60 Science & technology The EconomistJuly 27th 2019
2 Their study, carried out over the course of
nine days, proved that the stump under
scrutiny was still a participating member
of the local superorganism.
Sensors fitted to the two intact trees and
the stump showed that the stump’s flow of
sap and water ran inversely to that of the
trees. On sunny days, when the intact trees
were photosynthesising extensively and
drawing a great deal of water up their
trunks, there was almost no water move-
ment in the stump. At night, when the trees
were no longer transpiring in this way, wa-
ter flooded into the stump and sap flow
reached a maximum, indicating that it was
receiving a burst of resources.
Exactly why a stump’s neighbours dole
out their hard-won nutrients in this man-
ner remains a mystery, but Dr Bader and Dr
Leuzinger have ideas. Biologists know of
two ways co-operation between organisms
can evolve. One is kin selection, which re-
quires the collaborators to be related (as
neighbouring trees of the same species are
likely to be) and works if sacrifices by one
bring disproportionate reproductive bene-
fits to others. The effect of this is to propa-
gate a collaborator’s genes collaterally, in a
way that sociologists might refer to as nep-
otism, instead of directly from parent to
offspring. This may be why root connec-
tions happen in the first place, but cannot
explain their perpetuation, for trying to
help a trunkless stump reproduce would be
a fool’s errand.
The other route to co-operation is recip-
rocal altruism of the “you scratch my back
and I’ll scratch yours” variety. This requires
a stump’s neighbours, which are feeding it,
to benefit directly from the arrangement.
The suggestion Dr Bader and Dr Leuzinger
make is that they do—the stump’s role be-
ing to extend, at minimal cost, the root net-
works of its intact neighbours. From their
point of view, that makes keeping the
stump alive worthwhile.
If this is what is going on, however, it is
a good illustration of the dangers of an-
thropomorphic terminology. The arrange-
ment might look reciprocal to human eyes,
because it is keeping the stump alive. But
since the stump cannot reproduce it might
as well, in Darwinian terms, be dead any-
way, for it garners no evolutionary benefit
from its survival. Unless, of course, to go
back to the idea of kin selection, the neigh-
bours it is sustaining are its kin and it is
rendering nepotistic assistance to them
frombeyondthegrave. 7“L
ens” is theLatin word for lentil. And
it is indeed true that the shape of bi-
convex lenses—the familiar sort used as
magnifying glasses—resembles those le-
guminous seeds. But that resemblance
may soon be a thing of the past. For a group
of engineers at Columbia University, in
New York, led by Nanfang Yu, has worked
out how to make magnifying lenses that
are flat, and thinner than a hair.
A lens works by slowing down a light
wave as it traverses one of the lens’s faces
(the speed of light in glass is about two-
thirds of that in air). Slowing a wave
changes its direction, a process called re-
fraction. The angle through which it is re-
fracted depends on its angle of incidence to
the refracting surface—an angle that, on a
curved surface, varies continuously. When
the light leaves the lens it picks up speed
again, and thus goes through a second re-
fraction. The trick of the lensmaker’s art is
to grind the two surfaces into such shapes
that the sum of all this refraction brings the
light passing through the lens to a focus.
Dr Yu’s flat lens achieves a similar result
in a different way. Instead of holding the
change of speed constant while varying the
angle of incidence, the new lens holds the
angle of incidence constant while varying
the amount that the speed changes on dif-
ferent parts of the lens.
It can do this because its surface is cov-
ered with millions of tiny antennae. These
antennae are of different designs, each
with a cross section smaller than the aver-
age wavelength of the light it is interacting
with, and are arranged in concentric circles
(see picture). The antennae scatter the light
falling on them in such a way that, when
the individual changes are added up, the
combined effect is the same as if different
parts of the beam had passed through the
lens at different speeds.
Dr Yu is not the first person to make a
lens in this way, but previous efforts
worked only with single colours, and also
required the light to be polarised. Dr Yu’s
lens works with all colours and in natural
light, which is unpolarised.
In practice, few optical systems other
than eyeglasses rely on single lenses. Usu-
ally, different lenses with different proper-
ties are stacked on top of each other to re-
move aberrations and achieve full-colour
wide-angle images. Dr Yu’s lenses can be
stacked in this way, too. By sandwiching
three of them together, he has created a tri-plet that achieves almost all the control of
light waves that would be expected of big-
ger and heavier glass-lens systems.
Besides saving weight and volume, Dr
Yu’s flat lenses also promise to be cheaper
to mass produce than the conventional
sort. Grinding and polishing a glass lens is
complex and time-consuming. Flat lenses
are made using nanolithographic tech-
niques, which are also employed for mak-
ing computer chips. Given these advan-
tages, flat lenses could replace their bulkier
counterparts anywhere that cost or weight
is an issue—meaning pretty-well every-
where from microscopes and cameras, to
pairs of spectacles.
Flat lenses still need development be-
fore they can truly replace their glass coun-
terparts. In current designs, only around
half of the light falling on a flat lens triplet
makes it through to the other side. The rest
is reflected or absorbed by the material. In a
typical glass lens, by contrast, at least 90%
of the light passes through. However, the
researchers hope that, by tweaking the
shapes and positions of the antennae, they
will be able to improve on this.
In theory, there is no limit to the size of a
lens that could be made using Dr Yu’s tech-
niques. But there are practical challenges
in making ever-larger lenses that would
work well in full colour. In particular, the
bigger the lens, the more challenging it be-
comes to design the correct shape and dis-
tribution of antennae.
These technical obstacles will no doubt
be overcome—and probably quite quickly,
given the interest the project has attracted
from America’s armed forces. Meanwhile,
flat lenses for smaller applications are al-
ready on course to become the biggest in-
novation for manipulating rays of light
since someone, thousands of years ago,
first ground a piece of transparent crystal
into the shape of a leguminous seed.^7NEW YORK
The next generation of optical lenses
will be flat, and thinner than a hairOpticsThe seed of light
High magnificationScience correspondent’s job
The Economistis looking for a new Science and
Technology correspondent. Knowledge of the field,
an ability to write informatively, succinctly and
wittily, and an insatiable curiosity are more
important attributes than prior journalistic
experience. Please send a CV, a brief letter
introducing yourself and an article of 600 words
suitable for publication to [email protected].
The closing date for applications is August 23rd.