Abstract

Integrated optics is a far-reaching attempt to apply thin-film technology to optical circuits and devices, and, by using methods of integrated circuitry, to achieve a better and more economical optical system. The specific topics discussed here are physics of light waves in thin films, materials and losses involved, methods of couplings light beam into and out of a thin film, and nonlinear interactions in waveguide structures. The purpose of this paper is to review in some detail the important development of this new and fascinating field, and to caution the reader that the technology involved is difficult because of the smallness and perfection demanded by thin-film optical devices.

© 1971 Optical Society of America

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  1. S. E. Miller, Bell Syst. Tech. J. 48, 2059 (1969).
  2. R. Shubert, J. H. Harris, IEEE Trans. MMT 16, 1048 (1968).
    [CrossRef]
  3. P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
    [CrossRef]
  4. M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
    [CrossRef]
  5. H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).
  6. P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
    [CrossRef]
  7. R. Ulrich, J. Opt. Soc. Am. 60, 1337 (1970).
    [CrossRef]
  8. J. E. Midwinter, IEEE J. Quant. Electron. QE-6, 583 (1970).
    [CrossRef]
  9. J. H. Harris, R. Shubert, J. N. Polky, J. Opt. Soc. Amer. 60, 1007 (1970).
    [CrossRef]
  10. J. H. Harris, R. Shubert, IEEE Trans. MTT 19, 269 (1971).
    [CrossRef]
  11. R. Ulrich, to be published in J. Opt. Soc. Am.
  12. P. K. Tien, R. J. Martin, Appl. Phys. Lett. 18, 398 (1971).
    [CrossRef]
  13. J. E. Goell, R. D. Standley, Bell Syst. Tech. J. 48, 3445 (1969).
  14. D. H. Hensler, J. D. Cuthbert, R. J. Martin, P. K. Tien, Appl. Opt. 10, 1037 (1971).
    [CrossRef] [PubMed]
  15. P. K. Tien, G. Smolinsky, R. J. Martin, “Thin Organosilicon Films for Integrated Optics,” to be published in Appl. Opt.
  16. P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 17, 447 (1970).
    [CrossRef]
  17. L. Kuhn, M. L. Dakss, P. F. Heindrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
    [CrossRef]
  18. D. Hall, A. Yariv, E. Garmine, Appl. Phys. Lett. 17, 127 (1970).
    [CrossRef]
  19. H. Kogelnik, C. V. Shank, Appl. Phys. Lett. 18, 152 (1971).
    [CrossRef]
  20. J. E. Goell, R. D. Standley, Proc. IEEE 58, 1504 (1970).
    [CrossRef]
  21. D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969); Bell Syst. Tech. J. 48, 3233 (1969); Bell Syst. Tech. J. 49, 273 (1970); “Dependence of Reflection Loss on the Correlation Function” (private communication).
  22. H. K. V. Lotsch, J. Opt. Soc. Am. 58, 551 (1968).
    [CrossRef]
  23. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 49, Eq. (60).
  24. J. J. Burke, J. Opt. Soc. Am. 61, 676A (1971).
  25. N. F. Foster, G. A. Coquin, S. A. Rozgonyi, F. A. Vannatta, IEEE Trans. S4-15, 28 (1968).
  26. S. A. Rozgonyi, W. J. Polito, Appl. Phys. Lett. 8, 220 (1966).
    [CrossRef]
  27. P. Beckmann, A. Spizzichino, International Series of Monographs on Electromagnetic Waves (Oxford, New York, 1963), Chap. 5.

1971 (5)

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

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

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

H. Kogelnik, C. V. Shank, Appl. Phys. Lett. 18, 152 (1971).
[CrossRef]

J. J. Burke, J. Opt. Soc. Am. 61, 676A (1971).

1970 (10)

J. E. Goell, R. D. Standley, Proc. IEEE 58, 1504 (1970).
[CrossRef]

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 17, 447 (1970).
[CrossRef]

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

D. Hall, A. Yariv, E. Garmine, Appl. Phys. Lett. 17, 127 (1970).
[CrossRef]

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

H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).

