Super-resolution properties of the Spherical Geodesic Waveguides using the perfect drain

Perfect drain for the Maxwell Fish Eye (MFE) is a nonmagnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity ? that depends on frequency. However, this material is only a theoretical material, so it can not be used in practical devices. Recently, the perfect drain has been claimed as necessary to achieve super-resolution [Leonhard 2009, New J. Phys. 11 093040], which has increased the interest for practical perfect drains suitable for manufacturing. Here, we analyze the superresolution properties of a device equivalent to the MFE, known as Spherical Geodesic Waveguide (SGW), loaded with the perfect drain. In the SGW the source and drain are implemented with coaxial probes. The perfect drain is realized using a circuit (made of a resistance and a capacitor) connected to the drain coaxial probes. Superresolution analysis for this device is done in Comsol Multiphysics. The results of simulations predict the superresolution up to ? /3000 and optimum power transmission from the source to the drain.

Design of spherical symmetric gradient index lenses

Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.

Extreme super-resolution using the spherical geodesic waveguide

Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a "perfect point drain" located at the corresponding image point. Moreover, a prototype with λ/5 superresolution (SR) property for one microwave frequency has been manufactured and tested (Ma et al, 2010). Although this prototype has been loaded with an impedance different from the "perfect point drain", it has shown super-resolution property. However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here we present steady state simulations for two cases, using perfect drain as suggested by Leonhardt and without perfect drain as in the prototype. All the simulations have been done using a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW). The results show the super-resolution up to λ/3000, for the system loaded with the perfect drain, and up to λ/500 for a not perfect load. In both cases super-resolution only happens for discrete number of frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.

On the design of spherical gradient index lenses

Classical spherical gradient index (GRIN) lenses (such as Maxwell Fish Eye lens, Eaton lens, Luneburg lens, etc.) design procedure using the Abel integral equation is reviewed and reorganized. Each lens is fully defined by a function called the angle of flight which describes the ray deflection through the lens. The radial refractive index distribution is obtained by applying a linear integral transformation to the angle of flight. The interest of this formulation is in the linearity of the integral transformation which allows us to derive new solutions from linear combinations of known lenses. Beside the review of the classical GRIN designs, we present a numerical method for GRIN lenses defined by the Abel integral equation with fixed limits, which is an ill-posed problem.

Inverse bremsstrahlung absorption in spherical laser targets

Inverse bremsstrahlung has been incorporated into an analytical model of the expanding corona of a laser-irradiated spherical target. Absorption decreases slowly with increasing intensity, in agreement with some numerical simulations, and contrary to estimates from simple models in use up to now, which are optimistic at low values of intensity and very pessimistic at high values. Present results agree well with experimental data from many laboratories; substantial absorption is found up to moderate intensities,say below IOl5 W cm-2 for 1.06 pm light. Anomalous absorption, wher, included in the analysis, leaves practically unaffected the ablation pressure and mass ablation rate, for given absorbed intensity. Universal results are given in dimensionless fom.

Current collection by an active spherical electrode in an unmagnetized plasma

A theoretical model for the steady-state response of anodic contactors that emit a plasma current Ii and collect electrons from a collisionless, unmagnetized plasma is presented. The use of a (kinetic) monoenergetic population for the attracted species, well known in passive probe theory, gives both accuracy and tractability to the theory. The monoenergetic population is proved to behave like an isentropic fluid with radial plus centripetal motion, allowing direct comparisons with ad hoc fluid models. Also, a modification of the original monoenergetic equations permits analysis of contactors operating in orbit-limited conditions. Besides that, the theory predicts that, only for plasma emissions above certain threshold current a presheath/double layer/core structure for the potential is formed (the core mode), while for emissions below that threshold, a plasma contactor behaves exactly as a positive-ion emitter with a presheath/sheath structure (the no-core mode). Ion emitters are studied as a particular case. Emphasis is placed on obtaining dimensionless charts and approximate asymptotic laws of the current-voltage characteristic.

Non-periodic driving of coupled oscillators:a spherical swing

Nonlinearly coupled, damped oscillators at 1:1 frequency ratio, one oscillator being driven coherently for efficient excitation, are exemplified by a spherical swing with some phase-mismatch between drive and response. For certain damping range, excitation is found to succeed if it lags behind, but to produce a chaotic attractor if it leads the response. Although a period-doubhng sequence, for damping increasing, leads to the attractor, this is actually born as a hard (as regards amplitude) bifurcation at a zero growth-rate parametric line; as damping decreases, an unstable fixed point crosses an invariant plane to enter as saddle-focus a phase-space domain of physical solutions. A second hard bifurcation occurs at the zero mismatch line, the saddle-focus leaving that domain. Times on the attractor diverge when approaching either fine, leading to exactly one-dimensional and noninvertible limit maps, which are analytically determined.

