Abstract

Angle-resolved ellipsometry of light scattering is an original technique developed at the Fresnel Institute to identify scattering processes in substrates and multilayers. We extend the investigation because numerous experimental results proved that the technique can be of major interest for analysis of microcomponents and their scattering origins. Surface and bulk effects can be separated in most situations, as well as the oblique growth of materials and the presence of first-order contaminants.

© 2002 Optical Society of America

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References

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  1. R. M. A. Azzam, N. M. Bashara, Ellipsometry and polarized light (North-Holland, Amsterdam, 1977), pp. 364–416.
  2. H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, New York, 1997).
  3. D. Rönnow, S. K. Anderson, G. A. Niklasson, “Surface roughness effects in ellipsometry: comparison of truncated sphere and effective medium models,” Opt. Mater. 4(6), 815–821 (1995).
    [CrossRef]
  4. S. J. Fang, W. Chen, T. Yamanaka, C. R. Helms, “Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry,” Appl. Phys. Lett. 68, 2837–2839 (1996).
    [CrossRef]
  5. G. Videen, J.-Y. Hsu, W. S. Bickel, W. L. Wolfe, “Polarized light scattered from rough surfaces,” J. Opt. Soc. Am. A 9, 1111–1118 (1992).
    [CrossRef]
  6. M. I. Mishchenko, “Diffuse and coherent backscattering by discrete random media. I. Radar reflectivity, polarization ratios, and enhancement factors for a half-space of polydisperse, nonabsorbing and absorbing spherical particles,” J. Quant. Spectrosc. Radiat. Transfer 56, 673–702 (1996).
    [CrossRef]
  7. M. Dogariu, T. Asakura, “Polarized light scattering in dielectric layers with rough interfaces,” Opt. Commun. 131, 1–7 (1996).
    [CrossRef]
  8. C. Deumié, H. Giovannini, C. Amra, “Ellipsometry of light scattering from multilayer coatings,” Appl. Opt. 35, 5600–5608 (1996).
    [CrossRef] [PubMed]
  9. C. Amra, C. Grèzes-Besset, P. Roche, E. Pelletier, “Description of a scattering apparatus: application to the problems of characterization of opaque surfaces,” Appl. Opt. 28, 2723–2730 (1989).
    [CrossRef] [PubMed]
  10. C. Amra, D. Torricini, P. Roche, “Multiwavelength (0.45–10.6 µm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (1993).
    [CrossRef] [PubMed]
  11. D. Torricini, “Diffusion de la lumière par les empilements de couches minces. Mesures et calculs dans un large domaine spectral (4.45 µm à 10.6 µm),” Ph.D. dissertation (Université d’Aix-Marseille III, Marseille, France, 1992).
  12. C. Amra, “From light scattering to the microstructure of thin film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
    [CrossRef] [PubMed]
  13. C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
    [CrossRef]
  14. C. Amra, “Light scattering from multilayer optics. II. Application to experiment,” J. Opt. Soc. Am. A 11, 211–226 (1994).
    [CrossRef]
  15. C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
    [CrossRef] [PubMed]
  16. C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10, 365–374 (1993).
    [CrossRef]
  17. J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
    [CrossRef] [PubMed]
  18. S. Kassam, A. Duparré, K. Hehl, P. Bussemer, J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
    [CrossRef] [PubMed]
  19. H. Giovannini, M. Saillard, A. Sentenac, “Numerical study of scattering from rough inhomogeneous films,” J. Opt. Soc. Am. A 15, 1182–1190 (1998).
    [CrossRef]
  20. C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).
  21. C. Deumié, R. Richier, P. Dumas, C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
    [CrossRef] [PubMed]
  22. T. A. Germer, “Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness,” Appl. Opt. 36, 8798–8805 (1997).
    [CrossRef]
  23. T. A. Germer, C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
    [CrossRef]
  24. T. A. Germer, C. C. Asmail, G. W. Sheer, “Polarization of out-of-plane scattering from microrough silicon,” Opt. Lett. 22, 1284–1286 (1997).
    [CrossRef]
  25. C. Amra, C. Grèzes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5502 (1993).
    [CrossRef] [PubMed]
  26. S. Maure, G. Albrand, C. Amra, “Low-level scattering and localized defects,” Appl. Opt. 35, 5573–5582 (1996).
    [CrossRef] [PubMed]
  27. P. Croce, L. Prod’homme, “Etude par diffusion lumineuse de la nature des surfaces de verre poli,” J. Opt. (Paris) 7, 121–132 (1976).
  28. F. Flory, D. Endelema, E. Pelletier, I. J. 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]
  29. F. Horowitz, H. A. Macleod, “Form birefringence in thin films,” in Los Alamos Conference on Optics ’83, R. S. McDowell, S. C. Stotlar, eds., Proc. SPIE380, 83–87 (1983).

