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2014-05-15
PIER B
Vol. 59, 269-289, 2014
download: 349
Calculation of the Mutual Coupling Parameters and Their Effects in 1-D Planar Almost Periodic Structures
Bilel Hamdi Taoufik Aguili Nathalie Raveu Henri Baudrand
This paper proposes a new modal analysis based on Floquet's theorem which is needful for the study of a 1-D periodic phased array antenna excited by arbitrary located sources. This analysis requires an accurate estimation for calculation of the mutual coupling parameters (for example: mutual impedances or admittances...) between the array elements and their effects integrating a large planar radiating structure. Two different formulations are suggested, in spectral and spatial domains, to solve the problem and to calculate the coupling coefficients between the neighbouring elements in a periodic environment. Important gain in the running time and used memory is obtained using Floquet analysis. One numerical method is used for modeling the proposed structures: the moment method combined with Generalized Equivalent Circuit (MoM-GEC).
CALCULATION OF THE MUTUAL COUPLING PARAMETERS AND THEIR EFFECTS IN 1-D PLANAR ALMOST PERIODIC STRUCTURES
2014-04-30
PIER B
Vol. 59, 257-267, 2014
download: 109
Linear Momentum Density of a General Lorentz-Gauss Vortex Beam in Free Space
Yiqing Xu Guoquan Zhou
Based on the Collins integral, an analytical expression of a general Lorentz-Gauss vortex beam propagating in free space is derived, which allows one to calculate the linear momentum density of a general Lorentz-Gauss vortex beam in free space. The linear momentum density distribution of a general Lorentz-Gauss vortex beam propagating in free space is graphically demonstrated. The x- and y-components of the linear momentum density are composed of two lobes with the equivalent area and the opposite sign. Therefore, the overall x- and y-components of the linear momentum in an arbitrary reference plane are equal to zero. The longitudinal component of the linear momentum density is proportional to the intensity distribution. The influences of the Gaussian waist, the width parameters of the Lorentzian part, the axial propagation distance, and the topological charge on the linear momentum density distribution of a general Lorentz-Gauss vortex beam in free space are examined in detail.
LINEAR MOMENTUM DENSITY OF A GENERAL LORENTZ-GAUSS VORTEX BEAM IN FREE SPACE
2014-04-29
PIER B
Vol. 59, 245-256, 2014
download: 103
Inhomogeneous and Homogeneous Losses and Magnetic Field Effect in Planar Undulator Radiation
Konstantin V. Zhukovsky
We construct an analytical model for the description of emission of undulator radiation (UR) harmonics with account for several sources of line broadening, including the effect of a constant magnetic constituent. We compare it with that of the beam energy spread, emittance and focusing components. The analytical expressions obtained for the UR intensity and spectrum allow for profound analysis of homogeneous and inhomogeneous losses in their explicit form. We analyse the contributions to the fundamental frequency as well as to higher harmonics in long undulators. We study a possibility to compensate for the off-axis effects in undulators by a properly imposed constant magnetic field and obtain an expression for the intensity of such compensating effect. The results obtained are discussed in the context of their possible applications to free electron lasers (FEL). Recommendations for improvement of an UR harmonic line quality, profitable for FEL, are also proposed.
INHOMOGENEOUS AND HOMOGENEOUS LOSSES AND MAGNETIC FIELD EFFECT IN PLANAR UNDULATOR RADIATION
2014-04-25
PIER B
Vol. 59, 231-244, 2014
download: 109
Enhanced the Complete Photonic Band Gaps for Three-Dimensional Photonic Crystals Consisting of Epsilon-Negative Materials in Pyrochlore Arrangement
Hai Feng Zhang Shaobin Liu Hui-Chao Zhao
In this paper, the properties of photonic band gaps (PBGs) for three-dimensional (3D) photonic crystals (PCs) composed of isotropic positive-index materials and epsilon-negative materials with pyrochlore lattices are theoretically investigated by a modified plane wave expansion method. The eigenvalue equations of calculating the band structure for such 3D PCs in the first irreducible Brillouin zone (spheres with the isotropic positive-index materials inserted in the epsilon-negative materials background) are theoretically deduced. Numerical simulations show that the PBG and a flatbands region can be achieved. It is also found that the larger PBG can be obtained in such PCs structure than the conventional lattices, such as diamond, face-centered-cubic, body-centered-cubic and simple-cubic lattices. The influences of the relative dielectric constant of spheres, filling factor, electronic plasma frequency, dielectric constant of epsilon-negative materials and damping factor on the properties of the PBG for such 3D PCs are studied in detail, respectively, and some corresponding physical explanations are also given. The calculated results also show that the PBG can be manipulated by the parameters mentioned above except for the damping factor. Introducing the epsilon-negative materials into 3D dielectric PCs can obtain the complete and larger PBGs as such 3D PCs with pyrochlore lattices, and also provides a way to design the potential devices.
