few inverse problems in classical statistical mechanics and photonics
Mikael Rechtsman, CIMS
developments in colloidal science have allowed experimentalists to
tailor the isotropic interactions between nanometer and micron-sized
objects, yielding a variety of exotic many-body phases of (soft)
matter. A ``holy grail'' of the field has been the self-assembly
dielectric structures with full photonic bandgaps, which have enormous
technological application (waveguiding, optical computing, etc.), a
typical example being the diamond lattice of spheres.
first part of the talk, I will discuss the problem of deriving
isotropic inter-particle pair potentials that yield targeted,
technologically relevant and exotic crystal structures (including
diamond); I will also show how isotropic potentials may be derived to
give rise to negative thermal expansion and negative Poisson's ratio
materials. These exceptional materials properties have not
been found in isotropic systems.
In the second
part, I will go
deeper into the problem of finding and optimizing dielectric patterns
that have large photonic bandgaps. Quasicrystals are aperioidic
structures with long-ranged orientational order; I will explain why
they have tremendous potential to produce bandgaps and how they have
been optimized to yield the largest known bandgaps in certain cases.