Abstract

Narrowband spectral filters operating in reflection and consisting of multilayers containing both dielectric and metallic films are of interest for fiber–optical communication systems at wavelengths from 1250 to 1600 nm. Formulas are derived which relate the potential transmittances of the main metallic film to important specifications of the filter, namely, bandwidth and rejection, and it is shown how the parameters of the layers are chosen to meet these and other requirements such as free spectral range. Monitoring procedures are discussed, and the results of photometric observations on five filters are compared to theoretical predictions.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Winzer, “Wavelength Multiplexing Components—A Review of Single-Mode Devices and Their Applications,” IEEE/OSA J. Lightwave Technol. LT-2, 369–378 (1984).
    [CrossRef]
  2. D. B. Payne, J. R. Stern, “Transparent Single Mode Fiber Optical Networks,” IEEE/OSA J. Lightwave Technol. LT-4, 864–869 (1986).
    [CrossRef]
  3. S. R. Mallinson, “Wavelength-Selective Filters for Single-Mode Fiber WDM Systems Using Fabry-Perot Interferometers,” Appl. Opt. 26, 430–436 (1987).
    [CrossRef] [PubMed]
  4. G. Lippmann, “La Photographie des Couleurs,” C. R. Acad. Sci. Paris 112, 274–275 (1891).
  5. D. J. McCartney, D. B. Payne, S. S. Duncan, “Position-Tunable Holographic Filters in Dichromated Gelatin for Use in Single-Mode-Fiber Demultiplexers,” Opt. Lett. 10, 303–305 (1985).
    [CrossRef] [PubMed]
  6. Z. Knittl, Optics of Thin Films (Wiley, London, 1976), pp. 300–320.
  7. A. Thetford, “Absorbing Multilayers and Reflection Interference Filters,” Opt. Acta 25, 945–961 (1978).
    [CrossRef]
  8. S. Y. Zheng, J. W. Y. Lit, “Design of a Narrow-Band Reflection IR Multilayer,” Can. J. Phys. 61, 361–368 (1983).
    [CrossRef]
  9. A. Thetford, “Some Properties of Absorbing Multilayers,” Opt. Acta 19, 533–541 (1972).
    [CrossRef]
  10. P. H. Lissberger, “The Relationship Between Optical Absorptance and Electric Field of the Radiation in Multilayer Thin Films,” Opt. Acta 28, 187–200 (1981).
    [CrossRef]
  11. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).
  12. D. R. Gibson, P. H. Lissberger, I. W. Salter, D. G. Sparks, “A High Precision Adaptation of the ‘Turning-Point’ Method of Monitoring the Optical Thickness of Dielectric Layers Using Microprocessors,” Opt. Acta 29, 221–234 (1982).
    [CrossRef]
  13. D. R. Gibson, P. H. Lissberger, “Optical Properties of Narrowband Spectral Filter Coatings Related to Layer Structure and Preparation,” Appl. Opt. 22, 269–281 (1983).
    [CrossRef] [PubMed]
  14. P. H. Lissberger, A. K. Roy, I. W. Salter, J. A. Shan, “Thermal and Structural Constants of Magnesium Fluoride and Zinc Sulphide for Optical Coating Applications,” Opt. Acta 33, 925–938 (1986).
    [CrossRef]

1987

1986

P. H. Lissberger, A. K. Roy, I. W. Salter, J. A. Shan, “Thermal and Structural Constants of Magnesium Fluoride and Zinc Sulphide for Optical Coating Applications,” Opt. Acta 33, 925–938 (1986).
[CrossRef]

D. B. Payne, J. R. Stern, “Transparent Single Mode Fiber Optical Networks,” IEEE/OSA J. Lightwave Technol. LT-4, 864–869 (1986).
[CrossRef]

1985

1984

G. Winzer, “Wavelength Multiplexing Components—A Review of Single-Mode Devices and Their Applications,” IEEE/OSA J. Lightwave Technol. LT-2, 369–378 (1984).
[CrossRef]

1983

1982

D. R. Gibson, P. H. Lissberger, I. W. Salter, D. G. Sparks, “A High Precision Adaptation of the ‘Turning-Point’ Method of Monitoring the Optical Thickness of Dielectric Layers Using Microprocessors,” Opt. Acta 29, 221–234 (1982).
[CrossRef]

1981

P. H. Lissberger, “The Relationship Between Optical Absorptance and Electric Field of the Radiation in Multilayer Thin Films,” Opt. Acta 28, 187–200 (1981).
[CrossRef]

1978

A. Thetford, “Absorbing Multilayers and Reflection Interference Filters,” Opt. Acta 25, 945–961 (1978).
[CrossRef]

1972

A. Thetford, “Some Properties of Absorbing Multilayers,” Opt. Acta 19, 533–541 (1972).
[CrossRef]

1891

G. Lippmann, “La Photographie des Couleurs,” C. R. Acad. Sci. Paris 112, 274–275 (1891).

Duncan, S. S.

Gibson, D. R.

D. R. Gibson, P. H. Lissberger, “Optical Properties of Narrowband Spectral Filter Coatings Related to Layer Structure and Preparation,” Appl. Opt. 22, 269–281 (1983).
[CrossRef] [PubMed]

D. R. Gibson, P. H. Lissberger, I. W. Salter, D. G. Sparks, “A High Precision Adaptation of the ‘Turning-Point’ Method of Monitoring the Optical Thickness of Dielectric Layers Using Microprocessors,” Opt. Acta 29, 221–234 (1982).
[CrossRef]

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, London, 1976), pp. 300–320.

Lippmann, G.

G. Lippmann, “La Photographie des Couleurs,” C. R. Acad. Sci. Paris 112, 274–275 (1891).

Lissberger, P. H.

P. H. Lissberger, A. K. Roy, I. W. Salter, J. A. Shan, “Thermal and Structural Constants of Magnesium Fluoride and Zinc Sulphide for Optical Coating Applications,” Opt. Acta 33, 925–938 (1986).
[CrossRef]

D. R. Gibson, P. H. Lissberger, “Optical Properties of Narrowband Spectral Filter Coatings Related to Layer Structure and Preparation,” Appl. Opt. 22, 269–281 (1983).
[CrossRef] [PubMed]

D. R. Gibson, P. H. Lissberger, I. W. Salter, D. G. Sparks, “A High Precision Adaptation of the ‘Turning-Point’ Method of Monitoring the Optical Thickness of Dielectric Layers Using Microprocessors,” Opt. Acta 29, 221–234 (1982).
[CrossRef]

P. H. Lissberger, “The Relationship Between Optical Absorptance and Electric Field of the Radiation in Multilayer Thin Films,” Opt. Acta 28, 187–200 (1981).
[CrossRef]

Lit, J. W. Y.

S. Y. Zheng, J. W. Y. Lit, “Design of a Narrow-Band Reflection IR Multilayer,” Can. J. Phys. 61, 361–368 (1983).
[CrossRef]

Mallinson, S. R.

McCartney, D. J.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

Payne, D. B.

Roy, A. K.

P. H. Lissberger, A. K. Roy, I. W. Salter, J. A. Shan, “Thermal and Structural Constants of Magnesium Fluoride and Zinc Sulphide for Optical Coating Applications,” Opt. Acta 33, 925–938 (1986).
[CrossRef]

Salter, I. W.

P. H. Lissberger, A. K. Roy, I. W. Salter, J. A. Shan, “Thermal and Structural Constants of Magnesium Fluoride and Zinc Sulphide for Optical Coating Applications,” Opt. Acta 33, 925–938 (1986).
[CrossRef]

D. R. Gibson, P. H. Lissberger, I. W. Salter, D. G. Sparks, “A High Precision Adaptation of the ‘Turning-Point’ Method of Monitoring the Optical Thickness of Dielectric Layers Using Microprocessors,” Opt. Acta 29, 221–234 (1982).
[CrossRef]

Shan, J. A.

P. H. Lissberger, A. K. Roy, I. W. Salter, J. A. Shan, “Thermal and Structural Constants of Magnesium Fluoride and Zinc Sulphide for Optical Coating Applications,” Opt. Acta 33, 925–938 (1986).
[CrossRef]

Sparks, D. G.

D. R. Gibson, P. H. Lissberger, I. W. Salter, D. G. Sparks, “A High Precision Adaptation of the ‘Turning-Point’ Method of Monitoring the Optical Thickness of Dielectric Layers Using Microprocessors,” Opt. Acta 29, 221–234 (1982).
[CrossRef]

Stern, J. R.

D. B. Payne, J. R. Stern, “Transparent Single Mode Fiber Optical Networks,” IEEE/OSA J. Lightwave Technol. LT-4, 864–869 (1986).
[CrossRef]

Thetford, A.

A. Thetford, “Absorbing Multilayers and Reflection Interference Filters,” Opt. Acta 25, 945–961 (1978).
[CrossRef]

A. Thetford, “Some Properties of Absorbing Multilayers,” Opt. Acta 19, 533–541 (1972).
[CrossRef]

Winzer, G.

G. Winzer, “Wavelength Multiplexing Components—A Review of Single-Mode Devices and Their Applications,” IEEE/OSA J. Lightwave Technol. LT-2, 369–378 (1984).
[CrossRef]

Zheng, S. Y.

S. Y. Zheng, J. W. Y. Lit, “Design of a Narrow-Band Reflection IR Multilayer,” Can. J. Phys. 61, 361–368 (1983).
[CrossRef]

Appl. Opt.

C. R. Acad. Sci. Paris

G. Lippmann, “La Photographie des Couleurs,” C. R. Acad. Sci. Paris 112, 274–275 (1891).

Can. J. Phys.

S. Y. Zheng, J. W. Y. Lit, “Design of a Narrow-Band Reflection IR Multilayer,” Can. J. Phys. 61, 361–368 (1983).
[CrossRef]

IEEE/OSA J. Lightwave Technol.

G. Winzer, “Wavelength Multiplexing Components—A Review of Single-Mode Devices and Their Applications,” IEEE/OSA J. Lightwave Technol. LT-2, 369–378 (1984).
[CrossRef]

D. B. Payne, J. R. Stern, “Transparent Single Mode Fiber Optical Networks,” IEEE/OSA J. Lightwave Technol. LT-4, 864–869 (1986).
[CrossRef]

Opt. Acta

A. Thetford, “Absorbing Multilayers and Reflection Interference Filters,” Opt. Acta 25, 945–961 (1978).
[CrossRef]

A. Thetford, “Some Properties of Absorbing Multilayers,” Opt. Acta 19, 533–541 (1972).
[CrossRef]

P. H. Lissberger, “The Relationship Between Optical Absorptance and Electric Field of the Radiation in Multilayer Thin Films,” Opt. Acta 28, 187–200 (1981).
[CrossRef]

P. H. Lissberger, A. K. Roy, I. W. Salter, J. A. Shan, “Thermal and Structural Constants of Magnesium Fluoride and Zinc Sulphide for Optical Coating Applications,” Opt. Acta 33, 925–938 (1986).
[CrossRef]

D. R. Gibson, P. H. Lissberger, I. W. Salter, D. G. Sparks, “A High Precision Adaptation of the ‘Turning-Point’ Method of Monitoring the Optical Thickness of Dielectric Layers Using Microprocessors,” Opt. Acta 29, 221–234 (1982).
[CrossRef]

Opt. Lett.

Other

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

Z. Knittl, Optics of Thin Films (Wiley, London, 1976), pp. 300–320.

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 (7)

Fig. 1
Fig. 1

Parameters of central reflection band.

Fig. 2
Fig. 2

Parameters of the multilayer system of the reflection filter.

Fig. 3
Fig. 3

Detailed parameters of System I (Fig. 2).

Fig. 4
Fig. 4

Argand diagram for r = |r| exp() (Fig. 3).

Fig. 5
Fig. 5

Theoretical spectral reflectance (from glass side) of filter with layer parameters given in Table III: ----, wavelength scale expanded 15 times.

Fig. 6
Fig. 6

Measured spectral reflectance of filter (from glass side; reflection from uncoated substrate surface taken into account). Design as in Fig. 5: ----, wavelength scale expanded 15 times.

