Abstract

Residual absorption and scattering are loss mechanisms that degrade the performance of all thin films optical devices. By analogy to residual absorption, expressions are derived to evaluate losses due to surface and bulk scattering in dielectric multilayers. Based on these, proposals are made to improve the traditional performances of some basic filters. It is shown how, by means of index inhomogeneity, surface scattering is expected to be reduced considerably.

© 1977 Optical Society of America

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References

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  1. L. Young, J. Opt. Soc. Am. 52, 753 (1962).
    [CrossRef]
  2. G. Kopplemann, Ann. Phys. 5, 338 (1968) (in German).
  3. D. J. Hemingway, P. H. Lissberger, Opt. Acta 20, No. 2, 85 (1973).
    [CrossRef]
  4. A. K. Fung, Can. J. Phys. 48, 127 (1970).
    [CrossRef]
  5. I. Ohlídal, K. Navrátil, F. Luks, J. Opt. Soc. Am. 61, 1630 (1971).
    [CrossRef]
  6. K. H. Guenther, H. L. Gruber, H. K. Pulker, Thin Solid Films 34, 363 (1976).
    [CrossRef]
  7. L. P. Mott, “The effect of surface roughness on the optical properties of all dielectric interference filters,” MSC Dissertation, U. Arizona (1971) (unpublished).
  8. J. Eastman, “Surface scattering in optical interference coating,” Ph.D. Dissertation, U. Rochester, Rochester, N.Y. (1974).
  9. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), Chap. 5.
  10. J. O. Porteus, J. Opt. Soc. Am. 53, 1394 (1963).
    [CrossRef]
  11. G. Ross, Opt. Acta 15451 (1968).
    [CrossRef]
  12. T. H. Peak, Opt. Commun. 1, 341 (1970).
    [CrossRef]
  13. H. A. Macleod, Thin-Film Optical Filters (American Elsevier, New York, 1969), p. 177–8.
  14. E. Ritter, in Physics of Thin Films, G. Hass, M. Frencombe, R. Hoffman, Eds. (Academic, New York, 1975), Vol. 8.
  15. G. W. DeBell, Ph.D. Dissertation. U. Rochester, Rochester, N.Y. (1972) (unpublished).

1976 (1)

K. H. Guenther, H. L. Gruber, H. K. Pulker, Thin Solid Films 34, 363 (1976).
[CrossRef]

1973 (1)

D. J. Hemingway, P. H. Lissberger, Opt. Acta 20, No. 2, 85 (1973).
[CrossRef]

1971 (1)

1970 (2)

T. H. Peak, Opt. Commun. 1, 341 (1970).
[CrossRef]

A. K. Fung, Can. J. Phys. 48, 127 (1970).
[CrossRef]

1968 (2)

G. Ross, Opt. Acta 15451 (1968).
[CrossRef]

G. Kopplemann, Ann. Phys. 5, 338 (1968) (in German).

1963 (1)

1962 (1)

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), Chap. 5.

DeBell, G. W.

G. W. DeBell, Ph.D. Dissertation. U. Rochester, Rochester, N.Y. (1972) (unpublished).

Eastman, J.

J. Eastman, “Surface scattering in optical interference coating,” Ph.D. Dissertation, U. Rochester, Rochester, N.Y. (1974).

Fung, A. K.

A. K. Fung, Can. J. Phys. 48, 127 (1970).
[CrossRef]

Gruber, H. L.

K. H. Guenther, H. L. Gruber, H. K. Pulker, Thin Solid Films 34, 363 (1976).
[CrossRef]

Guenther, K. H.

K. H. Guenther, H. L. Gruber, H. K. Pulker, Thin Solid Films 34, 363 (1976).
[CrossRef]

Hemingway, D. J.

D. J. Hemingway, P. H. Lissberger, Opt. Acta 20, No. 2, 85 (1973).
[CrossRef]

Kopplemann, G.

G. Kopplemann, Ann. Phys. 5, 338 (1968) (in German).

Lissberger, P. H.

D. J. Hemingway, P. H. Lissberger, Opt. Acta 20, No. 2, 85 (1973).
[CrossRef]

Luks, F.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (American Elsevier, New York, 1969), p. 177–8.

Mott, L. P.

L. P. Mott, “The effect of surface roughness on the optical properties of all dielectric interference filters,” MSC Dissertation, U. Arizona (1971) (unpublished).

Navrátil, K.

Ohlídal, I.

Peak, T. H.

T. H. Peak, Opt. Commun. 1, 341 (1970).
[CrossRef]

Porteus, J. O.

Pulker, H. K.

K. H. Guenther, H. L. Gruber, H. K. Pulker, Thin Solid Films 34, 363 (1976).
[CrossRef]

Ritter, E.

E. Ritter, in Physics of Thin Films, G. Hass, M. Frencombe, R. Hoffman, Eds. (Academic, New York, 1975), Vol. 8.

Ross, G.

G. Ross, Opt. Acta 15451 (1968).
[CrossRef]

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), Chap. 5.

Young, L.

Ann. Phys. (1)

G. Kopplemann, Ann. Phys. 5, 338 (1968) (in German).

Can. J. Phys. (1)

A. K. Fung, Can. J. Phys. 48, 127 (1970).
[CrossRef]

J. Opt. Soc. Am. (3)

Opt. Acta (2)

D. J. Hemingway, P. H. Lissberger, Opt. Acta 20, No. 2, 85 (1973).
[CrossRef]

G. Ross, Opt. Acta 15451 (1968).
[CrossRef]

Opt. Commun. (1)

T. H. Peak, Opt. Commun. 1, 341 (1970).
[CrossRef]

Thin Solid Films (1)

K. H. Guenther, H. L. Gruber, H. K. Pulker, Thin Solid Films 34, 363 (1976).
[CrossRef]

Other (6)

L. P. Mott, “The effect of surface roughness on the optical properties of all dielectric interference filters,” MSC Dissertation, U. Arizona (1971) (unpublished).

