Abstract

<p>The absorption loss in a multilayer interference filter or antireflection coating can be calculated from the optical properties of its constituent materials. In the design of such a filter, the absorption and scattering losses are usually neglected. Even if these losses were taken into consideration at the design stage, the resulting performance would probably not be greatly improved; however, it is of interest to predict the change in filter performance when absorbing materials are substituted in an ideal nonabsorbing filter.</p><p>The multilayers treated include transmission-type interference filters, both with and without semi-transparent metal films, reflection-type interference filters, and antireflection coatings.</p><p>The analysis is made by transmission-line methods. The connection between optical and electrical filters with absorption losses is further treated in an appendix.</p>

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  1. A. Vasicek, Optics of Thin Films (North-Holland Publishing Company, Amsterdam, and Interscience Publishers, New York, 1960).
  2. O. S. Heavens, Optical Properties of Thin Solid Films (Academic Press, Inc., New York, 1955).
  3. L. Young, J. Opt. Soc. Am. 51, 967–974 (1961).
  4. J. S. Seeley, Proc. Phys. Soc. 78, 998–1008 (1961).
  5. R. J. Pegis, J. Opt. Soc. Am. 51, 1255–1264 (1961).
  6. H. Pohlack, "The synthesis of optical interference filters with specified spectral characteristics," Jenaer Jahrbuch, pp. 181–221 (1952) (in German).
  7. Two symbols will be used for reflection coefficient, ρ and Γ, and two for SWR, S and ν. The symbols S and ρ go together and will be used (with subscripts) to describe the standing wave patterns inside, as well as before and after, an actual filter. The symbols ν and Γ go together and will be used (with subscripts) as a measure of the discontinuity of individual interfaces; for instance Γ is defined as the reflection coefficient which would be measured at an interface if the two media on either side extended to infinity, instead of forming two thin layers [see Eqs. (2) to (4)].
  8. G. L. Ragan, Microwave Transmission Circuits, MIT Radiation Lab. Series (McGraw-Hill Publishing Company, Inc., New York, 1946), Vol. 9.
  9. The terms "band center" and "center frequency" will be used interchangeably for the center of the passband, which is symmetrical when plotted on a frequency scale.
  10. L. Young, IRE Trans. PGMTT-8, 483–489 (1960).
  11. S. B. Cohn, Proc. IRE 47, 1342–1348 (1959).
  12. L. Young, IRE Trans. PGMTT-8, 612–616 (1960).
  13. L. Young and G. L. Mattaei, "Microwave filters and coupling structures," Quart. Progr. Rept. No. 4, Contract DA-36-039 SC-97398, Stanford Research Institute (January 1962), Sec. IV.
  14. K. D. Mielenz, J. Research Natl. Bur. Standards 63A, 297–300 (1959). [There is a misprint in Eq. (17b): The lower left element in the matrix should be Sm-1α21.]
  15. P. H. Berning and A. F. Turner, J. Opt. Soc. Am. 47, 230–238 (1957).
  16. Reference 8, pp. 551–554.
  17. L. Young, IRE Trans. PGMTT-8, 436–439 (1960).
  18. Reference 1, p. 148.
  19. The transmission coefficient is of course the same in both directions by reciprocity (see reference 8, p. 552).
  20. L. Young, IRE Trans. PGCT-4, 3-5 (1957).
  21. S. B. Cohn, Proc. IRE 45, 187–196 (1957).
  22. Reference 11, Eq. (1).

Berning, P. H.

P. H. Berning and A. F. Turner, J. Opt. Soc. Am. 47, 230–238 (1957).

Cohn, S. B.

S. B. Cohn, Proc. IRE 47, 1342–1348 (1959).

S. B. Cohn, Proc. IRE 45, 187–196 (1957).

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Academic Press, Inc., New York, 1955).

Mattaei, G. L.

L. Young and G. L. Mattaei, "Microwave filters and coupling structures," Quart. Progr. Rept. No. 4, Contract DA-36-039 SC-97398, Stanford Research Institute (January 1962), Sec. IV.

Mielenz, K. D.

K. D. Mielenz, J. Research Natl. Bur. Standards 63A, 297–300 (1959). [There is a misprint in Eq. (17b): The lower left element in the matrix should be Sm-1α21.]