ENHANCED THE COMPLETE PHOTONIC BAND GAPS FOR THREE-DIMENSIONAL PHOTONIC CRYSTALS CONSISTING OF EPSILON-NEGATIVE MATERIALS IN PYROCHLORE ARRANGEMENT
2014-04-18
PIER B
Vol. 59, 219-229, 2014
download: 112
Optimization of a Plasmon-Assisted Waveguide Coupler Using FEM and Mmp
Mengyu Wang Aytac Alparslan Sascha M. Schnepp Christian Hafner
In this paper, we focus on the problem of optimizing plasmonic structures. A plasmon-assisted waveguide coupler is considered as a test problem, which leads to a five-dimensional optimization problem carried out by an evolution strategy (ES). The optimization results are verified by a comparative analysis between different solvers, i.e., the finite element package CONCEPTs and the multiple multipole program (MMP). We also compared with results obtained using a deterministic optimization algorithm, namely the Nedler-Mead method as implemented in the commercial software package COMSOL Multiphysics. Some issues concerning deterministic versus evolutionary optimization, in particular, in the field of plasmonics have been discussed.
OPTIMIZATION OF A PLASMON-ASSISTED WAVEGUIDE COUPLER USING FEM AND MMP
2014-04-18
PIER B
Vol. 59, 205-217, 2014
download: 129
Experimental Characterization of the Propagation Channel Along a Very Large Virtual Array in a Reverberation Chamber
Andres Alayon Glazunov Sathyaveer Prasad Peter Handel
We show that the combined use of radio frequency absorbers and directive antennas can produce significant changes of the radio propagation channel properties along the positions of a virtual array inside a reverberation chamber. A multidimensional characterization of the channel was performed at 40 antenna positions with spacing of 0.233λ at 1 GHz. The average power, the Ricean K-factor, the coherence bandwidth, the r.m.s. delay spread, the mean delay, the beamforming power angle spectrum and array antenna correlation have been studied for different arrangements in the reverberation chamber. The analysis shows that the joint average over time and frequency channel behavior is, as expected, rather homogeneous along the very large array. However, individual realizations of the channel present a pronounced selective behavior in space, time and frequency with parameters varying along the positions of the virtual array suggesting that a heterogeneous behavior of the radio channels can be emulated in reverberation chambers. An important application of the presented study comprises testing of antenna array designs and algorithms in multipath environments. Further development may lead to Over The Air testing of Multiple Input Multiple Output antenna systems of various sizes, i.e., from small to very large arrays.
EXPERIMENTAL CHARACTERIZATION OF THE PROPAGATION CHANNEL ALONG A VERY LARGE VIRTUAL ARRAY IN A REVERBERATION CHAMBER
2014-04-15
PIER B
Vol. 59, 193-204, 2014
download: 123
High-Frequency Method for Terahertz Radar Cross Section of Conductive Targets in Free Space
Houqiang Hua Yue-Song Jiang Yuntao He
The high-frequency method for the prediction of the terahertz (THz) radar cross section (RCS) of conductive targets with extremely electrically large size in free space was presented. In order to consider the scattering fields of the perfectly electric conducting (PEC) targets with extremely electrically large size in free space, the Green's function was introduced into the conventional physical optics (PO) method which was combined with the graphical electromagnetic computing (GRECO) method and improved using the partition display algorithm. The shadow regions were eliminated quickly by displaying lists of OpenGL to rebuild the targets, and the geometry information was attained by reading the color and depth of each pixel. The THz RCS of conductive targets can be exactly calculated in free space. The RCS comparison between the partition display GRECO prediction by the self-written Visual C++ 2010 program and the simulation of FEKO software with the large element PO method proves the validity and accuracy of the proposed method. The results provide an important basis and method for the potential applications of THz radar in many fields such as military, astronomy and remote sensing.