P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
[CrossRef]

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

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

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

1969 (4)

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

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

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969); Bell Syst. Tech. J. 48, 3233 (1969); Bell Syst. Tech. J. 49, 273 (1970); “Dependence of Reflection Loss on the Correlation Function” (private communication).

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

1968 (3)

N. F. Foster, G. A. Coquin, S. A. Rozgonyi, F. A. Vannatta, IEEE Trans. S4-15, 28 (1968).

H. K. V. Lotsch, J. Opt. Soc. Am. 58, 551 (1968).
[CrossRef]

R. Shubert, J. H. Harris, IEEE Trans. MMT 16, 1048 (1968).
[CrossRef]

1966 (1)

S. A. Rozgonyi, W. J. Polito, Appl. Phys. Lett. 8, 220 (1966).
[CrossRef]

Beckmann, P.

P. Beckmann, A. Spizzichino, International Series of Monographs on Electromagnetic Waves (Oxford, New York, 1963), Chap. 5.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 49, Eq. (60).

Burke, J. J.

J. J. Burke, J. Opt. Soc. Am. 61, 676A (1971).

Coquin, G. A.

N. F. Foster, G. A. Coquin, S. A. Rozgonyi, F. A. Vannatta, IEEE Trans. S4-15, 28 (1968).

Cuthbert, J. D.

Dakss, M. L.

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

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

Foster, N. F.

N. F. Foster, G. A. Coquin, S. A. Rozgonyi, F. A. Vannatta, IEEE Trans. S4-15, 28 (1968).

Garmine, E.

D. Hall, A. Yariv, E. Garmine, Appl. Phys. Lett. 17, 127 (1970).
[CrossRef]

Goell, J. E.

J. E. Goell, R. D. Standley, Proc. IEEE 58, 1504 (1970).
[CrossRef]

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

Hall, D.

D. Hall, A. Yariv, E. Garmine, Appl. Phys. Lett. 17, 127 (1970).
[CrossRef]

Harris, J. H.

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

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

R. Shubert, J. H. Harris, IEEE Trans. MMT 16, 1048 (1968).
[CrossRef]

Heidrich, P. F.

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

Heindrich, P. F.

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

Hensler, D. H.

Kogelnik, H.

H. Kogelnik, C. V. Shank, Appl. Phys. Lett. 18, 152 (1971).
[CrossRef]

H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).

Kuhn, L.

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

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

Lotsch, H. K. V.

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969); Bell Syst. Tech. J. 48, 3233 (1969); Bell Syst. Tech. J. 49, 273 (1970); “Dependence of Reflection Loss on the Correlation Function” (private communication).

Martin, R. J.

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

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

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 17, 447 (1970).
[CrossRef]

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

P. K. Tien, G. Smolinsky, R. J. Martin, “Thin Organosilicon Films for Integrated Optics,” to be published in Appl. Opt.

Midwinter, J. E.

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

Miller, S. E.

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

Polito, W. J.

S. A. Rozgonyi, W. J. Polito, Appl. Phys. Lett. 8, 220 (1966).
[CrossRef]

Polky, J. N.

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

Rozgonyi, S. A.

N. F. Foster, G. A. Coquin, S. A. Rozgonyi, F. A. Vannatta, IEEE Trans. S4-15, 28 (1968).

S. A. Rozgonyi, W. J. Polito, Appl. Phys. Lett. 8, 220 (1966).
[CrossRef]

Scott, B. A.

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

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

Shank, C. V.

H. Kogelnik, C. V. Shank, Appl. Phys. Lett. 18, 152 (1971).
[CrossRef]

Shubert, R.

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

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

R. Shubert, J. H. Harris, IEEE Trans. MMT 16, 1048 (1968).
[CrossRef]

Smolinsky, G.

P. K. Tien, G. Smolinsky, R. J. Martin, “Thin Organosilicon Films for Integrated Optics,” to be published in Appl. Opt.

Sosnowski, T.

H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).

Spizzichino, A.

P. Beckmann, A. Spizzichino, International Series of Monographs on Electromagnetic Waves (Oxford, New York, 1963), Chap. 5.