Fig. 7
Fig. 7

Theoretical spectral reflectance (from glass side) of filter with parameters given in Table VI: ----, wavelength scale expanded 15 times.

Tables (6)

Tables Icon

Table I Conditions for Solutions Corresponding to Various Integral Values of l and m

Tables Icon

Table II Properties of System I (Fig. 2) for Solutions Corresponding to Various Integral Values of l and m

Tables Icon

Table III Layer Parameters of a Reflection Filter with Dielectric Layers of Cryolite and ZnS

Tables Icon

Table IV Monitoring Data for Filter Design Given In Table III

Tables Icon

Table V Comparison of Measured and Theoretical Filter Performance Parameters

Tables Icon

Table VI Layer parameters of a reflection filter with dielectric layers of MgF2, ZnS, and Si

Equations (66)

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

L c = λ 2 / Δ λ = λ / f .
r G = r 1 + a / ( 1 | r 1 | | r 2 | exp ( 2 i ϕ ) ) ,
r G = exp ( i ρ 1 ) { | r 1 | + | r 2 | | g | exp [ i ( 2 ϕ + ) ] } 1 | r 1 | | r 2 | exp ( i 2 ϕ ) ,
g = | g | exp ( i γ ) = t 1 t 1 r 1 r 1 = exp { i ( ρ 1 + ρ 1 ) } [ | t 1 | | t 1 | exp ( i ω ) | r 1 | | r 1 | ] ,
ω = ( ρ 1 + ρ 1 ) ( τ 1 + τ 1 ) , = γ ( ρ 1 + ρ 1 ) .
| g | exp ( i ) = | t 1 | | t | exp ( i ω ) | r 1 | | r | ,
| g | 2 = ( | t 1 | | t | ) 2 + ( | r 1 | | r | ) 2 2 | t 1 | | t | | r 1 | | r | cos ω .
T 1 = | t 1 | | t |
R = | r G | 2 = C + D cos ( 2 ϕ + ) A B cos 2 ϕ ,
d R d ( 2 ϕ ) = B D sin E sin ( 2 ϕ + β ) ( A B cos 2 ϕ ) 2 ,
2 ϕ M = N π + ( 1 ) N sin 1 ( B D sin / E ) β ,
[ d 2 R d ( 2 ϕ ) 2 ] ϕ M = [ A D cos ( 2 ϕ M + ) + B C cos 2 ϕ M ] ( A B cos 2 ϕ M ) 2 .
= l π ,
2 ϕ M = N π .
[ d 2 R d ( 2 ϕ ) 2 ] ϕ M = ( A D B C ) cos 2 ϕ M ( A B cos 2 ϕ M ) 2 ,
ω = m π ,
| g | = ( 1 ) l + m T 1 ( 1 ) l | r 1 | | r 1 | .
R = C + ( 1 ) l D cos 2 ϕ A B cos 2 ϕ ,
R max = C + ( 1 ) l D A B = ( | r 1 | + ( 1 ) l | r 2 | | g | 1 | r 1 | | r 2 | ) 2
R min = C ( 1 ) l D A + B = ( | r 1 | ( 1 ) l | r 2 | | g | 1 + | r 1 | | r 2 | ) 2 .
ψ 1 = T 1 1 | r 1 | 2 = ( 1 ) m | r 1 | | r 1 | + ( 1 ) l + m | g | 1 | r 1 | 2 ,
ψ 1 = T 1 1 | r 1 | 2 = ( 1 ) m | r 1 | | r 1 | + ( 1 ) l + m | g | 1 | r 1 | 2 .
