Abstract

We present the results of computer simulation of the spatial distribution of the Poynting vector and illustrate motion of microparticles and nanoparticles in spatially inhomogeneously polarized fields. The influence of phase relations and the degree of mutual coherence of superimposing waves on the characteristics of the microparticle’s motion has been analyzed. For the first time, we have shown experimentally the possibility of diagnostics of optical currents in liquids caused by polarization characteristics of an optical field alone, using test metallic particles of nanoscale.

© 2011 Optical Society of America

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  1. M. V. Berry, “Optical currents,” J. Opt. A Pure Appl. Opt. 11, 094001 (2009).
    [CrossRef]
  2. O. V. Angelsky, N. N. Dominikov, P. P. Maksimyak, and T. Tudor, “Experimental revealing of polarization waves,” Appl. Opt. 38, 3112–3117 (1999).
    [CrossRef]
  3. T. Tudor, “Polarization waves as observable phenomena,” J. Opt. Soc. Am. A 14, 2013–2020 (1997).
    [CrossRef]
  4. M. V. Berry and K. T. Donald, “Exact and geometrical optics energy trajectories in twisted beams,” J. Opt. A Pure Appl. Opt. 10, 035005 (2008).
    [CrossRef]
  5. M. V. Berry and M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. London Ser. A 456, 2059–2079 (2000).
    [CrossRef]
  6. O. V. Angelsky, S. G. Hanson, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “On polarization metrology (estimation) of the degree of coherence of optical waves,” Opt. Express 17, 15623–15634 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
    [CrossRef]
  12. M. Mujait, A. Dogariu, and E. Wolf, “A law of interference of electromagnetic beams of any state of coherence and polarization and the Fresnel-Arago interference laws,” J. Opt. Soc. Am. A 21, 2414–2417 (2004).
    [CrossRef]
  13. J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005).
    [CrossRef]
  14. P. Refregier and F. Goudail, “Invariant degrees of coherence of partially polarized light,” Opt. Express 13, 6051–6060 (2005).
    [CrossRef] [PubMed]
  15. R. Khrobatin and I. Mokhun, “Shift application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A Pure Appl. Opt. 10, 064015 (2008).
    [CrossRef]
  16. R. Khrobatin, I. Mokhun, and J. Victorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
    [CrossRef]
  17. A. Y. Bekshaev and M. S. Soskin, “Transverse energy flows in vectorial fields of paraxial light beams,” Proc. SPIE 6729, 67290G (2007).
    [CrossRef]
  18. O. V. Angelsky, S. B. Yermolenko, C. Yu. Zenkova, and A. O. Agelskaya, “Polarization manifestations of correlation (intrinsic coherence) of optical fields,” Appl. Opt. 47, 5492–5499 (2008).
    [CrossRef] [PubMed]
  19. O. V. Angelsky, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “On the feasibility for estimating the degree of coherence of waves at near field,” Appl. Opt. 48, 2784–2788 (2009).
    [CrossRef] [PubMed]
  20. J. Turkevich, P. C. Stevenson, and J. Hiller, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55–75 (1951).
    [CrossRef]

2009 (3)

2008 (4)

R. Khrobatin and I. Mokhun, “Shift application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A Pure Appl. Opt. 10, 064015 (2008).
[CrossRef]

R. Khrobatin, I. Mokhun, and J. Victorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
[CrossRef]

M. V. Berry and K. T. Donald, “Exact and geometrical optics energy trajectories in twisted beams,” J. Opt. A Pure Appl. Opt. 10, 035005 (2008).
[CrossRef]

O. V. Angelsky, S. B. Yermolenko, C. Yu. Zenkova, and A. O. Agelskaya, “Polarization manifestations of correlation (intrinsic coherence) of optical fields,” Appl. Opt. 47, 5492–5499 (2008).
[CrossRef] [PubMed]

2007 (1)

A. Y. Bekshaev and M. S. Soskin, “Transverse energy flows in vectorial fields of paraxial light beams,” Proc. SPIE 6729, 67290G (2007).
[CrossRef]

2006 (1)

2005 (2)

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005).
[CrossRef]

P. Refregier and F. Goudail, “Invariant degrees of coherence of partially polarized light,” Opt. Express 13, 6051–6060 (2005).
[CrossRef] [PubMed]

2004 (1)

2000 (2)

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in biotissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

M. V. Berry and M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. London Ser. A 456, 2059–2079 (2000).
[CrossRef]

1999 (2)

O. V. Angelsky, N. N. Dominikov, P. P. Maksimyak, and T. Tudor, “Experimental revealing of polarization waves,” Appl. Opt. 38, 3112–3117 (1999).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

1997 (1)

1993 (2)

1951 (1)

J. Turkevich, P. C. Stevenson, and J. Hiller, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55–75 (1951).
[CrossRef]

Agelskaya, A. O.

