Abstract

Classical narrow-band interference dielectric filters with all-dielectric reflectors have quarter-wave stacks separated by a half-wave thickness (or a multiple-) spacer layer. These filters are essentially Fabry–Perot filters; hence the theory developed for those filters applies in full. The theory of narrow-band interference dielectric filters with unconventional spacer layers is presented. This spacer layer consists of two different materials. The optical features of these filters are compared with the features of Fabry–Perot filters. The influence of the errors of the layers on spectral characteristics is analyzed. The theory presented can be applied to any spectral range as well as to any thin-film material, including absorbing and nonlinear materials.

© 2000 Optical Society of America

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References

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  1. A. Macleod, Optical Coatings: Notes for a Short Course (Thin Film Center, Inc., 2745 East Via Rotonda, Tucson, Ariz., 85716-5227, 1997), Chap. 7.
  2. R. Guenther, Modern Optics (Wiley, New York, 1990).
  3. Z. Knittl, Optics of Thin Films (Wiley, London, 1976).
  4. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989).
  5. E. Pelletier, H. A. Macleod, “Interference filters with multiple peaks,” J. Opt. Soc. Am. 72, 683–687 (1982).
    [CrossRef]
  6. S. D. Smith, “Design of multilayer filters by considering two effective interfaces,” J. Opt. Soc. Am. 48, 43–50 (1958).
    [CrossRef]
  7. P. H. Lissberger, “Properties of all-dielectric interference filters. I. A new method of calculation,” J. Opt. Soc. Am. 49, 121–125 (1959).
    [CrossRef]
  8. H. D. Polster, “Symmetrical all-dielectric interference filter,” J. Opt. Soc. Am. 42, 21–24 (1952).
    [CrossRef]
  9. L. I. Epstein, “Design of optical filters,” J. Opt. Soc. Am. 42, 806–810 (1952).
    [CrossRef]
  10. R. R. Austin, “Polarizing beamsplitters and combiners,” in Optical Coatings: Applications and Utilization I, G. W. DeBell, D. H. Harrison, eds., Proc. SPIE50, 143–152 (1974).
  11. J. D. Rancourt, Optical Thin Films User’s Handbook (Macmillan, New York, 1987), pp. 112–116.
  12. W. H. Southwell, W. J. Gunning, R. L. Hall, “Narrow-bandpass filter using partitioned cavities,” in Optical Thin Films II: New Developments, R. I. Seddon, ed., Proc. SPIE678, 177–184 (1986).
  13. Sh. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (ADAGP, Paris, 1992), p. 100.
  14. J. Ciosek, “Narrow-band polarizing interference filter,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 255–260 (1996).
    [CrossRef]
  15. J. Ciosek, “Narrow-band interference filter with polarizing feature,” Opt. Commun. 136, 357–359 (1997).
    [CrossRef]
  16. J. Ciosek, “Design of the polarizing interference filters,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 317–320 (1997).
    [CrossRef]
  17. J. Ciosek, “Theory of narrow-band polarizing interference filters,” in Optical Interference Coatings, Vol. 9 of OSA 1998 Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 164–166.
  18. A. Thelen, “Design of optical minus filters,” J. Opt. Soc. Am. 61, 365–369 (1971).
    [CrossRef]
  19. H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, London, 1969).

1997 (1)

J. Ciosek, “Narrow-band interference filter with polarizing feature,” Opt. Commun. 136, 357–359 (1997).
[CrossRef]

1982 (1)

1971 (1)

1959 (1)

1958 (1)

1952 (2)

Austin, R. R.

R. R. Austin, “Polarizing beamsplitters and combiners,” in Optical Coatings: Applications and Utilization I, G. W. DeBell, D. H. Harrison, eds., Proc. SPIE50, 143–152 (1974).

Ciosek, J.

J. Ciosek, “Narrow-band interference filter with polarizing feature,” Opt. Commun. 136, 357–359 (1997).
[CrossRef]

J. Ciosek, “Narrow-band polarizing interference filter,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 255–260 (1996).
[CrossRef]

J. Ciosek, “Design of the polarizing interference filters,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 317–320 (1997).
[CrossRef]

J. Ciosek, “Theory of narrow-band polarizing interference filters,” in Optical Interference Coatings, Vol. 9 of OSA 1998 Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 164–166.