HIGH-FREQUENCY METHOD FOR TERAHERTZ RADAR CROSS SECTION OF CONDUCTIVE TARGETS IN FREE SPACE
2014-04-11
PIER B
Vol. 59, 181-191, 2014
download: 161
Effect of Snow Density Irregularities on Radar Backscatter from a Layered Dry Snow Pack
Boris S. Yurchak
The contribution of electromagnetic wave scattering on density irregularities in the volume component of radar backscatter was analyzed for a thick snow pack containing internal hoar/ice layers. To evaluate the effect of this scattering, Density Deviation Factor (DDF), a statistical parameter, was introduced into the backscattering coefficient using the ``slice'' approach. DDF is proportional to the intensity of the density fluctuation and inverse to the mean density. The inverse dependence of backscatter with accumulation rate was discussed based on the DDF parameterization of snow inhomogeneities.
EFFECT OF SNOW DENSITY IRREGULARITIES ON RADAR BACKSCATTER FROM A LAYERED DRY SNOW PACK
2014-04-11
PIER B
Vol. 59, 167-179, 2014
download: 613
Ground Fault Current Distribution When a Ground Fault Occurs in Hv Substations Located in an Urban Area
Ljubivoje M. Popovic
The paper presents a method of determination of ground fault current distribution when HV (high voltage) substations are located in urban or suburban areas, or where many relevant data necessary for determination of this distribution are uncertain or completely unknown. The problem appears as a consequence of the fact that many of urban metal installations are situated under the surface of the ground and cannot be visually determined or verified. On the basis of on-the-site measurements, the developed method enables compensating all deficiencies of the relevant data about metal installations involved with the fluctuating magnet field appearing around and along a feeding power line during an unbalanced fault. The presented analytical procedure is based on the fact that two measurable quantities, currents in one phase conductor and in one neutral line conductor, cumulatively involve the inductive effects of all, known and unknown surrounding metal installations. Once, this quantity has been determined, the problem of determination of different parts of a ground fault current becomes solvable by using a relatively simple calculation procedure. The presented quantitative analysis indicates at the benefits that can be obtained by taking into account the presence of surrounding metal installations.
GROUND FAULT CURRENT DISTRIBUTION WHEN A GROUND FAULT OCCURS IN HV SUBSTATIONS LOCATED IN AN URBAN AREA
2014-04-09
PIER B
Vol. 59, 151-166, 2014
download: 253
A Comparative Study of Material Leucaena Leucocephala Stem Wood Plastic Composite (Wpc) Substrate with Fr4 Substrate Throughout Single Patch Antenna Design
AHMAD AZLAN AB AZIZ Muhammad Kamal Badrun Mohd Tarmizi Ali Zaiki Awang Zakiah Bt. Md Saad Aziati Husna Awang
The fabrication of single square patch antenna for proposed Leucaena Leucocephala (``Petai Belalang'') Wood Plastic Composite (WPC) substrate board (PB Substrate board) and FR4 substrate board is presented in this paper. The experiment objective is to measure the performance of an antenna fabricated on the FR4 and PB substrate (proposed substrate) by comparing the performance in terms of material's dielectric constant and electron mobility and antennas' loss tangent, return loss (S11), radiation pattern and practical antenna transmitting performance. The new substrate compositions of Leucaena Leucocephala stem and polypropylene (PP) are 30% and 70% consecutively. The result for 150 μm (sample B) indicates stability on most dielectric constant (εr =3.02), loss tangent (Tanδ=0.029) and electron mobility (5.31x103 cm2/Vs), with the consistency of antenna result, between simulation and measurement. All results obtained will be analyzed and displayed in the form of data and graphs.