Standley, R. D.

J. E. Goell, R. D. Standley, Proc. IEEE 58, 1504 (1970).
[CrossRef]

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

Tien, P. K.

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

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

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 17, 447 (1970).
[CrossRef]

P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
[CrossRef]

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

P. K. Tien, G. Smolinsky, R. J. Martin, “Thin Organosilicon Films for Integrated Optics,” to be published in Appl. Opt.

Ulrich, R.

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 17, 447 (1970).
[CrossRef]

P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
[CrossRef]

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

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

R. Ulrich, to be published in J. Opt. Soc. Am.

Vannatta, F. A.

N. F. Foster, G. A. Coquin, S. A. Rozgonyi, F. A. Vannatta, IEEE Trans. S4-15, 28 (1968).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 49, Eq. (60).

Yariv, A.

D. Hall, A. Yariv, E. Garmine, Appl. Phys. Lett. 17, 127 (1970).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (8)

S. A. Rozgonyi, W. J. Polito, Appl. Phys. Lett. 8, 220 (1966).
[CrossRef]

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]

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

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 17, 447 (1970).
[CrossRef]

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

D. Hall, A. Yariv, E. Garmine, Appl. Phys. Lett. 17, 127 (1970).
[CrossRef]

H. Kogelnik, C. V. Shank, Appl. Phys. Lett. 18, 152 (1971).
[CrossRef]

Bell Syst. Tech. J. (4)

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

H. Kogelnik, T. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).

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

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969); Bell Syst. Tech. J. 48, 3233 (1969); Bell Syst. Tech. J. 49, 273 (1970); “Dependence of Reflection Loss on the Correlation Function” (private communication).

IEEE J. Quant. Electron. (1)

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

IEEE Trans. (1)

N. F. Foster, G. A. Coquin, S. A. Rozgonyi, F. A. Vannatta, IEEE Trans. S4-15, 28 (1968).

IEEE Trans. MMT (1)

R. Shubert, J. H. Harris, IEEE Trans. MMT 16, 1048 (1968).
[CrossRef]

IEEE Trans. MTT (1)

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

J. Opt. Soc. Am. (4)

J. Opt. Soc. Amer. (1)

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

Proc. IEEE (1)

J. E. Goell, R. D. Standley, Proc. IEEE 58, 1504 (1970).
[CrossRef]

Other (4)

R. Ulrich, to be published in J. Opt. Soc. Am.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 49, Eq. (60).

P. K. Tien, G. Smolinsky, R. J. Martin, “Thin Organosilicon Films for Integrated Optics,” to be published in Appl. Opt.

P. Beckmann, A. Spizzichino, International Series of Monographs on Electromagnetic Waves (Oxford, New York, 1963), Chap. 5.

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Figures (31)

Fig. 1
Fig. 1

Coordinate system that will be used throughout the paper. The light wave propagates in the film parallel to the x axis. The surface of the film is in the xy plane and its thickness in the z direction.

Fig. 2
Fig. 2

Light beam in an organic film. The film is coated on a 2.5-cm by 7.6-cm microscope glass slide and it serves as a dielectric waveguide for the light wave.

Fig. 3
Fig. 3

To show that the light wave was truly propagating in the film, we scratched the film and observed that the light beam stopped immediately at the scratched point, which then radiated brightly.

Fig. 4
Fig. 4

(a) When θ1 < sin−1(n2/n1), the light wave shown represents the air mode. According to ray optics, the light wave originated in the film is refracted into both the substrate and air space. (b) As θ1 increases so that sin−1(n2/n1) < θ1 < sin−1(n0/n1), the light wave shown now represents the substrate mode. It is refracted into the substrate but is totally reflected at the film–air interface. (c) When θ1 increases further so that θ1 > sin−1(n0/n1), the light wave shown is totally reflected at both the film–air and film–substrate interfaces. It is confined in the film as is to be expected in the waveguide mode.

