Abstract

A five-cavity bandpass is designed. The spectral transmittance simulates a Chebyshev polynomial. The same principles are used to design a bandpass that resides in a cemented cube at a 45° angle of incidence that has minimal polarization splitting.

© 1992 Optical Society of America

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References

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  1. A. J. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989), Chap. 10.
  2. H. Pohlack, “Synthesis of optical coatings with prescribed spectral characteristics,” in Jenaer Jahrbuch (Carl Zeiss, Jena, 1952).
  3. P. Kard, Analysis and Synthesis of Multilayer Interference Coatings (Valgus, Tallinn, Estonia, 1971).
  4. P. W. Baumeister, “Simplified equations for maximally flat all dielectric bandpass design,” Appl. Opt. 22, 1960 (1983).
    [CrossRef] [PubMed]
  5. J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893
    [PubMed]
  6. P. W. Baumeister, “Transmission and degree of polarization of quarterwave stacks at nonnormal incidence,” Opt. Acta 8, 105–119 (1961).
    [CrossRef]
  7. A. J. Thelen, “Nonpolarizing interference films inside a glass cube,” Appl. Opt. 15, 2983–2985 (1976).
    [CrossRef] [PubMed]
  8. P. W. Baumeister, “Optical coating technology,” lecture notes for the five-day short course engineering 823.17 at the UCLA Extension, University of California, Los Angeles, 14January, 1991, Chap. 7.
  9. A. F. Turner, “Infrared transmission filters,” Quarterly technical report number 5 of Contract DA-44-009-eng-1113 with US Army Engineer Research and Development Laboratories, Fort Belvoir VA. Published by Bausch and Lomb, Rochester NY, July1953.
  10. S. D. Smith, “Design of multilayer filters by considering two effective interfaces,” J. Opt. Soc. Am. 48, 43–50 (1958).
    [CrossRef]
  11. A. J. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 56, 1533–1538 (1966).
    [CrossRef]
  12. J. S. Seeley, “Synthesis of interference filters,” Proc. Phys. Soc. (London) 78, 998–1008 (1961).
    [CrossRef]

1983 (1)

1976 (1)

1966 (1)

1961 (2)

J. S. Seeley, “Synthesis of interference filters,” Proc. Phys. Soc. (London) 78, 998–1008 (1961).
[CrossRef]

P. W. Baumeister, “Transmission and degree of polarization of quarterwave stacks at nonnormal incidence,” Opt. Acta 8, 105–119 (1961).
[CrossRef]

1958 (1)

Baumeister, P. W.

P. W. Baumeister, “Simplified equations for maximally flat all dielectric bandpass design,” Appl. Opt. 22, 1960 (1983).
[CrossRef] [PubMed]

P. W. Baumeister, “Transmission and degree of polarization of quarterwave stacks at nonnormal incidence,” Opt. Acta 8, 105–119 (1961).
[CrossRef]

P. W. Baumeister, “Optical coating technology,” lecture notes for the five-day short course engineering 823.17 at the UCLA Extension, University of California, Los Angeles, 14January, 1991, Chap. 7.

Dobrowolski, J. A.

Kard, P.

P. Kard, Analysis and Synthesis of Multilayer Interference Coatings (Valgus, Tallinn, Estonia, 1971).

Kemp, R. A.

Pohlack, H.

H. Pohlack, “Synthesis of optical coatings with prescribed spectral characteristics,” in Jenaer Jahrbuch (Carl Zeiss, Jena, 1952).

Seeley, J. S.

J. S. Seeley, “Synthesis of interference filters,” Proc. Phys. Soc. (London) 78, 998–1008 (1961).
[CrossRef]

Smith, S. D.

Thelen, A. J.

Turner, A. F.

A. F. Turner, “Infrared transmission filters,” Quarterly technical report number 5 of Contract DA-44-009-eng-1113 with US Army Engineer Research and Development Laboratories, Fort Belvoir VA. Published by Bausch and Lomb, Rochester NY, July1953.

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

Opt. Acta (1)

P. W. Baumeister, “Transmission and degree of polarization of quarterwave stacks at nonnormal incidence,” Opt. Acta 8, 105–119 (1961).
[CrossRef]

Proc. Phys. Soc. (London) (1)

J. S. Seeley, “Synthesis of interference filters,” Proc. Phys. Soc. (London) 78, 998–1008 (1961).
[CrossRef]

Other (5)

P. W. Baumeister, “Optical coating technology,” lecture notes for the five-day short course engineering 823.17 at the UCLA Extension, University of California, Los Angeles, 14January, 1991, Chap. 7.

