Abstract

We present the computer simulation results of the spatial distribution of the Poynting vector and illustrate motion of micro and nanoparticles in spatially inhomogeneously polarized fields. The influence of phase relations and the degree of mutual coherence of superimposing waves in the arrangements of two-wave and four-wave superposition on the characteristics of the microparticle’s motion has been analyzed. The prospects of studying temporal coherence using the proposed approach are made. For the first time, the possibility of diagnostics of optical currents in liquids caused by polarization characteristics of an optical field alone, using nanoscale metallic particles has been shown experimentally.

© 2011 OSA

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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(14), 3112–3117 (1999).
    [CrossRef]
  3. T. Tudor, “Polarization waves as observable phenomena,” J. Opt. Soc. Am. A 14(8), 2013–2020 (1997).
    [CrossRef]
  4. M. V. Berry and K. T. McDonald, “Exact and geometrical optics energy trajectories in twisted beams,” J. Opt. A, Pure Appl. Opt. 10(3), 035005 (2008).
    [CrossRef]
  5. M. V. Berry and M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. Lond. A 456, 2059–2079 (2001).
  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(18), 15623–15634 (2009).
    [CrossRef] [PubMed]
  7. I. Mokhun and R. Khrobatin, “Shift of application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A, Pure Appl. Opt. 10(6), 064015 (2008).
    [CrossRef]
  8. R. Khrobatin, I. Mokhun, and J. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9(3), 182–186 (2008).
    [CrossRef]
  9. A. Y. Bekshaev and M. Soskin, “M.S.Soskin Transverse energy flows in vectorial fields of paraxial light beams,” Proc. SPIE, 6729, 67290G, 67290G-12 (2007).
    [CrossRef]
  10. O. V. Angelsky, S. B. Yermolenko, C. Yu. Zenkova, and A. O. Angelskaya, “Polarization manifestations of correlation (intrinsic coherence) of optical fields,” Appl. Opt. 47(29), 5492–5499 (2008).
    [PubMed]
  11. O. V. Angelsky, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “Feasibility of estimating the degree of coherence of waves at the near field,” Appl. Opt. 48(15), 2784–2788 (2009).
    [CrossRef] [PubMed]
  12. M. Born, and E. Wolf, Principles of optics. New York: Cambridge University Press (1999)
  13. J. Turkevich, P. C. Stevenson, and J. Hillier, “A study of the nucleation and growth processes in the synthesis of colloidal gold // J,” Discuss. Faraday Soc. 11, 55–75 (1951).
    [CrossRef]

2009

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

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(18), 15623–15634 (2009).
[CrossRef] [PubMed]

O. V. Angelsky, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “Feasibility of estimating the degree of coherence of waves at the near field,” Appl. Opt. 48(15), 2784–2788 (2009).
[CrossRef] [PubMed]

2008

O. V. Angelsky, S. B. Yermolenko, C. Yu. Zenkova, and A. O. Angelskaya, “Polarization manifestations of correlation (intrinsic coherence) of optical fields,” Appl. Opt. 47(29), 5492–5499 (2008).
[PubMed]

I. Mokhun and R. Khrobatin, “Shift of application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A, Pure Appl. Opt. 10(6), 064015 (2008).
[CrossRef]

R. Khrobatin, I. Mokhun, and J. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9(3), 182–186 (2008).
[CrossRef]

M. V. Berry and K. T. McDonald, “Exact and geometrical optics energy trajectories in twisted beams,” J. Opt. A, Pure Appl. Opt. 10(3), 035005 (2008).
[CrossRef]

2007

A. Y. Bekshaev and M. Soskin, “M.S.Soskin Transverse energy flows in vectorial fields of paraxial light beams,” Proc. SPIE, 6729, 67290G, 67290G-12 (2007).
[CrossRef]

2001

M. V. Berry and M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. Lond. A 456, 2059–2079 (2001).

1999

O. V. Angelsky, N. N. Dominikov, P. P. Maksimyak, and T. Tudor, “Experimental revealing of polarization waves,” Appl. Opt. 38(14), 3112–3117 (1999).
[CrossRef]

1997

T. Tudor, “Polarization waves as observable phenomena,” J. Opt. Soc. Am. A 14(8), 2013–2020 (1997).
[CrossRef]

1951

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

Angelskaya, A. O.

