Abstract

A new approach using the diffraction method of linear superposition is used for the analytical description of an imperfect Fabry-Perot etalon. Derived simple relations for the transfer coefficients of a corrugated thin-film system may find a broader field of application.

© 1984 Optical Society of America

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  1. J. E. Mack, D. P. McNutt, F. L. Roesler, R. J. Chabbal, Appl. Opt. 2, 873 (1963).
  2. E. B. Armstrong, Planet. Space Sci. 16, 211 (1968).
    [CrossRef]
  3. M. A. Biondi, W. A. Feibelman, Planet. Space Sci. 16, 431 (1968).
    [CrossRef]
  4. G. Hernandez, Appl. Opt. 9, 1225 (1970).
    [CrossRef] [PubMed]
  5. A. Title, Fabry-Perot Interferometers as Narrow Band Optical Filters—Part 1 (Harvard Observatory Publication, Cambridge, 1970).
  6. P. B. Hays, R. G. Roble, Appl. Opt. 10, 193 (1971).
    [CrossRef] [PubMed]
  7. T. R. Hicks, N. K. Reay, R. J. Scaddon, J. Phys. E 7, 27 (1974).
    [CrossRef]
  8. F. L. Roesler, in Methods of Experimental Physics, Vol. 12A, N. Carlton, Ed. (Academic, New York, 1974), p. 531.
    [CrossRef]
  9. H. F. Dobele, J. H. Massig, Appl. Opt. 15, 69 (1976).
    [CrossRef] [PubMed]
  10. J. Meaburn, Detection and Spectrometry of Faint Light (Reidel, Boston, 1976).
    [CrossRef]
  11. T. L. Killeen, P. B. Hays, B. C. Kennedy, J. Opt. Soc. Am. 70, 1588 (1980).
  12. P. B. Hays, Appl. Opt. 21, 1136 (1982).
    [CrossRef] [PubMed]
  13. D. Rees, T. J. Fuller-Rowell, A. Lyons, T. L. Killeen, P. B. Hays, Appl. Opt. 21, 3896 (1982).
    [CrossRef] [PubMed]
  14. T. L. Killeen, P. B. Hays, B. C. Kennedy, D. Rees, Appl. Opt. 21, 3903 (1982).
    [CrossRef] [PubMed]
  15. G. Hernandez, Appl. Opt. 5, 1745 (1966).
    [CrossRef] [PubMed]
  16. R. Petit, M. Cadilhae, C. R. Acad. Sci. 262, 468 (1966).
  17. R. F. Millar, Proc. Cambridge Philos. Soc. 65, 773 (1969).
    [CrossRef]
  18. R. F. Millar, Proc. Cambridge Philos. Soc. 69, 175 (1971).
    [CrossRef]
  19. P. M. van den Berg, J. T. Fokemer, J. Opt. Soc. Am. 69, 27 (1979).
    [CrossRef]
  20. Z. Knittl, Optics of Thin Films (Wiley, New York, 1976).

1982 (3)

1980 (1)

T. L. Killeen, P. B. Hays, B. C. Kennedy, J. Opt. Soc. Am. 70, 1588 (1980).

1979 (1)

1976 (1)

1974 (1)

T. R. Hicks, N. K. Reay, R. J. Scaddon, J. Phys. E 7, 27 (1974).
[CrossRef]

1971 (2)

R. F. Millar, Proc. Cambridge Philos. Soc. 69, 175 (1971).
[CrossRef]

P. B. Hays, R. G. Roble, Appl. Opt. 10, 193 (1971).
[CrossRef] [PubMed]

1970 (1)

1969 (1)

R. F. Millar, Proc. Cambridge Philos. Soc. 65, 773 (1969).
[CrossRef]

1968 (2)

E. B. Armstrong, Planet. Space Sci. 16, 211 (1968).
[CrossRef]

M. A. Biondi, W. A. Feibelman, Planet. Space Sci. 16, 431 (1968).
[CrossRef]

1966 (2)

R. Petit, M. Cadilhae, C. R. Acad. Sci. 262, 468 (1966).

G. Hernandez, Appl. Opt. 5, 1745 (1966).
[CrossRef] [PubMed]

1963 (1)

Armstrong, E. B.

E. B. Armstrong, Planet. Space Sci. 16, 211 (1968).
[CrossRef]

Biondi, M. A.

M. A. Biondi, W. A. Feibelman, Planet. Space Sci. 16, 431 (1968).
[CrossRef]

Cadilhae, M.

R. Petit, M. Cadilhae, C. R. Acad. Sci. 262, 468 (1966).

Chabbal, R. J.

Dobele, H. F.

Feibelman, W. A.

