OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 37, Iss. 16 — Jun. 1, 1998
  • pp: 3527–3532

Discrete thin-film layer thickness modulation

Bruce E. Perilloux  »View Author Affiliations

Applied Optics, Vol. 37, Issue 16, pp. 3527-3532 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (250 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A novel analytical thin-film design method is presented that is based on electrical engineering communication theory. The proposed thickness modulation describes the thickness modulation of discrete, homogeneous thin-film layers of a multilayer coating. One modulation scheme, amplitude modulation, is presented in which analytical equations determine individual layer thicknesses for a given modulation amplitude, carrier frequency (f c ), direct-current bias, as well as several layers and refractive indices. The spectral performance (especially stop bands) of multilayer coatings with alternating layers of two refractive indices is presented for different carrier frequencies and modulation amplitudes. For f c ≤ 1, the ratio of the center frequencies of the first-order (f1) and the next present stop band (f2) is determined analytically from the modulation frequency for which f2/f1 = 2f c + 1. Particular cases of the carrier frequency produce virtual stop bands below the spectral frequency of the first-order stop band as well as high-frequency harmonics. Degenerate and other cases of thickness-modulated designs are presented, along with other modulation methods.

© 1998 Optical Society of America

OCIS Codes
(120.2440) Instrumentation, measurement, and metrology : Filters
(310.0310) Thin films : Thin films

Original Manuscript: August 19, 1997
Revised Manuscript: January 15, 1998
Published: June 1, 1998

Bruce E. Perilloux, "Discrete thin-film layer thickness modulation," Appl. Opt. 37, 3527-3532 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989), Chap. 1, pp. 2–3.
  2. H. M. Liddell, Computer-Aided Techniques for the Design of Multilayer Filters (Hilger, Bristol, 1981), Chap. 2.4, pp. 46–47.
  3. J. A. Dobrowolski, “Numerical methods for optical thin films,” Opt. Photon. News 8(6), 25 (1997).
  4. W. H. Southwell, “Use of gradient index for spectral filters,” in Solid State Optical Control Devices, P. Yeh, ed., Proc. SPIE464, 110–114 (1984). [CrossRef]
  5. W. H. Southwell, “Spectral response calculations of rugate filters using coupled-wave theory,” J. Opt. Soc. Am. A 5, 1558–1564 (1988). [CrossRef]
  6. B. G. Bovard, “Derivation of a matrix describing a rugate dielectric thin film,” Appl. Opt. 27, 1998–2005 (1988). [CrossRef] [PubMed]
  7. W. H. Southwell, “Extended-bandwidth reflector designs by using wavelets,” Appl. Opt. 36, 314–318 (1997). [CrossRef] [PubMed]
  8. J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt. 17, 3039–3050 (1978). [CrossRef] [PubMed]
  9. P. Baumeister, Optical Coating Technology, Short Course, University of California at Los Angeles, 13–17 January 1997 (P. Baumeister, Sebastopol, Calif., 1997).
  10. See, for example, E. Cojocaru, “Analytical solutions for zero-phase-shift transparent coatings on metallic reflectors at 10.6 μm,” Appl. Opt. 32, 4843–4845 (1993).
  11. Ref. 2, pp. 55–73.
  12. S. Haykin, Communication Systems (Wiley, New York, 1978), Chap. 3, p. 244.
  13. Ref. 1, p. 25.
  14. J. Millman, Microelectronics (McGraw-Hill, New York, 1979), Chap. 10-5, pp. 343–348.
  15. R. M. A. Azzam, B. E. Perilloux, “Polarized-light techniques for generating electrical signals of controllable waveform,” in Solid State Optical Control Devices, P. Yeh, ed., Proc. SPIE464, 88–95 (1984). [CrossRef]
  16. M. Thomsen, Z. L. Wu, “Polarizing and reflective coatings based on half-wave layer pairs,” Appl. Opt. 36, 307–313 (1997). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited