DOW-UAP-D122, AAWSAP DIRD, Invisibility Cloaking Theory and Experiments, March 2010

This document is a Defense Intelligence Reference Document (DIRD), a technical reference format used by the Defense Intelligence Agency (DIA) to capture baseline knowledge on a specific topic for later analytic use. DIRDs are best understood as reference and synthesis products rather than as original research. It is one of 38 DIRDs produced under the Advanced Aerospace Weapon System Applications Program (AAWSAP) between 2009 and 2011. Because AAWSAP’s scope permitted a broad range of supporting topics, not every DIRD in the series directly concerns aerospace systems or future threat assessment. The following summary reflects the DIRD’s scope and framing at the time of writing and should not be read as implying current validation of the concepts discussed. This DIRD surveys the theory and early experiments behind invisibility cloaking, describing several ways an object might be hidden from visual or sensor detection, including camouflage, transparency effects, and optical cloaking that bends light around an object. It focuses mainly on metamaterials, negative refraction, and transformation optics, and reviews experiments that had already demonstrated limited cloaking at microwave frequencies. The report argues that “imperfect” cloaking is physically achievable in some parts of the electromagnetic spectrum, especially for microwaves, but that “perfect” cloaking is not practical because it would require material properties that conflict with the underlying physics. Its overall conclusion is that cloaking is a scientific field with plausible narrow applications, but that useful visible-light cloaking depends more on future theoretical breakthroughs than on conventional advances in materials science.

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Defense
Intelligence
Reference
Document
Acquisition Threat Support
2 March 2010
ICOD: 1 December 2009
DIA-08-1003-001
Invisibility Cloaking: Theory
and Experiments
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Invisibility Cloaking: Theory and Experiments
Prepared by:
Acquisition Support Division (DW0-3)
Defense Warning Office
Directorate for Analysis
Defense Intelligence Agency
Author:
AAP Person 68
Administrative Note
COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized.
This product is one in a series of advanced technology reports produced in FY 2009
under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace
Weapon System Applications (AAWSA Pro ram. Comments or uestions pertaining to
this document should be addressed to AAP Person 1 AAWSA Program
Manager, Defense Intelligence Agency, ATTN: CLAR/DWO-3, Bldg 6000, Washington,
DC 20340-5100.
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Contents
Introduction ............................................................................................................v
Camouflage ............................................................................................................ 1
Transparency ......................................................................................................... 3
Cloaking ................................................................................................................. 5
Metamaterials ........................................................................................................ 9
Optical Metamaterials .......................................................................................... 11
Fundamental Problem .......................................................................................... 15
Curved Space ....................................................................................................... 17
Broadband Invisibility .......................................................................................... 19
Implementation ................................................................................................... 20
Optical Cloaking ................................................................................................... 22
Summary.............................................................................................................. 23
References ........................................................................................................... 23
Figures
Figure 1. B2 Stealth Bomber .................................................................................. 1
Figure 2. Optical Camouflage ................................................................................. 2
Figure 3. The Secret Optical Camouflage................................................................ 2
Figure 4. H. G. Wells's The Invisible Man: Invisibility by Transparency .................. 3
Figure 5. Complementary Media Invisibility Cloak .................................................. 4
Figure 6. Cloaking Shell.......................................................................................... 5
Figure 7. The Invisible Woman ............................................................................... 6
Figure 8. Fermat's Principle ................................................................................... 7
Figure 9. An Optical Material Deforms the Coordinates of Space ............................ 8
Figure 10. Light Waves at Cloaking Device............................................................. 9
Figure 11. Cloaking Device for Microwaves .......................................................... 10
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Figure 12. Lycurgus Cup (British Museum; AD Fourth Century)........................... 11
Figure 13. Idea for a Cloaking Device for Visible Light ......................................... 12
Figure 14. Advances in Metamaterials.................................................................. 13
Figure 15. Demonstration of Negative Refraction With "Bulk" Optical
Metamaterials Made of Nano-Fishnets................................................. 14
Figure 16. Demonstration of Negative Refraction With "Bulk" Optical
Metamaterials Made of Nanowires....................................................... 15
Figure 17. Fundamental Problem of Transformation-Based Cloaking Devices ...... 16
Figure 18. Wave Packets are Made by Combining Waves With Different
Frequencies......................................................................................... 17
Figure 19. Stereographic Projection ..................................................................... 18
Figure 20. Non-Euclidean Cloaking Device in Two Dimensions ............................. 19
Figure 21. Three-Dimensional Cloaking................................................................ 20
Figure 22. Coordinate Transformation Implemented by a Ground-Plate Cloak..... 21
Figure 23. Implementation of the Ground-Plate Cloak ......................................... 21
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Invisibility Cloaking: Theory and Experiments
Introduction
The idea of invisibility has fascinated people for millennia, inspiring many
myths, novels, and films. Invisibility cloaking has recently become a subject of
science and technology. This paper describes the important current theoretical
and experimental developments and tries to project into the future.