M. A. Biondi, W. A. Feibelman, Planet. Space Sci. 16, 431 (1968).
[CrossRef]

Fokemer, J. T.

Fuller-Rowell, T. J.

Hays, P. B.

Hernandez, G.

Hicks, T. R.

T. R. Hicks, N. K. Reay, R. J. Scaddon, J. Phys. E 7, 27 (1974).
[CrossRef]

Kennedy, B. C.

T. L. Killeen, P. B. Hays, B. C. Kennedy, D. Rees, Appl. Opt. 21, 3903 (1982).
[CrossRef] [PubMed]

T. L. Killeen, P. B. Hays, B. C. Kennedy, J. Opt. Soc. Am. 70, 1588 (1980).

Killeen, T. L.

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, New York, 1976).

Lyons, A.

Mack, J. E.

Massig, J. H.

McNutt, D. P.

Meaburn, J.

J. Meaburn, Detection and Spectrometry of Faint Light (Reidel, Boston, 1976).
[CrossRef]

Millar, R. F.

R. F. Millar, Proc. Cambridge Philos. Soc. 69, 175 (1971).
[CrossRef]

R. F. Millar, Proc. Cambridge Philos. Soc. 65, 773 (1969).
[CrossRef]

Petit, R.

R. Petit, M. Cadilhae, C. R. Acad. Sci. 262, 468 (1966).

Reay, N. K.

T. R. Hicks, N. K. Reay, R. J. Scaddon, J. Phys. E 7, 27 (1974).
[CrossRef]

Rees, D.

Roble, R. G.

Roesler, F. L.

J. E. Mack, D. P. McNutt, F. L. Roesler, R. J. Chabbal, Appl. Opt. 2, 873 (1963).

F. L. Roesler, in Methods of Experimental Physics, Vol. 12A, N. Carlton, Ed. (Academic, New York, 1974), p. 531.
[CrossRef]

Scaddon, R. J.

T. R. Hicks, N. K. Reay, R. J. Scaddon, J. Phys. E 7, 27 (1974).
[CrossRef]

Title, A.

A. Title, Fabry-Perot Interferometers as Narrow Band Optical Filters—Part 1 (Harvard Observatory Publication, Cambridge, 1970).

van den Berg, P. M.

Appl. Opt. (8)

C. R. Acad. Sci. (1)

R. Petit, M. Cadilhae, C. R. Acad. Sci. 262, 468 (1966).

J. Opt. Soc. Am. (2)

P. M. van den Berg, J. T. Fokemer, J. Opt. Soc. Am. 69, 27 (1979).
[CrossRef]

T. L. Killeen, P. B. Hays, B. C. Kennedy, J. Opt. Soc. Am. 70, 1588 (1980).

J. Phys. E (1)

T. R. Hicks, N. K. Reay, R. J. Scaddon, J. Phys. E 7, 27 (1974).
[CrossRef]

Planet. Space Sci. (2)

E. B. Armstrong, Planet. Space Sci. 16, 211 (1968).
[CrossRef]

M. A. Biondi, W. A. Feibelman, Planet. Space Sci. 16, 431 (1968).
[CrossRef]

Proc. Cambridge Philos. Soc. (2)

R. F. Millar, Proc. Cambridge Philos. Soc. 65, 773 (1969).
[CrossRef]

R. F. Millar, Proc. Cambridge Philos. Soc. 69, 175 (1971).
[CrossRef]

Other (4)

Z. Knittl, Optics of Thin Films (Wiley, New York, 1976).

A. Title, Fabry-Perot Interferometers as Narrow Band Optical Filters—Part 1 (Harvard Observatory Publication, Cambridge, 1970).

F. L. Roesler, in Methods of Experimental Physics, Vol. 12A, N. Carlton, Ed. (Academic, New York, 1974), p. 531.
[CrossRef]

J. Meaburn, Detection and Spectrometry of Faint Light (Reidel, Boston, 1976).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Electromagnetic field on a boundary of the corrugated thin-film system.

