Abstract

Micron-sized structures on flat substrates supporting sub-micron defects are analyzed by means of a parameter based on integrated backscattering calculations. This analysis is performed for different particle and defect sizes, optical properties and for two different configurations (defect on the microstructure or on the substrate). Calculations in the far field are complemented by some near field results. It is shown that information about the defect (presence, size and optical properties) can be obtained from the proposed backscattering parameter.

© 2007 Optical Society of America

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References

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  1. P. N. Prasad, Nanophotonics (John Wiley and Sons, 2004).
    [CrossRef]
  2. P. R. Young, "Low scatter mirror degradation by particle contamination," Opt. Eng. 15, 516 (1976).
  3. J. C. Stover, ed., Optical Scattering: Measurements and Analysis, (SPIE Press Monographs SPIE, Bellingham, Wash., 1995) Vol. PM 24.
    [CrossRef]
  4. F. Moreno, J. M. Saiz, P. J. Valle, and F. Gonzalez, "Metallic particle sizing on flat surfaces. Application to conducting substrates," Appl. Phys. Lett 68, 3087 (1996).
    [CrossRef]
  5. J. L. de la Pena, F. Gonzalez, J. M. Saiz, F. Moreno, and P. J. Valle, "Sizing particles on substrates. Ageneral method for oblique incidence," J. Appl. Phys. 85, 432 (1999).
    [CrossRef]
  6. J. M. Saiz, P. Valle, F. Gonzalez, F. Moreno, and D. Jordan, "Backscattering from particulate surfaces: experiment and theoretical modeling," Opt. Eng 33(4), 1261 (1994).
    [CrossRef]
  7. J. L. de la Pena, J. M. Saiz, and F. Gonzalez, "Profile of a fiber from backscattering measurements," Opt. Lett 25, 1699 (2000).
    [CrossRef]
  8. J. L. de la Pena, J. M. Saiz, P. J. Valle, F. Gonzalez, and F. Moreno, "Tracking scattering minima to size metallic particles on flat substrates," Part. Part. Syst. Charact 16, 113-118 (2000).
    [CrossRef]
  9. P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "Monitoring small defect on microstructures through backscattering measurements," Opt. Lett 31, 1744 (2006).
    [CrossRef] [PubMed]
  10. P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "2D Double interaction method for modeling small particles contaminating microstructures located on substrates," J. Quant. Spectrosc. Radiat. Transfer.(Accepted for publication, 2007).
    [CrossRef]
  11. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (John Wiley and Sons, 1991).
  12. F. Gonzalez, J. M. Saiz, P. J. Valle, and F. Moreno, "Multiple scattering in particulate surfaces: Cross-polarization ratios and shadowing effects," Opt. Commun 137, 359-366 (1997).
    [CrossRef]
  13. Z. Chen, X. Li, A. Taflove, and V. Backman, "Backscattering enhancement of light by nanoparticles positioned in localized optical intensity peaks," Appl. Opt. 45, 633-638 (2006).
    [CrossRef] [PubMed]

2007

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "2D Double interaction method for modeling small particles contaminating microstructures located on substrates," J. Quant. Spectrosc. Radiat. Transfer.(Accepted for publication, 2007).
[CrossRef]

2006

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "Monitoring small defect on microstructures through backscattering measurements," Opt. Lett 31, 1744 (2006).
[CrossRef] [PubMed]

Z. Chen, X. Li, A. Taflove, and V. Backman, "Backscattering enhancement of light by nanoparticles positioned in localized optical intensity peaks," Appl. Opt. 45, 633-638 (2006).
[CrossRef] [PubMed]

2000

J. L. de la Pena, J. M. Saiz, and F. Gonzalez, "Profile of a fiber from backscattering measurements," Opt. Lett 25, 1699 (2000).
[CrossRef]

J. L. de la Pena, J. M. Saiz, P. J. Valle, F. Gonzalez, and F. Moreno, "Tracking scattering minima to size metallic particles on flat substrates," Part. Part. Syst. Charact 16, 113-118 (2000).
[CrossRef]

1999

J. L. de la Pena, F. Gonzalez, J. M. Saiz, F. Moreno, and P. J. Valle, "Sizing particles on substrates. Ageneral method for oblique incidence," J. Appl. Phys. 85, 432 (1999).
[CrossRef]

1997

F. Gonzalez, J. M. Saiz, P. J. Valle, and F. Moreno, "Multiple scattering in particulate surfaces: Cross-polarization ratios and shadowing effects," Opt. Commun 137, 359-366 (1997).
[CrossRef]

1996

F. Moreno, J. M. Saiz, P. J. Valle, and F. Gonzalez, "Metallic particle sizing on flat surfaces. Application to conducting substrates," Appl. Phys. Lett 68, 3087 (1996).
[CrossRef]

1994

J. M. Saiz, P. Valle, F. Gonzalez, F. Moreno, and D. Jordan, "Backscattering from particulate surfaces: experiment and theoretical modeling," Opt. Eng 33(4), 1261 (1994).
[CrossRef]

1976

P. R. Young, "Low scatter mirror degradation by particle contamination," Opt. Eng. 15, 516 (1976).

Albella, P.

