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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 5 — May. 1, 1998
  • pp: 1202–1211

Birefringence in rapidly rotating glass disks

Peter de Groot  »View Author Affiliations


JOSA A, Vol. 15, Issue 5, pp. 1202-1211 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001202


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Abstract

Centripetal forces modify the optical properties of a rotating glass disk, thus creating a circularly symmetric distortion in the refractive index. This centripetal birefringence has a strong radial dependency and increases with the square of the spin speed. The effect on a polarized beam transmitted through the glass may be reduced mathematically to that of an effective wave plate whose retardance and orientation may be calculated from knowledge of the stress distribution in the disk. Alternatively, one can directly measure the Jones-matrix elements that correspond to the effective wave plate by use of polarization phase measurements at two or more locations on the disk. This direct measurement compensates the centripetal birefringence in the instrumentation employed by the data-storage industry to measure the flying height of read–write heads.

© 1998 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(160.2750) Materials : Glass and other amorphous materials
(260.1440) Physical optics : Birefringence
(260.5430) Physical optics : Polarization

History
Original Manuscript: April 15, 1997
Revised Manuscript: November 7, 1997
Manuscript Accepted: November 3, 1997
Published: May 1, 1998

Citation
Peter de Groot, "Birefringence in rapidly rotating glass disks," J. Opt. Soc. Am. A 15, 1202-1211 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-5-1202


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References

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  17. For an analysis based on the index ellipsoid, see, for example, M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 674.
  18. The matrix v is the differential portion of the electric impermeability tensor in the principal axis frame. Because the index changes are small (<10-4), this differential form is a sufficient description of the optical anisotropy of the glass.
  19. A formal justification of the neglect of the u terms in the transformed index matrix v′ follows from Eqs. (6.3–6.13) of B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), p. 217.
  20. The symmetry argument that allows us to equate waveplates B1 and B2 in Fig. 3 requires that we neglect the slight difference in position within the glass of the incident and the reflected beams. This approximation simplifies the model but introduces an error that may be significant at small radii.
  21. G. Fowles, Introduction to Modern Optics, 2nd ed. (Dover, New York, 1975), pp. 33–36.
  22. Estimates of the accuracy of approximations in this paper all assume the disk geometry defined in Section 2, i.e., inner radius qins=3.18 mm, outer radius qout=53 mm, disk thickness T=7 mm.
  23. As an alternative to linear input polarization, Lacey, Womack have proposed using circular polarization [U.S. patent5,638,178, “Imaging polarimeter detector for measurement of small spacings” (June10, 1997)]. However, a linear input polarization substantially reduces the effect of polarization mixing attributable to disk birefringence.
  24. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 62 and 40.
  25. H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, Boston, 1993), p. 17.
  26. Centripetal birefringence measurement and compensation are covered by U.S. patent5,644,562 to P. de Groot entitled “Method and apparatus for measuring and compensating birefringence in rotating disks” (July1, 1997).
  27. T. Fukuzawa, T. Hisano, K. Ikarugi, Y. Ozawa, H. Watabe, K. Noda, “Two-dimensional flying-height measurement for new-generation heads,” in Digest of the IEEE International Magnetics Conference (Institute of Electronical and Electronics Engineers, Piscataway, N.J., 1995), HC-01.

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