Equations (54)

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a ( x , y ) = { 1 within the aperture domain 0 otherwise ,
z = g ( x , y ) ,
x 1 ( 2 π ) 2 - F R ( α R , β R ) exp [ - i k R ( α R , β R ) · r ] d α R d β R , x 1 ( 2 π ) 2 - F L ( α L , β L ) exp [ - i k L ( α L , β L ) · r ] d α L d β L ,
x 1 ( 2 π ) 2 - F R ( α R , β R ) exp [ - i k R ( α R , β R ) · r ] d α R d β R , x 1 ( 2 π ) 2 - F L ( α L , β L ) exp [ - i k L ( α L , β L ) · r ] d α L d β L ,
x f R ( x , y ) , x f L ( x , y ) , x f R ( x , y ) , x f L ( x , y )
x f R ( x , y ) exp [ - i ϕ R ( x , y ) ] , x f L ( x , y ) exp [ - i ϕ L ( x , y ) ] , x f R ( x , y ) exp [ - i ϕ R ( x , y ) ] , x f L ( x , y ) exp [ - i ϕ L ( x , y ) ] , }
ϕ R , L ( x , y ) = β 0 y ± γ 0 g ( x , y ) [ = ± 2 π λ n g ( x , y ) ] , ϕ R , L ( x , y ) = β 0 y ± γ 0 g ( x , y ) [ = ± 2 π λ n g ( x , y ) ] , }
y X f R ( x , y ) exp [ - i ϕ R ( x , y ) ] , - y X f L ( x , y ) exp [ - i ϕ L ( x , y ) ] , y X f R ( x , y ) exp [ - i ϕ R ( x , y ) ] , - y X f L ( x , y ) exp [ - i ϕ L ( x , y ) ] , }
X = 1 μ ω z · k 0 [ = n μ c ] , X = 1 μ ω z · k 0 [ = n μ c ] , }
X = c 2 μ n 2 ω z · k 0 [ = c μ n ] , X = c 2 μ n 2 ω z · k 0 [ = c μ n ] , }
x { f R ( x , y ) exp [ - i ϕ R ( x , y ) ] + f L ( x , y ) exp [ - i ϕ L ( x , y ) ] } = x { f R ( x , y ) exp [ - i ϕ R ( x , y ) ] + f L ( x , y ) exp [ - i ϕ L ( x , y ) ] } ,
y X { f R ( x , y ) exp [ - i ϕ R ( x , y ) ] - f L ( x , y ) exp [ - i ϕ L ( x , y ) ] } = y X { f R ( x , y ) exp [ - i ϕ R ( x , y ) ] - f L ( x , y ) exp [ - i ϕ L ( x , y ) ] } .
B R ( α R , β R ) = F R ( α R , β R ) G R ( α R , β R ) , B L ( α L , β L ) = F L ( α L , β L ) G L ( α L , β L ) , B R ( α R , β R ) = F R ( α R , β R ) G R ( α R , β R ) , B L ( α L , β L ) = F L ( α L , β L ) G L ( α L , β L ) , }
F R ( α R , β R ) = - f R ( x , y ) exp i ( α R x + β R y ) d x d y , F L ( α L , β L ) = - f L ( x , y ) exp i ( α L x + β L y ) d x d y , F R ( α R , β R ) = - f R ( x , y ) exp i ( α R x + β R y ) d x d y , F L ( α L , β L ) = - f L ( x , y ) exp i ( α L x + β L y ) d x d y , }
G R ( α R , β R ) = - a ( x , y ) exp [ - i ϕ R ( x , y ) ] × exp i ( α R x + β R y ) d x d y , G L ( α L , β L ) = - a ( x , y ) exp [ - i ϕ L ( x , y ) ] × exp i ( α L x + β L y ) d x d y , G R ( α R , β R ) = - a ( x , y ) exp [ - i ϕ R ( x , y ) × exp i ( α R x + β R y ) d x d y , G L ( α L , β L ) = - a ( x , y ) exp [ - i ϕ L ( x , y ) ] × exp i ( α L x + β L y ) d x d y . }
- B R ( α R , β R ) exp - i ( α R x + β R y ) d α R β R + - B L ( α L , β L ) exp - i ( α L x + β L x ) d α L d β L = - B R ( α R , β R ) exp - i ( α R x + β R y ) d α R d β R + - B L ( α L , β L ) exp - i ( α L x + β L y ) d α L d β L ,
X { - B R ( α R , β R ) exp - i ( α R x + β R y ) d α R d β R - - B L ( α L , β L ) exp - ( α L x + β L y ) d α L d β L } = X { - B R ( α R , β R ) exp - i ( α R x + β R y ) d α R d β R - - B L ( α L , β L ) exp - i ( α L x + β L y ) d α L d β L } ,
