Abstract

When the surface roughness is comparable with the wavelength of the probing radiation, the scattered field contains both the regular (forward-scattered) component of coherent nature and the diffusely scattered part. Coloring of the regular component of white light scattered by a colorless dielectric slab with a rough surface is considered as a peculiar effect of singular optics with zero (infinitely extended) interference fringes. To explain the observed alternation of colors with respect to the increasing depth of the surface roughness, we apply a model of transition layers associated with the surface roughness. By applying the chromascopic technique, it is shown that the modifications of the normalized spectrum of the forward-scattered white light can be interpreted as the effect of a quarter-wavelength (anti-reflecting) layer for some spectral component of a polychromatic probing beam.

© 2006 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2006

S. R. Wilk, "Once in a blue moon," Opt. Photonics News 17, 20-21 (2006).

2005

2004

Ch. V. Felde, "Young’s diagnostics of phase singularities of the spatial coherence function at partially coherent singular beams," Ukr. J. Phys. 49, 473-480 (2004).

G. Gbur, T. D. Visser, and E. Wolf, "Hidden singularities in partially coherent and polychromatic wavefields," J. Opt. A 6, 239-242 (2004).
[CrossRef]

2003

2002

G. Gbur, T. D. Visser, and E. Wolf, "Anomalous behaviour of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

G. Popescu and A. Dogariu, "Spectral anomalies at wave-front dislocations," Phys. Rev. Lett. 88,183902 (2002).
[CrossRef] [PubMed]

V. K. Polyanskii, O. V. Angelsky, P. V. Polyanskii, "Scattering-induced spectral changes as a singular-optical effect," Optica Applicata 32, 843-848 (2002).

S. A. Ponomarenko and E. Wolf, "Spectral anomalies in a Fraunhofer diffraction pattern," Opt. Lett. 27, 1211-1213 (2002).
[CrossRef]

2001

Angelsky, O. V.

Bogatyryova, G. V.

Desyatnikov, A. S.

Dogariu, A.

G. Popescu and A. Dogariu, "Spectral anomalies at wave-front dislocations," Phys. Rev. Lett. 88,183902 (2002).
[CrossRef] [PubMed]

Fadeeva, T. A.

A. V. Volyar and T. A. Fadeeva, "Generation of singular beams in uniaxial crystals," Opt. Spectrosc. 94, 235-244 (2003).
[CrossRef]

Felde, C. V.

Felde, Ch. V.

Ch. V. Felde, "Young’s diagnostics of phase singularities of the spatial coherence function at partially coherent singular beams," Ukr. J. Phys. 49, 473-480 (2004).

Freund, I.

Gbur, G.

G. Gbur, T. D. Visser, and E. Wolf, "Hidden singularities in partially coherent and polychromatic wavefields," J. Opt. A 6, 239-242 (2004).
[CrossRef]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, "Phase singularities of the coherence functions in Young’s interference pattern," Opt. Lett. 28, 968-970 (2003).
[CrossRef] [PubMed]

G. Gbur, T. D. Visser, and E. Wolf, "Anomalous behaviour of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Hanson, S. G.

Kivshar, Yu. S.

Krolokowski, W.

Maksimyak, A. P.

Maksimyak, P. P.

Neshev, D. N.

Polyanskii, P. V.

G. V. Bogatyryova, C. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, "Partially coherent vortex beams with a separable phase," Opt. Lett. 28, 878-880 (2003).
[CrossRef] [PubMed]

V. K. Polyanskii, O. V. Angelsky, P. V. Polyanskii, "Scattering-induced spectral changes as a singular-optical effect," Optica Applicata 32, 843-848 (2002).

Polyanskii, V. K.

V. K. Polyanskii, O. V. Angelsky, P. V. Polyanskii, "Scattering-induced spectral changes as a singular-optical effect," Optica Applicata 32, 843-848 (2002).

Ponomarenko, S. A.

Popescu, G.

G. Popescu and A. Dogariu, "Spectral anomalies at wave-front dislocations," Phys. Rev. Lett. 88,183902 (2002).
[CrossRef] [PubMed]

Schouten, H. F.

Shvedov, V.

Soskin, M. S.

Visser, T. D.