Angel’skii, O. V.

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in biotissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Angelsky, O. V.

Arkhelyuk, A. D.

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Arkhelyuk, O. D.

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in biotissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

Bekshaev, A. Y.

A. Y. Bekshaev and M. S. Soskin, “Transverse energy flows in vectorial fields of paraxial light beams,” Proc. SPIE 6729, 67290G (2007).
[CrossRef]

Berry, M. V.

M. V. Berry, “Optical currents,” J. Opt. A Pure Appl. Opt. 11, 094001 (2009).
[CrossRef]

M. V. Berry and K. T. Donald, “Exact and geometrical optics energy trajectories in twisted beams,” J. Opt. A Pure Appl. Opt. 10, 035005 (2008).
[CrossRef]

M. V. Berry and M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. London Ser. A 456, 2059–2079 (2000).
[CrossRef]

Burkovets, D. N.

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in biotissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Dennis, M. R.

M. V. Berry and M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. London Ser. A 456, 2059–2079 (2000).
[CrossRef]

Dogariu, A.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005).
[CrossRef]

M. Mujait, A. Dogariu, and E. Wolf, “A law of interference of electromagnetic beams of any state of coherence and polarization and the Fresnel-Arago interference laws,” J. Opt. Soc. Am. A 21, 2414–2417 (2004).
[CrossRef]

Dominikov, N. N.

Donald, K. T.

M. V. Berry and K. T. Donald, “Exact and geometrical optics energy trajectories in twisted beams,” J. Opt. A Pure Appl. Opt. 10, 035005 (2008).
[CrossRef]

Ellis, J.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005).
[CrossRef]

Ermolenko, S. B.

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Gorodyns’ka, N. V.

Gorsky, M. P.

Goudail, F.

Hanson, S. G.

Hiller, J.

J. Turkevich, P. C. Stevenson, and J. Hiller, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55–75 (1951).
[CrossRef]

Khrobatin, R.

R. Khrobatin, I. Mokhun, and J. Victorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
[CrossRef]

R. Khrobatin and I. Mokhun, “Shift application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A Pure Appl. Opt. 10, 064015 (2008).
[CrossRef]

Maksimyak, P. P.

Mokhun, I.

R. Khrobatin, I. Mokhun, and J. Victorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
[CrossRef]

R. Khrobatin and I. Mokhun, “Shift application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A Pure Appl. Opt. 10, 064015 (2008).
[CrossRef]

Mujait, M.

Perun, T. O.

Polyanskii, P. V.

Ponomarenko, S.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005).
[CrossRef]

Refregier, P.

Soskin, M. S.

A. Y. Bekshaev and M. S. Soskin, “Transverse energy flows in vectorial fields of paraxial light beams,” Proc. SPIE 6729, 67290G (2007).
[CrossRef]

Stevenson, P. C.

J. Turkevich, P. C. Stevenson, and J. Hiller, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55–75 (1951).
[CrossRef]

Tudor, T.

Turkevich, J.

J. Turkevich, P. C. Stevenson, and J. Hiller, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55–75 (1951).
[CrossRef]

Ushenko, A. G.

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Ushenko, O. G.

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in biotissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

Ushenko, Yu. A.

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in biotissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

Victorovskaya, J.

R. Khrobatin, I. Mokhun, and J. Victorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
[CrossRef]

Wolf, E.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005).
[CrossRef]

M. Mujait, A. Dogariu, and E. Wolf, “A law of interference of electromagnetic beams of any state of coherence and polarization and the Fresnel-Arago interference laws,” J. Opt. Soc. Am. A 21, 2414–2417 (2004).
[CrossRef]

Yermolenko, S. B.

Zenkova, C. Yu.

Appl. Opt. (4)

Discuss. Faraday Soc. (1)

J. Turkevich, P. C. Stevenson, and J. Hiller, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55–75 (1951).
[CrossRef]

J. Opt. A Pure Appl. Opt. (3)

M. V. Berry, “Optical currents,” J. Opt. A Pure Appl. Opt. 11, 094001 (2009).
[CrossRef]

M. V. Berry and K. T. Donald, “Exact and geometrical optics energy trajectories in twisted beams,” J. Opt. A Pure Appl. Opt. 10, 035005 (2008).
[CrossRef]

R. Khrobatin and I. Mokhun, “Shift application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A Pure Appl. Opt. 10, 064015 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Laser Phys. (1)

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in biotissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

Opt. Commun. (1)

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. R. Soc. London Ser. A (1)

M. V. Berry and M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. London Ser. A 456, 2059–2079 (2000).
[CrossRef]

Proc. SPIE (1)

A. Y. Bekshaev and M. S. Soskin, “Transverse energy flows in vectorial fields of paraxial light beams,” Proc. SPIE 6729, 67290G (2007).
[CrossRef]

Quantum Electron. (1)

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Ukr. J. Phys. Opt. (1)

R. Khrobatin, I. Mokhun, and J. Victorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Superposition of plane waves of equal amplitudes linearly polarized at the incidence plane, with an interference angle of 90 ° . Periodical spatial polarization modulation takes place in the plane of incidence. (b) Spatial distribution of the averaged Poynting vectors resulting from superposition of two orthogonally linearly polarized waves with an interference angle of 90 ° .