R ( ϕ 1 / 2 ) = 1 2 ( R max + R min ) ,
sin ξ = ( A B ) / 2 A ,
ξ = 1 Y 2 ( 1 + Y 2 ) ,
2 ξ = 1 Y = 1 | r 1 | | r 2 | .
ϕ max = k π = 2 π ν max n 2 d 2 + ( ρ 1 + ρ 2 ) / 2 , ϕ 1 / 2 = k π ± ξ = 2 π ( ν max ± Δ ν 2 ) n 2 d 2 + ( ρ 1 + ρ 2 ) / 2 .
2 ξ = π Δ ν ν max [ k ( ρ 1 + ρ 2 ) / ( 2 π ) ] .
2 σ = ( | g | 2 + 1 | r 1 | 2 | r 1 | 2 ) / T 1 ,
σ = ( cosh 2 δ + Γ 2 cos 2 δ ) 1 + Γ 2 ,
Γ = n / n
σ = cosh [ ln ( 1 / ψ max ) ] .
X = | R min | = | r 1 | + | g | 1 + | r 1 |
| g | = X ( 1 + | r 1 | ) | r 1 | .
T 1 = | r 1 | | r 1 | | g | ;
T 1 = ( | r 1 | X ) ( 1 + | r 1 | ) .
| r 1 | = X 2 ( 1 + | r 1 | ) + 2 σ X + ( 1 | r 1 | ) 2 ( σ + X ) ,
T 1 = ( 1 X 2 ) ( 1 | r 1 | 2 ) 2 ( σ + X ) ,
ψ 1 = T 1 1 | r 1 | 2 = 1 X 2 2 ( σ + X ) .
R max = ( | r 1 | | g | 1 | r 1 | ) 2
| r 1 | | g | = 2 | r 1 | X ( 1 + | r 1 | ) = ( 1 | r 1 | ) ( 1 + σ X ) / ( σ + X )
Z = | R max | = 1 + σ X σ + X
σ = ( 1 Z X ) / ( Z X ) .
ψ 1 = ( Z X ) / 2 ,
| r 1 | = [ Z ( 1 | r 1 | ) + X ( 1 + | r 1 | ) ] / 2 .
| r 1 | = 1 2 ξ .
| r 1 | = X + ξ Z
ψ 1 = ψ 1 ( 1 | r 1 | 2 ) / ( 1 | r 1 | 2 ) = 2 ξ
r A M = r f + r exp ( 2 i δ ) 1 + r f r exp ( 2 i δ ) ,
r B = | r B | exp ( 2 i δ B ) = r f + r 1 + r f r ,
r B M = r f + r exp ( 2 i δ ) 1 + r f r exp ( 2 i δ ) ,
r A = | r A | exp ( 2 i δ A ) = r f + r 1 + r f r ,
x 0 = Γ ψ 1 sin 2 δ / [ ψ 1 exp ( 2 δ ) 1 ] ,
y 0 = Γ ( ψ 1 cos 2 δ 1 ) / [ ψ 1 exp ( 2 δ ) 1 ] ,
r 0 2 = ( 1 + Γ 2 ) ( ψ 1 2 2 σ ψ 1 + 1 ) / [ ψ 1 exp ( 2 δ ) 1 ] 2 .
| r | = x 0 2 + y 0 2 + r 0 2 + 2 r 0 ( x 0 cos θ + y 0 sin θ ) ,
ρ = tan 1 [ ( y 0 + r 0 sin θ ) / ( x 0 + r 0 cos θ ) ] .
| r 1 | = ( 1 T 0 1 + F sin 2 ρ ) 1 / 2 ,
T 0 = ( 1 | r A | 2 ) ( 1 | r A M | 2 ) / ( 1 | r A | | r A M | ) 2 , F = 4 | r A | | r A M | / ( 1 | r A | | r A M | ) 2 , ρ = δ A + ρ A M / 2 , | r 1 | = ( 1 T 0 1 + F sin 2 ρ ) 1 / 2 ,
T 0 = ( 1 | r B | 2 ) ( 1 | r B M | 2 ) / ( 1 | r B | | r B M | ) 2 , F = 4 | r B | | r B M | / ( 1 | r B | | r B M | ) 2 , ρ = δ B + ρ B M / 2 .
M ( θ , θ ) = ( 1 | r 1 | / | r 1 | D ) 2 + ( 1 | r 1 | / | r 1 | D ) 2
A = 4 π n n λ 0 d η 2 d y
A = 4 π n n η 2 ( d / λ ) .
d s = λ / 4 π n ,
d d s .
R = 1 4 n n D n D 2 + | n | 2

Metrics