A COMPARATIVE STUDY OF MATERIAL LEUCAENA LEUCOCEPHALA STEM WOOD PLASTIC COMPOSITE (WPC) SUBSTRATE WITH FR4 SUBSTRATE THROUGHOUT SINGLE PATCH ANTENNA DESIGN
2014-04-09
PIER B
Vol. 59, 135-150, 2014
download: 272
Analysis of the Impedance Behaviour for Broadband Dipoles in Proximity of a Body Tissue: Approach by Using Antenna Equivalent Circuits
Tommi Tuovinen Markus Berg Jari Iinatti
Ultra wideband (UWB) antenna operation close to tissue is examined by using lumped-element equivalent circuits in the present paper. The impact of tissue within the reactive near-field of the antenna is introduced in terms of efficiency, impedance and matching to 50 Ω. The parasitic components for the series- and parallel-resonant stages of the equivalent models are proposed for taking the impact of tissue into account on the antenna design. The first time the antenna impedance behaviour is presentedin terms of capacitance, inductance and resistance as a function of the radiator distance on the tissue surface for UWB antennas. The capacitance was observed to increase with the distance on the tissue surface by achieving the maximum value close to the reactive near-field boundary. The inductance has the maximum on contact the tissue, decreasing strongly with the first millimetres and remaining constant with the higher distance. The maximum value of input resistance was seen to clearly increase with the distance, having the maximum value in the first third of the studied range, descending close to the value in free space at the boundary at the end. The results are achieved by realising electromagnetic simulations for the antennas and comparing the performance with the operation of the equivalent models.
ANALYSIS OF THE IMPEDANCE BEHAVIOUR FOR BROADBAND DIPOLES IN PROXIMITY OF A BODY TISSUE: APPROACH BY USING ANTENNA EQUIVALENT CIRCUITS
2014-04-04
PIER B
Vol. 59, 123-133, 2014
download: 141
Microwave Model of Radiation from the Multilayer ``Ocean-Atmosphere'' System for Remote Sensing Studies of the Polar Regions
Vasiliy V. Tikhonov Dmitriy A. Boyarskii Evgene Sharkov Mikhael Raev Irina A. Repina Vladimir Ivanov Tatyana A. Alexeeva Natalia Y. Komarova
Microwave model for simulation of radiation from the multilayer system ``sea surface - sea ice - snow cover - atmosphere'' is introduced. In the general case, ice and snow cover is modelled by multilayer medium, where every layer is characterized by its specific physical parameters. Electrodynamical properties of each layer are determined from the original authors' model of the effective permittivity of heterogeneous medium. This model takes into account effects of radiation scattering on irregularities of environment. Measurable physical characteristics of sea ice and snow are used as the model input data. This advantage allows using this model for interpretation of remote sensing images of the ice cover in the Polar Regions. Major attention is drawn to comparison of model calculations with satellite data and visual observations from ships. The collection of SSM/I and SSMIS images from GLOBAL-RT data base, and processed visual observations from ships in Arctic cruises were used. Observations data served as the input parameters for electrodynamical model. Comparison of model results with SSM/I images demonstrated good coincidence at various frequencies.
MICROWAVE MODEL OF RADIATION FROM THE MULTILAYER ``OCEAN-ATMOSPHERE'' SYSTEM FOR REMOTE SENSING STUDIES OF THE POLAR REGIONS
2014-04-04
PIER B
Vol. 59, 103-121, 2014
download: 179
Real Time Implemenation for DOA Estimation Methods on Ni-Pxi Platform
Nizar Tayem
In this paper, we present five different approaches to estimate direction of arrival (DOA) of multiple incident RF sources. The proposed methods are based on extracting the signal and noise subspaces from the Q matrix, R matrix, or both Q and R matrices of the QR decomposed received data matrix. The angle of the signal arrival is extracted from the signal subspace by using similar techniques as employed by MUSIC and ESPRIT methods. The simulation results are shown which verify accurate DOA estimates for both single and two sources. In addition, an experimental verification of the proposed methods is also presented. The methods are implemented in LabVIEW software and a prototype is built using National Instruments (NI) hardware. Furthermore, the details of experimental procedures are presented which includes interfacing the uniform linear array (ULA) of antennas with the NI-PXI platform, phase difference calibration between the RF receivers, and selection of transmitter and receiver parameters. The experimental results are shown for a single and two RF sources lying at arbitrary angles from the array reference, which verify the successful real-time implement-ability of the proposed DOA estimation methods.
