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On Sat, 2 Apr 2005, FrediFizzx wrote:
What is really interesting to me is how a single photon can have
differing orbital angular momentum.
Consider this:
Take a Gaussian TEM00 laser beam (ie Hermite-Gauss mode HG00). Orbital
angular momentum about the beam axis is zero. In the Laguerre-Gauss basis,
it's also LG00. Now, stetch the beam spot along the x-axis (perpendicular
to the beam axis) to make a beam with an elliptical cross-section. It's no
longer a pure single-mode in either the HG or LG basis. In the LG basis,
it's a sum like
LG00 + LG0,+2 + LG0,-2 + LG0,+4 + LG0,-4 + ...
In the same way that plane polarised light is a superposition of left- and
right-circularly polarised light, each with opposite spin, detectable by
sending the light through a circular-polarisation filter/beamsplitter, the
elliptical beam is also a sum of OAM components of opposite helicity. Send
the beam through an OAM filter, and, hey presto!, the photons indeed have
such values of their OAM about the beam axis.
Actually, I think a lot of people who write about photon OAM only think
about the component of the OAM about the beam axis, and forget the other 2
vector components. The first measurements of photon momentum (Lebedev
and Nichols and Hull) were actually measurements of these other two
components of photon OAM - a torsion balance is a torque detector - so
they're not unimportant in practice. And you can pretty much make these
components of photon OAM as large as you want, or as small as you want, by
suitable choice of origin.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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