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "2D Double interaction method for modeling small particles contaminating microstructures located on substrates," J. Quant. Spectrosc. Radiat. Transfer.(Accepted for publication, 2007).
[CrossRef]

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "Monitoring small defect on microstructures through backscattering measurements," Opt. Lett 31, 1744 (2006).
[CrossRef] [PubMed]

Backman, V.

Chen, Z.

Gonzalez, F.

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "2D Double interaction method for modeling small particles contaminating microstructures located on substrates," J. Quant. Spectrosc. Radiat. Transfer.(Accepted for publication, 2007).
[CrossRef]

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "Monitoring small defect on microstructures through backscattering measurements," Opt. Lett 31, 1744 (2006).
[CrossRef] [PubMed]

F. Gonzalez, J. M. Saiz, P. J. Valle, and F. Moreno, "Multiple scattering in particulate surfaces: Cross-polarization ratios and shadowing effects," Opt. Commun 137, 359-366 (1997).
[CrossRef]

F. Moreno, J. M. Saiz, P. J. Valle, and F. Gonzalez, "Metallic particle sizing on flat surfaces. Application to conducting substrates," Appl. Phys. Lett 68, 3087 (1996).
[CrossRef]

J. M. Saiz, P. Valle, F. Gonzalez, F. Moreno, and D. Jordan, "Backscattering from particulate surfaces: experiment and theoretical modeling," Opt. Eng 33(4), 1261 (1994).
[CrossRef]

Jordan, D.

J. M. Saiz, P. Valle, F. Gonzalez, F. Moreno, and D. Jordan, "Backscattering from particulate surfaces: experiment and theoretical modeling," Opt. Eng 33(4), 1261 (1994).
[CrossRef]

Li, X.

Moreno, F.

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "2D Double interaction method for modeling small particles contaminating microstructures located on substrates," J. Quant. Spectrosc. Radiat. Transfer.(Accepted for publication, 2007).
[CrossRef]

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "Monitoring small defect on microstructures through backscattering measurements," Opt. Lett 31, 1744 (2006).
[CrossRef] [PubMed]

F. Gonzalez, J. M. Saiz, P. J. Valle, and F. Moreno, "Multiple scattering in particulate surfaces: Cross-polarization ratios and shadowing effects," Opt. Commun 137, 359-366 (1997).
[CrossRef]

F. Moreno, J. M. Saiz, P. J. Valle, and F. Gonzalez, "Metallic particle sizing on flat surfaces. Application to conducting substrates," Appl. Phys. Lett 68, 3087 (1996).
[CrossRef]

J. M. Saiz, P. Valle, F. Gonzalez, F. Moreno, and D. Jordan, "Backscattering from particulate surfaces: experiment and theoretical modeling," Opt. Eng 33(4), 1261 (1994).
[CrossRef]

Saiz, J. M.

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "2D Double interaction method for modeling small particles contaminating microstructures located on substrates," J. Quant. Spectrosc. Radiat. Transfer.(Accepted for publication, 2007).
[CrossRef]

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "Monitoring small defect on microstructures through backscattering measurements," Opt. Lett 31, 1744 (2006).
[CrossRef] [PubMed]

F. Gonzalez, J. M. Saiz, P. J. Valle, and F. Moreno, "Multiple scattering in particulate surfaces: Cross-polarization ratios and shadowing effects," Opt. Commun 137, 359-366 (1997).
[CrossRef]

F. Moreno, J. M. Saiz, P. J. Valle, and F. Gonzalez, "Metallic particle sizing on flat surfaces. Application to conducting substrates," Appl. Phys. Lett 68, 3087 (1996).
[CrossRef]

J. M. Saiz, P. Valle, F. Gonzalez, F. Moreno, and D. Jordan, "Backscattering from particulate surfaces: experiment and theoretical modeling," Opt. Eng 33(4), 1261 (1994).
[CrossRef]

Taflove, A.

Valle, P.

J. M. Saiz, P. Valle, F. Gonzalez, F. Moreno, and D. Jordan, "Backscattering from particulate surfaces: experiment and theoretical modeling," Opt. Eng 33(4), 1261 (1994).
[CrossRef]

Valle, P. J.

F. Gonzalez, J. M. Saiz, P. J. Valle, and F. Moreno, "Multiple scattering in particulate surfaces: Cross-polarization ratios and shadowing effects," Opt. Commun 137, 359-366 (1997).
[CrossRef]

F. Moreno, J. M. Saiz, P. J. Valle, and F. Gonzalez, "Metallic particle sizing on flat surfaces. Application to conducting substrates," Appl. Phys. Lett 68, 3087 (1996).
[CrossRef]

Young, P. R.