O. V. Angelsky, S. B. Yermolenko, C. Yu. Zenkova, and A. O. Angelskaya, “Polarization manifestations of correlation (intrinsic coherence) of optical fields,” Appl. Opt. 47(29), 5492–5499 (2008).
[PubMed]

Angelsky, O. V.

O. V. Angelsky, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “Feasibility of estimating the degree of coherence of waves at the near field,” Appl. Opt. 48(15), 2784–2788 (2009).
[CrossRef] [PubMed]

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(18), 15623–15634 (2009).
[CrossRef] [PubMed]

O. V. Angelsky, S. B. Yermolenko, C. Yu. Zenkova, and A. O. Angelskaya, “Polarization manifestations of correlation (intrinsic coherence) of optical fields,” Appl. Opt. 47(29), 5492–5499 (2008).
[PubMed]

O. V. Angelsky, N. N. Dominikov, P. P. Maksimyak, and T. Tudor, “Experimental revealing of polarization waves,” Appl. Opt. 38(14), 3112–3117 (1999).
[CrossRef]

Bekshaev, A. Y.

A. Y. Bekshaev and M. Soskin, “M.S.Soskin Transverse energy flows in vectorial fields of paraxial light beams,” Proc. SPIE, 6729, 67290G, 67290G-12 (2007).
[CrossRef]

Berry, M. V.

M. V. Berry and K. T. McDonald, “Exact and geometrical optics energy trajectories in twisted beams,” J. Opt. A, Pure Appl. Opt. 10(3), 035005 (2008).
[CrossRef]

M. V. Berry and M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. Lond. A 456, 2059–2079 (2001).

Berry,, M. V.

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

Dennis, M. R.

M. V. Berry and M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. Lond. A 456, 2059–2079 (2001).

Dominikov, N. N.

O. V. Angelsky, N. N. Dominikov, P. P. Maksimyak, and T. Tudor, “Experimental revealing of polarization waves,” Appl. Opt. 38(14), 3112–3117 (1999).
[CrossRef]

Gorodyns’ka, N. V.

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(18), 15623–15634 (2009).
[CrossRef] [PubMed]

O. V. Angelsky, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “Feasibility of estimating the degree of coherence of waves at the near field,” Appl. Opt. 48(15), 2784–2788 (2009).
[CrossRef] [PubMed]

Gorsky, M. P.

O. V. Angelsky, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “Feasibility of estimating the degree of coherence of waves at the near field,” Appl. Opt. 48(15), 2784–2788 (2009).
[CrossRef] [PubMed]

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(18), 15623–15634 (2009).
[CrossRef] [PubMed]

Hanson, S. G.

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(18), 15623–15634 (2009).
[CrossRef] [PubMed]

Hillier, J.

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

Khrobatin, R.

I. Mokhun and R. Khrobatin, “Shift of application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A, Pure Appl. Opt. 10(6), 064015 (2008).
[CrossRef]

R. Khrobatin, I. Mokhun, and J. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9(3), 182–186 (2008).
[CrossRef]

Maksimyak, P. P.

O. V. Angelsky, N. N. Dominikov, P. P. Maksimyak, and T. Tudor, “Experimental revealing of polarization waves,” Appl. Opt. 38(14), 3112–3117 (1999).
[CrossRef]

McDonald, K. T.

M. V. Berry and K. T. McDonald, “Exact and geometrical optics energy trajectories in twisted beams,” J. Opt. A, Pure Appl. Opt. 10(3), 035005 (2008).
[CrossRef]

Mokhun, I.

R. Khrobatin, I. Mokhun, and J. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9(3), 182–186 (2008).
[CrossRef]

I. Mokhun and R. Khrobatin, “Shift of application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A, Pure Appl. Opt. 10(6), 064015 (2008).
[CrossRef]

Soskin, M.

A. Y. Bekshaev and M. Soskin, “M.S.Soskin Transverse energy flows in vectorial fields of paraxial light beams,” Proc. SPIE, 6729, 67290G, 67290G-12 (2007).
[CrossRef]

Stevenson, P. C.

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

Tudor, T.

O. V. Angelsky, N. N. Dominikov, P. P. Maksimyak, and T. Tudor, “Experimental revealing of polarization waves,” Appl. Opt. 38(14), 3112–3117 (1999).
[CrossRef]

T. Tudor, “Polarization waves as observable phenomena,” J. Opt. Soc. Am. A 14(8), 2013–2020 (1997).
[CrossRef]

Turkevich, J.

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

Viktorovskaya, J.