Fig. 5
Fig. 5

(a) Light wave in the waveguide mode can be considered as a plane wave which propagates along a zigzag path in the film. The wave can be represented by two wave vectors A1 and B1. (b) The wave vectors A1 and B1 can be decomposed into vertical and horizontal components. The horizontal components kn1 sinθ1 determine the wave velocity parallel to the film. The vertical components ± kn1 cos θ1 determine the field distribution across the thickness of the film.

Fig. 6
Fig. 6

(a) In wave optics, a light wave in the waveguide mode is an infinitely wide sheet of plane wave which folds back and forth in a zigzag manner between the top and the bottom surface of the film. (b) A light wave propagating inside the film is totally reflected at the two film surfaces. The figure shows that in order for the wave and its reflections to add in phase, the total phase change for the light wave to travel across the thickness of the film, up and down in one round trip, must be equal to 2. The figure also shows that the light wave suffers a phase change of −2Φ12 and −2Φ10 at the upper and lower film surfaces, respectively. These phase changes determine the field distribution across the thickness of the film, which is shown at the right of the figure for the m = 3 waveguide mode.

Fig. 7
Fig. 7

Any radius of the quarter-circle at the right side of the figure represents a possible direction for the wave vector B1. In the black region of the circle, the wave vector represents the substrate or air mode. In the white region of the circle, the wave vector represents the waveguide mode, but only a discrete set of the directions in this region satisfies the equation of the waveguide modes. Each direction of this discrete set represents one waveguide mode and each waveguide mode has its own field distribution as shown in the left side of the figure.

Fig. 8
Fig. 8

The electric field distribution of (a) a TE waveguide mode; (b) a TE substrate mode; (c) a TE (even) air mode.

Fig. 9
Fig. 9

In a prism–film coupler, the light wave from a laser is totally reflected at the prism base. The field distributions in the prism and in the film show that their evanescent fields overlap each other in the gap region.

Fig. 10
Fig. 10

In order that a waveguide mode be excited in a film by a prism–film coupler, the horizontal component of the wave vector for the wave in the prism must be equal to that of the wave in the film. The prism–film coupler, therefore, excites a single waveguide mode only, and by changing the direction of the incoming light wave, any waveguide mode can be excited.

Fig. 11
Fig. 11

(a) The light energy transferred from the prism to the film in the region 0 < X < l is returned to the prism in the region X > l; the net energy retained in the film is therefore zero. (b) By using a right-angle prism, the coupling between the prism and the film discontinues in the region X > l. The light wave coupled into the film in the region 0 < X < l is therefore retained in the film and continues to propagate in the film.

Fig. 12
Fig. 12

The figure shows that the prism–film coupler is a perfect output coupler. All the light energy in the film is coupled out and appears as the b3 wave in the prism. b1(x) and b3(x) show respectively how the filed amplitudes in the film and in the prism vary along the coupling length. B3(x) is the distribution of an incoming laser beam, which is used to demonstrate how to calculate the coupling efficiency.

Fig. 13
Fig. 13

The top photograph shows how a thin film coated on the glass substrate is pressed against the base of the prism in a prism–film coupler. The lower photograph shows that the entire prism–film assemblage is mounted on a turntable so that the incident laser beam can enter into the prism at any angle.

Fig. 14
Fig. 14

When the prism–film coupler is used as an input coupler, the pressure is applied at a point about a few tenths of a millimeter from the rectangular corner of the prism. Because of this pressure, the glass substrate bends slightly so that the gap between the prism base and the film is the smallest at the pressure point. To achieve a high coupling efficiency, the incident laser beam should fill the region between the pressure point and the rectangular corner of the prism.

Fig. 15
Fig. 15

The photograph shows a light beam which is fed into an organic film by the prism–film coupler at the right. The light wave propagates inside the film and is then coupled out of the film at the left by another prism-film coupler. (This figure is reproduced in color on the cover of the November 1971 Applied Optics issue.)

Fig. 16
Fig. 16

A grating light-wave coupler.

Fig. 17
Fig. 17

(a) A tapered film light-wave coupler is simply a tapered film edge deposited on a substrate. The figure shows that the film is tapered to nothing between X a and X c . (b) As a light wave originally propagating inside the film enters into the tapered region of the film, the angle between the zigzag light path and the vertical Z axis becomes smaller and smaller. At the cut-off point, X = X c , the angle is smaller than the critical angle of the film–substrate interface and the light wave is refracted into the substrate. The tapered film edge then serves as an output light-wave coupler.