P. R. Young, "Low scatter mirror degradation by particle contamination," Opt. Eng. 15, 516 (1976).

Appl. Opt.

Appl. Phys. Lett

F. Moreno, J. M. Saiz, P. J. Valle, and F. Gonzalez, "Metallic particle sizing on flat surfaces. Application to conducting substrates," Appl. Phys. Lett 68, 3087 (1996).
[CrossRef]

J. Appl. Phys.

J. L. de la Pena, F. Gonzalez, J. M. Saiz, F. Moreno, and P. J. Valle, "Sizing particles on substrates. Ageneral method for oblique incidence," J. Appl. Phys. 85, 432 (1999).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer.

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "2D Double interaction method for modeling small particles contaminating microstructures located on substrates," J. Quant. Spectrosc. Radiat. Transfer.(Accepted for publication, 2007).
[CrossRef]

Opt. Commun

F. Gonzalez, J. M. Saiz, P. J. Valle, and F. Moreno, "Multiple scattering in particulate surfaces: Cross-polarization ratios and shadowing effects," Opt. Commun 137, 359-366 (1997).
[CrossRef]

Opt. Eng

J. M. Saiz, P. Valle, F. Gonzalez, F. Moreno, and D. Jordan, "Backscattering from particulate surfaces: experiment and theoretical modeling," Opt. Eng 33(4), 1261 (1994).
[CrossRef]

Opt. Eng.

P. R. Young, "Low scatter mirror degradation by particle contamination," Opt. Eng. 15, 516 (1976).

Opt. Lett

P. Albella, F. Moreno, J. M. Saiz, and F. Gonzalez, "Monitoring small defect on microstructures through backscattering measurements," Opt. Lett 31, 1744 (2006).
[CrossRef] [PubMed]

J. L. de la Pena, J. M. Saiz, and F. Gonzalez, "Profile of a fiber from backscattering measurements," Opt. Lett 25, 1699 (2000).
[CrossRef]

Part. Part. Syst. Charact

J. L. de la Pena, J. M. Saiz, P. J. Valle, F. Gonzalez, and F. Moreno, "Tracking scattering minima to size metallic particles on flat substrates," Part. Part. Syst. Charact 16, 113-118 (2000).
[CrossRef]

Other

P. N. Prasad, Nanophotonics (John Wiley and Sons, 2004).
[CrossRef]

J. C. Stover, ed., Optical Scattering: Measurements and Analysis, (SPIE Press Monographs SPIE, Bellingham, Wash., 1995) Vol. PM 24.
[CrossRef]

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (John Wiley and Sons, 1991).

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Figures (9)

Fig. 1.
Fig. 1.

System geometry including both configurations. Inset: angular sign criterium.

Fig. 2.
Fig. 2.

Comparison of the backscattered intensity of a silver cylinder (D = 2λ) with either a dielectric defect (upper graph) or a metallic defect (bottom graph). Both defects of size d = 0.15λ and located at different angular positions, φ.

Fig. 3.
Fig. 3.

σbr ± comparison for two different type of defects as a function of the defect position for a silver cylinder of D=2λ.

Fig. 4.
Fig. 4.

Evolution of σbr ± with ε for a fix defect position (50°).

Fig. 5.
Fig. 5.

Comparison of σbr for a silver cylinder of diameter 2λ in configuration A considering two defect sizes and located on either silver substrate (plain lines) or dielectric substrate (dashed lines).

Fig. 6.
Fig. 6.

Backscattering patterns obtained for two different defect positions, together with the “perfect” case.

Fig. 7.
Fig. 7.

σbr ± for two different cylinder sizes, D=λ and D=2λ and three different defect sizes. Defect position x ranging from 0.5λ to 3λ.

Fig. 8.
Fig. 8.

(a) Near field for a siver cylinder sized D=2λ located on a silver substrate and normal incidence. (b), (c) The same for configuration A (defect on cylinder) with d=0.2λ and φ=60°, φ=150° for (b) and (c) respectively. (d),(e) The same for configuration B (defect on substrate) with d=0.2λ and x=1.2λ, x=2λ for (d) and (e) cases respectively. Each plot has its corresponding far-field at the bottom compared to the “perfect” case pattern.

Fig. 9.
Fig. 9.

Comparison of σbr for a silver cylinder of diameter 2λ considering two defect sizes and located on either silver substrate (plain lines) or dielectric substrate (dotted lines).

Equations (3)

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σ b ± = 0 ± 90 I back ( θ s ) d θ s
σ br ± = σ b ± σ b 0 ± σ b 0 ± = σ b ± σ b 0 ± 1
[ σ br ] max = 2.51 d 0.14

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