R. Khrobatin, I. Mokhun, and J. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9(3), 182–186 (2008).
[CrossRef]

Yermolenko, S. B.

O. V. Angelsky, S. B. Yermolenko, C. Yu. Zenkova, and A. O. Angelskaya, “Polarization manifestations of correlation (intrinsic coherence) of optical fields,” Appl. Opt. 47(29), 5492–5499 (2008).
[PubMed]

Zenkova, C. Yu.

O. V. Angelsky, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “Feasibility of estimating the degree of coherence of waves at the near field,” Appl. Opt. 48(15), 2784–2788 (2009).
[CrossRef] [PubMed]

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(18), 15623–15634 (2009).
[CrossRef] [PubMed]

O. V. Angelsky, S. B. Yermolenko, C. Yu. Zenkova, and A. O. Angelskaya, “Polarization manifestations of correlation (intrinsic coherence) of optical fields,” Appl. Opt. 47(29), 5492–5499 (2008).
[PubMed]

Appl. Opt.

O. V. Angelsky, N. N. Dominikov, P. P. Maksimyak, and T. Tudor, “Experimental revealing of polarization waves,” Appl. Opt. 38(14), 3112–3117 (1999).
[CrossRef]

O. V. Angelsky, S. B. Yermolenko, C. Yu. Zenkova, and A. O. Angelskaya, “Polarization manifestations of correlation (intrinsic coherence) of optical fields,” Appl. Opt. 47(29), 5492–5499 (2008).
[PubMed]

O. V. Angelsky, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “Feasibility of estimating the degree of coherence of waves at the near field,” Appl. Opt. 48(15), 2784–2788 (2009).
[CrossRef] [PubMed]

Discuss. Faraday Soc.

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

J. Opt. A, Pure Appl. Opt.

M. V. Berry and K. T. McDonald, “Exact and geometrical optics energy trajectories in twisted beams,” J. Opt. A, Pure Appl. Opt. 10(3), 035005 (2008).
[CrossRef]

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

I. Mokhun and R. Khrobatin, “Shift of application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A, Pure Appl. Opt. 10(6), 064015 (2008).
[CrossRef]

J. Opt. Soc. Am. A

T. Tudor, “Polarization waves as observable phenomena,” J. Opt. Soc. Am. A 14(8), 2013–2020 (1997).
[CrossRef]

Opt. Express

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(18), 15623–15634 (2009).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A

M. V. Berry and M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. Lond. A 456, 2059–2079 (2001).

Proc. SPIE,

A. Y. Bekshaev and M. Soskin, “M.S.Soskin Transverse energy flows in vectorial fields of paraxial light beams,” Proc. SPIE, 6729, 67290G, 67290G-12 (2007).
[CrossRef]

Ukr. J. Phys. Opt.

R. Khrobatin, I. Mokhun, and J. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9(3), 182–186 (2008).
[CrossRef]

Other

M. Born, and E. Wolf, Principles of optics. New York: Cambridge University Press (1999)

Supplementary Material (11)

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» Media 6: MOV (75 KB)     
» Media 7: MOV (1329 KB)     
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» Media 9: MOV (1099 KB)     
» Media 10: MOV (1769 KB)     
» Media 11: MOV (2472 KB)     

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Figures (15)

Fig. 1
Fig. 1

(a) Superposition of plane waves of equal amplitudes, linearly polarized in the plane of incidence having 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°. Red and green axes (0.25 µm of length) correspond to x- and z-coordinates, respectively Media 1. Media 2. The points in the map of the averaged Poynting vectors correspond to the areas (indicated by yellow) through which energy transfer is absent.

Fig. 2
Fig. 2

Illustration of velocities of microparticles in a 2D distribution of the averaged Poynting vectors formed in arrangement Fig. 1a for completely mutually coherent waves. Red and green axes (0.5 µm of length) correspond to x- and z-coordinates, respectively. Media 3.

Fig. 3
Fig. 3

Illustration of microparticles motion velocities in a 2D field distribution of the averaged Poynting vectors formed by the arrangement in Fig. 1 for a degree of mutual coherence of the components equal to 0.2. Red and green axes (0.5 µm of length) correspond to x- and z-coordinates, respectively. Media 4.

Fig. 4
Fig. 4

Illustration of microparticles motion velocities in the 2D field distribution of the averaged Poynting vectors shown in Fig. 1 for the degree of mutual coherence of the components equal to 0.5. Red and green axes (0.5 µm of length) correspond to x- and z-coordinates, respectively. Media 5.