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Camouflage
Invisibility may be achieved through three principal methods: camouflage,
transparency, and cloaking. Many animals and some plants use camouflage to disguise
themselves from predators-for example, by assuming the shapes and colors of objects
in their surroundings. The military has long used forms of camouflage; a recent military
application of camouflage is stealth technology.
Stealth planes have aerodynamically
unusual, edgy shapes and are coated
with a special material. Both features
serve the same purpose: to make the
plane "invisible" to radar. How does it
work? In radar, electromagnetic
microwaves are emitted by a source, and
their reflection by an object-an
airplane, for example-is detected. From
the direction and the time delay of the
reflected waves, the direction and
distance of the object are inferred. If the
object does not reflect the
electromagnetic microwaves back to the
source, it will not appear on the radar.
This is precisely what stealth technology
achieves. Owing to the edgy shape of Figure 1. B2 Stealth Bomber
the stealth plane, most of the incident
electromagnetic waves are reflected in different directions; the coating of the plane
absorbs the rest. In this way, the stealth plane has become completely black in the
spectral range of radar. As for radar waves, the sky is black, not blue, and the plane
has assumed the color of the background: the stealth plane is camouflaged.
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Another recent example of camouflage is
optical camouflage, developed by the
University of Tokyo's Tachi Laboratory.
Figure 2 shows an example of optical
camouflage. A camera captures the
background scene behind the person.
The image is processed and projected
onto the person via a semitransparent
mirror. The person wears an "invisibility
cloak" made of a retroreflective material
that reflects light back in the direction
whence it came, like cats-eye-reflectors
do. As the cloak carries the projected
image of the background, the person
seems to disappear, but surely the
equipment standing around the person is
clearly visible. In addition, optical
camouflage works only in one direction;
seen from the side, the person is visible.
Nevertheless, optica l camouflage may
become a useful tool in some situations
where obstacles are in the way of sight- Figure 2. Optical Camouflage (Tachi Laboratory,
for example in surgery, where the Tokyo}
surgeon's hands and instruments may
obstruct the view. Figure 3 shows how optical camouflage works.
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Figure 3. The Secret Optical Camouflage (Tachi Laboratory, Tokyo)
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Transparency
H. G. Wells's novel The Invisible Man
represents another strategy for
becoming invisible: transparency.
In Wells's novel, the invisible man, a
disgruntled college professor, invents a
substance that somehow changes the
refractive index1 of his body. Most
transparent substances, like glass, air,
or water, modify the speed of light,
because the atoms or molecules of these
substances absorb and re-emit light,
which takes time. The delay caused by
the atoms and molecules results in a
reduced speed of light and hence in a
refractive index larger than 1. It is,
however, also possible to achieve a
refractive index smaller than 1, although
only in narrow bands of the spectrum. In
these cases, the atoms or molecules
advance the wave fronts of light because Figure 4. H. G. Wells's The Invisible
Man: Invisibility by Transparency
they are excited such that their electron
clouds oscillate ahead of the light. If the refractive index is uniform in a material, light
is reflected and refracted at the boundary but otherwise is traveling straight through.