Fig. 18
Fig. 18

(a) Electron micrograph of an oriented sputtered ZnO film showing that the sizes of the crystal sites are on the order of 0.5 μm. The entire width of the micrograph is 5 μm. (b) Electron-micrograph showing the surface of the same film after polishing.

Fig. 19
Fig. 19

Electron micrograph of a Ta2O5 film showing that the film is generally amorphous, though a number of small crystals visible in the micrograph still exist.

Fig. 20
Fig. 20

Losses in decibels per centimeter measured at 6328-Å light wavelength for several semiconductor and organic films.

Fig. 21
Fig. 21

Measurement (circles) and calculation (crosses) of the losses in a Ta2O5 film at 6328-Å light wavelength. The figure shows that the loss in db/cm or attenuation in cm−1 for the m = 3 waveguide mode is as much as 14 times that of the m = 0 waveguide mode. The dashed line is the volume loss in the film and the vertical distance between the dashed line and the solid curve is the surface scattering.

Fig. 22
Fig. 22

Plane wave specularly reflected at the top film surface.

Fig. 23
Fig. 23

Thickness W of a ZnS film deposited on a glass substrate is plotted vs the ratio of (β/k) for both TE and TM waveguide modes. Here, the ratio β/k can be considered as the effective refractive index. The left shaded region is for β/k < n0, the right, shaded region is for β/k > n1, and in the space between the two shaded regions the waveguide modes are possible.

Fig. 24
Fig. 24

(a) dW/d(β/k) and (b) d(β/k)/dn j vs (β/k) curves for the m = 0 TE mode.

Fig. 25
Fig. 25

Weff and W vs (β/k) curves for m = 0 and m = 1 TE modes.

Fig. 26
Fig. 26

The phase-match condition is shown as the crossing point of the two W vs (β/k) curves. The solid curve is the m = 0 TE mode of the fundamental and the dashed curve is the m = 1 TE mode of the harmonic.

Fig. 27
Fig. 27

The phase-match condition for SHG in a LiNbO3 film on a quartz substrate is indicated as the crossing point of the two W vs (β/k) curves. The fundamental at 1.064 μm uses m = 0 TE mode and the harmonic at 0.532 μm uses m = 0 TM mode.

Fig. 28
Fig. 28

Experimental arrangement of second harmonic generation in the form of Cerenkov radiation. A fundamental light wave at 1.064 μm is fed into a ZnS polycrystal film which is deposited on a single-crystal ZnO substrate. The evanescent field of the fundamental wave generates a second harmonic Cerenkov radiation in the substrate.

Fig. 29
Fig. 29

Any horizontal line on this table indicates the corresponding values for the thickness of the ZnS film, β/k of the fundamental wave, and the Cerenkov angle α.

Fig. 30
Fig. 30

Experiment of the second harmonic generation. The bright star in the figure is the second harmonic Cerenkov radiation emerging from the side surface of the ZnO substrate. The second harmonic beam thus generated is a coherent light beam of a very small aperture; the fundamental light wave at 1.064 μm is invisible.

Fig. 31
Fig. 31

Photograph of the second harmonic Cerenkov radiation taken through a microscope focused on the side surface of the ZnO substrate where the radiation emerges.

Tables (1)

Tables Icon

Table I Electric Field Distribution in (a) a Waveguide Mode, (b) a Substrate Mode, and (c) the Even and Odd Air Modes a

Equations (33)

