Michael Berry is a Royal Society research
professor in the physics department at the University of Bristol
in the U.K., where he has been for many years. He has received
numerous awards, including the Dirac medals and prizes awarded
by both the Institute of Physics (1990) and the Abdus Salam
International Centre for Theoretical Physics, Trieste (1996), a
knighthood (1996) and the Wolf Prize in Physics (1998).
Michael is a dear friend and a staunch advocate of the principle
underlying Sightings—the power of visually
representing ideas in science. Here, he and I have a short
conversation about one of the first images I saw of his
F. F. You describe the material you used to
photograph this image as "a black-light sandwich." Tell us more.
M.B. The "bread" consists of two
polarizing sheets with their optic axes at right angles, and the
"filling" is a sheet of transparent viewgraph foil.
Different parts of the image correspond to light traveling through
the sandwich in different directions. Without the filling, the
polarizer closer to the camera would cut out the light transmitted
by the other one, so the sandwich would appear black. But the
filling acts like a transparent crystal and transforms the state of
polarization so that some light gets transmitted. Inside the
crystal, two light waves travel at different speeds, which depend on
direction; therefore the waves get out of phase and can interfere.
The colored rings are interference fringes, centered on a bull's-eye
indicating a particular direction where the two speeds are the same.
The black "brush" through the bull's-eye arises from a
geometric peculiarity of the polarizations of the two waves.
F. F. We see a number of colors. Is there any
particular information we get from those colors?
M.B. The colors always appear in the same order, as
a result of the interference of light with different wavelengths. In
the slightly different situation of a crystal with optical activity
(twisted internal structure), the center of the bull's-eye is not
black, and its color gives information about the amount of twist.
F. F. Can you tell us how you made/captured this
M.B. In optics these colored bull's-eyes are well
known as "conoscopic figures." Usually they are produced
by filling the sandwich with a thin slice of crystal (such as
aragonite). It was Rajendra Bhandari, in his laboratory in India,
who showed me how easily the bull's-eyes could be produced with
transparency foil. We worked on the phenomenon with Susanne Klein.
Because the bull's-eye is not localized anywhere, it always appears
along with whatever the eye or camera is focused on (in this
picture, it is the trees).
F. F. Did you find that visually expressing this
particular phenomenon clarified some of the physics involved?
M.B. Certainly. The sandwich beautifully
illustrates interference and polarization, geometric phases and an
aspect of crystal optics that was historically important in the
understanding of light. Moreover, it is a model for the preparation,
propagation and measurement of a quantum state (of spinning photons
in this case). It illustrates mathematics too: matrix algebra,
needed to describe the polarization states (the sandwich can be
interpreted as a nontrivial square root of zero), and singularities
(the bull's-eye and the black brush). I like to discover "the
arcane in the mundane," and this is one of the best examples I know.
F. F. Did new questions crop up when you actually
studied this visual representation?
M.B. Yes. Seeing the bull’s-eye led to a
general reformulation of crystal optics, developed with Mark Dennis,
making comprehensible the complications occurring when the material
is absorbing and twisted as well as anisotropic. And if the
polarizer farther from the eye is removed, the "open
sandwich" becomes a device for revealing and exploring the
polarization of the blue sky through the faint bull’s-eyes
that are still visible, leading to clarification of the pattern of
polarization singularities in the sky (still incompletely understood
after its discovery nearly 200 years ago).
F. F. When you work with a formula, do you ever
actually imagine a pictorial representation of that formula, or is
it a different kind of thinking?
M.B. When I was starting out as a physicist, I
thought sequentially and algebraically. But, under the influence of
a strong geometric culture in the Bristol physics department, I soon
learned to visualize much of the mathematics I needed to use, to the
benefit of my physical understanding. This process accelerated in
the late 1980s, with easy computer visualizations made possible by
Mathematica, etc. Peter Atkins has written: "Determining where
mathematics ends and science begins is as difficult, and as
pointless, as mapping the edge of a morning mist." I spend my
life wandering in and out of that mist; in such obscure terrain,
visualization is a very helpful navigational device.