Abstract

A periodic sequence of layers with alternately high and low refractive indices can guide loosely bound surface waves parallel to the layers. Most of the power flows in free space, and, thus, the losses may be considerably smaller than the bulk losses of the dielectric materials used. Possible applications are briefly discussed.

© 1974 Optical Society of America

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References

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  1. W. L. Weeks, Electromagnetic Theory for Engineering Applications (Wiley, New York, 1964), pp. 246–259.
  2. R. B. Adler, L. J. Chu, R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, New York, 1965), pp. 354–362.
  3. In the configurations considered by R. P. Larsen, A. A. Oliner, Microwave Symp. G-MTT, 17 (May1967) and by E. A. J. Marcatili, Patent 3,583,786, multiple layers are effectively used in the reflection mode rather than in the surface wave mode, considered in the present paper.
  4. E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969) and J. A. Arnaud, Bell Syst. Tech. J. 53 (Sept.1974).
  5. This was suggested to us by I. P. Kaminow and H. P. Weber.

1969 (1)

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969) and J. A. Arnaud, Bell Syst. Tech. J. 53 (Sept.1974).

1967 (1)

In the configurations considered by R. P. Larsen, A. A. Oliner, Microwave Symp. G-MTT, 17 (May1967) and by E. A. J. Marcatili, Patent 3,583,786, multiple layers are effectively used in the reflection mode rather than in the surface wave mode, considered in the present paper.

Adler, R. B.

R. B. Adler, L. J. Chu, R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, New York, 1965), pp. 354–362.

Chu, L. J.

R. B. Adler, L. J. Chu, R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, New York, 1965), pp. 354–362.

Fano, R. M.

R. B. Adler, L. J. Chu, R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, New York, 1965), pp. 354–362.

Larsen, R. P.

In the configurations considered by R. P. Larsen, A. A. Oliner, Microwave Symp. G-MTT, 17 (May1967) and by E. A. J. Marcatili, Patent 3,583,786, multiple layers are effectively used in the reflection mode rather than in the surface wave mode, considered in the present paper.

Marcatili, E. A. J.

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969) and J. A. Arnaud, Bell Syst. Tech. J. 53 (Sept.1974).

Oliner, A. A.

In the configurations considered by R. P. Larsen, A. A. Oliner, Microwave Symp. G-MTT, 17 (May1967) and by E. A. J. Marcatili, Patent 3,583,786, multiple layers are effectively used in the reflection mode rather than in the surface wave mode, considered in the present paper.

Weeks, W. L.

W. L. Weeks, Electromagnetic Theory for Engineering Applications (Wiley, New York, 1964), pp. 246–259.

Bell Syst. Tech. J. (1)

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969) and J. A. Arnaud, Bell Syst. Tech. J. 53 (Sept.1974).

Microwave Symp. (1)

In the configurations considered by R. P. Larsen, A. A. Oliner, Microwave Symp. G-MTT, 17 (May1967) and by E. A. J. Marcatili, Patent 3,583,786, multiple layers are effectively used in the reflection mode rather than in the surface wave mode, considered in the present paper.

Other (3)

This was suggested to us by I. P. Kaminow and H. P. Weber.

W. L. Weeks, Electromagnetic Theory for Engineering Applications (Wiley, New York, 1964), pp. 246–259.

R. B. Adler, L. J. Chu, R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, New York, 1965), pp. 354–362.

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Figures (4)

Fig. 1
Fig. 1

(a) Besides their reflecting properties periodic layers (x < 0) can guide surface waves for suitable values of the refractive indices n1, n2 and thickness l1, l2. (b) Approximate field distribution in the layers and in free space.

Fig. 2
Fig. 2

Diagram showing under what conditions loosely bound surface waves with the electric field in the x, z plane (E) or along the y axis (E) can propagate. (The intersection point is at n1 = n2 = √2.)

Fig. 3
Fig. 3

Optical beams can be confined transversely or focused through slow changes in layer thickness or deformation of the surface.

Fig. 4
Fig. 4

Method of fabrication using a Littrow prism (suggested by I. P. Kaminow and H. P. Weber). Typical numbers of layers are given for E and E.

Equations (20)

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Z i n = { A D ± [ ( A + D ) 2 4 ] 1 / 2 } / 2 C ,
A cos β 1 l 1 cos β 2 l 2 Z 2 1 Z 1 sin β 1 l 1 sin β 2 l 2 , D cos β 1 l 1 cos β 2 l 2 Z 1 1 Z 2 sin β 1 l 1 sin β 2 l 2 , C j [ Z 1 1 sin β 1 l 1 cos β 2 l 2 + Z 2 1 sin β 2 l 2 cos β 1 l 1 ] ,
β i = k n i [ 1 ( sin θ / n i ) 2 ] 1 / 2 , i = 1,2 ,
Z i = n i 1 [ 1 ( sin θ / n i ) 2 ] 1 / 2 , i = 1,2 ( E ) ,
Z i = n i 1 [ 1 ( sin θ / n i ) 2 ] 1 / 2 , i = 1,2 ( E ) .
cos θ = β x / k .
cos θ = Z i n , ( E ) ,
1 / cos θ = Z i n , ( E ) .
l i = ( λ 0 / 4 ) ( n i 2 1 ) 1 / 2 , i = 1,2.
n 1 2 ( n 1 2 1 ) 1 / 2 < n 2 2 ( n 2 2 1 ) 1 / 2 , ( E ) ,
n 1 < n 2 , ( E ) .
λ = λ 0 + Δ λ ,
Z i n i 2 ( n i 2 1 ) 1 / 2 , i = 1,2 , ( E ) ,
Z i ( n i 2 1 ) 1 / 2 , i = 1,2 , ( E ) .
j β x λ 0 1 π 2 ( Z 1 1 Z 2 1 ) 1 ( Δ λ / λ 0 ) , ( E ) ,
j β x λ 0 1 π 2 ( Z 1 Z 2 ) 1 ( Δ λ / λ 0 ) , ( E ) .
d 1 = ( j β x ) 1 .
α = real part of { cosh 1 [ ( A + D ) / 2 ] } .
d 2 ( l 1 + l 2 ) { cosh 1 [ ( Z 1 / Z 2 + Z 2 / Z 1 ) / 2 ] } 1 ,
N 2 d 2 / ( l 1 + l 2 ) .

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