Abstract

The feasibilities of using interferometric and chromascopic techniques in the diagnostics of phase singularities and in the study of a phase structure of the field in their vicinity are demonstrated. The peculiar evolution of singularities into caustics produced by phase elements of singularity-generating objects of spherical and cylindrical shape is studied.

© 2005 Optical Society of America

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References

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    [CrossRef]
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  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
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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]
  22. J. Leach, M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 1–7 (2003).
    [CrossRef]

2004 (3)

2003 (5)

J. Leach, M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 1–7 (2003).
[CrossRef]

M. Mujat, A. Dogariu, “Polarimetric and spectral changes in random electromagnetic fields,” Opt. Lett. 28, 2153–2155 (2003).
[CrossRef] [PubMed]

M. V. Berry, M. R. Dennis, “The optical singularities of birefringent dichroic chiral crystals,” Proc. Roy. Soc. London A 459, 1261–1292 (2003).
[CrossRef]

J. Nye, “Evolution from Fraunhofer to a Pearcey diffraction pattern,” J. Opt. A: Pure Appl. Opt. 5, 495–502 (2003).
[CrossRef]

O. V. Angelsky, D. N. Burkovets, P. P. Maksimyak, S. G. Hanson, “Applicability of the singular-optics concept for diagnostics of random and fractal rough surfaces,” Appl. Opt. 42, 4529–4540 (2003).
[CrossRef] [PubMed]

2002 (3)

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

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66, 1–16 (2002).
[CrossRef]

M. V. Berry, “Exploring the colours of dark light,” New J. Phys. 4, 1–14 (2002).
[CrossRef]

1994 (1)

I. Freund, N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. 50, 5164–5172 (1994).
[CrossRef]

1992 (1)

1983 (1)

N. B. Baranova, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zeldovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
[CrossRef]

1981 (1)

N. B. Baranova, B. Ya. Zeldovich, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, “Dislocation of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP. 33, 1789–1797 (1981).

1979 (1)

M. V. Berry, J. F. Nye, F. J. Wright, “The elliptic umbilic diffraction catastrophe,” Phil. Trans. R. Soc. A 291, 453–484 (1979).
[CrossRef]

1962 (2)

1946 (1)

T. Pearcey, “The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic,” Philos. Mag. 37, 311–317 (1946).

Angelsky, O. V.

Apostol, A.

Baranova, N. B.

N. B. Baranova, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zeldovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
[CrossRef]

N. B. Baranova, B. Ya. Zeldovich, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, “Dislocation of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP. 33, 1789–1797 (1981).

Berry, M. V.

M. V. Berry, M. R. Dennis, “The optical singularities of birefringent dichroic chiral crystals,” Proc. Roy. Soc. London A 459, 1261–1292 (2003).
[CrossRef]

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66, 1–16 (2002).
[CrossRef]

M. V. Berry, “Exploring the colours of dark light,” New J. Phys. 4, 1–14 (2002).
[CrossRef]

M. V. Berry, J. F. Nye, F. J. Wright, “The elliptic umbilic diffraction catastrophe,” Phil. Trans. R. Soc. A 291, 453–484 (1979).
[CrossRef]

Burkovets, D. N.

Dennis, M. R.

M. V. Berry, M. R. Dennis, “The optical singularities of birefringent dichroic chiral crystals,” Proc. Roy. Soc. London A 459, 1261–1292 (2003).
[CrossRef]

Dogariu, A.

Egorov, Y. A.

Y. A. Egorov, T. A. Fadeeva, A. V. Volyar, “The fine structure of singular beams in crystal: colors and polarization,” J. Opt. A: Pure Appl. Opt. 6, S217–S228 (2004).
[CrossRef]

Fadeeva, T. A.

Y. A. Egorov, T. A. Fadeeva, A. V. Volyar, “The fine structure of singular beams in crystal: colors and polarization,” J. Opt. A: Pure Appl. Opt. 6, S217–S228 (2004).
[CrossRef]

Freund, I.

