Within the framework of an exact analytical solution of Maxwell equations in a space domain, it is shown that optical scheme based on a slab with negative refractive index ($n=-1$) (Veselago lens or Pendry lens) does not possess focusing properties in the usual sense . In fact, the energy in such systems does not go from object to its "image", but from object and its "image" to an intersection point inside a metamaterial layer, or vice versa. A possibility of applying this phenomenon to a creation of entangled states of two atoms is discussed.
A bilayer lens is proposed based on transformation optics. It is shown that Pendry's perfect lens, perfect bilayer lens made of indefinite media, and the concept of compensated media are well unified under the scope of the proposed bilayer lens. Using this concept, we also demonstrate how one is able to achieve perfect imaging beyond passive objects or active sources which are present in front of the lens.
The canonical perfect lens--comprising three slabs, each made of a linear, homogeneous, bianisotropic material with orthorhombic symmetry--is Lorentz covariant.
We carefully examine the negative refractive index slab perfect lens theory by Pendry and point out an inconsistency that can be resolved. As a result, we find negative index slabs do not amplify or enhance evanescent waves and therefore they do not make a perfect lens in the sense that was originally suggested.
In this paper, the optical properties and imaging performance of a non-ideal Pendry's negative index flat lens with a practical value for loss are studied. Analytical calculations of the optical properties of the lens are performed, and those results are used to further study the lens and corresponding imaging system numerically. The plasmon injection scheme for loss compensation in negative index metamaterials is applied to the results from the imaging system, resulting in a perfect reconstruction of a previously unresolved image that demonstrates sub-diffraction-limit resolution.
We reply to the comments on our paper Perfect Drain for the Maxwell fish eye lens (NJP 13 (2011) 023038) made by Fei Sun. We believe that Sun comments have several mistakes in theoretical concepts and simulation results.
The coordinate transformation technique is applied to the design of perfect lenses and superlenses. In particular, anisotropic metamaterials that magnify two-dimensional planar images beyond the diffraction limit are designed by the use of oblate spheroidal coordinates. The oblate spheroidal perfect lens or superlens can naturally be used in reverse for lithography of planar subwavelength patterns.
In this letter, we show how transformation optics makes it possible to design what we call conjugate metamaterials. We show that these materials can also serve as substrates for making a subwavelength-resolution lens. The so-called "perfect lens", which is a lens that could focus all components of light (including propagating and evanescent waves), can be regarded as a limiting case, in which the respective conjugate metamaterials approach the characteristics of left-handed metamaterials, which have a negative refractive index.
The non-magnetic loss material has been proposed (2011 New J. Phys. 13 023038) to mimic a passive perfect drain in the Maxwell's fish eye lens (MFL). In this comment, we argue that this passive medium can only be treated as a perfect absorber which can totally absorb all incident radiation without scattering by it, but it cannot mimic a perfect focusing point. As a result, this passive medium cannot help to achieve a perfect focusing in MFL.
The resolution associated with the so-called perfect lens of thickness $d$ is $-2πd/\ln(|χ+2|/2)$. Here the susceptibility $χ$ is a Hermitian function in $H^2$ of the upper half-plane, i.e., a $H^2$ function satisfying $χ(-ω)=\bar{χ(ω)}$. An additional requirement is that the imaginary part of $χ$ be nonnegative for nonnegative arguments. Given an interval $I$ on the positive half-axis, we compute the distance in $L^\infty(I)$ from a negative constant to this class of functions. This result gives a surprisingly simple and explicit formula for the optimal resolution of the perfect lens on a fin…
Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electric field, emitted by the object surface, towards the image surface producing the same field distribution in both surfaces. In particular, a Dirac delta electric field in the object surface is focused without diffraction limit to the Dirac delta electric field in the image surface. The Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive r…
In this paper we show that a negative index of refraction is not a direct implication of transformation optics with orientation-reversing diffeomorphisms. Rather a negative index appears due to a specific choice of sign freedom. Furthermore, we point out that the transformation designed lens, which relies on the concept of spacetime folding, does not amplify evanescent modes, in contrast to the Pendry-Veselago lens. Instead, evanescent modes at the image point are produced by a duplicated source and thus no imaging of the near field (perfect lensing) takes place.
The transmission of evanescent waves in a gain-compensated perfect lens is discussed. In particular, the impact of gain saturation is included in the analysis, and a method for calculating the fields of such nonlinear systems is developed. Gain compensation clearly improves the resolution; however, a number of nonideal effects arise as a result of gain saturation. The resolution associated with the lens is strongly dependent on the saturation constant of the active medium.
