Abstract

The calculated spectral transmittance of a multilayer laser mirror is used to determine the effective index of the single layer equivalent to the multilayer stack. We measure the artificial anisotropy of photoresist thin films whose structure is a one-dimensional, subwavelength grating obtained from interference fringes. The limitation of the theory of the first-order effective index homogenization is discussed. We designed normal-incidence, polarizing coating and a polarization rotator by embedding anisotropic films in simple multilayer structures.

© 2002 Optical Society of America

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References

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  1. I. Hodgkinson, Q. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, Singapore, 1997).
  2. F. Flory, D. Endelema, E. Pelletier, I. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO2 films,” Appl. Opt. 32, 5649–5659 (1993).
    [CrossRef] [PubMed]
  3. F. Flory, “Consequences of the microstructure of thin films on their optical properties,” in Thin Film Physics and Applications, S. Zhou, Y. Hsang, Y.-K. Chen, S. Mao, eds., Proc. SPIE2364, 27–35, (1994).
  4. T. Motohiro, Y. Taga, “Thin film retardation plate by oblique deposition,” Appl. Opt. 28, 2466–2482 (1989).
    [CrossRef] [PubMed]
  5. E. Grann, M. Moharam, A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695–2703 (1994).
    [CrossRef]
  6. L. Escoubas, F. Flory, F. Lemarchand, A. During, L. Roux, “Enhanced diffraction efficiency of gratings in multilayer,” Opt. Lett. 25, 194–196 (2000).
    [CrossRef]
  7. W. Southwell, “Pyramid-array surface-relief structures producing antireflection index matching on optical surfaces,” J. Opt. Soc. Am. A 8, 549–553 (1991).
    [CrossRef]
  8. S. Rytov, “Electromagnetic properties of finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).
  9. P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod Opt 43, 2063–2085 (1996).
    [CrossRef]
  10. E. Pelletier, P. Roche, B. Vidal, “Determination automatique des constantes optiques et de l’épaisseur de couches minces: application aux couches diélectriques,” Nouv. Rev. Opt. 7, 353–362 (1976).
    [CrossRef]
  11. S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys 83, 5150–5153 (1998).
    [CrossRef]

2000 (1)

1998 (1)

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys 83, 5150–5153 (1998).
[CrossRef]

1996 (1)

P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod Opt 43, 2063–2085 (1996).
[CrossRef]

1994 (1)

1993 (1)

1991 (1)

1989 (1)

1976 (1)

E. Pelletier, P. Roche, B. Vidal, “Determination automatique des constantes optiques et de l’épaisseur de couches minces: application aux couches diélectriques,” Nouv. Rev. Opt. 7, 353–362 (1976).
[CrossRef]

1956 (1)

S. Rytov, “Electromagnetic properties of finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).

Adamik, M.

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys 83, 5150–5153 (1998).
[CrossRef]

During, A.

Endelema, D.

Escoubas, L.

Flory, F.

L. Escoubas, F. Flory, F. Lemarchand, A. During, L. Roux, “Enhanced diffraction efficiency of gratings in multilayer,” Opt. Lett. 25, 194–196 (2000).
[CrossRef]

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys 83, 5150–5153 (1998).
[CrossRef]

F. Flory, D. Endelema, E. Pelletier, I. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO2 films,” Appl. Opt. 32, 5649–5659 (1993).
[CrossRef] [PubMed]

F. Flory, “Consequences of the microstructure of thin films on their optical properties,” in Thin Film Physics and Applications, S. Zhou, Y. Hsang, Y.-K. Chen, S. Mao, eds., Proc. SPIE2364, 27–35, (1994).

Gatto, A.

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys 83, 5150–5153 (1998).
[CrossRef]

Grann, E.

Hodgkinson, I.

Kovacs, I.

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys 83, 5150–5153 (1998).
[CrossRef]

Lalanne, P.

P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod Opt 43, 2063–2085 (1996).
[CrossRef]

Lemarchand, F.

Lemercier-Lalanne, D.

P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod Opt 43, 2063–2085 (1996).
[CrossRef]

Moharam, M.

Motohiro, T.

Pelletier, E.