I. Freund, N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. 50, 5164–5172 (1994).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hanson, S. G.

Heckenberg, N. R.

Leach, J.

J. Leach, M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 1–7 (2003).
[CrossRef]

Maksimyak, A. P.

Maksimyak, P. P.

Mamayev, A. V.

N. B. Baranova, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zeldovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
[CrossRef]

N. B. Baranova, B. Ya. Zeldovich, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, “Dislocation of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP. 33, 1789–1797 (1981).

McDuff, R.

Miyamoto, K.

Mujat, M.

Nye, J.

J. Nye, “Evolution from Fraunhofer to a Pearcey diffraction pattern,” J. Opt. A: Pure Appl. Opt. 5, 495–502 (2003).
[CrossRef]

J. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (Institute of Physics, Bristol, 1999).

Nye, J. F.

M. V. Berry, J. F. Nye, F. J. Wright, “The elliptic umbilic diffraction catastrophe,” Phil. Trans. R. Soc. A 291, 453–484 (1979).
[CrossRef]

Padgett, M. J.

J. Leach, M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 1–7 (2003).
[CrossRef]

Pearcey, T.

T. Pearcey, “The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic,” Philos. Mag. 37, 311–317 (1946).

Pilipetsky, N. F.

N. B. Baranova, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zeldovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
[CrossRef]

N. B. Baranova, B. Ya. Zeldovich, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, “Dislocation of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP. 33, 1789–1797 (1981).

Popescu, G.

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

Shkunov, V. V.

N. B. Baranova, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zeldovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
[CrossRef]

N. B. Baranova, B. Ya. Zeldovich, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, “Dislocation of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP. 33, 1789–1797 (1981).

Shvartsman, N.

I. Freund, N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. 50, 5164–5172 (1994).
[CrossRef]

Smith, C. P.

Sommerfeld, A.

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

Ushenko, Y. A.

Volyar, A. V.

Y. A. Egorov, T. A. Fadeeva, A. V. Volyar, “The fine structure of singular beams in crystal: colors and polarization,” J. Opt. A: Pure Appl. Opt. 6, S217–S228 (2004).
[CrossRef]

White, A. G.

Wolf, E.

Wright, F. J.

M. V. Berry, J. F. Nye, F. J. Wright, “The elliptic umbilic diffraction catastrophe,” Phil. Trans. R. Soc. A 291, 453–484 (1979).
[CrossRef]

Zeldovich, B. Ya.

N. B. Baranova, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zeldovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
[CrossRef]

N. B. Baranova, B. Ya. Zeldovich, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, “Dislocation of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP. 33, 1789–1797 (1981).

Appl. Opt. (2)

J. Opt. A: Pure Appl. Opt. (2)

J. Nye, “Evolution from Fraunhofer to a Pearcey diffraction pattern,” J. Opt. A: Pure Appl. Opt. 5, 495–502 (2003).
[CrossRef]

Y. A. Egorov, T. A. Fadeeva, A. V. Volyar, “The fine structure of singular beams in crystal: colors and polarization,” J. Opt. A: Pure Appl. Opt. 6, S217–S228 (2004).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

N. B. Baranova, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zeldovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
[CrossRef]

JETP. (1)

N. B. Baranova, B. Ya. Zeldovich, A. V. Mamayev, N. F. Pilipetsky, V. V. Shkunov, “Dislocation of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP. 33, 1789–1797 (1981).