1999 (1)

T. A. Germer, C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[CrossRef]

1998 (1)

1997 (2)

1996 (6)

S. Maure, G. Albrand, C. Amra, “Low-level scattering and localized defects,” Appl. Opt. 35, 5573–5582 (1996).
[CrossRef] [PubMed]

C. Deumié, R. Richier, P. Dumas, C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
[CrossRef] [PubMed]

C. Deumié, H. Giovannini, C. Amra, “Ellipsometry of light scattering from multilayer coatings,” Appl. Opt. 35, 5600–5608 (1996).
[CrossRef] [PubMed]

S. J. Fang, W. Chen, T. Yamanaka, C. R. Helms, “Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry,” Appl. Phys. Lett. 68, 2837–2839 (1996).
[CrossRef]

M. I. Mishchenko, “Diffuse and coherent backscattering by discrete random media. I. Radar reflectivity, polarization ratios, and enhancement factors for a half-space of polydisperse, nonabsorbing and absorbing spherical particles,” J. Quant. Spectrosc. Radiat. Transfer 56, 673–702 (1996).
[CrossRef]

M. Dogariu, T. Asakura, “Polarized light scattering in dielectric layers with rough interfaces,” Opt. Commun. 131, 1–7 (1996).
[CrossRef]

1995 (1)

D. Rönnow, S. K. Anderson, G. A. Niklasson, “Surface roughness effects in ellipsometry: comparison of truncated sphere and effective medium models,” Opt. Mater. 4(6), 815–821 (1995).
[CrossRef]

1994 (2)

1993 (5)

1992 (3)

1989 (1)

1980 (1)

1976 (1)

P. Croce, L. Prod’homme, “Etude par diffusion lumineuse de la nature des surfaces de verre poli,” J. Opt. (Paris) 7, 121–132 (1976).

Albrand, G.

Amra, C.

S. Maure, G. Albrand, C. Amra, “Low-level scattering and localized defects,” Appl. Opt. 35, 5573–5582 (1996).
[CrossRef] [PubMed]

C. Deumié, H. Giovannini, C. Amra, “Ellipsometry of light scattering from multilayer coatings,” Appl. Opt. 35, 5600–5608 (1996).
[CrossRef] [PubMed]

C. Deumié, R. Richier, P. Dumas, C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
[CrossRef] [PubMed]

C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
[CrossRef]

C. Amra, “Light scattering from multilayer optics. II. Application to experiment,” J. Opt. Soc. Am. A 11, 211–226 (1994).
[CrossRef]

C. Amra, “From light scattering to the microstructure of thin film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
[CrossRef] [PubMed]

C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10, 365–374 (1993).
[CrossRef]

C. Amra, C. Grèzes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5502 (1993).
[CrossRef] [PubMed]

C. Amra, D. Torricini, P. Roche, “Multiwavelength (0.45–10.6 µm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (1993).
[CrossRef] [PubMed]

C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[CrossRef] [PubMed]

C. Amra, C. Grèzes-Besset, P. Roche, E. Pelletier, “Description of a scattering apparatus: application to the problems of characterization of opaque surfaces,” Appl. Opt. 28, 2723–2730 (1989).
[CrossRef] [PubMed]

C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).

Anderson, S. K.

D. Rönnow, S. K. Anderson, G. A. Niklasson, “Surface roughness effects in ellipsometry: comparison of truncated sphere and effective medium models,” Opt. Mater. 4(6), 815–821 (1995).
[CrossRef]

Apfel, J. H.

Asakura, T.