A. F. Turner, “Infrared transmission filters,” Quarterly technical report number 5 of Contract DA-44-009-eng-1113 with US Army Engineer Research and Development Laboratories, Fort Belvoir VA. Published by Bausch and Lomb, Rochester NY, July1953.

A. J. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989), Chap. 10.

H. Pohlack, “Synthesis of optical coatings with prescribed spectral characteristics,” in Jenaer Jahrbuch (Carl Zeiss, Jena, 1952).

P. Kard, Analysis and Synthesis of Multilayer Interference Coatings (Valgus, Tallinn, Estonia, 1971).

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Figures (9)

Fig. 1
Fig. 1

Transmittance versus phase thickness of the design air ABCBA air, where the refractive indices of air, A, B, and C are 1.00, 4.71, 0.226, and 7.314, respectively. Each layer has the same phase thickness. T x is the transmittance ripple in the passband.

Fig. 2
Fig. 2

Refractive index versus optical thickness of the filter given in Fig. 1. The numbers 1, 2, 3, 4, and 5 refer to the layers, I to the incident medium, and E to the emergent medium.

Fig. 3
Fig. 3

Transmittance versus wavelength of a bandpass with the following design: cement 1.357L 0.255H 1.357LH 2LHL 1.312H 0.340L 1.312HL 2HLH 1.132L 0.705H 1.132LH 2LH 1.132L 0.705H 1.132LHL 2HL 1.312H 0.340L 1.312HLH 2LH 1.357L 0.255H 1.357L glass

Fig. 4
Fig. 4

Figure 3 obtains, except that the transmittance in the passband spectral region is shown.

Fig. 5
Fig. 5

Design of a prototype four-cavity bandpass (of a Chebyshev type) in which the refractive indices of Incident, layer 1, layer 2, layer 3, layer 4, and Emergent are 1.00, 8.96, 0.116, 13.4, 0.17, and 1.554, respectively. The η is 7.74 and the reflectance ripple in the passband is 4.7%.

Fig. 6
Fig. 6

Figure 3 obtains, except that the transmittance for TE polarized flux (solid curves) and TM (dashed curve) is shown. The metric thickness of each layer is adjusted so that each is matched at angle. The angle of incidence is 45° in a reference medium of air (see Fig. 7).

Fig. 7
Fig. 7

A bandpass (dotted line) is sandwiched with optical cement (shaded area) between two plane-parallel glass plates. The angle of incidence θref is measured in a reference medium of air. The thickness of the bandpass is exaggerated for purposes of illustration.

Fig. 8
Fig. 8

Bandpass (dotted line) sandwiched with optical cement (shaded area) between two Porro prisms. The thickness of the bandpass is exaggerated for purposes of illustration.

Fig. 9
Fig. 9

Transmittance of a bandpass for TE polarized flux (solid curve) and TM (dashed curve). The angle of incidence is 45° in the incident medium of index 1.63. The design is glass (MLMH)2LL(M1LM1)4LL(M2LM2H2)5LL(H2M2LM2)5LL(M1LM1H1)4LL(HMLM)2 glass,

Tables (4)

Tables Icon

Table I Coefficients in Eq. (11) for a Stack of Five Nonabsorbing Layers of Equal Optical Thickness, Where the Parameter u l is Related to the Refractive Index by Eq. (12)

Tables Icon

Table II SWR’s at λ0 of Nonabsorbing Layers a

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Table III Design of a Bandpass Whose Transmittance is Similar to that Shown in Fig. 3. a

Tables Icon

Table IV Coefficients in the R/T Polynomial for Prototype Bandpasses with Specified Numbers of Sections, Ranging from Three to Seven; The Equations are Expressed in fortran Computer Language

Equations (53)

