YSM Issue 95.2

FOCUS
Wave Physics
“The sky looks
blue because blue
light is scattered [more]
strongly than red light,
and the reason why
we look opaque is
that there’s strong
scattering by the cells
in biological tissues.
That’s why we cannot
see through most
biological tissues.” We
encounter many things
in everyday life that we
cannot see through or send
information through—all
because of this strong
scattering of light.
H o w e v e r ,
scattering can
cause challenges in
applications such
as medicine, where
the opacity—or lack
of transparency—of
human tissues can limit
their visualization and
manipulation.
In recent years, researchers
have explored different
ways to transmit energy
through diffusive systems.
In medical applications,
for example, it is critical
to focus on delivering
and depositing energy
inside systems such as
human tissue instead of
simply sending energy
through the system.
Medical applications
include procedures like
photothermal therapy,
which uses heat generated by
near-infrared light to treat cancer, or deep
tissue imaging, which allows researchers
to image whole tissues without dividing
them into thinner sections.
Can’t We Just Send Light Into the System?
One of the greatest challenges in depthtargeted
delivery of light—in other
words, sending light into a specific spot
in the system—is that energy scatters in
multiple directions and diffuses upon
entering the system.
Previous research relied on controlling
the wavefront of the input energy wave to
limit diffusion, which allowed researchers to
focus light on a specific spot in a scattering
medium. A wavefront is an imaginary
surface where all the points are at the same
phase in their wave cycle (think of the ripples
you see when you drop something in water).
Shaping the wavefront involves controlling
the distribution of wave intensities and
phases in the input beam.
However, this method was less practical
for real-world applications because medical
targets such as tumors or neurons often
sprawl over a region rather than remaining in
a single focal spot. The upper limit on energy
deposition in a region at a certain depth in a
diffusive system, which is important to know
for practical applications of this technique,
was also unclear using this method.
Another difficulty lies in observing the
delivery of light into the system. “Scientifically,
it’s really easy to study sending something
into a system and measure something coming
out of a system—you just put a camera on one
end and input on the other,” said Nicholas
Bender, formerly a Yale doctoral student in
Cao’s lab and now a postdoctoral researcher
at Cornell University. “What’s hard to do is
to understand what this light is doing inside
a system because by observing the system,
you may interfere with it.” Simply put, trying
to see what was going on in the system could
mean inadvertently altering whatever process
was underway within it.
Lasers and Math
To confront this issue of targeted energy
delivery into diffusive systems, researchers at
Yale University performed a comprehensive
series of experiments, numerical simulations,
and theory. “I like to call it ‘creating and
controlling disorder, randomness, and chaos
with lasers,’” Bender said.
The team began by defining a matrix that
mathematically described the relationship
between the laser beam input into a diffusive
system and the way the light was distributed
across a region of specific depth in the system.
By running repeated simulations of virtual
disordered systems, the research team plotted
what different input beams would look like at
various points within the system.
The maximum energy that could be
delivered to the target region corresponded
to the largest eigenvalue of the deposition
matrix. Eigenvalues are factors
representing the scales of eigenvectors,
which are characteristic vectors in linear
algebra. The input wavefront could be
found from the eigenvector associated
with that largest eigenvalue.
Causing Chaos (On Purpose)
One unique feature of this study was the
experimental setup. The researchers devised
an experimental platform consisting of
a two-dimensional disordered structure
(picture a rectangular slab with holes
that randomly let light through) where
the optical field could be analyzed by the
researcher looking down at the platform
from above (from the third dimension).
“ This is new,” Cao said. “Before, people
usually made a three-dimensional sample.
With three-dimensional scattering, when
you send in the light, you cannot see it, so
you don’t know [which wavefront is best]
to deliver light. But by using this system,
we’re able to peek in, to take a look from the
third dimension, and say, ‘Oh, we see! This
is where we can deposit and how much.’”
For example, if you rolled a marble into a
non-transparent box, you wouldn’t be able
to see its path or where it stopped. If you
rolled that marble onto a sheet of paper, you
would be able to look down onto the paper
and track the marble’s progress.
According to Cao, creating this
experimental setup was not an easy process.
“It’s absurd how much effort we had to put
into making this disordered system just the
way we want it,” he said. “I mean, calibrating
and controlling disorder is ridiculous…it’s
crazy and great and horrible to do,” Bender
said. This breakthrough experimental
technique allowed the researchers to observe
scattering and light delivery with a degree of
control that had never before been possible.
Using a spatial light modulator, a device
that controls the intensity and phase
of light emitted, the researchers could
shape the wavefront of a laser beam in
one dimension. They found the twodimensional
field distribution inside the
system—the field of randomly scattered
light in the platform.
The two-dimensional sample consisted of
a silicon-on-insulator wafer with photoniccrystal
sidewalls to keep light inside the
system. The team added random optical
scattering to this system by etching a
20 Yale Scientific Magazine May 2022 www.yalescientific.org