Electromagnetic Metamaterials and their
Approximations:
Practical and Theoretical Aspects
CSIC Building (#406),
Seminar Room 4122.
Directions: home.cscamm.umd.edu/directions

Alternative
Derivation of Electromagnetic Cloaks and
Concentrators
Professor
Arthur Yaghjian
Air Force Research Laboratory

Abstract:
To complement the 'transformation optics' approach
of Pendry, Schurig, and Smith and the ‘general
relativity’ approach of Leonhardt and Philbin, we
formulate electromagnetic cloaking as a
boundaryvalue problem involving a single Maxwell
firstorder differential equation. The boundary
value formulation, which does not involve
eigenfunctions or separation of variables, is based
on the requirements that the cloaking occurs for all
possible incident fields and that the cloaks with
frequency omega > 0 have continuous tangential
components of E and H fields across their outer
surfaces, and zero normal components of D and B
fields at their inner material surfaces.
The tangential field boundary conditions at the
outer surface of the cloak ensure zero scattered
fields, and the normalfield boundary conditions at
the inner surface of the cloak are compatible with
zero total fields inside the interior cavity of the
cloak. For spherical cloaks, unlike cylindrical
cloaks, these boundary conditions lead to all the
tangential components of the E and H fields being
continuously zero across their inner
surfaces?cylindrical cloaks having delta functions
in polarization densities at their inner surfaces (a
discovery first made by Greenleaf, Kurylev, Lassas,
and Uhlmann). For bodies with no interior freespace
cavities, the formulation is used to derive
nonscattering spherical and cylindrical
'concentrators' that magnify the incident fields
near their centers. For static fields (omega = 0),
the boundaryvalue formulation is appropriately
modified to obtain a relative permeability dyadic
that will cloak magnetostatic fields.
Causalityenergy conditions imply that, unlike
magnetostatic cloaking, electrostatic cloaking as
well as lowfrequency cloaking for omega > 0 is not
realizable.
It is also confirmed that perfect cloaking over any
nonzero bandwidth violates causalityenergy
conditions and thus the cloaking of realistic time
dependent fields must be approximate. 
