MOTION MOUNTAIN

138 3 what is light?
B
B
Beam
in
A
Beam
in
A
Polarization
Polarization
Vol. I, page 200
Challenge 147 s
Ref. 99
Challenge 148 s
To simplify the exploration, the mirrors and beam splitters used above conserve handedness :
F I G U R E 88 Two different three-dimensional interferometers, with all edges of equal lengths, the
mirrors/beam splitters used, and their outputs A and B. Where does the light exit?
tionedbefore,areduetothegeometricphase.Following MichaelBerry,thephenomenon
isnowcalledthegeometricphase.Olderexpressions,suchasadiabaticphase,topological
phase,quantal phase,Berry’sphaseand various other terms are not used any more.
After this excursion, here is a challenge of the real world. What is the smallest number
of mirrors needed in a device to change the polarization of a light beam that exits the
device in the same direction as it came in?
∗∗
An interferometer is a device that uses the interference of light to study the properties
of a light beam. A common interferometer, the Mach-Zehnderinterferometer,isshown
in Figure 86. If all sides have equal length, light interferes constructively in the output
direction A and destructively in the other output direction B.Thus light exits in direction
A.
Only in the 1990s people started asking what would happen in three-dimensional interferometers,such
as theoneshownin Figure 88. To clarify thesituation, a fewpoints
arenecessary.First,we needtospecifythepolarization ofthelightused, andrecall that
onlylightofthesamepolarizationcaninterfere.Secondly,tosimplifythediscussion,we
assumethatthemirrorsareofaspecialtype(namelycornercubesbasedontotalrefraction)sothat,incontrasttousualmirrors,theyconservepolarization.Thirdly,weassume
thatall edgeshave equal length. Can you deduce which exits are bright in the two cases
of Figure 88?
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net