Analytical results regarding electrostatic resonances of surface phonon/plasmon polaritons: separation of variables with a twist.

The boundary integral equation (BIE) method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of the Laplace equation can be used to calculate the full set of eigenvalues and eigenfunctions of the electrostatic operator for shapes and shells described by separable coordinate systems. These results not only unify and generalize many existing studies, but also offer us the opportunity to expand the study of phenomena such as cloaking by anomalous localized resonance. Hence, we calculate the eigenvalues and eigenfunctions of elliptic and circular cylinders. We illustrate the benefits of using the BIE method to interpret recent experiments involving localized surface phonon polariton resonances and the size scaling of plasmon resonances in graphene nanodiscs. Finally, symmetry-based operator analysis can be extended from the electrostatic to the full-wave regime. Thus, bound states of light in the continuum can be studied for shapes beyond spherical configurations.

Rapid fabrication and chemical patterning of polymer microstructures and their applications as a platform for cell cultures.

Much of the current knowledge regarding biological processes has been obtained through in-vitro studies in bulk aqueous solutions or in conventional Petri-dishes, with neither methodology accurately duplicating the actual in-vivo biological processes. Recently, a number of innovative approaches have attempted to address these shortcomings by providing substrates with controlled features. In particular, tunable surface chemistries and topographical micro and nanostructures have been used as model systems to study the complex biological processes. We herein report a versatile and rapid fabrication method to produce a variety of microstructured polymer substrates with precise control and tailoring of their surface chemistries. A poly(dimethylsiloxane) (PDMS) substrate, produced by replication over a master mold with specific microstructures, is modified by a fluoro siloxane derivative to enhance its anti-adhesion characteristics and used as a secondary replication mold. A curable material, deposited by spin coating on various substrates, is stamped with the secondary mold and crosslinked. The removal of the secondary mold produces a microstructured surface with the same topographical features as the initial master mold. The facile chemical patterning of the microstructured substrates is demonstrated through the use of microcontact printing methods and these materials are tested as a platform to guide cell attachment, growth and proliferation. The master mold and flexible fluorinated PDMS stamps can be used in a repeated manner without any degradation of the anti-adhesion characteristics opening the way to the development of high-throughput fabrication methods that can yield reliable and inexpensive microstructured and chemically patterned substrates.