YorkPergamon, 1965).

R. Ulrich, H. P. Weber, BTL; to be published.

In Ref. 2, Eqs. (20)–(22), the effective index is defined erroneously as the reciprocal of Eq. (2) here.

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Figures (11)

Fig. 1
Fig. 1

A light beam, guided in a planar dielectric guide, is refracted at a step of the film thickness W. The difference in film thickness between the regions I and II causes their effective indices of refraction NI, NII to be different. (a) Top view; (b) side view.

Fig. 2
Fig. 2

Experimental demonstration of the refraction of a guided laser beam. The light guide is formed by a ZnS film vacuum-deposited on a glass substrate. The thicknesses WI, WII of the ZnS film are indicated. The He–Ne laser beam propagates as a TE(m = 0) mode.

Fig. 3
Fig. 3

The effective index of refraction Nm of a planar dielectric waveguide as a function of the film thickness W, given here for the example of a ZnS film on a glass substrate (n0 = 1.51; n1 = 2.35; λ = 6328 Å). The parameter at the curves is the mode number m. — TE modes, ------ TM modes.

Fig. 4
Fig. 4

The total reflection of a guided beam at a step of film thickness can be understood from the curvature of the rays inside the region LT of nonuniform film thickness.

Fig. 5
Fig. 5

Experimental demonstration of the total reflection of a guided laser beam at a step of film thickness. The beam is launched in the thin region, refracted when entering the thick region, and totally reflected at the boundary to the thin region. (ZnS on glass, TE0 mode, λ = 6328 Å.)

Fig. 6
Fig. 6

Total reflection of a guided beam at the edge of the light-guiding film (WI = 0).

Fig. 7
Fig. 7

Thin film optical elements like a prism (a) or lens (b) are formed by suitably shaping the boundary lines between the regions of thin and thick film thickness.

Fig. 8
Fig. 8

A thin film prism deflecting a guided laser beam. This is the same prism as in Fig. 5, but the direction of the incident beam has been changed.

Fig. 9
Fig. 9

A thin film lens collimating a guided laser beam. The film thickness is increased in the lens-shaped area. The lens is slightly tilted with respect to the incident beam; the resulting aberrations are apparent.

Fig. 10
Fig. 10

Another collimating thin film lens. The lens has a planoconcave shape; its effective index is lower than that of the surrounding region, because the film is thinner in the lens region than in its surrounding.

Fig. 11
Fig. 11

This diagram shows the refractive index and dispersion at λ = 6328 Å of selected optical materials and of a thin film guide (ZnS film on BK7 glass, TE0 mode). The parameter along the curve is the film thickness in angstroms. Abscissa in logarithmic scale, ordinate linear scale. BK7 and SF6 are designations of some Schott optical glasses.

Equations (13)

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N I sin α I = N I I sin α I I .
N = c / v p h ,
d N m / d W = ( N m / W e q ) [ ( n 1 2 / N m 2 ) - 1 ] .
α i I I > α c where α c = arcsin ( N I / N I I ) .
α r I I = π - α i I I .
α i I I > arcsin ( n 0 / N I I )
d ln N R / d λ = ( d ln N I I / d λ ) - ( d ln N I / d λ ) .
¯ V ( x , y ) + k 2 N 2 V ( x , y ) = 0 ,
k ¯ N = ( N / W ) k ¯ W 1.
V ( x , y ) = A ( x , y ) exp [ i k S ( x , y ) ] ,
[ ¯ S ( x , y ) ] 2 = N 2 ( x , y ) .
( d / d s ) [ N ( r ) s ( r ) ] = ¯ N ( r ) .
κ ρ - 1 = ( 1 / N ) ( N / W ) s × ¯ W ,

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