Abstract

This paper establishes that any thin periodic metal grid on a plane boundary between two semi-infinite media, irradiated normally at any specified wavelength larger than its period, can be represented by an equivalent thin film. Explicit formulas for the parameters of this film are derived, and a numerical example of the equivalence is given.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Véron, L. B. Whitbourn, “Strip Gratings on Dielectric Substrates as Output Couplers for Submillimeter Lasers,” Appl. Opt. 25, 619 (1986); Errata, Appl. Opt. 25, 3974 (1986).
    [CrossRef] [PubMed]
  2. L. B. Whitbourn, R. C. Compton, “Equivalent-Circuit Formulas for Metal Grid Reflectors at a Dielectric Boundary,” Appl. Opt. 24, 217 (1985).
    [CrossRef] [PubMed]
  3. R. C. Compton, L. B. Whitbourn, R. C. McPhedran, “Strip Gratings at a Dielectric Interface and Application of Babinet’s Principle,” Appl. Opt. 23, 3236 (1984); Errata, Appl. Opt. 25, 3974 (1986).
    [CrossRef] [PubMed]
  4. H. A. Macleod, Thin Film Optical Filters (Adam Hilger, Bristol, 1986).
    [CrossRef]
  5. P. I. Somlo, J. D. Hunter, Microwave Impedance Measurement (Peregrinus, London, 1985), pp. 18 and 19.
  6. P. E. Ciddor, “Reciprocity of Phase on Transmission Through a Multilayer or Grid,” Appl. Opt. 28, 18 (1989).
    [CrossRef] [PubMed]
  7. M. Gajdardziska-Josifovska, R. C. McPhedran, D. R. McKenzie, R. E. Collins, “Silver Magnesium Fluoride Cermet Films, II: Optical and Electrical Properties,” to be published.

1989 (1)

1986 (1)

1985 (1)

1984 (1)

Ciddor, P. E.

Collins, R. E.

M. Gajdardziska-Josifovska, R. C. McPhedran, D. R. McKenzie, R. E. Collins, “Silver Magnesium Fluoride Cermet Films, II: Optical and Electrical Properties,” to be published.

Compton, R. C.

Gajdardziska-Josifovska, M.

M. Gajdardziska-Josifovska, R. C. McPhedran, D. R. McKenzie, R. E. Collins, “Silver Magnesium Fluoride Cermet Films, II: Optical and Electrical Properties,” to be published.

Hunter, J. D.

P. I. Somlo, J. D. Hunter, Microwave Impedance Measurement (Peregrinus, London, 1985), pp. 18 and 19.

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (Adam Hilger, Bristol, 1986).
[CrossRef]

McKenzie, D. R.

M. Gajdardziska-Josifovska, R. C. McPhedran, D. R. McKenzie, R. E. Collins, “Silver Magnesium Fluoride Cermet Films, II: Optical and Electrical Properties,” to be published.

McPhedran, R. C.

R. C. Compton, L. B. Whitbourn, R. C. McPhedran, “Strip Gratings at a Dielectric Interface and Application of Babinet’s Principle,” Appl. Opt. 23, 3236 (1984); Errata, Appl. Opt. 25, 3974 (1986).
[CrossRef] [PubMed]

M. Gajdardziska-Josifovska, R. C. McPhedran, D. R. McKenzie, R. E. Collins, “Silver Magnesium Fluoride Cermet Films, II: Optical and Electrical Properties,” to be published.

Somlo, P. I.

P. I. Somlo, J. D. Hunter, Microwave Impedance Measurement (Peregrinus, London, 1985), pp. 18 and 19.

Véron, D.

Whitbourn, L. B.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (22)

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

[ A B C D ] = [ cos φ i Y sin φ ( i / Y ) sin φ cos φ ] ,
[ A B C D ] = [ 1 0 Y g 1 ]
A = D 1 φ 2 / 2 = 1 ( e N ) 2 / 2 ,
B ( 2 π d / λ ) i / Y 0 = i e / Y 0 ,
C i e Y 2 / Y 0 .
Y 2 ( e ) = i Y g Y 0 / e ,
Y ( e ) = ± ( 1 i ) ( Y g Y 0 / 2 e ) 1 / 2 ,
N ( e ) = Y ( e ) / Y 0 = ± ( 1 i ) ( Y g / 2 Y 0 e ) 1 / 2 .
Y 2 = i Y 0 ( G + i B ) / e = B Y 0 / e i G Y 0 / e .
n 2 k 2 = B / Y 0 e ,
2 n k = G / Y 0 e ,
n 4 ( B / Y 0 e ) n 2 ( G / Y 0 e ) 2 / 4 = 0.
n 2 = [ B + ( B 2 + G 2 ) 1 / 2 ] / 2 Y 0 e ,
k 2 = [ B + ( B 2 + G 2 ) ½ ] / 2 Y 0 e ,
arg ( t ) = arg ( Y 2 / Y 1 ) + arg ( t ) ,
R = | Y 0 Y 1 Y 0 + Y 1 | 2 = 0.5 ,
r ( e ) = r ( 0 ) [ 1 + Q e i ] ,
R ( e ) = R ( 0 ) [ 1 2   Im ( Q ) e ]
Q = ( Y 1 / Y 0 ) ( Y 2 + Y g ) 2 / [ Y 1 2 ( Y 2 + Y g ) 2 ] ,
t ( e ) = t ( 0 ) / ( 1 + P e i ) ,
T ( e ) = T ( 0 ) [ 1 2   Im ( P ) e ] ,
P = ( Y 1 Y g + Y 1 Y 2 + Y 2 Y g ) / [ 2 Y 0 ( Y 1 + Y g + Y 2 ) ] .

Metrics