Is Maxwell's Electrodynamic Theory Violated?

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Main Question or Discussion Point

In Edward Collet's book "Polarized Light: Fundamentals and Applications", Chapter 3 states that:
One of the immediate results of solving his equations was that in free space only transverse components arose; there was no longitudinal component.
However, in recent years (as recent as 2008), I came across a paper published in Nature Photonics that a group of scientists, Haifeng Wang et al. from Data Storage Institute based in Singapore managed to generate a needle of longitudinally polarized light in free space with the help of binary optics and also radially polarized light. (nature photonics | VOL 2 | AUGUST 2008, Published online: 22 June 2008; doi:10.1038/nphoton.2008.127 pp. 501-505)

The conclusion of the paper states that:

In conclusion, we have proposed the generation of a
longitudinally polarized beam by focusing a radially polarized
beam using a binary optical element and a lens. This binary
optical element works like a special polarization filter, which
diffracts the radial field away from the centre of the beam more
than the longitudinal field, thus making the beam in the focal
region substantially longitudinally polarized. This beam
propagates without divergence for over 4l (a non-diffracting
beam). It is also highly localized in the transverse direction with
FWHM ¼ 0.43l (subdiffraction beam). The suggested method
achieves the required combination of conversion efficiency,
uniformity and field localization.
My question is, does the creation of this longitudinal component actually violated Maxwell's Electrodynamic Theory? Is this phenomenon allowed in the Quantum theory?

Thanks for the help on insight on this matter.
 

Answers and Replies

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Born2bwire
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No, not necessarily. Longitudinal modes and solutions can arise, just in very specific cases. One that I am familiar with is the Zenneck wave. If you place a dipole antenna on top of a conducting ground, you will excite a surface wave that travels outward, confined to the surface between the ground and air. This surface wave is evanescent off of the surface but it is longitudinal if I recall correctly. If you have a cavity or confinement of the wave in one or more dimensions you will get longitudinal components. Although, this is due to the interference between the original wave and its reflections. You can sometimes remove the longitudinal quality of the wave by decomposing it into the superposition of multiple traveling waves. The physical meaning of these traveling waves is that they are the reflections from the boundaries.

So longitudinal waves are not necessary a violation, but they are most certainly the exception and not the rule. The question here would be if they predict the longitudinal behavior based upon classical or quantum electrodynamics.
 
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While I can understand the longitudinal component from the point of view of reflections in cavity (example of the Zenneck wave), however, the main crux of this idea is that it still needs a medium for the reflections to occur.

In this paper which i cited, they created it in vacuum, or termed free space. What could be the cavity for reflections in this case?

If i were to visualise this beam propagating through space, what could it look like? Because the field now no longer oscillates between the E and H (or x and y) plane, can I visualise it as something like a sound wave propagating through air?
 

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