This paper presents a general approach to design surface wave cloaks which circumvent the problems associated with superluminal phase velocities and anisotropy. The cloaks proposed in this paper are very thin, just a fraction of a wavelength in thickness, yet can cloak electrically large objects. This solution combines curved, rotationally symmetric geometries with isotropic radially dependent refractive index profiles to achieve perfect cloaking. Three refractive index profiles are obtained: an anti-fish eye, a conical cloak and a cosine cloak, and each is simulated using a fullwave solver. The performance is analysed using dielectric filled waveguide geometries, and the curvature of the surface is shown to be rendered invisible, hiding any object positioned underneath. For the cosine cloak, a transformation of the required dielectric slab permittivity was performed for surface waves propagation, demonstrating the practical applicability of this technique.

In the last decade, a technique termed transformation optics has been developed for the design of novel electromagnetic devices. This method defines the exact modification of magnetic and dielectric constants required, so that the electromagnetic behaviour remains invariant after a transformation to a new coordinate system. Despite the apparently infinite possibilities that this mathematical tool introduces, one restriction has repeatedly recurred since its conception: limited frequency bands of operation. Here we circumvent this problem with the proposal of a full dielectric implementation of a transformed planar hyperbolic lens which retains the same focusing properties of an original curved lens. The redesigned lens demonstrates operation with high directivity and low side lobe levels for an ultra-wide band of frequencies, spanning over three octaves. The methodology proposed in this paper can be applied to revolutionise the design of many electromagnetic devices overcoming bandwidth limitations.

Transformation Optics asks Maxwell's equations what kind of electromagnetic medium recreate some smooth deformation of space. The guiding principle is Einstein's principle of covariance: that any physical theory must take the same form in any coordinate system. This requirement fixes very precisely the required electromagnetic medium. The impact of this insight cannot be overestimated. Many practitioners were used to thinking that only a few analytic solutions to Maxwell's equations existed, such as the monochromatic plane wave in a homogeneous, isotropic medium. At a stroke, Transformation Optics increases that landscape from 'few' to 'infinity', and to each of the infinitude of analytic solutions dreamt up by the researcher, corresponds an electromagnetic medium capable of reproducing that solution precisely. The most striking example is the electromagnetic cloak, thought to be an unreachable dream of science fiction writers, but realised in the laboratory a few months after the papers proposing the possibility were published. But the practical challenges are considerable, requiring meta-media that are at once electrically and magnetically inhomogeneous and anisotropic. How far have we come since the first demonstrations over a decade ago? And what does the future hold? If the wizardry of perfect macroscopic optical invisibility still eludes us in practice, then what compromises still enable us to create interesting, useful, devices? While 3D cloaking remains a significant technical challenge, much progress has been made in 2dimensions. Carpet cloaking, wherein an object is hidden under a surface that appears optically flat, relaxes the constraints of extreme electromagnetic parameters. Surface wave cloaking guides subwavelength surface waves, making uneven surfaces appear flat. Two dimensions is also the setting in which conformal and complex coordinate transformations are realisable, and the possibilities in this restricted domain do not appear to have been exhausted yet. Beyond cloaking, the enhanced electromagnetic landscape provided by Transformation Optics has shown how fully analytic solutions can be found to a number of physical scenarios such as plasmonic systems used in electron energy loss spectroscopy (EELS) and cathodoluminescence (CL). Are there further fields to be enriched? A new twist to Transformation Optics was the extension to the space-time domain. By applying transformations to space-time, rather than just space, it was shown that events rather than objects could be hidden from view; Transformation Optics had provided a means of effectively redacting events from history. The hype quickly settled into serious nonlinear optical experiments that demonstrated the soundness of the idea, and it is now possible to consider the practical implications, particularly in optical signal processing, of having an 'interrupt-without-interrupt' facility that the socalled temporal cloak provides. Inevitable issues of dispersion in actual systems have only begun to be addressed. Now that time is included in ...

In this article, a number of guiding structures are proposed which take advantage of higher symmetries to vastly reduce the dispersion. These higher symmetries are obtained by executing additional geometrical operations to introduce more than one period into the unit cell of a periodic structure. The specific symmetry operations employed here are a combination of p-fold twist and polar glide. Our dispersion analysis shows that a mode in a structure possessing higher symmetries is less dispersive than in a conventional structure. It is also demonstrated that, similar to the previously studied Cartesian glide-symmetric structures, polar glide-symmetric structures also exhibit a frequency independent response. Promising applications of these structures are leaky-wave antennas which utilize the low frequency dependence.

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