Optical angular momentum transfer to transparent isotropic particles using laser beam carrying zero average angular momentum

Enrico Santamato; Antonio Sasso; Bruno Piccirillo; Angela Vella

doi:10.1364/OE.10.000871

Optics Express
Vol. 10,
Issue 17,
pp. 871-878
(2002)
•https://doi.org/10.1364/OE.10.000871

Optical angular momentum transfer to transparent isotropic particles using laser beam carrying zero average angular momentum

Enrico Santamato, Antonio Sasso, Bruno Piccirillo, and Angela Vella

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Enrico Santamato, Antonio Sasso, Bruno Piccirillo, and Angela Vella, "Optical angular momentum transfer to transparent isotropic particles using laser beam carrying zero average angular momentum," Opt. Express 10, 871-878 (2002)

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Abstract

The torque exerted by an astigmatic optical beam on small transparent isotropic particles was dynamically measured observing the angular motion of the particles under a microscope. The data confirmed that torque was originated by the transfer of orbital angular momentum associated with the spatial changes in the phase of the optical field induced by the moving particle. This mechanism for angular momentum transfer works also with incident light beams with no net angular momentum.

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Media 1: MOV (530 KB)

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Fig. 1. Rotational dragging of three trapped latex spheres each 14 μm in diameter.

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Fig. 2. Movie showing the laser-induced spinning of a trapped small glass rod (length 13 μm, diameter 2 μm). [Media 1]

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Fig. 3. Nine frames of a trapped glass rods showing the alignment motion along the major axis of the trapping beam shape. As the optical torque acting on the particle depends on its orientation [see Eq. (8)], the rotation speed is not constant. The frames are 200 ms apart. The scale bar is 10 μm.

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Fig. 4. The angular position of the particle as a function of time during its motion. The laser power at the sample position was P = 200 mW.

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Equations (14)

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ψ (r, α) = - \frac{k r^{2}}{4 f} - \frac{k r^{2}}{4 a} \cos [2 (ϕ - α)]

E (r, ϕ, α) = \sum_{p = 0}^{\infty} \sum_{l = - \infty}^{\infty} c_{p, l} (α) \exp [il (ϕ - α)] f_{p, l} (r),

f_{p, l} (x) = {(- 1)}^{p} \sqrt{\frac{2 p!}{π w^{2} (p + ∣ l ∣)!}} x^{∣ l ∣} \exp (- x^{2}) L_{p}^{∣ l ∣} (x^{2})

{\dot{c}}_{p, l} (t) = il \dot{α} c_{p, l} - (\frac{k w^{2} \dot{α}}{8 a}) [\sqrt{(p + l) (p + l - 1)} c_{p, l - 2} - 2 \sqrt{(p + l) (p + 1)} c_{p + 1, l - 2}

+ \sqrt{(p + 1) (p + 2)} c_{p + 2, l - 2} - \sqrt{(p + l + 1) (p + l + 2)} c_{p, l + 2}

+ 2 \sqrt{p (p + l + 1)} c_{p - 1, l + 2} - \sqrt{p (p - 1)} c_{p - 2, l + 2}] .

(l = 0,2,4, \dots) (p = 0,1,2, \dots)

{\dot{c}}_{p, 0} (t) = (\frac{k w^{2} \dot{α}}{8 a}) [\sqrt{(p + 1) (p + 2)} c_{p, - 2} - 2 \sqrt{p (p + 1)} c_{p - 1, - 2} + \sqrt{p (p - 1)} c_{p - 2, - 2}

+ 2 \sqrt{p (p + 1)} c_{p - 1,2} - \sqrt{(p + 1) (p + 2)} c_{p, 2} - \sqrt{p (p - 1)} c_{p - 2,2}] .

γ \dot{α} = M_{z} (t) = (\frac{cn}{8 πω}) \sum_{p = 0}^{\infty} \sum_{l = - \infty}^{\infty} l {∣ c_{p, l} (t) ∣}^{2} =

= (\frac{P}{ω}) \frac{\sum_{p = 0}^{\infty} \sum_{l = - \infty}^{\infty} l {∣ c_{p, l} (t) ∣}^{2}}{\sum_{p = 0}^{\infty} \sum_{l = - \infty}^{\infty} {∣ c_{p, l} (t) ∣}^{2}}

M_{z} (t) = (\frac{cn}{8 πω}) Im \int \int (E^{*} \frac{\partial}{\partial ϕ} E) d x d y

= - A \sin 2 α (t)

\tan α (t) = e^{- \frac{t}{τ}} \tan α (0)

Abstract

Supplementary Material (1)

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Equations (14)

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