Epstein, L. I.

Furman, Sh. A.

Sh. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (ADAGP, Paris, 1992), p. 100.

Guenther, R.

R. Guenther, Modern Optics (Wiley, New York, 1990).

Gunning, W. J.

W. H. Southwell, W. J. Gunning, R. L. Hall, “Narrow-bandpass filter using partitioned cavities,” in Optical Thin Films II: New Developments, R. I. Seddon, ed., Proc. SPIE678, 177–184 (1986).

Hall, R. L.

W. H. Southwell, W. J. Gunning, R. L. Hall, “Narrow-bandpass filter using partitioned cavities,” in Optical Thin Films II: New Developments, R. I. Seddon, ed., Proc. SPIE678, 177–184 (1986).

Knittl, Z.

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

Lissberger, P. H.

Macleod, A.

A. Macleod, Optical Coatings: Notes for a Short Course (Thin Film Center, Inc., 2745 East Via Rotonda, Tucson, Ariz., 85716-5227, 1997), Chap. 7.

Macleod, H. A.

Pelletier, E.

Polster, H. D.

Rancourt, J. D.

J. D. Rancourt, Optical Thin Films User’s Handbook (Macmillan, New York, 1987), pp. 112–116.

Smith, S. D.

Southwell, W. H.

W. H. Southwell, W. J. Gunning, R. L. Hall, “Narrow-bandpass filter using partitioned cavities,” in Optical Thin Films II: New Developments, R. I. Seddon, ed., Proc. SPIE678, 177–184 (1986).

Thelen, A.

A. Thelen, “Design of optical minus filters,” J. Opt. Soc. Am. 61, 365–369 (1971).
[CrossRef]

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

Tikhonravov, A. V.

Sh. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (ADAGP, Paris, 1992), p. 100.

J. Opt. Soc. Am. (6)

Opt. Commun. (1)

J. Ciosek, “Narrow-band interference filter with polarizing feature,” Opt. Commun. 136, 357–359 (1997).
[CrossRef]

Other (12)

J. Ciosek, “Design of the polarizing interference filters,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 317–320 (1997).
[CrossRef]

J. Ciosek, “Theory of narrow-band polarizing interference filters,” in Optical Interference Coatings, Vol. 9 of OSA 1998 Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 164–166.

A. Macleod, Optical Coatings: Notes for a Short Course (Thin Film Center, Inc., 2745 East Via Rotonda, Tucson, Ariz., 85716-5227, 1997), Chap. 7.

R. Guenther, Modern Optics (Wiley, New York, 1990).

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

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

H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, London, 1969).

R. R. Austin, “Polarizing beamsplitters and combiners,” in Optical Coatings: Applications and Utilization I, G. W. DeBell, D. H. Harrison, eds., Proc. SPIE50, 143–152 (1974).

J. D. Rancourt, Optical Thin Films User’s Handbook (Macmillan, New York, 1987), pp. 112–116.

W. H. Southwell, W. J. Gunning, R. L. Hall, “Narrow-bandpass filter using partitioned cavities,” in Optical Thin Films II: New Developments, R. I. Seddon, ed., Proc. SPIE678, 177–184 (1986).

Sh. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (ADAGP, Paris, 1992), p. 100.

J. Ciosek, “Narrow-band polarizing interference filter,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 255–260 (1996).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Spectral characteristics and phase changes on reflection from the mirrors of Fabry–Perot filters at a wavelength of 632.8 nm with n H = 2.25, n L = 1.45, and n S = n 0 = 1. The mirror configurations are as follows for the curves shown. Curve 1: L. Curve 2: L H. Curve 3: (L H)2. Curve 4: (L H)2L. Curve 5: (L H)3. Curve 6: (L H)3L. Curve 7: (L H)4. Curve 8: (L H)4L. Curve 9: (L H)5. Curve 10: (L H)5L. Curve 11: (L H)6.

Fig. 2
Fig. 2

Spectral characteristics and phase changes on reflection from the mirrors of a NCNBPIF with λ0 = 632.8 nm, n H = 2.25, n L = 1.45, and n S = n 0 = 1. The mirrors are mL: 632.8(0.5L H 0.5L) m and mH: 632.8(0.5H 0.5H) m , where m = 1, … , 6. For example, 2L denotes 632.8(0.5L H 0.5L)2.