REAL TIME IMPLEMENATION FOR DOA ESTIMATION METHODS ON NI-PXI PLATFORM
2014-04-01
PIER B
Vol. 59, 89-102, 2014
download: 275
Patch and Ground Plane Design of Microstrip Antennas by Material Distribution Topology Optimization
Emadeldeen Hassan Eddie Wadbro Martin Berggren
We use a gradient-based material distribution approach to design conductive parts of microstrip antennas in an efficient way. The approach is based on solutions of the 3D Maxwell's equation computed by the finite-difference time-domain (FDTD) method. Given a set of incoming waves, our objective is to maximize the received energy by determining the conductivity on each Yee-edge in the design domain. The objective function gradient is computed by the adjoint-field method. A microstrip antenna is designed to operate at 1.5 GHz with 0.3 GHz bandwidth. We present two design cases. In the first case, the radiating patch and the finite ground plane are designed in two separate phases, whereas in the second case, the radiating patch and the ground plane are simultaneously designed. We use more than 58,000 design variables and the algorithm converges in less than 150 iterations. The optimized designs have impedance bandwidths of 13% and 36% for the first and second design case, respectively.
PATCH AND GROUND PLANE DESIGN OF MICROSTRIP ANTENNAS BY MATERIAL DISTRIBUTION TOPOLOGY OPTIMIZATION
2014-03-27
PIER B
Vol. 59, 71-87, 2014
download: 152
Analysis on Strongly Coupled Oscillator Arrays Using Modified Y-Parameters Approach
Yu-Tsung Lo Jean-Fu Kiang
A modified Y-parameters approach is proposed to model the behavior of coupled oscillator arrays (COA's). A coupling network with tunable coupling strength is proposed, which has a near-constant input conductance, to ensure the oscillation condition under different attenuation levels. The parameters of oscillators and the coupling network are derived on the TSMC 0.18 μm technology, and their Y parameters are extracted around 10 GHz for illustration. After being verified with full-circuit simulations and other behavior models, including the Adler's equation and the conventional Y-parameters approach, this method is applied to estimate the maximum allowable number of oscillators that can be coupled together. The inter-element phase shift of a COA is controlled by tuning the free-running frequencies of oscillators at both ends. Injection signals with proper phases are proposed to synchronize multiple COA's into a bigger COA.
ANALYSIS ON STRONGLY COUPLED OSCILLATOR ARRAYS USING MODIFIED Y-PARAMETERS APPROACH
2014-03-19
PIER B
Vol. 59, 59-70, 2014
download: 110
Electromagnetic Scattering by Approximately Cloaked Dielectric Cylinder
Hany Mahmoud Zamel Essam Eldiwany Hadia El-Hennawy
In cloaking, a body is hidden from detection by surrounding it by a coating consisting of an unusual anisotropic nonhomogeneous material. The permittivity and permeability of such a cloak are determined by the coordinate transformation of compressing a hidden 2D or cylindrical body into a line. Some components of the electrical parameters of the cloaking material (ε, μ) are required to have infinite or zero value at the boundary of the hidden object. In order to eliminate the zero or infinite values of the electrical parameters, approximate cloaking can be used by transforming the cylindrical body virtually into a small cylinder rather than a line, but this produces some scattering. The solution is obtained by rigorously solving Maxwell equations using angular harmonics expansion. In this work, the scattering pattern, and the backscattering cross section against the frequency for cloaked conducting and dielectric cylinders are studied for both transverse magnetic (TMz) and transverse electric (TEz) polarizations of the incident plane wave for different transformed body radii.
ELECTROMAGNETIC SCATTERING BY APPROXIMATELY CLOAKED DIELECTRIC CYLINDER
2014-03-18
PIER B
Vol. 59, 45-58, 2014
download: 113
Rainfall Microstructural Analysis for Microwave Link Networks: Comparison at Equatorial and Subtropical Africa
Akintunde Ayodeji Alonge Thomas Joachim Odhiambo Afullo
The quest to understand the variation of rainfall microstructures at subtropical and equatorial regions is vital to rain attenuation studies. In this study, point rainfall datasets obtained at Butare (2°36'S, 29°44'E) and Durban (29°52'S, 30°58'E), are compared at the reflectivity threshold of 38 dBz. Joss- Walvogel (JW) distrometer measurements collected from these two locations represent physical rainfall data from equatorial and subtropical climates respectively. The reflectivity threshold enables the classification of rainfall datasets into stratiform and convective (S-C) precipitation regimes. These thresholds, Rth, at Durban and Butare are analysed based on three known rainfall microphysical parameters: rain rate, rainfall Drop Size Distribution (DSD) and radar reflectivity. The results from rain rate distributions at the both regions are similar for both stratiform and convective classes. However, the sampled DSDs indicate the dominance of larger rain droplets at Butare compared to observations at Durban, irrespective of the rain classes. In addition, it is found that the reflectivity distributions at both regions, under stratiform and convective conditions, are distinct in their probability profiles. The overall S-C analysis implied that the structures of the reflectivity and DSD profiles at both regions - result in significant variation of predicted specific attenuation - at microwave and millimeter band. In comparison with other global locations, it is affirmed that the S-C transition occurs globally at rain rates between 6 mm/h and 13 mm/h.