( Δ α ) = 2 π / L x and ( Δ β ) = 2 π / L y ,
α R = α L = α R = α L , β R = β L = β R = β L , }
B R ( α , β ) + B L ( α , β ) = B R ( α , β ) + B L ( α , β ) ,
X [ B R ( α , β ) - B L ( α , β ) ] - X [ B R ( α , β ) - B L ( α , β ) ] ,
F R ν ( α , β ) = exp ( i γ 0 h ν ) · F R ν + 1 ( α , β ) , F L ν ( α , β ) = exp ( - i γ 0 h ν ) · F L ν + 1 ( α , β ) , }
G R ν ( α , β ) = G R ν + 1 ( α , β ) , G L ν ( α , β ) = G L ν + 1 ( α , β ) . }
B R ν ( α , β ) = exp ( i γ 0 ν h ν ) B R ν + 1 ( α , β ) , B L ν ( α , β ) = exp ( - i γ 0 ν h ν ) B L ν + 1 ( α , β ) , }
B R ( α , β ) = t R B R ( α , β ) ,
B L ( α , β ) = r R B R ( α , β ) ,
F R ( α , β ) = t R · F R ( α , β ) P R ( t ) ( α , β ) ,
F L ( α , β ) = r R · F R ( α , β ) P R ( r ) ( α , β ) ,
P R ( t ) ( α , β ) = - a ( x , y ) exp [ - i 2 π λ ( n - n ) g ( x , y ) ] × exp i ( α x + β y ) d x d y ,
P R ( r ) ( α , β ) = - a ( x , y ) exp [ - i 4 π λ n · g ( x , y ) ] × exp i ( α x + β y ) d x d y .
F L ( α , β ) = t L · F ( L ) ( α , β ) P L ( t ) ( α , β ) ,
F ( R ) ( α , β ) = r L · F ( L ) ( α , β ) P L ( r ) ( α , β ) ,
t R = t R I · t R I I I exp - i ψ d 1 - r L I r R I I exp - i 2 ψ d ,
ψ d ( α , β , h d ) = ( α , β ) · h d ,
= [ ( 2 π λ ) 2 - α 2 - β 2 ] 1 / 2 ,
t R = t R I t R I I exp ( - i ψ d ) · ( 1 + q + q 2 + ) ,
q = r L I r R I I exp ( - i 2 ψ d ) ,
t R = t R I t R I I [ F R P R I ( t ) ] exp ( - i ψ d ) P R I I ( t ) + t R I t R I I r R I I r L I ( { [ F R P R I ( t ) ] exp ( - i ψ d ) P R I I ( r ) } × exp ( - i ψ d ) P L I ( r ) ) exp ( - i ψ d ) P R I I ( t ) + t R I t R I I ( r R I I r L I ) 2 { [ ( { [ F R P R I ( t ) ] exp ( - i ψ d ) P R I I ( r ) } × exp ( - i ψ d ) P L I ( ( r ) ) exp ( - i ψ d ) P R I I ( r ) ] exp ( - i ψ d ) P L I ( r ) } × exp ( - i ψ d ) P R I I ( t ) + ,
P R I ( t ) = P R I ( t ) ( α , β ) = - a ( x , y ) exp [ - i 2 π λ ( n 1 - n 2 ) g I ( x , y ) ] × exp i ( α x + β y ) d x d y ,
P R I I ( t ) = P R I I ( t ) ( α , β ) = - a ( x , y ) exp [ - i 2 π λ ( n 2 - n 3 ) g I I ( x , y ) ] × exp i ( α x + β y ) d x d y ,
P L I ( r ) = P L I ( r ) ( α , β ) = - a ( x , y ) exp [ - i 4 π λ n 2 g I ( x , y ) ] × exp i ( α x + β y ) d x d y ,
P R I I ( r ) = P R I I ( r ) ( α , β ) = - a ( x , y ) exp [ - i 4 π λ n 2 g I I ( x , y ) ] × exp i ( α x + β y ) d x d y .
J ( α , β , h d ) = 2 t R ( α , β , h d ) 2 ,
I ( h d , ρ ) = - J ( α , β , h d ) · D ( α , β , ρ ) d α d β ,
D ( α , β , ρ ) = D 0 ( α , β , ρ ) - D I ( α , β , ρ ) ,
D 0 ( α , β , ρ ) = { 1 for α 2 + β 2 k 2 ( ρ 2 + S / π ) / f 2 0 otherwise ,
D I ( α , β , ρ ) = { 1 for α 2 + β 2 k 2 ρ 2 / f 2 0 otherwsise ,
I ( λ , λ = λ ) = I [ h d ( λ ) , ρ = const ] ,
h d ( λ ) = h d max 2 - e λ λ c ( h d max 2 - h d max 1 ) ,
I ( λ , λ = λ ) = I [ h d = const , ρ ( λ ) ] ,
ρ 2 ( λ ) = ρ max 1 2 + e λ λ c ( ρ max 2 2 - ρ max 1 2 ) .
L ( λ ) = I ( λ , λ ) L ( λ ) d λ
I ( λ , λ ) = I [ h d ( λ ) , ρ ( λ ) ]
I ( λ , λ ) = I [ h d ( λ ) , ρ ( λ ) ]

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