M. Dogariu, T. Asakura, “Polarized light scattering in dielectric layers with rough interfaces,” Opt. Commun. 131, 1–7 (1996).
[CrossRef]

Asmail, C. C.

T. A. Germer, C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[CrossRef]

T. A. Germer, C. C. Asmail, G. W. Sheer, “Polarization of out-of-plane scattering from microrough silicon,” Opt. Lett. 22, 1284–1286 (1997).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and polarized light (North-Holland, Amsterdam, 1977), pp. 364–416.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and polarized light (North-Holland, Amsterdam, 1977), pp. 364–416.

Bennett, J. M.

Bickel, W. S.

Bruel, L.

Bussemer, P.

Chen, W.

S. J. Fang, W. Chen, T. Yamanaka, C. R. Helms, “Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry,” Appl. Phys. Lett. 68, 2837–2839 (1996).
[CrossRef]

Croce, P.

P. Croce, L. Prod’homme, “Etude par diffusion lumineuse de la nature des surfaces de verre poli,” J. Opt. (Paris) 7, 121–132 (1976).

Deumié, C.

C. Deumié, H. Giovannini, C. Amra, “Ellipsometry of light scattering from multilayer coatings,” Appl. Opt. 35, 5600–5608 (1996).
[CrossRef] [PubMed]

C. Deumié, R. Richier, P. Dumas, C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
[CrossRef] [PubMed]

C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).

Dogariu, M.

M. Dogariu, T. Asakura, “Polarized light scattering in dielectric layers with rough interfaces,” Opt. Commun. 131, 1–7 (1996).
[CrossRef]

Dumas, P.

Duparré, A.

Elson, J. M.

Endelema, D.

Fang, S. J.

S. J. Fang, W. Chen, T. Yamanaka, C. R. Helms, “Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry,” Appl. Phys. Lett. 68, 2837–2839 (1996).
[CrossRef]

Flory, F.

Galindo, R.

C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).

Germer, T. A.

Giovannini, H.

Grèzes-Besset, C.

Hehl, K.

Helms, C. R.

S. J. Fang, W. Chen, T. Yamanaka, C. R. Helms, “Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry,” Appl. Phys. Lett. 68, 2837–2839 (1996).
[CrossRef]

Hodgkinson, I. J.

Horowitz, F.

F. Horowitz, H. A. Macleod, “Form birefringence in thin films,” in Los Alamos Conference on Optics ’83, R. S. McDowell, S. C. Stotlar, eds., Proc. SPIE380, 83–87 (1983).

Hsu, J.-Y.

Kassam, S.

Macleod, H. A.

F. Horowitz, H. A. Macleod, “Form birefringence in thin films,” in Los Alamos Conference on Optics ’83, R. S. McDowell, S. C. Stotlar, eds., Proc. SPIE380, 83–87 (1983).

Maure, S.

Mishchenko, M. I.

M. I. Mishchenko, “Diffuse and coherent backscattering by discrete random media. I. Radar reflectivity, polarization ratios, and enhancement factors for a half-space of polydisperse, nonabsorbing and absorbing spherical particles,” J. Quant. Spectrosc. Radiat. Transfer 56, 673–702 (1996).
[CrossRef]

Neubert, J.

Niklasson, G. A.

D. Rönnow, S. K. Anderson, G. A. Niklasson, “Surface roughness effects in ellipsometry: comparison of truncated sphere and effective medium models,” Opt. Mater. 4(6), 815–821 (1995).
[CrossRef]

Pelletier, E.

Prod’homme, L.

P. Croce, L. Prod’homme, “Etude par diffusion lumineuse de la nature des surfaces de verre poli,” J. Opt. (Paris) 7, 121–132 (1976).

Rahn, J. P.

Richier, R.

Roche, P.

Rönnow, D.

D. Rönnow, S. K. Anderson, G. A. Niklasson, “Surface roughness effects in ellipsometry: comparison of truncated sphere and effective medium models,” Opt. Mater. 4(6), 815–821 (1995).
[CrossRef]

Saillard, M.

Sentenac, A.

Sheer, G. W.

Tompkins, H. G.

H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, New York, 1997).

Torricini, D.

C. Amra, D. Torricini, P. Roche, “Multiwavelength (0.45–10.6 µm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (1993).
[CrossRef] [PubMed]

C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).