On the other hand, if the refractive index varies, light is scattered at the index
inhomogeneities and gets lost. Most white substances appear white because of such
scattering . Milk, for example, consists of minuscule oily droplets-fat-in water. The
refractive index of the droplets differs from water, and hence light is scattered at them;
it does not penetrate the substance, and the diffused light appears as white. Now,
human bodies are visible, because they absorb light. Most of the absorption is due to
the scattering of light in biological tissue, in the cells of which the bodies are made. If
the refractive indices of a person's cells could somehow be changed to the refractive
index of air, the person would become transparent and disappear from view-like the
Invisible Man.
Some animals (for example, some jellyfish) are transparent, but the cells of higher
order animals are usually much too complex and diverse for transparency to become a
serious option for disguise. Exceptions are the transparent parts of the body, most
notably eye lenses, which consist of uniform cells kept in a state between life and
death. If this balance is upset, the lenses become opaque as a cataract develops.
Transparency is the idea behind some proposed forms of invisibility by technology. For
example, in plasmonic covering, 1 a particle should be surrounded by layers made of
metals and transparent substances, such as glass. The layers are designed such that
they cancel the scattering of light at the particle, hence making both the particle and
the layers transparent-that is, invisible. Another proposal2 exploits the resonance of
the particle with a negative-refractive material that cancels out scattering. In a material
with negative refraction, the wave fronts of light appear to move in the opposite
1 The refractive index is the ratio between the speed of light in vacuum and the speed of light in a material.
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direction from the propagation. The clearest and most advanced form of this concept is
the complementary media invisibility cloak.3 Here, an optical antiobject is placed beside
the object one wishes to make disappear. The antiobject should be made of a
negatively refractive material that exactly compensates the optical appearance of the
object. An image is contained in the deformations of light-wave fronts caused by the
imaged object. If these deformations are reversed, the image disappears, and the
object becomes transparent- that is, invisible. The optical antiobject must be tailored to
the object and placed precisely at the correct distance-that is, the distance where it is
made to cancel the image of the object. The more complex the object is, the more
complex the antiobject must be for reversing all the scatterings of light. Such cloaking
at the distance cannot be instantaneous, as the light scattered by both object and
antiobject must settle to a stationary state where it becomes synchronized. A stationary
light field has only one color. So, in practice, these forms of transparency will work only
for small objects and for small parts of the spectrum and not for large objects in many
colors.
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Figure 5. Complementary Media Invisibility Cloak: (a) The slab of empty space x with O < x < Lis optically
canceled by a slab of negative-index material in -L < x < 0. (b) The same cancellation effect works with an object
in O < x < L if the negative-index slab contains an antiobject. (c) A spherical shell b < r < c is optically canceled by
a negative-index shell a < r < b. If the corer< a is optically equivalent to a sphere of radius c, then this device ls
invisible. (d) The same as (c), but with an object in the canceled shell b < r < c. The object is cloaked: both it and
the cloaking sphere are invisible.
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Cloaking
Cloaking4• 5 is a universal strategy for invisibility that works for objects of arbitrary
compositions and shapes within a given size. In cloaking, the hidden object is enclosed
by the cloaking device, a transparent shell that guides light around the object as if the
light would propagate through empty space. In this way, both the interior of the
cloaking device is hidden and the act of hiding is concealed.
Figure 6. Cloaking Shell6
How does one find the right design for such a cloaking device? As the Invisible Man
symbolizes transparency as a strategy for invisibility, inspiration for cloaking may come
from the Invisible Woman, a cartoon figure from the Fantastic Four. The Invisible
Woman is said to create a mysterious force field around her that bends space. Light
follows the curved space such that it smoothly flows around the Invisible Woman, like
water in a stream flowing around an obstacle. The key idea here is the concept of
curved space used for invisibility. The idea that turns the Invisible Woman with her
fabled force field from a fictitious character into something close to reality is the insight
that no force field is needed, that light-refracting materials like glass or water appear as
curved spaces by themselves