Spherical collectors versus bare tethers for drag, thrust, and power generation

Deorbit, power generation, and thrusting performances of a bare thin-tape tether and an insulated tether with a spherical electron collector are compared for typical conditions in low-Earth orbit and common values of length L = 4−20 km and cross-sectional area of the tether A = 1−5 mm2. The relative performance of moderately large spheres, as compared with bare tapes, improves but still lags as one moves from deorbiting to power generation and to thrusting: Maximum drag in deorbiting requires maximum current and, thus, fully reflects on anodic collection capability, whereas extracting power at a load or using a supply to push current against the motional field requires reduced currents. The relative performance also improves as one moves to smaller A, which makes the sphere approach the limiting short-circuit current, and at greater L, with the higher bias only affecting moderately the already large bare-tape current. For a 4-m-diameter sphere, relative performances range from 0.09 sphere-to-bare tether drag ratio for L = 4 km and A = 5 mm2 to 0.82 thrust–efficiency ratio for L = 20 km and A = 1 mm2. Extremely large spheres collecting the short-circuit current at zero bias at daytime (diameters being about 14 m for A = 1 mm2 and 31 m for A = 5 mm2) barely outperform the bare tape for L = 4 km and are still outperformed by the bare tape for L = 20 km in both deorbiting and power generation; these large spheres perform like the bare tape in thrusting. In no case was sphere or sphere-related hardware taken into account in evaluating system mass, which would have reduced the sphere performances even further.

Spherical collectors versus bare tethers for drag, thrust, and power generation

Performances of ED-tethers using either spherical collectors or bare tethers for drag, thrust, or power generation, are compared. The standard Parker-Murphy model of current to a full sphere, with neither space-charge nor plasmamotion effects considered, but modified to best fit TSS1R results, is used (the Lam, Al'pert/Gurevich space-charge limited model will be used elsewhere) In the analysis, the spherical collector is assumed to collect current well beyond its random-current value (thick-heath). Both average current in the bare-tether and current to the sphere are normalized with the short-circuit current in the absence of applied power, allowing a comparison of performances for all three applications in terms of characteristic dimensionless numbers. The sphere is always substantially outperformed by the bare-tether if ohmic effects are weak, though its performance improves as such effects increase.

Experimental evidence for super-resolution in the spherical geodesic waveguide

The previous publications (Miñano et al, 2011 and Gonzalez et al, 2012) have shown that using a Spherical Geodesic Waveguide (SGW) it can be achieved the super-resolution up to λ/3000, which is far below the classic Abbe diffraction limit, close to a set of discrete microwave frequencies. The SGW was designed and simulated in COMSOL as a thin geodesic waveguide bounded by an ideal and lossless metal. Herein we present the experimental results for a manufactured SGW, slightly modified due to fabrication requirements, showing the super-resolution up to λ/105.

Current-voltage response of a spherical plasma contactor

A theoretical model for a contactor, collecting electrons from an ambient, unmagnetized plasma and emitting a current Iiis discussed. The relation between Ii and the potential bias of the contactor is found to be crucial for the formation of a quasineutral core around the anode and, consequently, for the current colleted. Approximate analytical laws and charts for the current-voltage response are provided.

Experimental confirmation of FK concentrator insensitivity to chromatic aberrations

The FK concentrator has demonstrated during the last years that compares very well with other Fresnel-based concentrator optics for CPV. There are several features that provide the FK high performance: (1) high optical efficiency; (2) large tolerance to tracking misalignment and manufacturing errors, thanks to a high CAP (Concentration-Acceptance Product); (3) good irradiance uniformity and low chromatic dispersion on the cell surface. Non-uniformities in terms of absolute irradiance and spectral content produced by conventional CPV systems can originate electrical losses in multi-junction (MJ) solar cells. The aim of this work is to analyze the influence of these non-uniformities in the FK concentrator performance and how FK concentrator provides high electrical efficiencies thanks to its insensitivity to chromatic aberrations, especially when components move away from the module nominal position due to manufacturing misalignments. This analysis has been done here by means of both, experimental on-sun measurements and simulations based on 3D fully distributed circuit model for MJ cells.

Inverse kinematics of a humanoid robot with non-spherical hip: a hybrid algorithm approach

This paper describes an approach to solve the inverse kinematics problem of humanoid robots whose construction shows a small but non negligible offset at the hip which prevents any purely analytical solution to be developed. Knowing that a purely numerical solution is not feasible due to variable efficiency problems, the proposed one first neglects the offset presence in order to obtain an approximate “solution” by means of an analytical algorithm based on screw theory, and then uses it as the initial condition of a numerical refining procedure based on the Levenberg‐Marquardt algorithm. In this way, few iterations are needed for any specified attitude, making it possible to implement the algorithm for real‐time applications. As a way to show the algorithm’s implementation, one case of study is considered throughout the paper, represented by the SILO2 humanoid robot.

Analysis of the behavior of multijunction solar cells under high irradiance Gaussian light profiles showing chromatic aberration with emphasis on tunnel junction performance

In this work, we explain the behavior of multijunction solar cells under non-uniform (spatially and in spectral content) light profiles in general and in particular when Gaussian light profiles cause a photo-generated current density, which exceeds locally the peak current density of the tunnel junction. We have analyzed the implications on the tunnel junction's limitation, that is, in the loss of efficiency due to the appearance of a dip in the I–V curve. For that, we have carried out simulations with our three-dimensional distributed model for multijunction solar cells, which contemplates a full description of the tunnel junction and also takes into account the lateral resistances in the tunnel junction. The main findings are that the current density photo-generated spreads out through the lateral resistances of the device, mainly through the tunnel junction layers and the back contact. Therefore, under non-uniform light profiles these resistances are determinant not only to avoid the tunnel junction's limitation but also for mitigating losses in the fill factor. Therefore, taking into account these lateral resistances could be the key for jointly optimizing the concentrator photovoltaic system (concentrator optics, front grid layout and semiconductor structure)