Sidharath Jain

Flat-Lens Design Using Field Transformation and Its Comparison With Those Based on Transformation Optics and Ray Optics

This letter proposes a technique for designing flat lenses using field transformation (FT), as opposed to ray optics (RO) or transformation optics (TO). The lens design consists of 10 layers of graded index dielectric in the radial direction and 5 layers in the longitudinal direction. The central layer in the longitudinal direction primarily contributes to a bulk of the phase transformation, while the other four layers, above and below this middle layer on either side, act as matching layers that help reduce the reflections introduced by the impedance mismatch at the interfaces of the middle layer. The letter compares the performance of the lens, so designed, to those based on the RO and TO techniques. We show that the proposed lens design using FT is broadband, has a better than 1 dB higher gain compared to the RO- and TO-based designs over a wider frequency band, and that its scan capability is superior as well.

Broadband flat-base Luneburg lens antenna for wide angle scan

In this paper we present the design of a Luneburg type of lens antenna, with a flat base, designed for wide angle scan. The antenna consists of a 11-layer lens, fed at its base by a 6×6 array of waveguides. The lens is broadband and has a very high aperture efficiency, only 1 dB below that of a reference aperture antenna with a uniform amplitude and phase. Its sidelobe level is good, only -21 dB at boresight and -13 dB for a scan angle of 64°. Its performance is shown to be considerably superior to that of a flat Luneburg lens previously reported in the literature, both in terms of the gain and scan capability, as well as the ease of fabrication.

Enhancement of Angular Resolution of a Flat-Base Luneburg Lens Antenna by Using Correlation Method

We propose a technique for enhancing the angular resolution of a flat-base Luneburg lens antenna to enable it to detect multiple targets with arbitrary scattering cross-sections that are located in angular proximity. The technique involves measuring the electric field distribution on the flat plane of the Luneburg lens antenna, operating in the receive mode, at a specified number of positions, and correlating these distributions with the known distributions derived from the field distributions in the measurement plane generated by single target at different look angles. We show that the proposed approach can achieve enhanced resolution than the basis of the beam-width of the Luneburg lens antenna, and it is capable of distinguishing between two targets with different scattering cross-sections that have an angular separation as small as 1 ◦ for a Luneburg lens with 6.35λ aperture size, for Signal- to-Noise Ratio (SNR) better than 20 dB.

Doa estimation by using luneburg lens antenna with mode extraction and signal processing technique

We propose a framework based on the use of a flat-base Luneburg lens antenna with a waveguide array for Direction-of-Arrival (DOA) estimation, and also present a hybrid approach which combines waveguide mode extraction and signal processing techniques for enhancing the angular resolution of the lens antenna. The hybrid method involves sampling the electric field at specified positions when the lens is operating in the receive mode, and extracting the weights of the possible propagating modes in each waveguide. Following this, we correlate these weights with the known ones that have been derived by either simulated or measured signals from single targets located at different look angles, to make an initial estimate of the angular regions of possible DOAs. We then apply an algorithm based on the Singular Value Decomposition (SVD) of the simulated or measured database to estimate the angles of incidence. Numerical results show that the proposed framework, used in conjunction with the hybrid approach, can achieve an enhanced resolution over the conventional limit base on the 3dB beamwidth of the lens antenna. Furthermore, it is capable of locating targets with different scattering cross-sections and achieving an angular resolution as small as 2°, for a Luneburg lens antenna with an aperture size of 6.35λ and a Signal-to-Noise Ratio (SNR) of 30 dB.

Performance Enhancement of Microwave Sub-Wavelength Imaging and Lens-Type DOA Estimation Systems by Using Signal Processing Techniques

In this work, we show how we can improve the image resolution capabilities of a Phase Conjugating (PC) lens as well as the angular resolution of Luneburg lens antennas by employing signal processing techniques such as the Correlation Method (CM), the Minimum Residual Power Search Method (MRPSM), the sparse reconstruction method, and the Singular-Value-Decomposition (SVD)based basis matrix method. In the first part, we apply these techniques for sub-wavelength imaging in the microwave regime by combining them with the well-known phase conjugation principle. We begin by considering a one-dimensional microwave sub-wavelength imaging problem handled by using three signal processing methods, and then we move on to two- or three-dimensional problems by using the SVD-based basis matrix method. Numerical simulation results show that we can enhance the resolution significantly by using these methods, even if the measurement plane is not located in the very nearfield region of the source. We describe these proposed algorithms in detail and study their abilities to resolve at the sub-wavelength level. Next, we investigate the sparse reconstruction method for a normal Luneburg lens antenna and the Correlation Method and the SVD-based basis matrix method for a flat-base Luneburg lens antenna to estimate the Direction-of-Arrival (DOA). Numerical simulation results show that the signal processing techniques are capable of enhancing the angular resolution of the Luneburg lens antenna enabling the lens to locate multiple targets with different scattering cross-sections and achieving higher angular resolution.

