Vitaliy Lomakin

Thresholdless nanoscale coaxial lasers

The effects of cavity quantum electrodynamics (QED), caused by the interaction of matter and the electromagnetic field in subwavelength resonant structures, have been the subject of intense research in recent years. The generation of coherent radiation by subwavelength resonant structures has attracted considerable interest, not only as a means of exploring the QED effects that emerge at small volume, but also for its potential in applications ranging from on-chip optical communication to ultrahigh-resolution and high-throughput imaging, sensing and spectroscopy. One such strand of research is aimed at developing the ‘ultimate’ nanolaser: a scalable, low-threshold, efficient source of radiation that operates at room temperature and occupies a small volume on a chip. Different resonators have been proposed for the realization of such a nanolaser—microdisk and photonic bandgap resonators, and, more recently, metallic, metallo-dielectric and plasmonic resonators. But progress towards realizing the ultimate nanolaser has been hindered by the lack of a systematic approach to scaling down the size of the laser cavity without significantly increasing the threshold power required for lasing. Here we describe a family of coaxial nanostructured cavities that potentially solve the resonator scalability challenge by means of their geometry and metal composition. Using these coaxial nanocavities, we demonstrate the smallest room-temperature, continuous-wave telecommunications-frequency laser to date. In addition, by further modifying the design of these coaxial nanocavities, we achieve thresholdless lasing with a broadband gain medium. In addition to enabling laser applications, these nanoscale resonators should provide a powerful platform for the development of other QED devices and metamaterials in which atom–field interactions generate new functionalities.

Low threshold gain metal coated laser nanoresonators

We introduce a low refractive index layer between the metal and the gain medium in metal-coated laser resonators and demonstrate that it can significantly reduce the dissipation losses. Analysis of a gain medium waveguide shows that for a given waveguide radius, the low index layer has an optimal thickness for which the lasing threshold gain is minimal. The waveguide analysis is used for the design of a novel three-dimensional cylindrical resonator that is smaller than the vacuum wavelength in all three dimensions and exhibits a low enough threshold gain to lase at room temperature.

Fast solution of mixed-potential time-domain integral equations for half-space environments

A fast Fourier transform-accelerated integral-equation based algorithm to efficiently analyze transient scattering from planar perfect electrically conducting objects residing above or inside a potentially lossy dielectric half-space is presented. The algorithm requires O(N/sub t/N/sub s/(logN/sub s/+log/sup 2/N/sub t/)) CPU and O(N/sub t/N/sub s/) memory resources when analyzing electromagnetic wave interactions with uniformly meshed planar structures. Here, N/sub t/ and N/sub s/ are the numbers of simulation time steps and spatial unknowns, respectively. The proposed scheme is therefore far more efficient than classical time-marching solvers, the CPU and memory requirements of which scale as O(N/sub t//sup 2/N/sub s//sup 2/) and O(N/sub t/N/sub s//sup 2/). In the proposed scheme, all pertinent time-domain half-space Green functions are (pre) computed from their frequency-domain counterparts via inverse discrete Fourier transformation. In this process, in-band aliasing is avoided through the application of a smooth and interpolatory window. Numerical results demonstrate the accuracy and efficiency of the proposed algorithm.

FastMag: Fast micromagnetic simulator for complex magnetic structures (invited)

A fast micromagnetic simulator (FastMag) for general problems is presented. FastMag solves the Landau-Lifshitz-Gilbert equation and can handle problems of a small or very large size with a high speed. The simulator derives its high performance from efficient methods for evaluating the effective field and from implementations on massively parallel Graphics Processing Unit (GPU) architectures. FastMag discretizes the computational domain into tetrahedral elements and therefore is highly flexible for general problems. The magnetostatic field is computed via the superposition principle for both volume and surface parts of the computational domain. This is accomplished by implementing efficient quadrature rules and analytical integration for overlapping elements in which the integral kernel is singular. Thus discretized superposition integrals are computed using a non-uniform grid interpolation method, which evaluates the field from N sources at N collocated observers in ( ) O N operations. This approach allows handling any uniform or non-uniform shapes, allows easily calculating the field outside the magnetized domains, does not require solving linear system of equations, and requires little memory. FastMag is implemented on GPUs with GPU-CPU speed-ups of two orders of magnitude. Simulations are shown of a large array and a recording head fully discretized down to the exchange length, with over a hundred million tetrahedral elements on an inexpensive desktop computer.

Microwave assisted magnetization reversal in composite media

Magnetic reversal in exchange-coupled composite elements under microwave fields is characterized by several unique properties including reduced reversal fields, microwave fields, microwave resonant frequencies, and reduced sensitivity to anisotropy distributions as compared to homogeneous elements. We find that reversal can occur in uniform and nonuniform regimes. The uniform regime is characterized by coherent spin precession enhancement by the microwave field. In the nonuniform regime domain walls in the soft layer mediate reversal and under linearly polarized microwave fields, can lead to a formation of localized reversal/nonreversal areas in the “applied field-frequency” phase plane.