We propose a device with a positive isotropic refractive index that creates an approximate magnified perfect real image of an optically homogeneous three-dimensional region of space within geometrical optics. Its key ingredient is a new refractive index profile that can work as an approximate perfect lens on its own, having a very moderate index range.
Perfect imaging for electromagnetic waves using the Maxwell Fish Eye (MFE) requires a new concept: the perfect drain. From the mathematical point of view, a perfect point drain is just like an ideal point source, except that it drains power from the electromagnetic field instead of generating it. We show here that the perfect drain for the MFE can be seen as a dissipative region the diameter of which tends to zero. The complex permittivity $\varepsilon$ of this region cannot take arbitrary values, however, since it depends on the size of the drain as well as on the frequency. This interpretati…
We experimentally demonstrate a prototype of a cylindrical enlarging lens capable of enhancing and restoring evanescent fields. The enabling phenomenon is the resonant excitation of coupled surface modes in a system of two cylindrical arrays of small resonant particles. As was shown in [J. Appl. Phys. 96, 1293 (2004)], this phenomenon in planar arrays can be used in electromagnetic near-field imaging. Here, we use a similar structure in a cylindrically symmetric configuration, which gives us a possibility to obtain an enlarged near-field image.
Maxwell's fish eye has been known to be a perfect lens within the validity range of ray optics since 1854. Solving Maxwell's equations we show that the fish-eye lens in three dimensions has unlimited resolution for electromagnetic waves.
Both explicit analysis and FEM numerical simulation are used to analyze the field distribution of a line current in the so-called Maxwell's fish eye lens [bounded with a perfectly electrical conductor (PEC) boundary]. We show that such a 2D Maxwell's fish eye lens cannot give perfect imaging due to the fact that high order modes of the object field can hardly reach the image point in Maxwell's fish eye lens. If only zeroth order mode is excited, a good image of a sharp object may be achieved in some cases, however, its spot-size is larger than the spot size of the initial object field. The ima…
The widely-accepted theoretical treatment of the electromagnetic boundary problem of evanescent wave transfer at an interface between a normal medium of n=1 and an ideal negative index medium of n=-1 neglects the non-zero induced surface current and charge densities at the interface and is self-inconsistent. We re-solve the electromagnetic boundary problem by taking into account the non-zero induced surface current and charge densities that have been neglected so far by others. We give the exact induced surface current and charge distributions for this special case and solve the refracted and …
We show that a single-interface between regular and double-negative (DNG) media constitutes the core structure of a perfect lens and, furthermore, substantially outperforms the highly discussed DNG slab-based lens under imperfect conditions, maintaining unbounded resolution. We identify the perfect-lensing mechanism as the excitation of a Brewster (real improper) mode at the interface - a mode with a completely flat-band dispersion at media-matching conditions, perfectly transferring all incident waves including evanescent. A lossless DNG slab retains the single-interface perfect-lensing chara…
It is theoretically known that a pair of phase conjugating surfaces can function as a perfect lens, focusing propagating waves and enhancing evanescent waves. However, the known experimental approaches based on thin sheets of nonlinear materials cannot fully realize the required phase conjugation boundary condition. In this paper we show that the ideal phase conjugating surface is in principle physically realizable and investigate the necessary properties of nonlinear and nonreciprocal particles which can be used to build a perfect lens system. The physical principle of the lens operation is d…
We describe the properties of birefringent left-handed metamaterials and introduce the concept of a birefringent perfect lens. We demonstrate that, in a sharp contrast to the conventional left-handed perfect lens at $ε=μ=-1$, where $ε$ is the dielectric constant and $μ$ is the magnetic permeability, the birefringent left-handed lens can focus either TE or TM polarized waves or both of them, allowing a spatial separation of the TE and TM images. We discuss several applications of the birefringent left-handed lenses such as the beam splitting and near-field diagnostics at the sub-wavelength scal…
A discussion of a question, studied earlier by V.Veselago in 1967 and by J. Pendry in 2000, is given. The question is: can a slab of the material with negative refraction make a perfect lens? Pendry's conclusion was: yes, it can. Our conclusion is: no, in practice it cannot, because of the fluctuations of the refraction coefficient of the slab. Resolution ability of linear isoplanatic optical instruments is discussed.
We demonstrate experimentally that disordered scattering can be used to improve, rather than deteriorate, the focusing resolution of a lens. By using wavefront shaping to compensate for scattering, light was focused to a spot as small as one tenth of the diffraction limit of the lens. We show both experimentally and theoretically that it is the scattering medium, rather than the lens, that determines the width of the focus. Despite the disordered propagation of the light, the profile of the focus was always exactly equal to the theoretical best focus that we derived.
