Abstract

By abandoning the concept of detuned Fabry-Perot interference filters for the design of nonpolarizing edge filters at oblique incidence and applying classical Herpin equivalent layer theory, the number of usable structures can be greatly expanded, and exact equations for aligning the edges in all cases can be derived.

© 1984 Optical Society of America

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References

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  1. H. F. Mahlein, “Designing of Edge Interference Filters for Wavelength-Division-Multiplex Transmission over Multimode Optical Fibers,” Siemens Forsch. Entwicklungsber. 9, No. 3, 142 (1980).
  2. H. F. Mahlein, H. Michel, W. Rauscher, A. Reichelt, G. Winzer, “Interference Filter All-Fibre Directional Coupler for for W.D.M.,” Electron. Lett. 16, 584 (1980).
    [CrossRef]
  3. H. F. Mahlein, “Wavelength-Selective Beam Splitters with Minimum Polarizing Effects for Wavelength-Division Multiplexing in Optical Communications Systems,” Opt. Acta 28, 29 (1981).
    [CrossRef]
  4. H. Rausch, “Fiber Optics: Expectations Achieved but Some Optical Illusions Remain,” Opt. News6 (July/Aug.1983).
    [CrossRef]
  5. A. Thelen, “Avoidance or Enhancement of Polarization in Multilayers,” J. Opt. Soc. Am. 70, 118 (1980).
    [CrossRef]
  6. A. Thelen, “Nonpolarizing Edge Filters,” J. Opt. Soc. Am. 71, 309 (1981).
    [CrossRef]
  7. L. I. Epstein, “Design of Optical Filters,” J. Opt. Soc. Am. 42, 806 (1952).
    [CrossRef]
  8. A. Thelen, “Equivalent Layers in Multilayer Filters,” J. Opt. Soc. Am. 56, 1533 (1966).
    [CrossRef]

1983 (1)

H. Rausch, “Fiber Optics: Expectations Achieved but Some Optical Illusions Remain,” Opt. News6 (July/Aug.1983).
[CrossRef]

1981 (2)

H. F. Mahlein, “Wavelength-Selective Beam Splitters with Minimum Polarizing Effects for Wavelength-Division Multiplexing in Optical Communications Systems,” Opt. Acta 28, 29 (1981).
[CrossRef]

A. Thelen, “Nonpolarizing Edge Filters,” J. Opt. Soc. Am. 71, 309 (1981).
[CrossRef]

1980 (3)

A. Thelen, “Avoidance or Enhancement of Polarization in Multilayers,” J. Opt. Soc. Am. 70, 118 (1980).
[CrossRef]

H. F. Mahlein, “Designing of Edge Interference Filters for Wavelength-Division-Multiplex Transmission over Multimode Optical Fibers,” Siemens Forsch. Entwicklungsber. 9, No. 3, 142 (1980).

H. F. Mahlein, H. Michel, W. Rauscher, A. Reichelt, G. Winzer, “Interference Filter All-Fibre Directional Coupler for for W.D.M.,” Electron. Lett. 16, 584 (1980).
[CrossRef]

1966 (1)

1952 (1)

Epstein, L. I.

Mahlein, H. F.

H. F. Mahlein, “Wavelength-Selective Beam Splitters with Minimum Polarizing Effects for Wavelength-Division Multiplexing in Optical Communications Systems,” Opt. Acta 28, 29 (1981).
[CrossRef]

H. F. Mahlein, “Designing of Edge Interference Filters for Wavelength-Division-Multiplex Transmission over Multimode Optical Fibers,” Siemens Forsch. Entwicklungsber. 9, No. 3, 142 (1980).

H. F. Mahlein, H. Michel, W. Rauscher, A. Reichelt, G. Winzer, “Interference Filter All-Fibre Directional Coupler for for W.D.M.,” Electron. Lett. 16, 584 (1980).
[CrossRef]

Michel, H.

H. F. Mahlein, H. Michel, W. Rauscher, A. Reichelt, G. Winzer, “Interference Filter All-Fibre Directional Coupler for for W.D.M.,” Electron. Lett. 16, 584 (1980).
[CrossRef]

Rausch, H.

H. Rausch, “Fiber Optics: Expectations Achieved but Some Optical Illusions Remain,” Opt. News6 (July/Aug.1983).
[CrossRef]

Rauscher, W.

H. F. Mahlein, H. Michel, W. Rauscher, A. Reichelt, G. Winzer, “Interference Filter All-Fibre Directional Coupler for for W.D.M.,” Electron. Lett. 16, 584 (1980).
[CrossRef]

Reichelt, A.

