We introduce here a novel type of cloaking, based on a circular concentric meta-waguide struc- ture, where the metawaveguides are bent waveguides with porous metasurface walls. In contrast to the cloak implementation reported in Schurig et al. (/two.pnum/zero.pnum/zero.pnum/six.pnum), which only approximates the ideally perfect transformation-optics cloak because of prohibitive fabrication complexity, this cloak is designed ab ini- tio for optimal cloaking, and o/uniFB00ers therefore largely superior performance. Its combined simplicity and performance arguably makes it the most practical existing cloak reported so far. /one.pnum Introduction Cloaking is one of the most popular applications of metamaterials. Practical cloaking techniques may be classi/uniFB01ed in four main categories: /one.pnum) transformation optics Pendry et al. (/two.pnum/zero.pnum/zero.pnum/six.pnum), /two.pnum) plasmonic scattering can- cellation Alù and Engheta (/two.pnum/zero.pnum/zero.pnum/five.pnum), /three.pnum) transmission-line matching Alitalo and Tretyakov (/two.pnum/zero.pnum/zero.pnum/nine.pnum), and /four.pnum) redi- rection cloaking Dehmollaian and Caloz (/two.pnum/zero.pnum/two.pnum/zero.pnum). Unfortunately, each of these techniques su/uniFB00ers from some major drawback. Transformation optics cloaking requires a complex nonuniform and bianisotropic medium Schurig et al. (/two.pnum/zero.pnum/zero.pnum/six.pnum), scattering cancellation cloaking is restricted to electrically small objects Fleury et al. (/two.pnum/zero.pnum/one.pnum/five.pnum), transmission-line matching cloaking implies penetration though the object to cloak Alitalo and Tretyakov (/two.pnum/zero.pnum/zero.pnum/nine.pnum), and redirection cloaking is restricted to a speci/uniFB01c incidence angle Dehmollaian and Caloz (/two.pnum/zero.pnum/two.pnum/zero.pnum). The recent spectacular developments in metasurface technology Achouri and Caloz (/two.pnum/zero.pnum/two.pnum/one.pnum) may o/uniFB00er new avenues for cloaking that would be immune to the issues mentioned above. In this context, we present here a novel form of cloak, formed by a set of circular concentric porous metasurface cavities, or a concentric metawaveguide cloaking , which operates in a fundamentally di/uniFB00erent fashion than the approximation of the transformation optics cloak presented in Schurig et al. (/two.pnum/zero.pnum/zero.pnum/six.pnum). /two.pnum Operation Principle Transformation optics provides perfect cloaking Pendry et al. (/two.pnum/zero.pnum/zero.pnum/six.pnum). Unfortunately, it involves a complex nonuniform bianisotropic medium whose fabrication is prohibitively challenging. This issue constrained Schurig et al. to sacri/uniFB01ce some of the parameters of the perfect cloak in their proof-of-concept experimental prototype Schurig et al. (/two.pnum/zero.pnum/zero.pnum/six.pnum), and the resulting imperfect cloak displayed a forward scattering shadow even in the ideal case of perfect homogeneity Schurig et al. (/two.pnum/zero.pnum/zero.pnum/six.pnum). Our cloak has the same concentric topology as the imperfect cloak built in Schurig et al. (/two.pnum/zero.pnum/zero.pnum/six.pnum): it is also composed of thin concentric ‘metasurfaces’/one.pnum. However, its design and operation is fundamentally di/uniFB00erent. It is indeed designed ab initio for (quasi-)perfect cloaking, and is therefore immune from any approximation imperfection. As a result, as will be shown at the conference, it has di/uniFB00erent meta-parameters than those of the prototypes in Schurig et al. (/two.pnum/zero.pnum/zero.pnum/six.pnum), and exhibits largely superior performance. /one.pnumAt the time of the publication of Schurig et al. (/two.pnum/zero.pnum/zero.pnum/six.pnum), which is already /one.pnum/five.pnum years ago, metasurfaces were in their infancy, and the authors of that paper did not even refer to their concentric structures as metasurfaces. 