# How does circularly polarized light rotate a body?

1. Jul 27, 2010

### Khrapko

Everyone affirms that a circularly polarized plane wave has no angular momentum, though it contains density of spin. However, a circularly polarized beam of any big diameter has spin angular momentum, which is localized at the surface of the beam, though the spin is allocated in the interior of the beam.
Now imagine that we rotate a huge cosmic body by lighting it with a circularly polarized beam of the correspondingly huge diameter. I ask: Where does the torque act?

2. Jul 27, 2010

### GRDixon

Not everyone! For example, "Circularly polarized light ... carries angular momentum. ...when this beam is absorbed that angular momentum is delivered to the absorber." (Feynman Lectures on Physics," V1, Sect. 33-7. The entire chapter 33 may be instructive reading.

3. Jul 27, 2010

### Andy Resnick

Circularly polarized light does indeed carry spin angular momentum. In addition, it's possible for light to carry angular orbital momentum. There are several ways light can impart torque to a massive body, the most common uses birefringent materials. AFAIK, the earliest demonstration of this was by Richard Beth in 1936, although Barlow published a few papers in 1913. IIRC, Barlow was really observing linear momentum but the geometry created angular momentum.

More recently, people routinely use laser tweezers to rapidly spin micrometer-sized particles (optical spanners).

4. Jul 28, 2010

### Khrapko

Dear GRDixon! Thank you! You are completely right! But Feynman joined the Majority, and current Scientific community insists that a circularly polarized plane wave has no angular momentum because J=r\times(E\times H).
Well, but I am interested to know where, in the center or at the periphery, does the torque act?

5. Jul 28, 2010

### Andy Resnick

I don't understand what you are asking?

6. Jul 28, 2010

### Khrapko

Light pressure acts uniformly on the alight surface of the body. I ask: where, on what points, near the center of the alight surface, or at the periphery of the alight surface, maybe uniformly as well, does the torque act?

7. Jul 29, 2010

### DrDu

Khrapko, I don't know much about the energy-momentum tensor of light, but the pressure of light is given by the i=1,2,3 diagonal elements of the tensor. I suppose, the effect is due to the space like the non-diagonal elements of the tensor.

8. Jul 29, 2010

### Khrapko

Sorry, once more, I ask: where, on what points, near the center of the alight surface, or at the periphery of the alight surface, maybe uniformly as well, does the torque act?

9. Jul 29, 2010

### Andy Resnick

Are you asking how to reconcile the notions that a spot of light has a finite extent, but torque is usually defined as a force acting at a point?

10. Jul 29, 2010

### Khrapko

First, not a spot of light. We consider a huge cosmic body, and we light it up by a circularly polarized beam of the correspondingly huge diameter. So, all our body is alight.
Second, torque is moment of a couple. Couple is a system of two equal and antiparallel forces.
I ask: where do the forces act? Where are the forces applied? At what place are the forces applied?I ask: on what place do the forces act? Maybe they act near the center of the body surface, or at the periphery of the surface?

Last edited: Jul 29, 2010
11. Jul 30, 2010

### Khrapko

I submitted this question to several forums during several years. This question was published by Am. J. Phys. 69, 405 (2001) One can see it at http://khrapkori.wmsite.ru/. Nobody knows an answer. However, an experiment for determining the place of applying the torque are suggested http://khrapkori.wmsite.ru/ftpgetfile.php?module=files&id=34. Unfortunately, this paper was rejected by a dozen of journals without a consideration.

Last edited by a moderator: Apr 25, 2017
12. Jul 31, 2010

### Dr Lots-o'watts

Won't the forces act everywhere the beam is lit? This is not obvious? Beam and body diameter are irrelevant.

"...localized at the surface of the beam" ? What does that mean?

Some beams are uniform, some are gaussian, some are annular, it depends on the profile of your beam. You don't say this. All beams aren't identical.

13. Jul 31, 2010

### Khrapko

Mirabile dictu! The scientific community insists that spin angular momentum of a circularly polarized beam is localized at the surface of the beam. For example, [1]: “We have made E(r) and H(r) constant over a large central region of the beam and confined the variation of the functions from these constant values to zero to lie within a “skin” of small thickness which lies a distance R from the axis. The electric and magnetic fields can have a nonzero z-component only within the skin region of this beam. Having z-components within this region implies the possibility of a nonzero z-component of angular momentum within this region. Since the beam is identically zero outside the skin and constant inside the skin region, the skin region is the only one in which the z-component of angular momentum does not vanish”. [2] adds: “This angular momentum is the spin of the beam”
[1] Simmonds & Guttmann, States, Waves and Photons (1970), p.226
[2] Ohanian, What is spin? Am. J. Phys. 54 (1986) p. 502

14. Nov 25, 2010

### Khrapko

Can you give a reference concerning Barlow?

15. Nov 25, 2010

### Khrapko

Absorption of a circularly polarized light beam represents a critical problem. The point is that spin (of photons) is contained within the (wide) beam, but moment of linear momentum is localized in the surface layer (skin)of the beam. Therefore we cannot predict the behaviour of an absorber, which is divided concentrically into an inner part and corresponding outer part such that the skin of the beam is absorbed by the outer part. Will the inner part perceive a torque (and rotate)? It is a puzzle!
Really, if the inner part does not perceive a torque, spin angular momentum of a photon disappears or is absorbed on peripheries of the absorber while energy of the photon is absorbed on the inner region. If the inner part does perceive a torque, this cannot be explained by the use of the Maxwell stress tensor of electromagnetic field because this tensor provides no tangential forces in the inner part. Also note there is no angular momentum flux in the radial direction.
Welcome to the discussion [1 - 3].
[1] R. I. Khrapko, “Does plane wave not carry a spin?” Amer. J. Phys. 69, 405 (2001). http://khrapkori.wmsite.ru/ftpgetfile.php?module=files&id=10
[2] L. Allen, M. J. Padgett, “Response to Question #79. Does a plane wave carry spin angular momentum?” Am. J. Phys. 70, 567 (2002) http://khrapkori.wmsite.ru/ftpgetfile.php?id=53&module=files
[3] R. I. Khrapko, “Mechanical stresses produced by a light beam.” J. Modern Optics. 55 (2008) 1487-1500. http://khrapkori.wmsite.ru/ftpgetfile.php?module=files&id=9

16. Nov 25, 2010

### Andy Resnick

Barlow, G., On the Torque produced by a Beam of Light in Oblique Refraction through a Glass Plate. Proc. R. Soc. Lond., 1912. A87: p. 1.

17. Nov 26, 2010

### Khrapko

You are right. They did not use circular polarization

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