New J. Phys. (3)

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66, 1–16 (2002).
[CrossRef]

M. V. Berry, “Exploring the colours of dark light,” New J. Phys. 4, 1–14 (2002).
[CrossRef]

J. Leach, M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 1–7 (2003).
[CrossRef]

Opt. Lett. (3)

Phil. Trans. R. Soc. A (1)

M. V. Berry, J. F. Nye, F. J. Wright, “The elliptic umbilic diffraction catastrophe,” Phil. Trans. R. Soc. A 291, 453–484 (1979).
[CrossRef]

Philos. Mag. (1)

T. Pearcey, “The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic,” Philos. Mag. 37, 311–317 (1946).

Phys. Rev. (1)

I. Freund, N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. 50, 5164–5172 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

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

Proc. Roy. Soc. London A (1)

M. V. Berry, M. R. Dennis, “The optical singularities of birefringent dichroic chiral crystals,” Proc. Roy. Soc. London A 459, 1261–1292 (2003).
[CrossRef]

Other (3)

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

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

J. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (Institute of Physics, Bristol, 1999).

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Figures (18)

Fig. 1
Fig. 1

Formation of the field diffracted by a cylindrical lens.

Fig. 2
Fig. 2

(a) Intensity and (b) phase distributions of the fields passing a cylindrical lens; (c) interference distribution obtained as a result of superposition with a plane reference wave; (d) enlarged segments depicted in (a), (b), and (c).

Fig. 3
Fig. 3

(a) Intensity and (b) phase distributions of the field obtained for a spherical lens.

Fig. 4
Fig. 4

Intensity (left) and phase (right) distributions of the field obtained for cylindrical lens with a radius of curvature of 10 μm for apertures a/f: (a) 0.5, (b) 0.65, and (c) 0.75.

Fig. 5
Fig. 5

Dependence of a/f ratio on the radius of cylindrical lens R, for which the phase singularity disappears.

Fig. 6
Fig. 6

(a) Intensity and (b) phase distributions of the field for a tautochronic lens with a radius of curvature of 10 μm.

Fig. 7
Fig. 7

(a) Intensity and (b) phase distributions of the field for a cylindrical lens illuminated with a Gaussian beam.

Fig. 8
Fig. 8

(a) Intensity distributions of the field for cylindrical lens with a radius of curvature of 10 μm illuminated with a beam consisting of three spectral components. (b) The use of a chromoscope provides the pattern.

Fig. 9
Fig. 9

(a) Patterns obtained by the use of a chromascope for coinciding amplitude zeros of three spectral components, (b) for two spectral components.

Fig. 10
Fig. 10

Patterns processed by a chromascope for various scales for a cylindrical lens with a curvature radius 100 μm at the distances (a) 10 μm, (b) 30 μm, and (c) 110 μm from the apex point of the cylindrical lens.

Fig. 11
Fig. 11

Relief map for the modeled surface with a three-point smoothed random surface obeying a Gaussian height distribution.

Fig. 12
Fig. 12

(a) Intensity and (b) phase distributions of the field diffracted by a rough surface, and the pattern resulting from (c) chromascopic processing for a polychromatic field consisting of three wavelengths. The amplitude zeros for three spectral components coincide in the center of the pattern.

Fig. 13
Fig. 13

(a) Intensity and (b) phase distributions of the field diffracted by a rough surface, and the pattern resulting from (c) a chromascopic processing for a polychromatic field consisting of three wavelengths. Amplitude zeros for two spectral components coincide in the center of the pattern.

Fig. 14
Fig. 14

Experimental optical arrangement: 1, source of light; 2, 4, 8, objectives; 3, diaphragm; 5, polarizer; 6, film; 7, analyzer; 9, CCD camera; 10, computer.

Fig. 15
Fig. 15

Conoscopic patterns obtained in white light for (a) parallel and (b) crossed polarizer and analyzer.

Fig. 16
Fig. 16

Pattern shown in Fig. 14 processed by a chromascope.

Fig. 17
Fig. 17

Polychromatic radiation field scattered by a rough surface.

Fig. 18
Fig. 18

Pattern obtained by applying a chromascope to the experimentally found intensity distributions.

Equations (2)

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U ( ξ ) = z i λ F ( x ) R 3 / 2 ( x ) exp { - i k [ R ( x ) + h ( x ) ] } d x ,
( R G B ) ( R G B ) / max ( R ,     G ,     B ) .

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