D. Torricini, “Diffusion de la lumière par les empilements de couches minces. Mesures et calculs dans un large domaine spectral (4.45 µm à 10.6 µm),” Ph.D. dissertation (Université d’Aix-Marseille III, Marseille, France, 1992).

Videen, G.

Wolfe, W. L.

Yamanaka, T.

S. J. Fang, W. Chen, T. Yamanaka, C. R. Helms, “Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry,” Appl. Phys. Lett. 68, 2837–2839 (1996).
[CrossRef]

Appl. Opt. (12)

J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
[CrossRef] [PubMed]

C. Amra, C. Grèzes-Besset, P. Roche, E. Pelletier, “Description of a scattering apparatus: application to the problems of characterization of opaque surfaces,” Appl. Opt. 28, 2723–2730 (1989).
[CrossRef] [PubMed]

C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[CrossRef] [PubMed]

C. Amra, D. Torricini, P. Roche, “Multiwavelength (0.45–10.6 µm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (1993).
[CrossRef] [PubMed]

C. Amra, “From light scattering to the microstructure of thin film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
[CrossRef] [PubMed]

C. Deumié, H. Giovannini, C. Amra, “Ellipsometry of light scattering from multilayer coatings,” Appl. Opt. 35, 5600–5608 (1996).
[CrossRef] [PubMed]

S. Kassam, A. Duparré, K. Hehl, P. Bussemer, J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
[CrossRef] [PubMed]

C. Amra, C. Grèzes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5502 (1993).
[CrossRef] [PubMed]

F. Flory, D. Endelema, E. Pelletier, I. J. 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]

S. Maure, G. Albrand, C. Amra, “Low-level scattering and localized defects,” Appl. Opt. 35, 5573–5582 (1996).
[CrossRef] [PubMed]

C. Deumié, R. Richier, P. Dumas, C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
[CrossRef] [PubMed]

T. A. Germer, “Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness,” Appl. Opt. 36, 8798–8805 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

S. J. Fang, W. Chen, T. Yamanaka, C. R. Helms, “Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry,” Appl. Phys. Lett. 68, 2837–2839 (1996).
[CrossRef]

J. Opt. (Paris) (1)

P. Croce, L. Prod’homme, “Etude par diffusion lumineuse de la nature des surfaces de verre poli,” J. Opt. (Paris) 7, 121–132 (1976).

J. Opt. Soc. Am. A (5)

J. Quant. Spectrosc. Radiat. Transfer (1)

M. I. Mishchenko, “Diffuse and coherent backscattering by discrete random media. I. Radar reflectivity, polarization ratios, and enhancement factors for a half-space of polydisperse, nonabsorbing and absorbing spherical particles,” J. Quant. Spectrosc. Radiat. Transfer 56, 673–702 (1996).
[CrossRef]

Opt. Commun. (1)

M. Dogariu, T. Asakura, “Polarized light scattering in dielectric layers with rough interfaces,” Opt. Commun. 131, 1–7 (1996).
[CrossRef]

Opt. Lett. (1)

Opt. Mater. (1)

D. Rönnow, S. K. Anderson, G. A. Niklasson, “Surface roughness effects in ellipsometry: comparison of truncated sphere and effective medium models,” Opt. Mater. 4(6), 815–821 (1995).
[CrossRef]

Rev. Sci. Instrum. (1)

T. A. Germer, C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[CrossRef]

Other (5)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and polarized light (North-Holland, Amsterdam, 1977), pp. 364–416.

H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, New York, 1997).

D. Torricini, “Diffusion de la lumière par les empilements de couches minces. Mesures et calculs dans un large domaine spectral (4.45 µm à 10.6 µm),” Ph.D. dissertation (Université d’Aix-Marseille III, Marseille, France, 1992).

C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).

F. Horowitz, H. A. Macleod, “Form birefringence in thin films,” in Los Alamos Conference on Optics ’83, R. S. McDowell, S. C. Stotlar, eds., Proc. SPIE380, 83–87 (1983).