Fig. 2
Fig. 2

Distribution of polarization in the registration plane is marked by thin lines. The direction and value of the Poynting vector is marked by bold lines. The point at the end of the vector determines the direction of energy propagation. The modulation of the Poynting vector takes place according to the modulation polarization in the registration plane.

Fig. 3
Fig. 3

(a) Change of the particle motion velocity with time, obtained for different values of the degree of coherence of superposing waves in the case of particles moving along the peak of the field averaged value of the Poynting vector: curve 1 is obtained for the degree of coherence, which is equal to 1; curve 2, for the degree of coherence, which is equal to 0.5; curve 3, for the degree of coherence, which is equal to 0.25. (b) Change of the motion velocity with time, obtained for different values of the degree of coherence of superposing waves in the case of the motion of particles along the minimum of the averaged field value of the Poynting vector: curve 1 is obtained for the degree of coherence, which is equal to 1; curve 2, for the degree of coherence, which is equal to 0.5; curve 3, for the degree of coherence, which is equal to 0.25.

Fig. 4
Fig. 4

The diagram of particle velocity distribution with time.

Fig. 5
Fig. 5

(a) Arrangement of superposition of four plane waves. (b) 2D distribution of the averaged Poynting vectors resulting from the superposition of four waves shown in Fig. 5a.

Fig. 6
Fig. 6

Variation of motion velocity of a test particle in an averaged field of distributed Poynting vectors with the change of the degree of coherence of one of the waves (four superposing waves are in phase): curve 1, one of the waves is incoherent; curve 2, the degree of coherence of the same wave is 0.25; curve 3, the degree of coherence of the wave is 0.5; curve 4, the degree of coherence of the wave is 0.75

Fig. 7
Fig. 7

Change of the resultant force of the test particle motion in the averaged field of distributed Poynting vectors with the change of the degree of coherence of one of the waves (four superposing waves are in phase): curve 1, one of the waves is incoherent; curve 2, the degree of coherence of the same wave is 0.25; curve 3, the degree of coherence of the wave is 0.5; curve 4, the degree of coherence of the wave is 0.75.

Fig. 8
Fig. 8

Experimental setup: L1, L2, lasers; TS1, TS2, telescopic systems; M1, M2, M3, M4, mirrors; PW1, PW2, half-wave plates for λ = 635 nm ; PP, plane-parallel plate; BS, beam splitter; MO1, MO2, MO3, micro-objectives; C, cuvette with gold hydrosol; IF, interference filter at λ = 532 nm ; D1 ( 0.7 mm diameter), D2, diaphragms; S, opaque screen; PD, photodetector; A, amplifier; ADC, analog-to-digital converter; PC, computer.

Equations (7)

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S = ε ε 0 μ μ 0 i , j { φ i j ( 1 ) ( r ) + φ i j ( 2 ) ( r ) + 2 tr [ W ( r 1 , r 1 , 0 ) ] tr [ W ( r 2 , r 2 , 0 ) ] · | η i j ( 1 , 2 ) | cos [ α i j ( 1 , 2 ) ] · cos [ δ e ] } ,
W ( r 1 , r 2 , t ) = E i ( 1 ) ( r 1 , t ) E j ( 2 ) * ( r 2 , t ) ,
η i j ( r 1 , r 2 , t ) = W i j ( r 1 , r 2 , t ) tr [ W ( r 1 , r 1 , 0 ) ] · tr [ W ( r 2 , r 2 , 0 ) ] = W i j ( r 1 , r 2 , t ) i j W i i ( r 1 , r 1 , 0 ) W j j ( r 2 , r 2 , 0 ) .
E = | E ( 1 ) + E ( 2 ) | cos ( ω t + δ e ) a e ,
H = | H ( 1 ) + H ( 2 ) | cos ( ω t + δ h ) a h .
S inst = E × H = | E | · | H | cos ( ω t + δ e ) cos ( ω t + δ h ) ( a e × a h ) ,
S ave = | E | · | H | 2 ( a e × a h ) cos ( δ e δ h ) = 1 2 ( E × H ) · cos ( δ e δ h ) .

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