F. Flory, D. Endelema, E. Pelletier, I. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO2 films,” Appl. Opt. 32, 5649–5659 (1993).
[CrossRef] [PubMed]

E. Pelletier, P. Roche, B. Vidal, “Determination automatique des constantes optiques et de l’épaisseur de couches minces: application aux couches diélectriques,” Nouv. Rev. Opt. 7, 353–362 (1976).
[CrossRef]

Pommet, A.

Roche, P.

E. Pelletier, P. Roche, B. Vidal, “Determination automatique des constantes optiques et de l’épaisseur de couches minces: application aux couches diélectriques,” Nouv. Rev. Opt. 7, 353–362 (1976).
[CrossRef]

Roux, L.

L. Escoubas, F. Flory, F. Lemarchand, A. During, L. Roux, “Enhanced diffraction efficiency of gratings in multilayer,” Opt. Lett. 25, 194–196 (2000).
[CrossRef]

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys 83, 5150–5153 (1998).
[CrossRef]

Rytov, S.

S. Rytov, “Electromagnetic properties of finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).

Southwell, W.

Taga, Y.

Tisserand, S.

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys 83, 5150–5153 (1998).
[CrossRef]

Vidal, B.

E. Pelletier, P. Roche, B. Vidal, “Determination automatique des constantes optiques et de l’épaisseur de couches minces: application aux couches diélectriques,” Nouv. Rev. Opt. 7, 353–362 (1976).
[CrossRef]

Wu, Q.

I. Hodgkinson, Q. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, Singapore, 1997).

Appl. Opt. (2)

J. Appl. Phys (1)

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys 83, 5150–5153 (1998).
[CrossRef]

J. Mod Opt (1)

P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod Opt 43, 2063–2085 (1996).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nouv. Rev. Opt. (1)

E. Pelletier, P. Roche, B. Vidal, “Determination automatique des constantes optiques et de l’épaisseur de couches minces: application aux couches diélectriques,” Nouv. Rev. Opt. 7, 353–362 (1976).
[CrossRef]

Opt. Lett. (1)

Sov. Phys. JETP (1)

S. Rytov, “Electromagnetic properties of finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).

Other (2)

I. Hodgkinson, Q. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, Singapore, 1997).

F. Flory, “Consequences of the microstructure of thin films on their optical properties,” in Thin Film Physics and Applications, S. Zhou, Y. Hsang, Y.-K. Chen, S. Mao, eds., Proc. SPIE2364, 27–35, (1994).

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Figures (5)

Fig. 1
Fig. 1

Calculated broadband transmission spectra of a 19-layers TiO2 and SiO2, quarter-wave stack centered at 0.55 µm.

Fig. 2
Fig. 2

Refractive index of the layer equivalent to the 19-layers TiO2 and SiO2, quarter-wave stack centered at 0.55 µm and determined between 1.4 and 5.4 µm from the transmission spectra of Fig. 1.

Fig. 3
Fig. 3

Example of a measured transmittance between crossed polarizers of a grating etched in a photoresist layer.

Fig. 4
Fig. 4

Calculated transmittances in polarized light of a Fabry-Perot filter having an anisotropic spacer layer (ϕ = 0°). The coating design is substrate-M9 4B* M9-air, where M9 denotes a mirror made of nine alternated high and low refractive-index, quarter-wave layers and 4B* is assumed to be made of silica with a Ti-implanted grating in a depth of 0.150 µm. The s and p denote polarization states parallel and perpendicular to the gratings’ stripes.

Fig. 5
Fig. 5

Calculated reflectance between crossed and parallel polarizers of an asymmetric Fabry-Perot filter having an anisotropic spacer layer (ϕ = 45°). The design is substrate-M9BM9 4B* M9-air, where M9 denotes a mirror made of nine quarter-wave layers of alternated high and low refractive index and 4B* is assumed to be made of silica with a Ti-implanted grating in a depth of 0.150 µm. The s and p denote polarization states parallel and perpendicular to the gratings’ stripes.

Equations (2)

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n2=n12/2+n22/2, n2=n12×n22n12/2+n22/2.
Tsp=Tps=sin2Φ/2,

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