J. Eastman, “Surface scattering in optical interference coating,” Ph.D. Dissertation, U. Rochester, Rochester, N.Y. (1974).

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), Chap. 5.

H. A. Macleod, Thin-Film Optical Filters (American Elsevier, New York, 1969), p. 177–8.

E. Ritter, in Physics of Thin Films, G. Hass, M. Frencombe, R. Hoffman, Eds. (Academic, New York, 1975), Vol. 8.

G. W. DeBell, Ph.D. Dissertation. U. Rochester, Rochester, N.Y. (1972) (unpublished).

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Figures (4)

Fig. 1
Fig. 1

The distribution of the (time averaged) electric field square in a quarterwave dielectric reflector of nH = 2.10 (HfO2) and nL = 1.51 (silica) at λo = 320 nm.

Fig. 2
Fig. 2

The distribution of the (time averaged) electric field square in a Fabry-Perot bandpass filter of low index spacer (nH = 2.10, nL = 1.51). The central block of layers, from (−3) to (+3), is an example of a halfwave block absentee. This implies (SWR)−4 = (SWR)+4.

Fig. 3
Fig. 3

In a stepped index antireflection coating, n|E|2 (as well as the losses) are distributed uniformly along the layers of the stack.

Fig. 4
Fig. 4

Index inhomogeneity is used to shift reflecting power from antinode to node boundaries.

Equations (35)

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d P ( z ) [ c / ( 8 π ) ] n E + ( z ) 2 α a b d z .
d ( A L ) i [ c / ( 8 π ) ] n i E ( z ) 2 ( α a b ) i d z ,
E ( z ) = E + ( z ) + E - ( z ) = E + ( z ) [ 1 - ρ i ( z ) ] .
( A L ) i ( 1 - ρ o 2 ) ( α a b ) i l i U i .
U i = ( gross power flow net power flow ) i = ( SWR ) i 2 + 1 2 ( SWR ) i .
( SSL ) i c 8 π n i + n i + 1 2 E i 2 ( 1 - R s - T s ) i .
( R s ) i = ( R o ) i exp [ - ( 2 π λ o n i σ i ) 2 ]
( T s ) i = ( T o ) i exp { - [ 2 π λ o ( n i - n i + 1 ) σ i ] 2 }
( SSL ) i β i n i E i + 2 1 - ρ i 2 n o E o + 2 ,
β i = 8 π 2 ( n i - n i + 1 ) 2 ( σ i λ o ) 2 .
n o E o + 2 ( 1 - ρ o 2 ) n i E i + 2 ( 1 - ρ i 2 ) ;             i = 1 , 2 , 3 , ,
( SSL ) i ( 1 - ρ o 2 ) β i 1 + ρ i 2 1 - ρ i 2 .
( SSL ) i { ( 1 - ρ o 2 ) β i ( SWR ) i ( antinode ) ( 1 - ρ o 2 ) β i 1 ( SWR ) i ( node ) ,
( SWR ) i 1 + ρ i 1 - ρ i .
α = α a b + α s c .
( VL ) i ( 1 - ρ o 2 ) α i l i U i .
TL = VL + SSL ,
VL = layers ( V L ) i ;             SSL = boundaries ( SSL ) i .
( air ) ( H L ) m H ( sub ) ;             2 m + 1 = total # of layers .
ρ o 2 1.
( SSL ) D . M . = i = 0 2 m + 1 ( SSL ) i = [ 1 - ρ o 2 ] β i × [ i = 0 odd 2 m + 1 ( SWR ) i + i = 0 even 2 m 1 ( SWR ) i ]
1 - ρ o 2 4 ( SWR ) o ,
i = 1 odd 2 m + 1 ( SWR ) i = i = 1 odd 2 m + 1 V i V i + 1 V 2 m + 1 = ( SWR ) o i = 1 odd 2 m + 1 1 V 0 V 1 V 2 V i - 1 ,
V i = { n i + 1 n i for n i + 1 > n i n i n i + 1 for n i > n i + 1 .
( TL ) D . M = ( VL ) D . M + ( SSL ) D . M .
( VL ) D . M 2 π n o ( κ H + κ L ) eff n H 2 - n L 2 ,
( SSL ) D . M 8 π 2 n o n L T H , L ( n H 2 - n L 2 ) ( σ λ o ) 2 ,
n o = 1 ; n L = 1.51 ; n H = 2.10 ; ( κ i ) eff = 2.0 × 10 - 4 ; σ = 20 Å ; λ o = 3500 Å
T max = 1 - ( VL ) F . P . + ( SSL ) F . P . ,
( V L ) F . P . π ( n H n L ) 2 m + 1 n H n H 2 - n L 2 × [ ( κ L ) eff n H 2 n L 2 + ( κ H ) eff ] ,
( SSL ) F . P . 1 2 ( n H n L ) 2 m + 2 ( SSL ) D . M . ,
( VL ) F . P . + ( SSL ) F . P . 0.1.
n i E 2 n 0 E 0 + 2 = 1 ;             i = 0 , 1 , 2 P
( VL ) A . R . C . π i = 1 p ( κ i ) eff n i
( SSL ) A . R . C . 8 π 2 ( p + 1 ) ( Δ n ) 2 ( σ λ 0 ) 2 ,

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