Re: Phase cancellation --where does the energy go?


"Einar Andreas Rodland" <einarro@xxxxxxxxxx> wrote in message
news:fac3ub$gdo$1@xxxxxxxxxxxxxxxx
Much of the cited text came out horribly scrambled on my side, so I've
deleted it: hope I didn't miss any response within this.

Neil Bates wrote:
OK, I need to
correct some of what I've said earlier and elsewhere. The issue isn't
the symmetry of the combiner as such, it's the relative phase between
transmitted and reflected beams. Iff (sic) the difference is
consistently 90° on both sides, as you seem to imply here and as
"redbelly" noted in a similar sci.optics thread, then the added
amplitudes squared will indeed give the correct output power. But that
isn't (?) what we expect from a *thin* metal film diagonal inside a
glass cube. We expect a 180° change upon reflection. Depending on
relative input phase, that leads to results varying from both channels
getting constructively reinforced (simplistic amplitude addition would
provide 2x input power) to both destructive, to in between. And if there
was a zero degree change, there'd be an analogous problem. I always see
reference to either zero or 180° phase change, not others (and even if
90° was available, what if we used something that wasn't?) So, either we
find a way to get 90° phase change on reflection - how? What does that?
If not, then we can't just add up amplitudes naively, square them, and
get output powers.

It seems to me the problem rests entirely with the assumption that the
phase difference between the beam that passes through and the one that
is reflected is 180°. This is true for an ordinary mirror when comparing
the in-coming beam to the reflected beam; my previous deduction also
gives that result. However, I'm pretty sure this doesn't apply to the
two out-going beams from a beam-splitter, none of which are in phase
with the in-coming by the way: I see no reason why it should.

You are confusing the assymetrial conditon of say, a traditional
Mach-Zehnder BS that has a coating on one side of a glass plate, with the
problem that arises when in-phase beams strike a symmetrical
splitter/combiner of the sort described below.


As my deduction indicated, if you view the setup as an incoming beam
plus two beams produced by the metal of the beam-splitter (which must be
of the same phase and amplitude), then anything other than a 90° phase
difference between the two resulting out-going beams would violate
energy conservation.

Einar

You are right that "anything other than a 90° phase difference between the
two resulting out-going beams would violate energy conservation" if indeed
linearity must hold. (I use linearity in the broad sense, not just
"non-linear optics" tradition.) I don't think the phase difference could be
90° in the type of beam recombiner I noted (a thin film diagonal inside a
cube, or maybe also frustrated total internal reflection.) I think it would
have to be either zero or 180°, based on standard behavior of phase change
upon reflection. (Look at articles about that, do you ever see 90°
mentioned? No, it's either in phase reflection or 180° out of phase.) So
somehow Nature must find a way to conserve energy by means other than the
simple addition & squaring of separate amplitudes. It makes more sense to
look at that, than to continue defending the idea that the relative phases
really would be 90°.


.

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