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. . Red and green axes (0.25 µm of length) correspond to x- and z-coordinates, respectively.

Fig. 6
Fig. 6

Spatial distribution of the averaged Poynting vectors for four-wave superposition of components with initial phases from Eq. (9), illustrating a steady-state situation for the resulting field. (Time in sec.). Red and green axes (0.5 µm of length) correspond to x- and z-coordinates. Media 6.

Fig. 7
Fig. 7

Illustrating the movement of a microparticle when of one of four waves with a mutual degree of coherence of 0.5 with other three waves takes part in the forming of a spatial distribution of the averaged Poynting vectors. (Time in sec.). Initial phases defined from Eq. (9). Red and green axes (0.5 µm of length) correspond to x- and z-coordinates, respectively. Media 7.

Fig. 8
Fig. 8

Illustration of moving microparticles, when the spatial distribution of the averaged Poynting vector is formed by four mutually coherent waves with phases defined from Eq. (10). Time in sec.). Red and green axes (0.5 µm of length) correspond to x- and z-coordinates, respectively. Media 8.

Fig. 9
Fig. 9

Illustration of moving microparticles, when the spatial distribution of the averaged Poynting vector is formed by four beams, one of which is incoherent with respect to the other three. (Time in sec.). Initial phases defined from Eq. (10). Red and green axes (0.5 µm of length) correspond to x- and z-coordinates, respectively. Media 9.

Fig. 10
Fig. 10

“Cellular” distribution of the potential traps for microparticles in the case of superposition of four waves.

Fig. 11
Fig. 11

Illustration of the direction and mechanism of energy transfer for superposition of two linearly polarized waves of equal intensity; here the waves are polarized in the plane of incidence, meeting at right angle. (Time in sec.). Red and green axes (0.5 µm of length) correspond to x- and z-coordinates, respectively. Media 10.

Fig. 12
Fig. 12

Arrangement for forming the desired spatial interference distribution. Polarization of both crossed beams is linear, perpendicular to the figure plane.

Fig. 13
Fig. 13

Experimental setup: L1, L2 - lasers, TS1, TS2 - telescopic systems, M1, M2, M3, M4 - mirrors, PW1, W2 - half-wave plates for λ = 635 nm, PP - plane-parallel plate, MO1, MO2, MO3 - microobjectives, C - cuvette with gold hydrosol, IF - interference filter at λ = 532 nm, D1, D2 - diaphragms, S - opaque screen, PD - photodetector, A - amplifier, ADC - analog-to-digital converter, PC - computer.

Fig. 14
Fig. 14

Relative signal for a photodetector (a plate PP is inserted on 2 sec and then removed) in the case when radiation of red laser is linearly polarized: (a) both beams are polarized in the plane perpendicular to the figure plane; (b) both beams are polarized in the figure plane; (c) one beam is polarized at the figure plane, while another one is polarized perpendicularly to this plane.

Fig. 15
Fig. 15

Illustration of the directions of oscillations of the vectors E , H , S for superposition of two waves of equal intensity one of which is linearly polarized in the plane of incidence and another perpendicularly to this plane. The crossing angle between the two beams equals 90°. Red and green axes (0.25 µm of length) correspond to x- and z-coordinates, respectively. Media 11.

Equations (10)

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m d v c d t = i f i 6 π η R v c ,
0.4 m R 2 d Ω d t = i [ f i × r i ] π 2 η R 3 Ω .
E = E ( 1 ) + E ( 2 ) + E ( 3 ) + E ( 4 ) ,
H = H ( 1 ) + H ( 2 ) + H ( 3 ) + H ( 4 ) .
E ( i ) = E x ( i ) i + E y ( i ) j + E z ( i ) k ,
H ( i ) = H x ( i ) i + H y ( i ) j + H z ( i ) k ,
E j ( i ) = E j 0 ( i ) exp [ i ( ω t k j ( i ) j + φ 0 ( i ) ) ] ,
H j ( i ) = H j 0 ( i ) exp [ i ( ω t k j ( i ) j + φ 0 ( i ) ) ] ,
φ 0 ( 1 ) = φ 0 ( 2 ) = φ 0 ( 3 ) = φ 0 ( 4 ) = 0.
φ 0 ( 1 ) = φ 0 ( 2 ) = φ 0 ( 3 ) = 0 ,     φ 0 ( 4 ) = π .

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