OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 40, Iss. 4 — Feb. 1, 2001
  • pp: 452–457

Dispersion equations for vacuum-deposited tilted-columnar biaxial media

Ian Hodgkinson, Qi Hong Wu, and Simon Collett  »View Author Affiliations

Applied Optics, Vol. 40, Issue 4, pp. 452-457 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (129 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We consider the application of the Bragg–Pippard (BP) equations for form birefringence to a tilted-columnar biaxial thin film with columns of index n c and voids of known index n v . In such a situation the three forward BP equations that express the principal refractive indices n1, n2, and n3 as functions of n c , n v , the packing fraction p c , and the depolarization factors L1, L2, and L3 can be inverted. The procedure described for adding dispersion to the principal indices involves entry to the BP model via the inverted equations, modification of n c to allow for dispersion, and then exit from the model via the forward BP equations. We discuss the introduction of composite columns to the model to allow for angular dependence of n c and the selection of suitable dispersion functions for bulk tantalum oxide, titanium oxide, and zirconium oxide. Theory and experiment both show that the dispersion of the normal-incidence birefringence Δn of the thin films is several times larger than the dispersion of the individual principal refractive indices.

© 2001 Optical Society of America

OCIS Codes
(160.1190) Materials : Anisotropic optical materials
(160.4670) Materials : Optical materials
(260.1440) Physical optics : Birefringence
(310.6860) Thin films : Thin films, optical properties

Original Manuscript: July 5, 2000
Revised Manuscript: October 23, 2000
Published: February 1, 2001

Ian Hodgkinson, Qi Hong Wu, and Simon Collett, "Dispersion equations for vacuum-deposited tilted-columnar biaxial media," Appl. Opt. 40, 452-457 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. W. Mbise, D. Le Bellac, G. A. Niklasson, C. G. Granqvist, “Angular selective window coatings: theory and experiments,” J. Phys. D 30, 2103–2122 (1997). [CrossRef]
  2. I. J. Hodgkinson, Q. H. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, Singapore, 1998). [CrossRef]
  3. W. L. Bragg, A. B. Pippard, “The form birefringence of macromolecules,” Acta Crystallogr. 6, 865–867 (1953). [CrossRef]
  4. I. J. Hodgkinson, Q. H. Wu, J. C. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37, 2653–2659 (1998). [CrossRef]
  5. I. J. Hodgkinson, Q. H. Wu, “Vacuum deposited biaxial thin films with all principal axes inclined to the substrate,” J. Vac. Sci. Technol. A 17, 2928–2932 (1999). [CrossRef]
  6. I. J. Hodgkinson, Q. H. Wu, B. Knight, A. Lakhtakia, K. Robbie, “Vacuum deposition of chiral sculptured thin films with high optical activity,” Appl. Opt. 39, 642–649 (2000). [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959).
  8. H. K. Pulker, G. Paesold, E. Ritter, “Refractive indices of TiO2 films produced by reactive evaporation of various titanium–oxygen phases,” Appl. Opt. 15, 2986–2991 (1976). [CrossRef] [PubMed]
  9. Technical information from Patinal Newsletter No. 3, E. Merc, Patinal-Centre, 64578 Gernsheim, Germany, June1994.
  10. H. Kuster, J. Ebert, “Activated reactive evaporation of TiO2 layers and their absorption indices,” Thin Solid Films 70, 43–47 (1980). [CrossRef]
  11. P. J. Martin, “Ion-based methods for optical thin film deposition,” J. Mater. Sci. 21, 1–25 (1986). [CrossRef]
  12. D. Smith, P. Baumeister, “Refractive index of some oxide and fluoride coating materials,” Appl. Opt. 18, 111–115 (1979). [CrossRef] [PubMed]
  13. T. Motohiro, Y. Taga, “Thin film retardation plate by oblique deposition,” Appl. Opt. 28, 2466–2482 (1989). [CrossRef] [PubMed]
  14. I. J. Hodgkinson, Q. H. Wu, “Serial bideposition of anisotropic thin films with enhanced linear birefringence,” Appl. Opt. 38, 3621–3625 (1999). [CrossRef]
  15. A. Zuber, H. Jänchen, N. Kaiser, “Perpendicular-incidence photometric ellipsometry of biaxial anisotropic thin films,” Appl. Opt. 35, 5553–5556 (1996). [CrossRef] [PubMed]
  16. T. Motohiro, Y. Takeda, T. Hioki, S. Noda, “Simultaneous oblique deposition from opposite azimuthal directions for fabrication of thin film retardation plates,” in International Symposium on Polarization Analysis and Applications to Device Technology, H. Yokota, T. Yoshizawa, eds., Proc. SPIE2873, 214–217 (1996). [CrossRef]
  17. I. J. Hodgkinson, Q. H. Wu, K. E. Thorn, M. D. Arnold, “Vacuum-deposited thin film polarizing elements for use with linearly and circularly polarized light at visible and near infrared wavelengths,” in Complex Mediums, A. Lakhtakia, W. S. Weiglhofer, R. Messier, eds., Proc. SPIE4097, 266–279 (2000). [CrossRef]

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