Abstract

No abstract available.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Sossi, “On the Theory of the Synthesis of Multilayer Dielectric Light Filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171 (1976).
  2. W. H. Southwell, “Use of Gradient Index for Spectral Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 464, 11 (1984).
  3. E. Delano, “Fourier Synthesis of Multilayer Filters,” J. Opt. Soc. Am. 57, 1529 (1967).
    [Crossref]
  4. B. G. Bovard, “Derivation of a Matrix Describing a Rugate Dielectric Thin Film,” Appl. Opt. 27, 1998 (1988).
    [Crossref] [PubMed]
  5. H. A. Macleod, Thin-Film Optical Filters (MacMillan, New York, 1986).
    [Crossref]

1988 (1)

1984 (1)

W. H. Southwell, “Use of Gradient Index for Spectral Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 464, 11 (1984).

1976 (1)

L. Sossi, “On the Theory of the Synthesis of Multilayer Dielectric Light Filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171 (1976).

1967 (1)

Bovard, B. G.

Delano, E.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (MacMillan, New York, 1986).
[Crossref]

Sossi, L.

L. Sossi, “On the Theory of the Synthesis of Multilayer Dielectric Light Filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171 (1976).

Southwell, W. H.

W. H. Southwell, “Use of Gradient Index for Spectral Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 464, 11 (1984).

Appl. Opt. (1)

Eesti NSV Tead. Akad. Toim. Fuus. Mat. (1)

L. Sossi, “On the Theory of the Synthesis of Multilayer Dielectric Light Filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171 (1976).

J. Opt. Soc. Am. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

W. H. Southwell, “Use of Gradient Index for Spectral Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 464, 11 (1984).

Other (1)

H. A. Macleod, Thin-Film Optical Filters (MacMillan, New York, 1986).
[Crossref]

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.


Figures (3)

Fig. 1
Fig. 1

Comparison of the maximum reflectances obtained using various Q-functions in the case where nH = 1.55 and nL = 1.45. The outer media have a refractive index nL. Curve 1, matrix multiplication; curve 2, Delano; curve 3, Sossi; curve 4, logarithmic; and curve 5, the new Q function presented here.

Fig. 2
Fig. 2

Reflectance of a rejection filter designed using different approximations. The desired halfwidth is 20 nm, the desired maximum reflectance is 90%, and the total optical thickness is 20 μm. The substrate and incident medium refractive indices are 1.52. Diamonds, Q-function presented here; squares, Sossi; triangles, logarithmic; circles, Delano. The square function is the desired reflectance.

Fig. 3
Fig. 3

Comparison of the bandwidth of a mirror calculated with the matrix calculation technique with the bandwidth calculated using the Fourier transform approximation.

Equations (15)

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

- x 0 + x 0 n ( x ) 2 n ( x ) exp ( - 2 i π σ x ) · d x = Q ( σ ) exp [ i Φ ( σ ) ] ,
Q ( σ ) = R ( σ ) T ( σ ) ;
Q ( σ ) = 1 2 [ 1 T ( σ ) - T ( σ ) ] ;
Q ( σ ) = - log [ T ( σ ) ] .
r ( x ) = n ( x ) 2 n ( x )
r ( x ) = r · [ m = - m = + δ ( x - m σ 0 ) - m = - m = + δ ( x - 2 m + 1 2 σ 0 ) ]
r = ( n H - n L ) ( n H + n L ) ,
Q ( σ ) exp [ i ϕ ( σ ) ] = 2 r · [ m = - m = + δ ( σ σ 0 - 2 m - 1 ) ]
Q ( σ ) ¯ exp [ i Φ ( σ ) ¯ ] = 4 r σ 0 x 0 m = - m = + [ sin { 2 π [ σ - ( 2 m + 1 ) σ 0 ] x 0 } 2 π [ σ - ( 2 m + 1 ) σ 0 ] x 0 ] ,
q = 2 x 0 σ 0 ,
Q max = 2 r q .
R = [ 1 - ( n L n H ) 2 q - 1 1 + ( n L n H ) 2 q - 1 ] 2 = { 1 - exp [ 2 q - 1 · log ( n L n H ) ] 1 + exp [ 2 q - 1 · log ( n L n H ) ] } 2 .
R = [ 1 - exp ( - 4 q r ) 1 + exp ( - 4 q r ) ] 2 2 q r = 1 2 log 1 + R 1 - R .
Q ( σ ) = 1 2 log 1 + R ( σ ) 1 - R ( σ ) .
Δ g = 4 π sin - 1 ( n H - n L n H + n L ) .

Metrics