OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 66, Iss. 7 — Jul. 1, 1976
  • pp: 735–739

Frequency-mixing detection (FMD) of polarization-modulated light

R. M. A. Azzam  »View Author Affiliations

JOSA, Vol. 66, Issue 7, pp. 735-739 (1976)

View Full Text Article

Acrobat PDF (536 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



When a light beam whose polarization and intensity are weakly modulated at a frequency ωm passes through a periodic analyzer of frequency ωa(<ωm) and the transmitted flux is linearly detected, the resulting total signal St consists of two components: (i) a periodic baseband signal Sbb with harmonics of frequencies nωa (n = 0,1,2,…) and (ii) an amplitude-modulated-carrier signal δSmc with center (carrier) frequency ωm and sideband frequencies at ωm ± nωa(n = 1,2,…). In this paper we show that the average polarization of the beam is determined by a limited spectral analysis of Sbb, whereas the polarization and intensity modulation are determined by a limited spectral analysis of δSmc, or the associated envelope signal δSe, where δSmc = δSecosωmt. The theory of this frequency-mixing detection (FMD) of polarization modulation is developed for an arbitrary periodic analyzer. The specific case of a rotating analyzer is considered as an example. Applications of FMD include the retrieval of information impressed on light beams as polarization modulation in optical communication systems, and the automation of modulated ellipsometry, AIDER (angle-of- incidence-derivative ellipsometry and reflectometry), and modulated generalized ellipsometry.

© 1976 Optical Society of America

R. M. A. Azzam, "Frequency-mixing detection (FMD) of polarization-modulated light," J. Opt. Soc. Am. 66, 735-739 (1976)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. To prevent overlapping between the spectra of Sbb and δSmc, we select the frequency of the periodic analyzer ωa to be much smaller than the beam-modulation frequency ωm (e. g., ωm > 10ωa), and restrict ωma not to equal the ratio of two integers.
  2. Alternatively, we may measure the amplitudes of the cosine and sine components of one nonzero harmonic of Sbb. This is the case of the example considered in Sec. III.
  3. Dependent on the type of periodic analyzer that we choose, Eqs. (16) may or may not have an explicit, or a unique, solution for ¯ψ and ¯Δ.
  4. This requires, of course, that the three equations be linearly independent. This is satisfied in general, unless the periodic analyzer, the chosen harmonics (p, q), and/or the quiescent polarization (¯ψ,¯Δ) happen to be such that two (or all three) equations become linearly dependent.
  5. Such a constant can be absorbed in the multipler c that appears in Eq. (7).
  6. This is in agreement with results to be found in Refs. 8–10.
  7. See, for example, W. K. Pratt, Laser Communication Systems (Wiley, New York, 1969).
  8. P. S. Hauge and F. H. Dill, "Design and Operation of ETA, an Automated Ellipsometer," IBM J. Res. Devel. 17, 472–489 (1973).
  9. D. E. Aspnes, "Effects of Component Optical Activity in Data Reduction and Calibration of Rotating-Analyzer Ellipsometers," J. Opt. Soc. Am. 65, 812–819 (1975).
  10. R. M. A. Azzam and N. M. Bashara, "Analysis of Systematic Errors in Rotating-Analyzer Ellipsometers," 64, 1459–1469 (1974).
  11. R. M. A. Azzam, "Oscillating-Analyzer Ellipsometer," Rev. Sci. Instrum. 47, (1976) (in press).
  12. R. W. Stobie, B. Rao, and M. J. Dignam, "Analysis of a Novel Ellipsometer Technique for Infrared Spectroscopy," J. Opt. Soc. Am. 65, 25–28 (1975).
  13. P. S. Hauge and F. H. Dill, "A Rotating-Compensator Fourier Ellipsometer," Opt. Commun. 14, 431–435 (1975).
  14. D. E. Aspnes, "Photometric Ellipsometer for Measuring Partially Polarized Light," J. Opt. Soc. Am. 65, 1274–1278, 1975.
  15. R. M. A. Azzam, "Alternate Arrangement and Analysis of Systematic Errors for Dynamic Photometric Ellipsometers Employing an Oscillating-Phase Retarder," Optik. 45, (1976) (in press).
  16. A. B. Buckman and N. M. Bashara "Ellipsometry for Modulated Reflection Studies," J. Opt. Soc. Am. 58, 700–701 (1968).
  17. R. M. A. Azzam, "Modulated Generalized Ellipsometry," J. Opt. Soc. Am. 66, 520–524 (1976).
  18. R. M. A. Azzam, "AIDER: Angle-of-Incidence-Derivative Ellipsometry and Reflectometry," Opt. Commun. 16, 153–156 (1976).

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited