Mike E. Potter

On the Selection of the Number of Bits to Control a Dynamic Digital MEMS Reflectarray

The benefit of low loss exhibited in utilizing MEMS variable capacitors in a reconfigurable reflectarray is undermined by the inconsistency of the fabricated devices. A digitally controlled reflectarray with MEMS capacitive switches is proposed. This paper aims to determine an appropriate number of phase shifting bits for such implementation. Using array theory, the influence of the number of bits on the beam pointing performance is evaluated. A common feed horn is used to illuminate the reflectarrays. In addition, broadside plane wave illumination is also considered for comparison with existing works in phased arrays. Though at certain scan angles the results are different from those for traditional phased arrays, in general the results are found to be similar. This information lays the groundwork for designing a cost-effective digital MEMS reflectarray cell.

1-D Multipoint Auxiliary Source Propagator for the Total-Field/Scattered-Field FDTD Formulation

A multipoint auxiliary time-domain 1-D propagator is proposed for initiation of plane wave sources in the total-field/ scattered-field formulation (TFSF) of finite-difference time-domain (FDTD). The propagator is developed by making the 1-D and 2-D/3-D dispersion equations identical, leading to a multipoint 1-D stencil. A perfect match can be achieved for a plane wave propagating at an angle forming an integer gridcell ratio, which can in theory represent almost any angle. Numerical examples in 2-D show that leakage errors into the scattered field domain are on the order of finite precision (-300 dB for double precision)

FDTD Discrete Planewave (FDTD-DPW) Formulation for a Perfectly Matched Source in TFSF Simulations

A technique is proposed for the generation of planewaves in the total-field scattered-field (TFSF) formulation of the FDTD method. The method is developed using the 1D properties of a planewave and optimized projection of the 3D finite difference operators to the 1D domain. The result is an efficient and accurate planewave source that can be propagated on six 1D grids concurrent with the main simulation, and that is perfectly matched to the main 2D/3D FDTD domain for any source function. Numerical simulations show that the technique is valid for any angle of propagation, and for any gridcell aspect ratio, with non-physical reflections in the scattered field domain on the order of machine precision (-300 dB).

Two compact structures for perpendicular coupling of optical signals between dielectric and photonic crystal waveguides

Two structures are analyzed with numerical modeling as candidates for perpendicular coupling of optical signals from a dielectric waveguide to a photonic bandgap (PBG) waveguide. The first consists of a perfectly electric conducting (PEC) grating and PBG mirror to couple power out of the dielectric waveguide, along with a circular-like lens to couple that power into the PBG waveguide. The second consists of a slanted inline fiber Bragg grating to couple power out of the dielectric waveguide, and a graded-index (GRIN) lens to couple that power into the PBG waveguide. Power transfer efficiencies of 50% and 71%, respectively, are reported. Such structures would be useful in WDM applications, and/or where circuit real estate restrictions demand coupling perpendicular to the dielectric guide over small distances.

Optimized Analytic Field Propagator (O-AFP) for Plane Wave Injection in FDTD Simulations

Optimizations are proposed for the original frequency domain analytic field propagator (AFP) to source plane waves in a 1D/2D/3D total-field scattered-field (TF/SF) FDTD formulation. The proposed technique essentially produces no field leakage error (limited by-300 dB machine precision error) with finite sampling points dictated by temporal aliasing constraints. By taking advantage of the inherent 1D nature of a plane wave, the memory requirements for the original AFP are reduced significantly. The proposed optimized solution (O-AFP) greatly reduces the computational complexity by calculating a number of spatial fields of O(N) rather than O(N 2), which then makes the technique practical enough to include fully 3D simulations.

FDTD Method on a Lebedev Grid for Anisotropic Materials

The finite-difference time-domain method is derived on a Lebedev grid for lossy anisotropic media. The Lebedev grid uses collocated field components and supports spurious solutions but an intuitive method for removing the extra solutions is presented. Update equations at material discontinuities and metal planes are derived and shown to take the same form as updates in bulk media. Additionally, a dispersion relation and stability criteria are presented. A numerical comparison with the Yee grid shows that the Lebedev grid suffers from greater numerical dispersion but better represents material discontinuities when compared using equal memory requirements. Furthermore, the small stencil on the Lebedev grid decreases the required number of calls to memory and simplifies the programming structure.

An FDTD scheme on a face-centered-cubic (FCC) grid for the solution of the wave equation

A method is proposed to improve the numerical dispersion characteristics for simulations of the scalar wave equation in 3D using the FDTD method. The improvements are realized by choosing a face-centered-cubic (FCC) grid instead of the typical Cartesian (Yee) grid, which exhibits non-physical distortions of the wavefront due to the FD stencil. FCC grids are the logical extension of hexagonal grids in 2D, and have been shown previously to provide optimal sampling of space based on close packing of spheres (highest density). The difference equations are developed for the wave equation on this alternative grid, and the dispersion relationship and stability for grids of equal and non-equal aspect ratios are derived. A comparison is made between FCC and Cartesian formulations, based upon having an equal volume density of gridpoints in each method (i.e. the computational storage requirements of each method would be the same for the same simulated space). The comparison shows that the FCC grid exhibits a much more isotropic dispersion relation than the Cartesian grid of equivalent density. Furthermore, for an equivalent density, the FCC method has a more relaxed stability criterion by a factor of approximately 1.35, resulting in a further reduction in computational resources.

On the Nature of Numerical Plane Waves in FDTD

The nature of uniform plane waves in the standard finite-difference time domain (FDTD) grid is investigated. In particular, it is shown that for the waves to be truly planar in the grid, they can only propagate at a countably infinite set of rational angles defined by integer ratios of grid-cells. The plane wave can then be expressed on a one-dimensional (1D) grid with uniform spacing, where each 1D point is directly associated with field locations in the main three-dimensional (3D) grid. Furthermore, it is shown that angles used in the projection of field components that account for the field nonorthogonality are inherently contained in the dispersion equation, and hence, a consistent set of projection operators is defined from it.

Data detection algorithms for multiplexed quantum dot encoding

A group of quantum dots can be designed to have a unique spectral emission by varying the size of the quantum dots (wavelength) and number of quantum dots (intensity). This technique has been previously proposed for biological tags and object identification. The potential of this system lies in the ability to have a large number of distinguishable wavelengths and intensity levels. This paper presents a communications system model for MxQDs including the interference between neighbouring QD colours and detector noise. An analytical model of the signal-to-noise ratio of a Charge-Coupled Device (CCD) spectrometer is presented and confirmed with experimental results. We then apply a communications system perspective and propose data detection algorithms that increase the readability of the quantum dots tags. It is demonstrated that multiplexed quantum dot barcodes can be read with 99.7% accuracy using the proposed data detection algorithms in a system with 6 colours and 6 intensity values resulting in 46,655 unique spectral codes.

Configuration design of MEMS switches in a digitally controlled reflectarray element

This paper introduces a circuit of MEMS capacitive switches, which yields a set of phase states that are close to being equally separated. The optimal capacitance values of the switches are determined using a genetic algorithm (GA). In addition, a ternary design for controlling the switches is proposed to reduce the number of control lines required without decreasing the number of realizable phase states.