RAINFALL MICROSTRUCTURAL ANALYSIS FOR MICROWAVE LINK NETWORKS: COMPARISON AT EQUATORIAL AND SUBTROPICAL AFRICA
2014-03-13
PIER B
Vol. 59, 31-44, 2014
download: 101
Feasibility Investigation of Low Cost Substrate Integrated Waveguide (SIW) Directional Couplers
Tiziana Castellano Onofrio Losito Luciano Mescia Michele A. Chiapperino Giuseppe Venanzoni Davide Mencarelli Giacomo Angeloni Chiara Renghini Pasquale Carta Francesco Prudenzano
In this paper, the feasibility of Substrate Integrated Waveguide (SIW) couplers, fabricated using single-layer TACONIC RF-35 dielectric substrate is investigated. The couplers have been produced employing a standard PCB process. The choice of the TACONIC RF-35 substrate as alternative to other conventional materials is motivated by its lower cost and high dielectric constant, allowing the reduction of the device size. The coupler requirements are 90-degree phase shift between the output and the coupled ports and frequency bandwidth from about 10.5 GHz to 12.5 GHz. The design and optimization of the couplers have been performed by using the software CST Microwave Studio©. Eight different coupler configurations have been designed and compared. The better three couplers have been fabricated and characterized. The proposed SIW directional couplers could be integrated within more complex planar circuits or utilized as stand-alone devices, because of their compact size. They exhibit good performance and could be employed in communication applications as broadcast signal distribution and as key elements for the construction of other microwave devices and systems.
FEASIBILITY INVESTIGATION OF LOW COST SUBSTRATE INTEGRATED WAVEGUIDE (SIW) DIRECTIONAL COUPLERS
2014-03-07
PIER B
Vol. 59, 19-29, 2014
download: 131
Diffraction from a Grating on a Chiral Medium: Application of Analytical Regularization Method
Sergey B. Panin Bahattin Turetken Anatoly Poyedinchuk Yury A. Tuchkin
Theoretical results on the electromagnetic wave diffraction from a periodic strip grating placed on a chiral medium are obtained. Analytical regularization method based on the solution to the vector Riemann-Hilbert boundary value problem was used to get robust numerical results in the resonant domain, where direct solution methods typically fail. It was shown that in the case of normal incidence of linearly polarized wave the cross-polarized field appears in the reflected field. For elliptically polarized incident wave the diffraction character essentially depends on the polarization direction of the incident wave. These diffraction peculiarities are more pronounced in the resonant domain. Influence of the dichroism caused by chiral medium losses is thoroughly studied. The combination of a chiral medium and a grating can be effectively used for a frequency and polarization selection and for a mode conversion.
DIFFRACTION FROM A GRATING ON A CHIRAL MEDIUM: APPLICATION OF ANALYTICAL REGULARIZATION METHOD
2014-03-07
PIER B
Vol. 59, 1-18, 2014
download: 92
Multilayered Superlenses Containing Csbr OR Active Medium for Subwavelength Photolithography
Li-Hao Yeh Jean-Fu Kiang
The characteristics of periodic multilayered near-field superlenses are analyzed and optimized, using the dispersion relation derived from an effective medium theory and the transfer function in the spectral domain. The k'z-k''x and kz-kx contours are used to explain and predict the spectral width, amplitude and phase of the transfer function. Superlenses containing CsBr or active layers are proposed to reduce image distortion or to compensate for the propagation loss, respectively. The parameters of the superlenses can be optimized by simulations to resolve half-pitch features down to λ/36 using CsBr layers, and λ/20 using active layers.
MULTILAYERED SUPERLENSES CONTAINING CSBR OR ACTIVE MEDIUM FOR SUBWAVELENGTH PHOTOLITHOGRAPHY