Doubly negative metamaterials in the near infrared and visible regimes based on thin film nanocomposites

An optical metamaterial characterized simultaneously by negative permittivity and permeability, viz. doubly negative metamaterial (DNM), that comprises deeply subwavelength unit cells is introduced. The DNM can operate in the near infrared and visible spectra and can be manufactured using standard nanofabrication methods with compatible materials. The DNMs unit cell comprise a continuous optically thin metal film sandwiched between two identical optically thin metal strips separated by a small distance form the film. The incorporation of the middle thin metal film avoids limitations of metamaterials comprised of arrays of paired wires/strips/patches to operate for large wavelength / unit cell ratios. A cavity model, which is a modification of the conventional patch antenna cavity model, is developed to elucidate the structures electromagnetic properties. A novel procedure for extracting the effective permittivity and permeability is developed for an arbitrary incident angle and those parameters were shown to be nearly angle-independent. Extensions of the presented two dimensional structure to three dimensions by using square patches are straightforward and will enable more isotropic DNMs.

Fast evaluation of Helmholtz potential on graphics processing units (GPUs)

This paper presents a parallel algorithm implemented on graphics processing units (GPUs) for rapidly evaluating spatial convolutions between the Helmholtz potential and a large-scale source distribution. The algorithm implements a non-uniform grid interpolation method (NGIM), which uses amplitude and phase compensation and spatial interpolation from a sparse grid to compute the field outside a source domain. NGIM reduces the computational time cost of the direct field evaluation at N observers due to N co-located sources from O(N^2) to O(N) in the static and low-frequency regimes, to O(NlogN) in the high-frequency regime, and between these costs in the mixed-frequency regime. Memory requirements scale as O(N) in all frequency regimes. Several important differences between CPU and GPU implementations of the NGIM are required to result in optimal performance on respective platforms. In particular, in the CPU implementations all operations, where possible, are pre-computed and stored in memory in a preprocessing stage. This reduces the computational time but significantly increases the memory consumption. In the GPU implementations, where handling memory often is a critical bottle neck, several special memory handling techniques are used to accelerate the computations. A significant latency of the GPU global memory access is hidden by implementing coalesced reading, which requires arranging many array elements in contiguous parts of memory. Contrary to the CPU version, most of the steps in the GPU implementations are executed on-fly and only necessary arrays are kept in memory. This results in significantly reduced memory consumption, increased problem size N that can be handled, and reduced computational time on GPUs. The obtained GPU-CPU speed-up ratios are from 150 to 400 depending on the required accuracy and problem size. The presented method and its CPU and GPU implementations can find important applications in various fields of physics and engineering.

Graphics Processing Unit Accelerated

An efficient micromagnetic solver running on graphics processing units (GPU) is demonstrated. The solver implements a nonuniform grid interpolation method (NGIM) to compute the superposition integral for the magnetostatic field with operations and memory requirements. The NGIM divides the computational domain into a hierarchy of boxes containing sources and observers, and it uses spatial interpolation from sparse nonuniform grids to achieve computational savings. Efficiency of the GPU solver is achieved by using coalesced memory accessing requiring arranging data in contiguous addresses, one-block-per-box computations with a block of threads handling an observation box to achieve the best utilization of the GPU threads, and on-fly computation of all grids and interpolation coefficients leading to reduced memory and increased speed. The GPU-CPU speed-ups are shown to be in the range 40-100 depending on the problem size and accuracy. A simple and inexpensive GPU is shown to handle efficiently problems comprising discretizations of more than 16 million of spins.

O(N)

A novel algorithm to efficiently compute transient wave fields produced by known three-dimensional source constellations is proposed. The algorithm uses domain decomposition concepts and comprises two steps to be repeated for each subdomain considered. In the first step, delay- and amplitude- compensated fields, produced by sources residing inside each subdomain are computed at a sparse set of points surrounding the observation domain. In the second step, total fields in the observer domain are evaluated by interpolation, delay and amplitude restoration, and aggregation of subdomain fields. The proposed scheme is well-suited to accelerate the solution of time domain integral equations by marching on in time, to carry out time domain physical optics calculations, and to realize near- to far-field transformations of transients. Moreover, the scheme automatically adapts to, and takes advantage of, special geometrical features of the source-observer constellation studied, a key benefit when analyzing quasi-planar configurations. In addition, it realizes a seamless transition from the dynamic to the quasi-static regime, thus facilitating a unified treatment of electrically large and small problems. Last but not least, the scheme is remarkably simple to implement.

Micromagnetic Solver

Patterned media elements comprising coupled magnetically hard and soft sections of different horizontal size, referred to as ledge elements, are characterized by several unique properties. These elements allow for remarkably reduced reversal fields, which are an order of magnitude below the Stoner-Wohlfarth limit. They also allow for precessional reversal to occur for practical field rise times (100–200ps), which are two orders of magnitude larger than those in the case of homogeneous elements (∼2ps). These attractive properties are obtained even for elements of small height (4–8nm). Patterned media implementing such ledge elements can allow for recording densities above 10Tbit∕in2.