H. F. Mahlein, H. Michel, W. Rauscher, A. Reichelt, G. Winzer, “Interference Filter All-Fibre Directional Coupler for for W.D.M.,” Electron. Lett. 16, 584 (1980).
[CrossRef]

Thelen, A.

Winzer, G.

H. F. Mahlein, H. Michel, W. Rauscher, A. Reichelt, G. Winzer, “Interference Filter All-Fibre Directional Coupler for for W.D.M.,” Electron. Lett. 16, 584 (1980).
[CrossRef]

Electron. Lett. (1)

H. F. Mahlein, H. Michel, W. Rauscher, A. Reichelt, G. Winzer, “Interference Filter All-Fibre Directional Coupler for for W.D.M.,” Electron. Lett. 16, 584 (1980).
[CrossRef]

J. Opt. Soc. Am. (4)

Opt. Acta (1)

H. F. Mahlein, “Wavelength-Selective Beam Splitters with Minimum Polarizing Effects for Wavelength-Division Multiplexing in Optical Communications Systems,” Opt. Acta 28, 29 (1981).
[CrossRef]

Opt. News (1)

H. Rausch, “Fiber Optics: Expectations Achieved but Some Optical Illusions Remain,” Opt. News6 (July/Aug.1983).
[CrossRef]

Siemens Forsch. Entwicklungsber. (1)

H. F. Mahlein, “Designing of Edge Interference Filters for Wavelength-Division-Multiplex Transmission over Multimode Optical Fibers,” Siemens Forsch. Entwicklungsber. 9, No. 3, 142 (1980).

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Figures (5)

Fig. 1
Fig. 1

Reflectance in the two planes of polarization of the design 1.0|0.7S1(0.5161H 0.2876L 0.3725H 0.2876L 0.5161H)2 (0.4213H 0.4905L 0.1763H 0.4905L 0.4213H)5 (0.5161H 0.2876L 0.3725H 0.2876L 0.5161H)2 0.7S2|1.52 with nH = 3.5, nL = 1.45, nS1 = 1.72, nS2 = 2.13, and 45° light incidence as a function of the relative wave number λ0\λ. λ0 is the design wavelength defined as the wavelength where the layers described by capital letters (H,L,S1,S2) are a quarterwave thick. S1 and S2 are temporary matching layers which later are replaced by synthesized H–L combinations.

Fig. 2
Fig. 2

Reflectance in the two planes of polarization of the design 1.0|0.7S1 (0.4213H 0.4905L 0.1763H 0.4905L 0.4213H)6 0.7S2|1.52 with nH = 3.5, nL = 1.45, nS1 = 1.72, nS2 = 2.13, and 45° light incidence.

Fig. 3
Fig. 3

Reflectance in the two planes of polarization of the design 1.0|0.7S1 (0.4116H 0.5249L 0.1271H 0.5249L 0.4116H)6 0.7S2|1.52 with nH = 3.5, nL = 1.45, nS1 = 1.72, nS2 = 2.13, and 45° light incidance.

Fig. 4
Fig. 4

Reflectance in the two planes of polarization of the design 1.0|(0.1678H 0.5613L 0.1678H) (0.9143H 0.1867L 0.7880H 0.1867L 0.9143H) (0.7320H 0.4648L 0.4680H 0.4648L 0.7320H) (0.6153H 0.7847L 0.1900H 0.7847L 0.6153H)4 (0.7320H 0.4648L 0.4680H 0.4648L 0.7320H) (0.9143H 0.1867L 0.7880H 0.1867L 0.9143H) (0.2752H 0.3467L 0.2752H)|1.52 with nH = 3.5, nL = 1.45, and 45° light incidence. λ0 equals 1 μm. (Reflectance holes below 0.8 μm are omitted.)

Fig. 5
Fig. 5

Reflectance in the two planes of polarization of the design 1.0|0.2941H 1.02(0.3824H 0.1765L 0.3529H 0.1766L 0.3529H 0.1765L 0.3824H) (0.3824H 0.1765L 0.3529H 0.1766L 0.3529H 0.1765L 0.3824H)4 1.02(0.3824H 0.1765L 0.3529H 0.1766L 0.3529H 0.1765L 0.3824H) (0.2941H 0.2941L 0.2941H)|1.52 with nH = 2.28, nL = 1.45, and 45° light incidence.