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Figures (14)

Fig. 1
Fig. 1

Comparison of the angular behavior of the phase term η(θ) for a glass substrate illuminated at 0° and 56° incidence for surface and bulk scattering. The surface curve at 56° incidence exhibits a 180° discontinuity at high angles. The wavelength under study is 633 nm.

Fig. 2
Fig. 2

Same as Fig. 1, but the component is a single half-wave high-index TiO2 layer (see text).

Fig. 3
Fig. 3

Same as Fig. 1, but the component is an absentee 2H2L2H layer stack with materials TiO2 and SiO2 (see text).

Fig. 4
Fig. 4

Same as Fig. 1, but the component is a quarter-wave mirror with 17 layers of TiO2 and SiO2 (see text).

Fig. 5
Fig. 5

Same as Fig. 1, but the component is a single half-wave Fabry-Perot HLHLH(6L)HLHLH filter with materials TiO2 and SiO2 (see text).

Fig. 6
Fig. 6

Measurements of the angular variations of the phase term for substrates of (a) fused silica, (b) MgF2, (c) resin. Measurements were taken at the 633-nm wavelength and are to be compared with the calculations in Fig. 1. The results offer a direct discrimination of surface and bulk effects (see text).

Fig. 7
Fig. 7

Angular scattering of the resin sample before and after deposition of an Al layer. The reduction of scattering after the Al deposition clearly proves that scattering from the bare resin originates from a bulk effect.

Fig. 8
Fig. 8

Measurement of the polarimetric phase difference for the M17 mirror multilayer compared with the calculations presented in Fig. 4. The incidence angle is equal to 0°. In (a), the mirror is deposited on a 2-nm rough glass substrate; in (b) the mirror is deposited on a supersmooth (0.1-nm) silicon substrate.

Fig. 9
Fig. 9

Measurement of the polarimetric phase difference for the specific 2H2L2H structure deposited on a glass substrate, compared with the calculated curves presented in Fig. 3. The incidence angle is equal to 0°.

Fig. 10
Fig. 10

Geometry of a multilayer. The n i and e i represent, respectively, the index and the thickness of layer i.

Fig. 11
Fig. 11

Phase term η calculated for a single half-wave layer at 633 nm. The top interface profile is described as h 0 = h s + g 1, where h s is the substrate profile and g is the roughness brought by the layer (see text). The substrate roughness is 2 nm. Curve 1 was calculated for h 0 = h s , that is, g 1 = 0, which exhibits smooth variations. Curves 2 and 3 were calculated for g 1 = 0.1 and 1 nm, respectively, and reveal a significant ripple in the angular variations. Curves 4, 5, and 6 were calculated for g 1 = 10, 100, and 1000 nm, respectively (see text).

Fig. 12
Fig. 12

Phase term calculated for a bare substrate (2-nm roughness) in the absence (curve 1) or in the presence (curve 2) of four localized defects with 4-µm diameters and 10-nm height.

Fig. 13
Fig. 13

Geometry of oblique deposition on a single layer. β and γ are the deposition and growth angles from the sample normal (see text).

Fig. 14
Fig. 14

Phase term calculated for a single Ta2O5 layer with optical thickness 8λ/4 at 633 nm. The layer was grown under oblique deposition β equal to 0° (curve 1) and 20° (curve 2).

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

As or p= Cis or phˆi,
As or p= Cis or ppˆi
r=x, y,σ=2πv=2π/λsin θcos ϕ, sin ϕ,
As=Ns0.5 expjηsEs,
Ap=Np0.5 expjηpEp,
η=ηs-ηp=argAs-argAp=argAsAp*,
η=argC0s-argC0p,
η=argC0s-argC0p
hi=hs*ai,
η=argCs-argCp=arg Ci s-arg Ci p
ϕ=0°, θ=fi=n2n2-sin2i/n2+n4-1sin2i.
ηi, θ=0°=argCsCp*0.
η=argCs-argCp=arg Ci s-arg Ci p,
η=argCs-argCp=arg αiCi s-arg αiCi p=arg L,
hi-1=hi*ai+gi,
A=C0h0+C1h1=hsC0+C1+C0g1,
η=arg L,
L=AsAp*= hsC0s+C1s+C0sg1× hs* C0p*+C1p*+C0p*g1*.
t=0.5 e tan γ cos ψ, sin ψ,

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