Abstract

The relations for the components of the Poynting vector of a quasi-monochromatic wave are obtained. It is shown that in this case the behavior of the transversal Poynting component may be defined similarly to that in the coherent case. The total angular momentum of the quasi-monochromatic wave may be divided into the orbital and spin parts. The example of a Gaussian beam shows that the value of the spin angular momentum is connected to the coherence characteristics of the beam. Experimental results are presented.

© 2014 Optical Society of America

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References

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  1. M. J. Lang and S. M. Block, “Resource letter: LBOT-1: laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
    [CrossRef]
  2. L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1999), Vol. XXXIX, pp. 291–372.
  3. A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum. (Nova Science, 2008).
  4. I. I. Mokhun, “Introduction to linear singular optics,” in Optical Correlation Techniques and Applications, O. V. Angelsky, ed. (SPIE, 2007), pp. 1–132.
  5. A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation light beams,” J. Opt. 13, 053001 (2011).
    [CrossRef]
  6. J. Serna and J. M. Movilla, “Orbital angular momentum of partially coherent beams,” Opt. Lett. 26, 405–407 (2001).
    [CrossRef]
  7. O. V. Angelsky, M. P. Gorsky, P. P. Maksimyak, A. P. Maksimyak, S. G. Hanson, and C. Yu. Zenkova, “Investigation of optical currents in coherent and partially coherent vector fields,” Opt. Express 19, 660–672 (2011).
    [CrossRef]
  8. 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]
  9. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).
  10. J. Perina, Coherence of Light, 2nd ed. (D. Reidel, 1985).
  11. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics, (Wiley, 1981).
  12. R. Khrobatin, I. Mokhun, and Ju. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
    [CrossRef]
  13. M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Progress in Optics (Elsevier, 2009), Vol. 53, pp. 293–363.
  14. I. Mokhun and R. Khrobatin, “Shift of application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A 10, 064015 (2008).
    [CrossRef]
  15. F. S. Crawford, Waves, Berkeley Physics Course (McGraw-Hill, 1968), Vol. 3, pp. 337–341.
  16. O. V. Angelsky, A. Ya. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Yu. Zenkova, and A. V. Tyurin, “Circular motion of particles suspended in a Gaussian beam with circular polarization validates the spin part of the internal energy flow,” Opt. Express 20, 11351–11356 (2012).
    [CrossRef]

2012 (1)

2011 (2)

2009 (1)

2008 (2)

R. Khrobatin, I. Mokhun, and Ju. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 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 10, 064015 (2008).
[CrossRef]

2003 (1)

M. J. Lang and S. M. Block, “Resource letter: LBOT-1: laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

2001 (1)

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1999), Vol. XXXIX, pp. 291–372.

Angelsky, O. V.

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1999), Vol. XXXIX, pp. 291–372.

Bekshaev, A.

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum. (Nova Science, 2008).

Bekshaev, A. Ya.

Bliokh, K.

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

Block, S. M.

M. J. Lang and S. M. Block, “Resource letter: LBOT-1: laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Crawford, F. S.

F. S. Crawford, Waves, Berkeley Physics Course (McGraw-Hill, 1968), Vol. 3, pp. 337–341.

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Progress in Optics (Elsevier, 2009), Vol. 53, pp. 293–363.

Gorodyns’ka, N. V.

Gorsky, M. P.

Hanson, S. G.

Khrobatin, R.

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

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

Lang, M. J.

M. J. Lang and S. M. Block, “Resource letter: LBOT-1: laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

Maksimyak, A. P.

Maksimyak, P. P.

Mokhun, I.

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

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

Mokhun, I. I.

Movilla, J. M.

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics, (Wiley, 1981).

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Progress in Optics (Elsevier, 2009), Vol. 53, pp. 293–363.

Padgett, M. J.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Progress in Optics (Elsevier, 2009), Vol. 53, pp. 293–363.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1999), Vol. XXXIX, pp. 291–372.

Perina, J.

J. Perina, Coherence of Light, 2nd ed. (D. Reidel, 1985).

Serna, J.

Soskin, M.

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum. (Nova Science, 2008).

Tyurin, A. V.