The response of the ``perfect lens'', consisting of a slab of lossless material of thickness $d$ with $ε=μ=-1$ at one frequency $ω_0$ is investigated. It is shown that as time progresses the lens becomes increasingly opaque to any physical TM line dipole source located a distance $d_0<d/2$ from the lens and which has been turned on at time $t=0$. Here a physical source is defined as one which supplies a bounded amount of energy per unit time. In fact the lens cloaks the source so that it is not visible from behind the lens either. For sources which are turned on exponentially slowly there is a…
We extend the ideas of the recently proposed perfect lens [J.B. Pendry, Phys. Rev. Lett. {\bf 85}, 3966 (2000)] to an alternative structure. We show that a slab of a medium with negative refractive index bounded by media of different positive refractive index also amplifies evanescent waves and can act as a near-perfect lens. We examine the role of the surface states in the amplification of the evanescent waves. The image resolution obtained by this asymmetric lens is more robust against the effects of absorption in the lens. In particular, we study the case of a slab of silver, which has nega…
An isotropic three-dimentional perfect lens based on cubic meshes of interconnected transmission lines and bulk loads is proposed. The lens is formed by a slab of a loaded mesh placed in between two similar unloaded meshes. The dispersion equations and the characteristic impedances of the eigenwaves in the meshes are derived analytically, with an emphasis on generality. This allows designing of transmission-line meshes with desired dispersion properties. The required backward-wave mode of operation in the lens is realized with simple inductive and capacitive loads. An analytical expression for…
We use both FEM (finite element method) and FDTD (finite difference time domain method) to simulate the field distribution in Maxwell's fish eye lens with one or more passive drains around the image point. We use the same Maxwell's fish eye lens structure as the one used in recent microwave experiment [arXiv:1007.2530]: Maxwell's fish eye lens bounded by PEC (perfect electric conductor) is inserted between two parallel PEC plates (as a waveguide structure). Our simulation results indicate that if one uses an active coaxial cable as the object and set an array of passive drains around the image…
Cylinder-shaped perfect lens deduced from the coordinate transformation method is proposed. The previously reported perfect slab lens is noticed to be a limiting form of the cylindrical lens when the inner radius approaches infinity with respect to the lens thickness. Connaturality between a cylindrical lens and a slab lens is affirmed by comparing their eigenfield transfer functions. We numerically confirm the subwavelength focusing capability of such a cylindrical lens with consideration of material imperfection. Compared to a slab lens, a cylindrical lens has several advantages, including f…
In this letter, we show that a perfect lens can be employed to make multiple objects appear like only one in the far field, leading to a new concept of illusion optics. Numerical simulations are performed to verify the functionalities for both passive and active objects. The conceptual device can be utilized to enhance the illumination brightness for both incoherent and coherent systems.
Both explicit analysis and FEM numerical simulation are used to analyze the field distribution of a line current in the so-called Maxwell's fish eye lens, which has been claimed recently to be able to achieve perfect imaging. We show that such a Maxwell's fish eye lens cannot give perfect imaging due to the fact that high order modes of the object field can hardly reach the image point in the Maxwell's fish eye. If only zero order mode is excited, a subwavelength image can be achieved, however, its spot-size is larger than the spot size of the source field. The image resolution is determined b…
A perfect lens with unlimited resolution has always posed a challenge to both theoretical and experimental physicists. Recent developments in optical meta-materials promise an attractive approach towards perfect lenses using negative refraction to overcome the diffraction limit, improving resolution. However, those artificially engineered meta-materials usually company by high losses from metals and are extremely difficult to fabricate. An alternative proposal using negative refraction by four-wave mixing has attracted much interests recently, though most of existing experiments still require …
An analytical closed-form formula for the design of freeform lenses free of spherical aberration is presented. Given the equation of the freeform input surface, the formula gives the equation of the second surface in order to correct the spherical aberration. The derivation is based on the formal application of the variational Fermat principle under the standard geometrical optics approximation.
The perfect vortex is a new class of optical vortex beam having ring radius independent of its topological charge (order). One of the simplest techniques to generate such beams is the Fourier transformation of the Bessel-Gauss beam. The variation in ring radius of such vortices require Fourier lenses of different focal lengths and or complicated imaging setup. Here we report a novel experimental scheme to generate perfect vortex of any ring radius using a convex lens and an axicon. As a proof of principle, using a lens of focal length f=200mm, we have varied the radius of the vortex beam acros…
Wide field-of-view (FOV) optics are widely used in various imaging, display, and sensing applications. While conventional wide FOV optics rely on cascading multiple elements to suppress coma and other aberrations, it has recently been demonstrated that diffraction-limited, near-180 degree FOV operation can be achieved with a single-piece flat fisheye lens designed via iterative numerical optimization [Nano Lett. 20, 7429(2020)]. Here we derive an analytical solution to enable computationally efficient design of flat wide FOV lenses based on metasurfaces or diffractive optical elements (DOEs). …
To overcome the resolution limit of conventional optics, near field imaging techniques using a negative index flat lens (NIFL) have been previously developed that amplify the evanescent components of the incident field. Here, a technique is developed and demonstrated to compensate for losses in a non-ideal NIFL by determining the transfer function of the lens and subsequently applying the inverse to the unresolved raw image. The result is a compensated image with sub-diffraction-limited resolution.