Pegis, R. J.

R. J. Pegis, J. Opt. Soc. Am. 51, 1255–1264 (1961).

Pohlack, H.

H. Pohlack, "The synthesis of optical interference filters with specified spectral characteristics," Jenaer Jahrbuch, pp. 181–221 (1952) (in German).

Ragan, G. L.

G. L. Ragan, Microwave Transmission Circuits, MIT Radiation Lab. Series (McGraw-Hill Publishing Company, Inc., New York, 1946), Vol. 9.

Seeley, J. S.

J. S. Seeley, Proc. Phys. Soc. 78, 998–1008 (1961).

Turner, A. F.

P. H. Berning and A. F. Turner, J. Opt. Soc. Am. 47, 230–238 (1957).

Vasicek, A.

A. Vasicek, Optics of Thin Films (North-Holland Publishing Company, Amsterdam, and Interscience Publishers, New York, 1960).

Young, L.

L. Young, J. Opt. Soc. Am. 51, 967–974 (1961).

L. Young, IRE Trans. PGMTT-8, 483–489 (1960).

L. Young, IRE Trans. PGMTT-8, 436–439 (1960).

L. Young, IRE Trans. PGCT-4, 3-5 (1957).

L. Young, IRE Trans. PGMTT-8, 612–616 (1960).

L. Young and G. L. Mattaei, "Microwave filters and coupling structures," Quart. Progr. Rept. No. 4, Contract DA-36-039 SC-97398, Stanford Research Institute (January 1962), Sec. IV.

Other

A. Vasicek, Optics of Thin Films (North-Holland Publishing Company, Amsterdam, and Interscience Publishers, New York, 1960).

O. S. Heavens, Optical Properties of Thin Solid Films (Academic Press, Inc., New York, 1955).

L. Young, J. Opt. Soc. Am. 51, 967–974 (1961).

J. S. Seeley, Proc. Phys. Soc. 78, 998–1008 (1961).

R. J. Pegis, J. Opt. Soc. Am. 51, 1255–1264 (1961).

H. Pohlack, "The synthesis of optical interference filters with specified spectral characteristics," Jenaer Jahrbuch, pp. 181–221 (1952) (in German).

Two symbols will be used for reflection coefficient, ρ and Γ, and two for SWR, S and ν. The symbols S and ρ go together and will be used (with subscripts) to describe the standing wave patterns inside, as well as before and after, an actual filter. The symbols ν and Γ go together and will be used (with subscripts) as a measure of the discontinuity of individual interfaces; for instance Γ is defined as the reflection coefficient which would be measured at an interface if the two media on either side extended to infinity, instead of forming two thin layers [see Eqs. (2) to (4)].

G. L. Ragan, Microwave Transmission Circuits, MIT Radiation Lab. Series (McGraw-Hill Publishing Company, Inc., New York, 1946), Vol. 9.

The terms "band center" and "center frequency" will be used interchangeably for the center of the passband, which is symmetrical when plotted on a frequency scale.

L. Young, IRE Trans. PGMTT-8, 483–489 (1960).

S. B. Cohn, Proc. IRE 47, 1342–1348 (1959).

L. Young, IRE Trans. PGMTT-8, 612–616 (1960).

L. Young and G. L. Mattaei, "Microwave filters and coupling structures," Quart. Progr. Rept. No. 4, Contract DA-36-039 SC-97398, Stanford Research Institute (January 1962), Sec. IV.

K. D. Mielenz, J. Research Natl. Bur. Standards 63A, 297–300 (1959). [There is a misprint in Eq. (17b): The lower left element in the matrix should be Sm-1α21.]

P. H. Berning and A. F. Turner, J. Opt. Soc. Am. 47, 230–238 (1957).

Reference 8, pp. 551–554.

L. Young, IRE Trans. PGMTT-8, 436–439 (1960).

Reference 1, p. 148.

The transmission coefficient is of course the same in both directions by reciprocity (see reference 8, p. 552).

L. Young, IRE Trans. PGCT-4, 3-5 (1957).

S. B. Cohn, Proc. IRE 45, 187–196 (1957).

Reference 11, Eq. (1).

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