example. When you look inside the fish tank, you notice that
the fish inside the water do not appear at their actual positions;
they are at virtual positions. ;is is because the light that carries their image has been refracted at the water’s surface and
the walls of the tank. ;erefore, their image appears to come
from a di;erent direction.
Using this model, one may also say that the water has created a virtual space with geometry di;erent from ordinary space.
;is virtual geometry is quite peculiar: the virtual positions of
the fish change, depending on your viewpoint (whether you
look at them through the water’s surface or from the side),
something that is impossible in ordinary flat space. ;e fact
that the water of the fish tank distorts space tells you that the
fish are surrounded by an optical material—in this case, water.
Now imagine the fish tank is filled with a material not
normally found in nature that appears to move every point in
the tank to a new virtual position independent of the viewing
angle. ;is is something very special. ;e fish still appear at
positions di;erent from where they actually are, but these positions are always the same. You would not be able to see a difference between the fish tank and empty space, except that the
sizes and shapes of the fish might change. ;is is because the
tank may expand or condense space, making the fish appear
larger or smaller. Now imagine the tank shrinks everything
inside a certain region to the size of a single point. A single
point is invisibly small: ;e fish inside this region disappear.
;e fish tank is now an invisibility device.
Metamaterials
;e materials for manipulating the geometry of space in such
drastic ways have to be rather advanced. ;ese metamaterials consist of artificial structures that act like atoms. ;e
shape and size of these structures determine their optical and
electromagnetic properties. Unlike natural atoms, they can be
manipulated to create optical materials like cloaking devices.
Metamaterials are fantastic, but not infinitely malleable. ;ey
are still subject to the laws of physics.
Imagine what happens to a light ray that is skimming along
the inner surface of a cloaking device. In virtual space, the
entire inner region of the device has become a single point.
How much time does it take to cross a single point? No time
at all. Now, the light propagation in physical and virtual space
must be synchronized, because the device performs a coordinate transformation from one space to the other. Light should
go around the inner surface of the cloaking device instantaneously. In other words, the velocity of light must be infinite.
Having a nearly infinite speed of light in a material is not
prohibited by Einstein’s relativity, provided that speed is the
phase velocity, which it is in practical demonstrations of cloak-
ing devices. However, no information can be transmitted and
in practice the device is reduced to operating in a stationary
regime for only one frequency. If the virtual space is curved
these limitations do not apply.
[ Fermat’s principle in a fish bowl ]
Phil Saunders, spacechannel.org
Ordinary materials such as water (left) may distort the
appearance of space, whereas transformation optics (right)
can shrink a region of physical space to a single point,
making its contents invisible.
[ Cloaking device deforms the grid of space ]
Courtesy of Ulf Leonhardt
The cloaking device deforms the grid of space (white lines)
around its interior. Light rays (yellow lines) are bent and leave
as if they have travelled through empty space. Anything inside
the device is hidden, but without affecting the light that carries
the image of the background scenery, which creates the
ultimate optical illusion: invisibility.