Both explicit analysis and FEM numerical simulation are used to analyze the field distribution of a line current in the so-called Maxwell's fish eye lens [bounded with a perfectly electrical conductor (PEC) boundary]. We show that such a 2D Maxwell's fish eye lens cannot give perfect imaging due to the fact that high order modes of the object field can hardly reach the image point in Maxwell's fish eye lens. If only zeroth order mode is excited, a subwavelength image of a sharp object may be achieved in some cases, however, its spot-size is larger than the spot size of the initial object field…
We design an all-dielectric Lüneburg lens as an adiabatic space-variant lattice explicitly accounting for finite film thickness. We describe an all-analytical approach to compensate for the finite height of subwavelength dielectric structures in the pass-band regime. This method calculates the effective refractive index of the infinite-height lattice from effective medium theory, then embeds a medium of the same effective index into a slab waveguide of finite height and uses the waveguide dispersion diagram to calculate a new effective index. The results are compared with the conventional nume…
We reconsider the refraction of evanescent waves at an interface between air and negative index medium under the assumption that negative index medium is necessarily dispersive and lossy. We show that all evanescent waves in air will be refracted into decaying propagating waves inside a negative index medium, with different spatial frequency components having different propagation directions which are separated both in time and space; hence no refocus of these evanescent waves is possible. Accordingly, all information encoded by evanescent waves will be lost in the image making sub-diffraction…
We propose a new method for integrating metasurfaces in optical design using semi-analytical modelling of dielectric nanostructures. The latter computes the output phase of an electric field incident on the metasurface, allowing their use with ray-tracing software. This tool provides a method to use metasurfaces in optical systems while using built-in optimization processes to avoid time-consuming computation. To demonstrate the applicability and versatility of our method, we present variations of a triplet composed of refractive elements and a metasurface. For each of the systems, similar opt…
Whether or not perfect imaging is obtained in the mirrored version of Maxwell's fisheye lens is debated in the comment/reply sequence [Blaikie-2010njp, Leonhardt-2010njp] discussing Leonhardt's original paper [Leonhardt-2009njp]. Here we show that causal solutions can be obtained without the need for an "active localized drain", contrary to the claims in [Leonhardt-2010njp].
It has been shown that a slab of materials with refractive index = -1 behaves like a perfect lens focussing all light to an exact electromagnetic copy of an object. The original lens is limited to producing images the same size as the object, but here we generalise the concept so that images can be magnified. For two dimensional systems, over distances much shorter than the free space wavelength, we apply conformal transformations to the original parallel sided slab generating a variety of new lenses. Although the new lenses are not `perfect' they are able to magnify two dimensional objects. T…
It has been shown that negative refraction makes a perfect lens. However, with little loss, the imaging functionality will be strongly compromised. Later on, it was proved that positive refraction from Maxwell's fish-eye lens can also makes a perfect lens. However, strong debating happens on the introduced drain problem at the imaging position. In this work, we for the first time find that a solid immersion Maxwell's fish-eye lens could be used for super-resolution imaging. We find that it is due to the perfect focusing and total reflection at the outer interface, such that a super-resolution …
We present quasi-analytical solutions (QANS) of hybrid platform (HP) comprising metallic grating (MG) and stacked-dielectric layers for terahertz (THz) radiation. The QANS are validated by finite difference time domain simulation. It is found that the Wood anomalies induce the high-order spoof surface plasmon resonances in the HP. The QANS are applied to optimize new perfect absorber for THz sensing of large-area thin film with ultrahigh figure of merit reaching fifth order of magnitude for the film thickness 0.0001p (p: MG period). The first-order Wood's anomaly of the insulator layer and the…
In this study, the design of a directional cloaking based on the Luneburg lens system is proposed and its operating principle is experimentally verified. The cloaking concept is analytically investigated via geometrical optics and numerically realized with the help of the finite-difference time-domain method. In order to benefit from its unique focusing and/or collimating characteristics of light, the Luneburg lens is used. We show that by the proper combination of Luneburg lenses in an array form, incident light bypasses the region between junctions of the lenses, i.e., the "dark zone." Hence…