G. Gbur, T. D. Visser, and E. Wolf, "Hidden singularities in partially coherent and polychromatic wavefields," J. Opt. A 6, 239-242 (2004).
[CrossRef]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, "Phase singularities of the coherence functions in Young’s interference pattern," Opt. Lett. 28, 968-970 (2003).
[CrossRef] [PubMed]

G. Gbur, T. D. Visser, and E. Wolf, "Anomalous behaviour of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Volyar, A.

Volyar, A. V.

A. V. Volyar and T. A. Fadeeva, "Generation of singular beams in uniaxial crystals," Opt. Spectrosc. 94, 235-244 (2003).
[CrossRef]

Wilk, S. R.

S. R. Wilk, "Once in a blue moon," Opt. Photonics News 17, 20-21 (2006).

Wolf, E.

J. Opt. A

G. Gbur, T. D. Visser, and E. Wolf, "Hidden singularities in partially coherent and polychromatic wavefields," J. Opt. A 6, 239-242 (2004).
[CrossRef]

J. Opt. Soc. Am. A

News

S. R. Wilk, "Once in a blue moon," Opt. Photonics News 17, 20-21 (2006).

Opt. Express

Opt. Lett.

Opt. Spectrosc.

A. V. Volyar and T. A. Fadeeva, "Generation of singular beams in uniaxial crystals," Opt. Spectrosc. 94, 235-244 (2003).
[CrossRef]

Optica Applicata

V. K. Polyanskii, O. V. Angelsky, P. V. Polyanskii, "Scattering-induced spectral changes as a singular-optical effect," Optica Applicata 32, 843-848 (2002).

Phys. Rev. Lett.

G. Gbur, T. D. Visser, and E. Wolf, "Anomalous behaviour of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

G. Popescu and A. Dogariu, "Spectral anomalies at wave-front dislocations," Phys. Rev. Lett. 88,183902 (2002).
[CrossRef] [PubMed]

Ukr. J. Phys.

Ch. V. Felde, "Young’s diagnostics of phase singularities of the spatial coherence function at partially coherent singular beams," Ukr. J. Phys. 49, 473-480 (2004).

Other

P. V. Polyanskii, "Some current views on singular optics," in Sixth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE 5477, 31-40 (2004).
[CrossRef]

M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, "Computer-synthesized hologram-based rainbow optical vortices," New J. Phys. 6, 196.1-196-8 (2004).
[CrossRef]

M. Berry, "Coloured phase singularities," New J. Phys. 4, 66.1-66.14 (2002).
[CrossRef]

M. Berry, "Exploring the colours of dark light," New J. Phys. 4, 74.1-74.14 (2002).
[CrossRef]

J. Leach and M. J. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 154.1-154.7 (2003).
[CrossRef]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," in Progress in optics, E. Wolf, ed., (Elsevier, Amsterdam, 2005) Vol. 47.

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, Cambridge, 1999.)

M. S. Soskin and M. V. Vasnetsov, "Singular Optics" in Progress in Optics E, Wolf, ed., (North-Holland, Amsterdam, 2001) Vol. 42, 219-276.

R. J. Collier, Ch. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, London, 1979).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

A. Sommerfeld, Optics (Academic, New York, 1954).

F. S. Grawford, Jr., Waves: Berkley Physics Course (McGraw-Hill, New York, 1968) Vol 3.

R. M. Evans, An Introduction to Color (Wiley, New York, 1959).

M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954).

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Figures (2)

Fig. 1.
Fig. 1.

Chromascopic simulation of the spectral changes of the forward-scattered component of a white light induced by a colorless glass rough surface (n i=1.52, n 2=1.233, and n 3=1) following the model of the transition layer.

Fig. 2.
Fig. 2.

Photos of a natural Moon (a), a blue Moon (b), and a red Moon (c).

Equations (6)

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

T g = exp [ iq cos ( 2 π p x ) ] = l = i l J l ( q ) exp ( i l 2 π p x ) ,
T r = exp [ i m q m cos ( 2 π p m x ) ] m [ l = i l J l ( q m ) exp ( i l 2 π p m x ) ] ,
η 0 = m J 0 2 ( q m ) .
I r I i = 4 [ 1 n 1 1 + n 1 ] 2 sin 2 [ π 2 ( λ i λ 0 1 ) ] ,
I f I i = 1 I r I i .
( R G B ) ( R G B ) max R G B .

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