When a planar dielectric medium has a permittivity profile that is an analytic function in the upper or lower half of the complex position plane x = x′ + ix″ then the real and imaginary parts of its permittivity are related by the spatial Kramers-Kronig relations. We find that such a medium will not reflect radiation incident from one side, whatever the angle of incidence. Using the spatial Kramers-Kronig relations, one can derive a real part of a permittivity profile from some given imaginary part (or vice versa) such that the reflection is guaranteed to be zero. This result is valid for both scalar and vector wave theories and may have relevance for designing materials that efficiently absorb radiation or for the creation of a new type of anti-reflection surface.A wave propagating through an inhomogeneous medium is usually partially reflected, which is often undesirable from a practical point of view. Although the reflection from a sharp interface can be suppressed by applying an anti-reflection coating 1 , less is understood about what is required in order for a generic inhomogeneous medium not to reflect any radiation. There are some well-known examples of non-reflecting material profiles, such as the hyperbolic secant profile described by Landau and Lifshitz 2 , which has been discussed by Lekner 3 (see ref. 4 for an experimental realization). More recently, the design technique of transformation optics 5,6 has made significant strides forward, giving us a strategy for finding inhomogeneous, anisotropic materials (transformation media) that reflect no radiation, whatever the incident field 5,7,8 . In the same vein, perfectly matched layers 9 are a family of anisotropic lossy media that are often used in computer simulations to mimic an infinitely extended system and are closely connected to transformation media, absorbing a wave without producing any reflection [10][11][12] . The last few years have seen increasing interest in the property of parity-time (PT) symmetry in optics [13][14][15] , partly because media with this property can suppress reflection 16,17 . For complex permittivities this requires regions of gain (Im[ϵ(x)] < 0) as well as loss (Im[ϵ(x)] > 0) and has been connected to the use of complex coordinates in transformation optics 18 . Realizing any of these non-reflecting materials is challenging, but suitably structured metamaterials 19 are promising, because a wide range of material parameters can be achieved through the use of specially designed sub-wavelength elements. In particular, recent work on 'dispersion engineering' 20 has seen simultaneous control of the real and imaginary parts of the permittivity and permeability, which is necessary to realize PT-symmetric media, as well as the materials proposed in this work.Here, we find a new and very general relation between the real and imaginary parts of a (locally isotropic) planar permittivity profile ϵ(x) that guarantees zero reflection. The result makes use of the properties of ϵ(x) at complex values of the spatial coordinate x = x′ + ...

We investigate the analytic continuation of wave equations into the complex position plane. For the particular case of electromagnetic waves we provide a physical meaning for such an analytic continuation in terms of a family of closely related inhomogeneous media. For bounded permittivity profiles we find the phenomenon of reflection can be related to branch cuts in the wave that originate from poles of (z) at complex positions. Demanding that these branch cuts disappear, we derive a large family of inhomogeneous media that are reflectionless for a single angle of incidence. Extending this property to all angles of incidence leads us to a generalized form of the Pöschl Teller potentials. We conclude by analyzing our findings within the phase integral (WKB) method.

Nonlinear optical devices and their implementation into modern nanophotonic architectures are constrained by their usually moderate nonlinear response. Recently, epsilon-near-zero (ENZ) materials have been found to have a strong optical nonlinearity, which can be enhanced through the use of cavities or nano-structuring. Here, we study the pump dependent properties of the plasmon resonance in the ENZ region in a thin layer of indium tin oxide (ITO). Exciting this mode using the Kretschmann-Raether configuration, we study reflection switching properties of a 60 nm layer close to the resonant plasmon frequency. We demonstrate a thermal switching mechanism, which results in a shift in the plasmon resonance frequency of 20 THz for a TM pump intensity of 70 GW cm−2. For degenerate pump and probe frequencies, we highlight an additional two-beam coupling contribution, not previously isolated in ENZ nonlinear optics studies, which leads to an overall pump induced change in reflection from 1% to 45%.

When light propagates through opaque material, the spatial information it holds becomes scrambled, but not necessarily lost. Two classes of techniques have emerged to recover this information: methods relying on optical memory effects, and transmission matrix (TM) approaches. Here we develop a general framework describing the nature of memory effects in structures of arbitrary geometry. We show how this framework, when combined with wavefront shaping driven by feedback from a guide-star, enables estimation of the TM of any such system. This highlights that guide-star assisted imaging is possible regardless of the type of memory effect a scatterer exhibits. We apply this concept to multimode fibres (MMFs) and identify a ‘quasi-radial’ memory effect. This allows the TM of an MMF to be approximated from only one end - an important step for micro-endoscopy. Our work broadens the applications of memory effects to a range of novel imaging and optical communication scenarios.

Reciprocity is fundamental to light transport and is a concept that holds also in rather complex systems. Yet, reciprocity can be switched off even in linear, isotropic and passive media by setting the material structure into motion. In highly dispersive multilayers this leads to a fairly large forwardbackward asymmetry in the pulse transmission. Moreover, in multilevel systems, this transport phenomenon can be all-optically enhanced. For atomic multilayer structures made of three-level cold 87 Rb atoms, for instance, forward-backward transmission contrast around 95% can be obtained already at atomic speeds in the meter per second range. The scheme we illustrate may open up avenues for optical isolation that were not previously accessible.PACS numbers: 42.50. Wk, 42.70.Qs, 42.50.Gy, 37.10.Vz Much attention has been devoted to the development of advanced materials and composite systems to achieve optical functionalities not readily available in natural media. Such optical metamaterials can be engineered to stretch the rules that govern light propagation and lightmatter interaction, potentially seeding a new paradigm in all-optical, optoelectronic and optomechanical devices. Photonic crystals and negatively refracting media are prominent instances of man-made systems the optical properties of which can be tailored to a great extent. Nevertheless, some tasks are more difficult than others. Already in the familiar process of linear reflection and transmission of light [1] it is in general hard to achieve non-reciprocity. In particular, multilayer photonic structures made with linear isotropic media with dissipation and/or gain may exhibit reflection non-reciprocity, i.e., an unbalance between the forward and backward reflectivities. There are even cases in which one of them can be made negligible and the other one can increase without limit with the sample thickness [2]; this occurs in the so called P T -symmetric media which exhibit a variety of peculiar optical properties [3,4]. Yet, it is not possible to achieve a non-reciprocal transmissivity in such linear and passive systems. Transmission reciprocity is almost ubiquitous in optics [1,5].Non-reciprocal transmission is however rather desirable for information processing and crucial to the development of optical-based functional components in photonics. In much the same way in which electrical nonreciprocity has been realized through diodes, devising an optical diode is challenging, even in theory. Ideally, an optical diode would allow total light transmission over a bundle of wavelengths in one direction, providing total isolation in the reverse direction. Previous * s.horsley@exeter.ac.uk work on non-reciprocal transmission has been based on either magneto-optical effects [6][7][8] or non linear processes [9,10]. Other mechanisms have also been explored [11][12][13] and realized experimentally [14], including more involved diode designs based on two-dimensional square-lattice photonic crystals [15] or non-symmetric photonic crystal gratings exhibiting anomal...