<div dir="ltr"><div><div><div><div>Thursday<br></div>Dear Kirk,<br><br></div>I think I would say it differently and I would appreciate your comment: "Wrong!, Okay, Partially."<br><br></div>The photon number doesn't increase at each reflection, so the only effect is that the photon is bounced back and forth until it hits the hole and gets out. So, the effect is simply reducing the emittance from 4 pi (the whole sphere) to the area of the hole. Even simple to calculate the amplification. So, my view is not a re-using of photons, but a change in desired emittance.<br>
<br></div>Andy<br></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Wed, Dec 19, 2012 at 8:36 PM, Kirk T McDonald <span dir="ltr"><<a href="mailto:kirkmcd@princeton.edu" target="_blank">kirkmcd@princeton.edu</a>></span> wrote:<br>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">Folks,</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">I have become fortuitously aware of an old trick in the lamp
industry that is now sometimes called “light recycling” – with the goal of
enhancing the optical brightness of light sources.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">Remember, brightness = power / area in transverse phase
space</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">(although the opticians don’t generally say it this way,
perhaps using the buzzword “etendue” instead of “area in transverse phase
space”)<br></font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">In our project, we try to increase the brightness by
“cooling”/shrinking the area in transverse phase space.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">The opticians’ trick is to “recycle” the light so that one
photon gets counted many times in the same area in phase space, effectively
increasing the power, while leave the emittance the same.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">The historical way of doing this (dating back at least to
1936) involves a cylindrical cavity lined with a phosphor (i.e., a fluorescent
lamp) with a small slit in the phosphor to let light out.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">A photon has only a small probability P to escape out the slit
directly after being emitted by the phosphor.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">Generally, the photon hits another region of the phosphor, is
absorbed, and then re-emitted. [The cavity can be lined with a reflector
to assist in this process.]</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">On average, the photon bounces around N = 1 / P times before
it escapes through the slit.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">Hence, the steady-state emission of photons by the phosphor
surface is N times greater than if the photons flew away on their first emission
– as holds for an ordinary fluorescent lamp.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">The net effect is that the light coming out of the slit is N
times brighter than the light from an ordinary fluorescent bulb of the same
output power.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">The brightness has been enhanced N-fold (with no emittance
reduction) to the extent that the absorption and re-emission involves no
losses.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">[I think the lamps in Xerox machines and scanners are of this
type.]</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">I’ve written up a pedagogic note on this:</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><a title="http://puhep1.princeton.edu/~mcdonald/examples/lamp.pdf" href="http://puhep1.princeton.edu/~mcdonald/examples/lamp.pdf" target="_blank">http://puhep1.princeton.edu/~mcdonald/examples/lamp.pdf</a></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"><font>--------------------------------------</font></font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"><font>This trick seems different from what we do to enhance
the brightness of particle beams.</font></font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"><font></font></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"><font>However, a comment by Fred Mills, dated 9/98, near the
bottom of my web page</font></font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"><a title="http://puhep1.princeton.edu/~mcdonald/mumu/physics/" href="http://puhep1.princeton.edu/~mcdonald/mumu/physics/" target="_blank">http://puhep1.princeton.edu/~mcdonald/mumu/physics/</a></font></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"><font>has me wondering if part of the effect of the “Piccione
lip” seen on p. 4 of</font></font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><a title="http://puhep1.princeton.edu/~mcdonald/mumu/physics/lichtenberg_mura-110.pdf" href="http://puhep1.princeton.edu/~mcdonald/mumu/physics/lichtenberg_mura-110.pdf" target="_blank">http://puhep1.princeton.edu/~mcdonald/mumu/physics/lichtenberg_mura-110.pdf</a><font face="Arial"> </font></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">was to use multiple scattering in the “lip” to kick some
particles into a desired area of phase space.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">That is, perhaps we can say that ionization cooling also
includes a small effect equivalent to the opticians’ trick of “light
recycling”.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">What do you think?</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">--Kirk</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">PS The opticians are after big game = use of such tricks
to make better solar energy concentrators for photovoltaic energy generation (or
even just heating water).</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">In the past, such efforts have not involved brightness
enhancement, but only clever rearrangement of light in phase space (as in
Winston cones).</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">The next generation of brightness enhancement schemes uses
materials with differing absorption and emission spectra to play additional
“tricks”. New engineered optical materials, called photonic band gap
materials, could play a key role here.</font></div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial"></font> </div></div>
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<div style="font-size:small;font-style:normal;text-decoration:none;font-family:'Calibri';display:inline;font-weight:normal"><font face="Arial">If these solar brightness-enhancement schemes pay off, they
will be able to fund all of high energy
physics....</font></div></div></div></div></div>
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