Disordered hyperuniform PBG structures

1
Disordered Photonic Band Gap Heterostructures
Marian Florescu1, Salvatore Torquato2,3, Paul J.
Steinhardt1,3 1Department of Physics
2Department of Chemistry 3Princeton Center
for Theoretical Science
Does the design work? The design was tested by
fabricating the predicted structure from
dielectric polymer and air. Below is shown the
first-ever disordered photonic heterostructure
found to have a complete photonic band
gap. Measured
transmission as a function of frequency and angle
for the disordered hyperuniform structure shown
in the middle column, upper right. Why are
disordered photonic materials useful? Disordered
photonic band gap heterostructures capable of
blocking light equally from all directions
facilitate a variety of applications, such as
waveguides for photonic communication, new types
of isotropic light sources and highly-efficient
thermophotovoltaic devices.
What are the inventions? (1) We have designed and
tested the first example of a disordered photonic
heterostructure that blocks light equally in all
directions. Left Protocol for
mapping point patterns into tessellations for
photonic structure designs. Right Disordered
hyperuniform photonic band gap heterostructure
fabricated from dielectric polymer. (2) The
disordered heterostructure arose from our
invention of a new general mathematical protocol
for finding structures with  optimal band gap
properties.  The protocol works for crystals,
quasicrystals, and disordered heterostructures.
How can the heterostructures be
distinguished? The different types of
heterostructures are distinguished by their
symmetries which can be determined from the
Fourier transforms of the structures.

Hyperuniform Crystal
Quasicrystal
Disordered What is a hyperuniform
disordered structure? Disordered means random
positions distributed uniformly in all directions
(along two or three-dimensions, depending on the
case). Hyperuniform means the density variations
are constrained on large distances so that the
Fourier transform has zero intensity near the
center (wavenumber k0). The example above is a
stealthy hyperuniform pattern with no intensity
within a finite radius of the center, one of the
invented structures predicted by our mathematical
design method to have a complete photonic
bandgap.
What is the purpose? To design and construct new
and improved types of photonic heterostructures,
the equivalent of semiconductors for light that
can be used to manipulate and control the flow of
light in photonic circuits. What is
photonics? Photonics refers to the use of light
in place of electrons in communication and
computer devices and in other applications in
which electronics is conventionally used.
Fiber-optics replaces wires and photonic
heterostructures replace semiconductors.
. What are heterostructures? Heterostr
uctures are man-made designer materials
composed of two or more dielectric materials in
an interpenetrating arrangement. The ability of
a photonic heterostructure to block and
manipulate light depends on the symmetry and
geometry of the arrangement. Two examples of
non-crystalline heterostructures composed of
polymer and air are shown below.
Left Optimal design of a disordered
hyperuniform photonic band gap heterostructure.
Right Design for a three-dimensional
quasicrystalline photonic heterostructure. What
is a photonic band gap? A photonic band gap is
the range of frequencies that are blocked
(reflected) by a photonic heterostructure no
matter the incoming direction or polarization
(analogous to the way a semiconductor blocks
electrons for a range of energies to form an
electronic band gap). By introducing
strategically placed defects in the structure,
blocked frequencies can be manipulated in various
selected ways to enable information communication
and computation.
References 1 Marian Florescu, Salvatore
Torquato, Paul J Steinhardt, Proceedings of the
National Academy of Sciences, 106, 20658
(2009). 2 Marian Florescu, Salvatore Torquato,
Paul J Steinhardt, Physical Review B 80, 155112
(2009). 3 Weining Man, Marian Florescu, Kazue
Matsuyama, Polin Yadak, Salvatore Torquato, Paul
J Steinhardt, and Paul Chaikin, submitted to
CLEO/QELS. Acknowledgements This work was
supported by the NSF Grant No. DMR-0606415.