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The analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require O(N2) operations, N being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in O(N) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.

A new cascade impactor has been designed specifically for pharmaceutical inhaler testing. This impactor, called the Next Generation Pharmaceutical Impactor (NGI), has seven stages and is intended to operate at any inlet flow rate between 30 and 100 L/min. It spans a cut size (D50) range from 0.54-microm to 11.7-microm aerodynamic diameter at 30 L/min and 0.24 microm to 6.12 microm at 100 L/min. The aerodynamics of the impactor follow established scientific principles, giving confident particle size fractionation behavior over the design flow range. The NGI has several features to enhance its utility for inhaler testing. One such feature is that particles are deposited on collection cups that are held in a tray. This tray is removed from the impactor as a single unit, facilitating quick sample turn-around times if multiple trays are used. For accomplishing drug recovery, the user can add up to approximately 40 mL of an appropriate solvent directly to the cups. Another unique feature is a micro-orifice collector (MOC) that captures in a collection cup extremely small particles normally collected on the final filter in other impactors. The particles captured in the MOC cup can be analyzed in the same manner as the particles collected in the other impactor stage cups. The user-friendly features and the aerodynamic design principles together provide an impactor well suited to the needs of the inhaler testing community.