Equations (18)

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a 1 A 1 a 2 A 2 a ν - 1 A ν - 1 a ν A ν a ν A ν a ν - 1 A ν - 1 a 1 A 1
a 1 A 1 a 2 A 2 a ν - 1 A ν - 1 a ν A ν
( B ) = ( B 1 ) ( B 2 ) ( B ν - 2 ) ,
( Q ) = ( B ) ( cos ψ ν - 1 j sin ψ ν - 1 / n ν - 1 j n ν - 1 sin ψ ν - 1 cos ψ ν - 1 ) × ( cos ψ ν j sin ψ ν / n ν j n ν sin ψ ν cos ψ ν )
Q 11 = B 11 ( cos ψ ν - 1 cos ψ ν - sin ψ ν - 1 sin ψ ν n ν / n ν - 1 ) - B 12 ( n ν - 1 sin ψ ν - 1 cos ψ ν + n ν cos ψ ν - 1 sin ψ ν )
( M ) = ( M 11 j M 12 j M 21 M 22 ) = ( Q 11 j Q 12 j Q 21 Q 22 ) ( Q 22 j Q 12 j Q 21 Q 11 ) × ( Q 11 Q 22 - Q 12 Q 21 2 j Q 11 Q 12 2 j Q 22 Q 21 - Q 12 Q 21 + Q 11 Q 22 ) .
Q 11 or Q 12 or Q 21 or Q 22 = 0.
tan ψ ν - 1 = B 11 / B 12 - n ν tan ψ ν n ν - 1 + B 11 n ν tan ψ ν / ( B 12 n ν - 1 ) .
[ B 11 / B 12 - n ν tan ψ ν n ν - 1 + B 11 n ν tan ψ ν / ( B 12 n ν - 1 ) ] - [ B 11 / B 12 - n ν tan ψ ν n ν - 1 + B 11 n ν tan ψ ν / ( B 12 n ν - 1 ) ] = 0 ,
Q 12 = 0 : [ B 12 / B 11 + tan ψ ν / n ν - 1 / n ν - 1 + B 12 n ν - 1 tan ψ ν / ( B 11 n ν ) ] - [ B 12 / B 11 + tan ψ ν / n ν - 1 / n ν - 1 + B 12 n ν - 1 tan ψ ν / ( B 11 n ) ] = 0 ;
Q 21 = 0 : [ B 21 / B 22 + n ν tan ψ ν - n ν - 1 + B 21 n ν tan ψ ν / ( B 22 n ν - 1 ) ] - [ B 21 / B 22 + n ν tan ψ ν - n ν - 1 + B 21 n ν tan ψ ν / ( B 22 n ν - 1 ) ] = 0 ;
Q 22 = 0 : [ B 22 / B 21 - tan ψ ν / n ν 1 / n ν - 1 + B 22 n ν - 1 tan ψ ν / ( B 21 n ν ) ] - [ B 22 / B 21 - tan ψ ν / n ν 1 / n ν - 1 + B 22 n ν - 1 tan ψ ν / ( B 21 n ν ) ] = 0.
a 1 A 1 a 2 A 2 a 3 A 1 a 3 A 1 a 2 A 2 a 1 A 1 .
B 11 = cos ψ 1 , B 21 = n 1 sin ψ 1 , B 12 = sin ψ 1 / n 1 , B 22 = cos ψ 1 .
F ( n 1 , n 2 , , n ν ; ψ 1 , ψ 2 , , ψ ν - 2 , ψ ν ) - F ( n 1 , n 2 , , n ν ; ψ 1 , ψ 2 , , ψ ν - 2 , ψ ν ) = 0.
tan - 1 { F ( n 1 , n 2 , , n ν ; ψ 1 , ψ 2 , , ψ ν - 2 , ψ ν ) } - tan - 1 { F ( n 1 , n 2 , , n ν ; ζ ψ 1 , ζ ψ 2 , , ζ ψ ν - 2 , ζ ψ ν ) } / ζ = 0 ,
a 1 A 1 a 2 A 2 a 3 A 1 a 4 A 2 a 4 A 2 a 3 A 1 a 2 A 2 a 1 A 1 ,
B 11 = cos ψ 1 cos ψ 2 - ( n 2 / n 1 ) sin ψ 1 sin ψ 2 , B 12 = ( 1 / n 2 ) cos ψ 1 sin ψ 2 + ( 1 / n 1 ) sin ψ 1 cos ψ 2 , B 21 = n 1 sin ψ 1 cos ψ 2 + n 2 cos ψ 1 sin ψ 2 , B 22 = - ( n 1 / n 2 ) sin ψ 1 sin ψ 2 + cos ψ 1 cos ψ 2 .

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