1 In fact, our cloak, instead of gradually de/uniFB02ecting waves according to an equivalent curvature of spacetime achieved by nonuniform bianisotropy, guides the illuminating wave around the object to cloak via curved waveguides made of penetrable metasurface walls, which we refer here to as porous or leaky metawaveg- uides , as illustrated in Fig. /one.pnum. The metasurfaces are separated by a quarter of the wavelength, so as to form a kind of two-dimensional Fabry-Perot resonator with perfect re/uniFB02ection cancellation, and the wave is perfectly routed to the output of the system thanks to an optimal interplay between local re/uniFB02ection and transmission on each metasurface. Note that the structure is circularly symmetric, i.e., composed of uniform metasurfaces, and therefore omnidirectional, as typical cloaks. Figure /one.pnum: Waveguide routing operation (ray picture) of the proposed concentric metawaveguide cloak. /three.pnum Design We design the concentric metawaveguide cloak by optimizing the susceptibilities of its metasurfaces for minimal scattering. We assume that the metasurfaces have only transverse electric and magnetic surface polarization densities, ~Pkand~Mk, in which case the harmonic ( ej!t) Generalized Sheet Transition Condi- tions (GSTCs) reduce to Achouri and Caloz (/two.pnum/zero.pnum/two.pnum/one.pnum) ^n~E=j! 0~Mk;^n~H=j!~Pk; (/one.pnum) where ^nis the unit vector normal to the metasurface, ~Eand~Hare the di/uniFB00erence of the /uniFB01elds at both sides of the metasurface, and ~Mkand~Pkwill be expressed in terms of the average /uniFB01elds at both sides of the metasurface, ~Ek;avand~Hk;av, and of the bianisotropic surface susceptibility tensors mmk, mek, emk, eek?. Let us assume a two-dimensional cloaking structure (perpendicular to the Cartesian coordinate z), composed of Nmetasurfaces and operating in the TM zpolarization regime. We shall synthesize the metasurface, i.e., determine its surface susceptibilities, by iterative analysis optimization. To analyse the cloaking structure, i.e., to compute the /uniFB01elds that it scatters for given susceptibilities, we proceed as follows. First, we expand the tangential electromagnetic /uniFB01elds involved in Eqs. (/one.pnum), namely EzandH , within each cloak layer (or metawaveguide) in generalized Fourier series, namely in terms of cylindrical Bessel basis functions and sinusoidal basis functions for the radial and azimuthal dependencies, respectively. Assuming Mmetasurfaces and 2Nunknown Fourier coe/uniFB03cients, these expansions include 2MN unknown coe/uniFB03cients for the two tangential /uniFB01elds. Then, we insert these expressions for the /uniFB01elds into (/one.pnum) and use the orthogonality of the sinusoidal basis functions. This results into 2Nscalar equations at the interface of each metasurface, and the inversion of the related matrix system provides the sought-after /uniFB01eld solutions. This is of course an exact analysis technique, which accounts for the exact electromagnetic scattering in the structure. We next perform the synthesis by iteratively applying the analysis tool described in the previous paragraph for di/uniFB00erent susceptibility parameters until the scattering cross section falls below a determined threshold. The lossless and gainless susceptibilities found by this synthesis procedure are plotted in Fig. /two.pnum. /four.pnum Results and Discussion Figure /three.pnum presents the main results. Figure /three.pnum(a) plots the real part of the total electric /uniFB01eld, which reveals an essentially perfect cloaking performance. The scattered power was computed to be as low as 1:7105! /two.pnum Figure /two.pnum: Optimized susceptibilities versus radial distance from the innermost metasurface to the outer- most metasurface. (a) zz ee, (b) mm, and (c) z em= z meof the /five.pnum concentric metasurfaces. Figure /three.pnum: (a) The real part of the total electric /uniFB01eld and (b) the Poynting vector inside the metawaveguide cloak. Figure /three.pnum(b) plots the Poynting vector /uniFB01eld, which con/uniFB01rms the waveguiding mechanism indicated by the simpli/uniFB01ed ray picture of Fig. /one.pnum. We acknowledge the contribution of the Innovation for Defense Excellence and Security (IDEaS) Program of the Department of National Defense related to this project.