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

sin θ 2 / sin θ 1 = n 1 / n 2 ,
sin θ 0 / sin θ 1 = n 1 / n 0 .
2 k n 1 W cos θ 1 - 2 Φ 10 - 2 Φ 12 - 2 Φ 12 = 2 m π ,
tan Φ 12 = ( n 1 2 sin 2 θ 1 - n 2 2 ) 1 2 / ( n 1 cos θ 1 ) ; tan Φ 10 = ( n 1 2 sin 2 θ 1 - n 0 2 ) 1 2 / ( n 1 cos θ 1 )
tan Φ 12 = n 1 2 ( n 1 2 sin 2 θ 1 - n 2 2 ) 1 2 / ( n 2 2 n 1 cos θ 1 ) ; tan Φ 10 = n 1 2 ( n 1 2 sin 2 θ 1 - n 0 2 ) 1 2 / ( n 0 2 n 1 cos θ 1 )
β = k n 1 sin θ 1 , v = c ( k / β ) .
2 E / x 2 + 2 E / z 2 = - ( k n j ) 2 E ,             j = 0 , 1 , or 2 ,
k x j 2 + k z j 2 = ( k n ) j 2 .
k x 0 = k x 1 = k x 2 = β .
k z j = ( k 2 n j 2 - β 2 ) 1 2 .
E y = A cos Φ 12 exp [ - p 2 ( z - W 12 ) ]
E y = A cos ( Φ 10 + m π ) exp [ - p 0 ( z - W 10 ) ]
1 2 A [ cos ( b 1 W 10 ) - i ( b 1 / b 0 ) sin ( b 1 W 10 ) ] exp [ - i b 0 ( z - W 10 ) ] + the complex conjugate .
1 2 A [ cos ( b 1 W 1 j ) - i ( b 1 / b j ) sin ( b 1 W 1 j ) ] exp [ - i b j ( z - W 1 j ) ] + the complex conjugate ,
± 1 2 A [ sin ( b 1 W 1 j ) + i ( b 1 / b j ) cos ( b 1 W 1 j ) ] exp [ - i b j ( z - W 1 j ) ] + the complex conjugate ,
d a 1 / d x = T a 3 - S a 1 ,
b 1 ( x ) = b 1 ( 0 ) exp [ - S x ] , x > 0 , = b 1 ( 0 ) , x < 0.
b 3 ( x ) = b 3 ( 0 ) exp [ - S x ] , x > 0 = 0 , x < 0.
η = [ - x + x B 3 ( x ) b 3 * ( x ) d x ] 2 - x + x B 3 ( x ) B 3 * ( x ) d x - x + x b 3 ( x ) b 3 * ( x ) d x ,
η = 2 / S l [ 1 - e - S l ] 2 ,
S = e - 2 p 2 d sin 2 Φ 12 sin 2 Φ 32 / ( W eff tan θ 1 ) ,
c 8 π n 1 E y 2 cos θ 1 exp [ - ( 4 π σ 12 λ 1 cos θ 1 ) 2 ] .
( c / 8 π ) n 1 E y cos θ 1 { 1 - exp [ - K 2 ( cos θ 1 ) 2 ] } ( c / 8 π ) n 1 E y 2 K 2 cos 3 θ 1 ,
K = ( 4 π / λ 1 ) ( σ 12 2 + σ 10 2 ) 1 2 .
( c / 4 π ) n 1 E y 2 sin θ 1 [ W + ( 1 / p 10 ) + ( 1 / p 12 ) ] ,
Attenuation = K 2 ( 1 2 cos 3 θ 1 sin θ 1 ) { 1 [ W + ( 1 / p 10 ) + ( 1 / p 12 ) ] } .
d W d ( β / k ) = β k b 1 2 ( W + 1 p 0 + 1 p 2 ) ;
d ( β / k ) d n 1 = k n 1 β W + [ p 10 / ( p 10 2 + b 1 2 ) ] + [ p 12 / ( p 12 2 + b 1 2 ) ] W + 1 p 10 + 1 p 12 ;
d ( β / k ) d n j = k n j β · b 1 2 / [ p j ( p j 2 + b 1 2 ) ] W + 1 p 0 + 1 p 2 ,
P = c 4 π n 1 sin θ 1 E y 2 ( W + 1 p 0 + 1 p 2 ) d ,
W = 0.314 ± 2.65 × 10 - 3 0.44 = 0.314 ± 0.006 μ m .
n 0 ( 1 ) < ( β / k ) < n 0 ( 2 ) .
cos α = β / k n 0 ( 2 ) .

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