Abstract

Optical properties of overcoated microspheres are calculated and compared to those of planar multilayers, in regard to the sphere diameter. The classical criteria for in-situ optical monitoring is analyzed to control the growth of films on the spheres. Most coatings are multi-dielectric quarter-wave stacks used in the thin film community.

© 2004 Optical Society of America

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References

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Appl. Opt.

J. Opt. Soc. Am.

C. Amra, �??Light scattering from multilayer optics. Part A: investigation tools,�?? J. Opt. Soc. Am. 11, 197-210 (1994).
[CrossRef]

C. Amra, �??Light scattering from multilayer optics. Part B: application to experiment,�?? J. Opt. Soc. Am. 11, 211-226 (1994).
[CrossRef]

Opt. Commun.

G. Burlak, S. Koshevaya, J. Sanchez- Mondragon, V. Grimalsky, �??Electromagnetic oscillations in a multilayer spherical stack,�?? Opt. Commun. 180, 49-58 (2000).
[CrossRef]

Proceedings of SPIE

C. Deumié, P. Voarino, C. Amra, �??Interferential powders for the spectral control of light scattering,�?? Advances in Optical Thin Films 2003, Proceedings of SPIE 5250.

Other

H.A. Macleod, Thin Film Optical Filters, (London Adam Hilger, 1986).

H.C. van de Hulst, Light Scattering by Small Particles, (Dover Publications, Inc. New York, 1981).

J.A. Stratton, Electromagnetic theory,( Mc Graw-Hill Book Company, New York, 1941).

C.F. Bohren and D.R. Hufman, Absoption and scattering of light by small particules, (Wiley-Interscience, New York, 1983).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Definition of angular ranges by transmission (0°-90°) and reflection (90°-180°). (b) Angular and wavelength variations of scattering from a SiO2 sphere of diameter 500 nm, overcoated with a quarterwave mirror of design: M7 = Air/HBHBHBH/Glass. The incident wave is TE polarized. The incident wavelength is the design wavelength of the mirror (633 nm).

Fig. 2.
Fig. 2.

Integrated angular scattering ST and SR at wavelength λ0 = 633 nm calculated for a single SiO2 sphere overcoated with a high index Ta2O5 layer. The abscissa is the thickness of the Ta205 thin film. The initial sphere radius is 15 μm (a), 5 μm (b), 2.5 μm (c) and 500 nm (d).

Fig. 3.
Fig. 3.

Angular scattering ST and SR at wavelength λ0 = 633 nm calculated for a single SiO2 sphere overcoated with a low index YF3 layer. The abscissa is the thickness of the YF3 thin film. The initial sphere radius is 15 μm (a), 5 μm (b), 2,5 μm (c) and 500 nm (d).

Fig. 4.
Fig. 4.

Comparison between reflection of a planar mirror of design M7, and SR scattering from the same concentric mirror M7. The wavelength range is 400–800 nm. Curves are calculated for different initial sphere radia: 15 μm (a), 5 μm (b), 2,5 μm (c) and 500 nm (d).

Fig. 5.
Fig. 5.

Planar reflection and transmission of a beam splitter.

Fig. 6.
Fig. 6.

ST and SR scattering from the beam splitter of figure 5 but deposited on a microsphere. The wavelength range is 400–800 nm. Curves are calculated for different initial sphere radia: 15 μm (a), 5 μm (b), 2,5 μm (c) and 500 nm (d).

Fig. 7.
Fig. 7.

Comparison between planar reflection of a band-pass filter, and SR scattering from the same concentric filter. The wavelength range is 400–800 nm. Curves are calculated for different initial sphere radia: 15 μm (a), 5 μm (b), 2,5 μm (c) and 500 nm (d).

Equations (8)

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M 7 = Air / HBHBHBH / Glass
S T = θ , ϕ I θ ϕ sin θ with < θ < 90 ° and 0 ° < ϕ < 360 °
S R = θ , ϕ I θ ϕ sin θ with 90 ° < θ < 180 ° and 0 ° < ϕ < 360 °
n ( λ 0 ) e k = k λ 0 4
n ( λ q ) e = q λ q 4
BS = Air / e H = 61,67 nm / e B = 106,54 nm / e H = 70,07 nm / e B = 10,14 nm
/ e H = 45,57 nm / e B = 43,23 nm / e H = 10,56 nm / Glass
FP = Air / HBHBH ( 2 B ) HBHBH / Glass

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