Dispersive full-wave finite-difference time-domain analysis of the bipolar cylindrical cloak based on the effective medium approach

Abstract

A dispersive full-wave finite-difference time-domain model is used to study the performance of bipolar cylindrical invisibility cloaking devices. We have considered two different cloaking structures generated by the mapping of the σ axis and the mapping of the τ axis of bipolar coordinates. The permittivity and permeability tensors for the cloaking devices are obtained from an effective medium approach in general relativity. The σ-axis mapped bipolar cylindrical cloak is found to be imperfect, and the cloaking performance is found to depend on the polarization of the incident waves, the direction of propagation of the waves, and the loss tangents of the metamaterial. Only the case of TM waves for the specific propagation direction shows good cloaking performance. On the other hand, the τ-mapped cloaking device shows good cloaking performance for all polarizations and directions of propagation. However, this structure has a singular boundary at the inner radius. Realistic cloaking materials with loss still show a cloak that is working, but attenuated backscattering waves exist.

FDTD Study of Half Cloak in Bipolar Cylindrical Shape With Compressed Geometry and Complementary Media

“…Before we proceed to the design of exterior cloak, we first need to obtain the constitutive parameters of a bipolar cylindrical cloak from the effective medium approach in general relativity [11,13]. We use primed coordinates for the empty curved space-time.…”

“…As a result, the transformation map is defined by (1) Once the transformation is defined, the constitutive parameters can be obtained straightforwardly [13]. In this work, the region σ 1 < σ < π which would have been filled with perfect electric conductor (PEC) in the ordinary bipolar cylindrical half cloak shown in Fig.…”

“…INTRODUCTION RECENTLY, invisibility cloaking via the control of electromagnetic fields, using meta-materials, is becoming of substantial interest . Study of the invisibility cloaking was first inspired by the idea of transformation optics [1][2][3][4][5] and then by the effective medium approach of general relativity [10][11][12][13][24][25][26][27][28][29][30]. In these transformation based cloaking, the interior of the region to hide the object is essentially compressed into a point, a line or to a plane.…”

“…However, previous proposals for cloaks with compressed geometries into a point contain extreme material parameters at the cloak's interior boundaries [8,23]. And that's not their only issue: while the cloak which is obtained by the transformation to a plane or line-segment such as the elliptical cylindrical cloak does not show singular material parameters, the cloaking performances, especially the transverse electric (TE) illumination is not so good because the scattering coefficients do not vanish completely [8,13,22]. On the other hand, there is an alternative approach based on complementary media [15][16][17], which cancels the region containing the object and can also be applied to exterior cloaking.…”

“…We first obtain the permittivity and permeability tensors for cloaking devices by using the effective medium approach [10][11][12][13][14][25][26][27][28][29][30][31]. In this approach, one can transform the space-time metric into the constitute parameters and from which one can find the specific conditions for the invisibility cloaking [11].…”