Fig. 3
Fig. 3

Transmittance changes at the peak wavelength of 652.2 nm in a Fabry–Perot filter: 652.2[(H L)7(L H)7] as a result of a relative change of 0.01 in the individual layers.

Fig. 4
Fig. 4

Transmittance changes at the peak wavelength of 652.2 nm in a NCNBPIF: 632.8[(0.5L H 0.5L)7(0.5H L 0.5H)7] as a result of a relative change of 0.01 in the individual layers.

Fig. 5
Fig. 5

Spectral characteristics and phase changes on reflection for Fabry–Perot filters of the following types. Curve 1: 632.8[(H L)7(L H)7]. Curve 2: 632.8[(0.98H 0.98L)7(1.02L 1.02H)7]. Curve 3: 632.8[(0.95H 0.95L)7(1.05L 1.05H)7]. Curve 4: 632.8[(0.9H 0.9L)7(1.1L 1.1H)7]. The materials have the same values as those of Fig. 1.

Fig. 6
Fig. 6

Spectral characteristics and phase changes on reflection for NCNBPIF’s of the following types. Curve 1: 632.8[(0.5L H 0.5L)7(0.5H L 0.5H)7]. Curve 2: 632.8[(0.49L 0.98H 0.49L)7(0.51H 1.02L 0.51H)7]. Curve 3: 632.8[(0.475L 0.95H 0.475L)7(0.525H 1.05L 0.525H)7]. Curve 4: 632.8[(0.45L 0.9H 0.45L)7(0.55H 1.1L 0.55H)7].

Fig. 7
Fig. 7

Comparison of the spectral characteristics of the Fabry–Perot filters and the NCNBPIF’s with n H = 2.25, n L = 1.45, and n S = n 0 = 1. Curve 1: 652.2[(H L)7(L H)7]. Curve 2: 652.2[(H L)6 2H(L H)6]. Curve 3: 632.8[(0.5L H 0.5L)7(0.5H L 0.5H)7]. Curve 4: 632.8[(0.5H L 0.5H)7(0.5L H 0.5L)7].

Fig. 8
Fig. 8

Comparison of the spectral characteristics of the same filters as in Fig. 7.

Fig. 9
Fig. 9

Comparison of the spectral characteristics of different NCNBPIF’s. Curve 1 (single spacer): 632.8[(0.5L H 0.5L)6(0.5H L 0.5H)6]. Curve 2 (symmetrical double spacer): 632.8[(0.5L H 0.5L)3(0.5H L 0.5H)6(0.5L H 0.5L)3]. Curve 3 (asymmetrical double spacer): 632.8[(0.5L H 0.5L)3(0.5H L 0.5H)3 0.5H 0.5L(0.5L H 0.5L)3(0.5H L 0.5H)30.5H 0.5L]. The constants of the materials are the same as those of Fig. 1.

Tables (1)

Tables Icon

Table 1 Comparison of the Coefficients of Reflection and Phase Change on Reflection of Two Minus Filters as Mirrors of Unconventional Filters at a Peak Wavelength of Transmittance of 652.218 nma

Equations (17)

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TF=T1T21-R1R21/21+F sin2 θ-1,
F=4R1R21/21-R1R21/2-2,
θ=ϕ1+ϕ2-2δ/2,
PS0.5L H 0.5Lm0.5H L 0.5Hnλ0P,
M=cosmΓ1i sinmΓ1/NE1iNE1 sinmΓ1cosmΓ1×cosmΓ2i sinmΓ2/NE2iNE2 sinmΓ2cosmΓ2,
NE1=NE2=NE.
Γ=mΓ1+Γ2.
ϕ1+ϕ2=2π.
δ=2π.
sinϕ1+ϕ2/2-δ=0.
T0λ=1-R11-R21-R1R21/2-2,
Fλ=4R1R21/21-R1R21/2-2.
R1=R2=R
T0λ=Tmax=1,
Fλ=4R1-R-2.
0.5L H 0.5Lm0.5H L 0.5H2m0.5L H 0.5Lm.
0.5L H 0.5Lm0.5H L 0.5Hm0.5H 0.5L0.5L H 0.5Lm0.5H L 0.5Hm0.5H 0.5L.

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