Vasnetsov, M.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum. (Nova Science, 2008).

Viktorovskaya, Ju.

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

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Zenkova, C. Yu.

Am. J. Phys. (1)

M. J. Lang and S. M. Block, “Resource letter: LBOT-1: laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

J. Opt. (1)

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

J. Opt. A (1)

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

Opt. Express (3)

Opt. Lett. (1)

Ukr. J. Phys. Opt. (1)

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

Other (8)

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Progress in Optics (Elsevier, 2009), Vol. 53, pp. 293–363.

F. S. Crawford, Waves, Berkeley Physics Course (McGraw-Hill, 1968), Vol. 3, pp. 337–341.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

J. Perina, Coherence of Light, 2nd ed. (D. Reidel, 1985).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics, (Wiley, 1981).

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1999), Vol. XXXIX, pp. 291–372.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum. (Nova Science, 2008).

I. I. Mokhun, “Introduction to linear singular optics,” in Optical Correlation Techniques and Applications, O. V. Angelsky, ed. (SPIE, 2007), pp. 1–132.

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Figures (4)

Fig. 1.
Fig. 1.

1, He–Ne laser; 2,5,9,11, beam splitters; 3,4, mirrors; 6,7, intensity “regulators” (two polarizers); 8, quarter-wave plate; 10, reference photo detector; 12,13, system of incoherent illumination; 14, focusing micro-objective; 15, sample with micro-objects; 16, objective of microscope; 17, blue filter; 18, CCD camera.

Fig. 2.
Fig. 2.

Optical trap configuration and stages of micro-object (red blood cell) capturing.

Fig. 3.
Fig. 3.

Rotation of a red blood cell due to the spin angular momentum in the clockwise direction.

Fig. 4.
Fig. 4.

Rotation of a red blood cell due to the spin angular momentum in the anticlockwise direction.

Equations (20)

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p⃗=E⃗×H⃗,
Ei(t)=0a(ν)cos[φ(ν)2πνt]dν,
Δνν¯1,
Ei(t)=Ai(t)cos[Φi(t)2πν¯t],
{Pxc4πk{ExT2EyT1}Pyc4πk{EyT2+ExT1}Pzc4π{Ex2+Ey2},
{T1=ExΦxyEyΦyx+AxyAxEx,π2AyxAyEy,π2T2=ExΦxx+EyΦyy+AxxAxEx,π2+AyyAyEy,π2,
{Ei=Ai(t)cos[Φi(t)2πν¯t]Ei,π2=Ai(t)sin[Φi(t)2πν¯t].
{cos2(Φi2πν¯t)=12sin(Φi2πν¯t)cos(Φi2πν¯t)=0cos(Φi2πν¯t)cos(Φl2πν¯t)=12cosΔ¯=12cos(Φ¯iΦ¯l)sin(Φi2πν¯t)cos(Φl2πν¯t)=12sinΔ¯=12sin(Φ¯iΦ¯l),
{P¯x116πω¯{[(s0+s1)Φ¯xx+(s0s1)Φ¯yx]s3y}P¯y116πω¯{[(s0+s1)Φ¯xy+(s0s1)Φ¯yy]+s3x}P¯zc8πs0,
j¯z=xP¯yyP¯x,
{Ex=12π3/2σ2σνexp{x2+y22σ2}×exp{(νν¯)22σν2}×exp{j[Φ0ν2πνt]}dνEy=12π3/2σ2σνexp{x2+y22σ2}×exp{(νν¯)22σν2}×exp{j[Φ0ν2πνt+Δν]}dν,
Δv=π2νν¯.
{P¯x116πω¯s3yP¯y116πω¯s3xP¯zc8πs0,
s3=j(JyxJxy)=1πσ2exp{x2+y2σ2}exp(π2σν216ν¯2).
{P¯x116π2ω¯σ4exp(π2σν216ν¯2)exp{x2+y2σ2}yP¯y116π2ω¯σ4exp(π2σν216ν¯2)exp{x2+y2σ2}x.
α=exp(π2σν216ν¯2)1
Δντ01,
T0=λ¯c,
τ0aT0,
Δνν¯1/a.

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