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V i = 1 + R i 1 R i .
F = F m [ τ 5 ( sin β sin β ) ] 2 [ τ 5 ( 1 sin β ) ] 2 ,
F m ( 1 + V m ) 2 / ( 4 V m ) .
V m i = 0 q V i .
η log ( V m ) .
τ 5 ( x ) 16 x 5 20 x 3 + 5 x .
β i 2 π n i h i cos θ i ,
F x R x / T x = 0 . 05 / 0 . 95 = 0 . 053 .
F = F m G 1 [ 16 sin 5 β 20 sin 3 β sin 2 β + 5 sin β sin 4 β ] ,
G 16 20 sin 2 β + 5 sin 4 β .
F = [ a 1 sin β cos 4 β a 3 sin 3 β cos 2 β + a 5 sin 5 β ] 2 + [ a 0 cos 5 β a 2 sin 2 β cos 3 β + a 4 sin 4 β cos β ] 2 .
u i 1 2 ln ( n i / n s )
F = a 1 sin β cos 4 β a 3 sin 3 β cos 2 β + a 5 sin 5 β,
F = a 1 sin β ( 1 sin 2 β ) 2 a 3 sin 3 β ( 1 sin 2 β ) + a 5 sin 5 β .
a 1 = 5 F m G 1 sin 4 β ,
a 3 = 20 F m G 1 sin 2 β 2 a 1 ,
a 5 = 16 F m G 1 a 1 a 3 .
n i = n s exp ( 2 u i ) .
a 1 = sinh ( 2 u 3 ) 2 [ sinh ( 2 u 1 ) + sinh ( 2 u 2 ) ] ,
a 3 = 2 { sinh [ 2 ( u 1 + u 2 u 3 ) ] + sinh ( 2 u 1 ) + sinh ( 4 u 1 + 2 u 2 ) + sinh [ 2 ( u 1 u 2 + u 3 ) ] } + sinh ( 4 u 1 + 2 u 3 ) + sinh ( 4 u 2 + 2 u 3 ) ,
a 5 = sinh ( 4 u 1 + 4 u 2 2 u 3 ) .
τ 5 ( 1 sin β ) = ( F m F x ) 1 / 2 .
( 16 20 sin 2 β + 5 sin 4 β ) ( F x F m ) 1 / 2 = sin 5 β .
n i = n i 1 ( V i 1 ) ± 1 ,
y = [ n l 1 n l n l 3 n l 2 n 3 n 4 n 1 n 2 ] 2 n s n 0 ,
y = [ n l n l 1 n l 2 n l 3 n 3 n 2 n 1 ] 2 1 n s n 0 ,
V = y ± 1 ,
low HL E 1 L HL high ,
n H 5 n E 1 2 n L 7 = 32 . 3 .
low HL E 3 L substrate ,
n H 2 n E 3 2 n s n L 5 = 4 . 71 .
n s = 1 + R x 1 R x .
u 0 = u 1 + u 4 , u 0 = u 2 + u 3 ,
n 1 n 4 = n 0 n s , n 2 n 3 = n 0 n s .
F = u 0 cos 4 β a 2 sin 2 β cos 2 β + a 4 sin 4 β,
a 2 = sinh ( 3 u 0 4 u 1 ) + sinh ( 3 u 0 4 u 2 ) + 2 { sinh [ 3 u 0 2 ( u 1 + u 2 ) ] + sinh [ u 0 2 ( u 1 u 2 ) ] } ,
a 4 = sinh [ u 0 4 ( u 1 u 2 ) ] .
L = n ref sin θ ref ,
U = ( n 1 n 2 n 3 n 4 n l 3 n l 2 n l 1 n l ) 2 n s n 0 ,
W = ( cos θ 1 cos θ 2 cos θ 3 cos θ 4 cos θ l 3 cos θ l 2 cos θ l 1 cos θ l ) 2 cos θ s cos θ 0 .
R s = ( 1 U W 1 + U W ) 2 ,
R p = ( 1 U / W 1 + U / W ) 2 .
R p = R s ,
incident ( HMLM ) m emergent
U = n H 2 m n L 2 m n s n 0 n M 4 m = 15 ,
W = cos θ s ( 1 L 2 n H 2 ) m ( 1 L 2 n L 2 ) m ( 1 L 2 n M 2 ) 2 m cos θ 0 = 1 .
a H n H 2 , a M n M 2 .
a H = γ a M 2 ,
γ n L 2 ( n s U 1 n 0 1 ) 1 / m ,
cos θ s ( 1 L 2 a H ) m ( 1 L 2 n L 2 ) m ( cos θ 0 ) 1 = ( 1 L 2 a M ) 2 m .
( 1 L 2 a H ) κ = ( 1 L 2 a M ) 2 ,
κ ( 1 L 2 n L 2 ) [ ( cos θ 0 ) 1 cos θ s ] 1 / m .
κ L 2 κγ a M 2 = 1 2 L 2 a M + L 4 a M 2 .

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