Field Transformation Approach to Designing Lenses

This chapter presents a technique--referred to herein as the Field Transformation method--for designing flat lenses, as well as flat-base Luneburg lens antennas for wide-angle scanning using waveguide array feeds. The performance characteristics of these lenses are compared with those based on Transformation Optics (TO) paradigm, which has been recently developed as a tool for designing lenses of the same type. It is shown, via several examples, that the Field Transformation approach leads to designs which use conventional materials that are conveniently realizable, as opposed to metamaterials or those with anisotropic properties, that are often called for and are difficult to realize in TO-based designs. Furthermore, the Field Transformation approach enables one to control both the phase and amplitude distributions in the aperture of an antenna, which is difficult to do when employing the geometry transformation approach prescribed in the TO paradigm.

Design of flat lenses using Field Manipulation

This paper proposes a technique for designing flat lenses using Field Manipulation (FM), as opposed to Ray Optics (RO) or Transformation Optics (TO). The lens design consists of 10 layers of graded index dielectric in the radial direction and 5 layers in the longitudinal direction. The central layer in the longitudinal direction primarily contributes to a bulk of the phase transformation, while the other four layers, above and below this middle layer on either side, act as matching layers that help reduce the reflections introduced by the impedance mismatch at the interfaces of the middle layer. We show that the proposed lens design is broadband and has a better than 1 dB higher gain compared to the conventional designs.

Efficient and accurate approximation of infinite series summation using asymptotic approximation and fast convergent series

We present an approach for very quick and accurate approximation of infinite series summation arising in electromagnetic problems. This approach is based on using asymptotic expansions of the arguments and the use of fast convergent series to accelerate the convergence of each term. It has been validated by obtaining very accurate solution for propagation constant for shielded microstrip lines using spectral domain approach (SDA). In the spectral domain analysis of shielded microstrip lines, the elements of the Galerkin matrix are summations of infinite series of product of Bessel functions and Green’s function. The infinite summation is accelerated by leading term extraction using asymptotic expansions for the Bessel function and the Green’s function, and the summation of the leading terms is carried out using the fast convergent series.

Full Wave Modeling of Brain Waves as Electromagnetic Waves (Invited Paper)

(Invited Paper) Abstract—This paper describes a novel technique which has the potential to make a significant impact on the mapping of the human brain. This technique has been designed for 3D full-wave electromagnetic simulation of waves at very low frequencies and has been applied to the problem of modeling of brain waves which can be modeled as electromagnetic waves lying in the frequency range of 0.1-100 Hz. The use of this technique to model the brain waves inside the head enables one to solve the problem on a regular PC within 24 hrs, and requires just 1 GB of memory, as opposed to a few years of run time and nearly 200 Terabyte (200,000 GB) needed by the conventional FDTD (Finite Difference Time Domain) methods. The proposed technique is based on scaling the material parameters inside the head and solving the problem at a higher frequency (few tens of MHz) and then obtaining the actual fields at the frequency of interest (0.1-100 Hz) by using the fields computed at the higher frequency. The technique has been validated analytically by using the Mie Series solution for a homogeneous sphere, as well as numerically for a sphere, a finite lossy dielectric slab and the human head using the conventional Finite Difference Time Domain (FDTD) Method. The presented technique is universal and can be used to obtain full-wave solution to low-frequency problems in electromagnetics by using any numerical technique.

Low Frequency Modelling of Layered Media for Logging While DrillingApplications Using FDTD

In a typical Logging While Drilling (LWD) ap- plication, several coils operating in the frequency range of a few KHz to MHz are used as transmitters and receivers to appropriately characterize the earth formation. Electromagnetic modelling of such a low frequency system poses serious computational challenges. In the Method of Moment (MoM) formulation, contribution of vector potential to the total field becomes several orders of magnitude smaller than that of the scalar potential, thus making the resultant matrix highly ill-conditioned. Finite Difference Time Domain (FDTD) method, on the other hand, requires enormous number of time steps to capture the low frequency information. In this paper, we consider a layered-earth model and compute the electromagnetic field due to electric and magnetic dipoles embedded in the formation. To address the low frequency problem in FDTD, we consider the source and the receiver dipoles to be infinitesimally small and aligned with the computational grid, and we modify the update equations accordingly. This approach reduces the time convergence of FDTD by two-to-three orders of magnitude, and also reduces the memory requirements by the same factor. Numerical results for the fields reflected from the layered interfaces and the corresponding voltages induced in the receive coils are presented for multiple scenarios involving shale and sand zones.