Abstract

According to Herpin’s theorem, a symmetrical thin-film combination is equivalent, at one wavelength, to a single film, characterized by an equivalent index and equivalent thickness. If a large number of identical nonabsorbing thin-film combinations are combined, the resulting periodically stratified medium acts as a band-stop filter. In a stop band, the equivalent index of a symmetrical period is a pure imaginary; in a pass band, it is real. Equivalent indices are given for some commonly used periods. These may have values not possessed by any existing substance. These periods have proved useful in the design of optical filters and antireflection coatings.

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  1. A. Herpin, Compt. rend. 225, 182 (1947).
  2. F. Abelès, Ann. phys. [12] 5, 596 and 706 (1950).
  3. L. Brillouin, Wave Propagation in Periodic Structures (Mc- Graw-Hill Book Company, Inc., New York, 1946), first edition, Chapter IX.
  4. S. A. Schelkunoff, Bell System Tech. J. 17, 17 (1938).
  5. R. B. Muchmore, J. Opt. Soc. Am. 38, 20 (1948).
  6. H. A. Kramers, Physica 2, 483 (1935).
  7. See E. L. Ince, Ordinary Differential Equations (Longmans, Green and Company, London, 1926), first edition, pp. 242–248.
  8. See, for example, L. Brillouin, Quart. Appl. Math. VII, 363 (1950).
  9. Lord Rayleigh, Proc. Roy. Soc. (London) A93, 565 (1917).

Abelès, F.

F. Abelès, Ann. phys. [12] 5, 596 and 706 (1950).

Brillouin, L.

L. Brillouin, Wave Propagation in Periodic Structures (Mc- Graw-Hill Book Company, Inc., New York, 1946), first edition, Chapter IX.

See, for example, L. Brillouin, Quart. Appl. Math. VII, 363 (1950).

Herpin, A.

A. Herpin, Compt. rend. 225, 182 (1947).

Ince, E. L.

See E. L. Ince, Ordinary Differential Equations (Longmans, Green and Company, London, 1926), first edition, pp. 242–248.

Kramers, H. A.

H. A. Kramers, Physica 2, 483 (1935).

Muchmore, R. B.

R. B. Muchmore, J. Opt. Soc. Am. 38, 20 (1948).

Rayleigh, Lord

Lord Rayleigh, Proc. Roy. Soc. (London) A93, 565 (1917).

Schelkunoff, S. A.

S. A. Schelkunoff, Bell System Tech. J. 17, 17 (1938).

Other (9)

A. Herpin, Compt. rend. 225, 182 (1947).

F. Abelès, Ann. phys. [12] 5, 596 and 706 (1950).

L. Brillouin, Wave Propagation in Periodic Structures (Mc- Graw-Hill Book Company, Inc., New York, 1946), first edition, Chapter IX.

S. A. Schelkunoff, Bell System Tech. J. 17, 17 (1938).

R. B. Muchmore, J. Opt. Soc. Am. 38, 20 (1948).

H. A. Kramers, Physica 2, 483 (1935).

See E. L. Ince, Ordinary Differential Equations (Longmans, Green and Company, London, 1926), first edition, pp. 242–248.

See, for example, L. Brillouin, Quart. Appl. Math. VII, 363 (1950).

Lord Rayleigh, Proc. Roy. Soc. (London) A93, 565 (1917).

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