Frequency dependence and passive drains in fish-eye lenses

Quevedo–Teruel, Oscar; Mitchell‐Thomas, R. C.; Hao, Yang

doi:10.1103/physreva.86.053817

Cited by 18 publications

(19 citation statements)

References 31 publications

(63 reference statements)

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“…The first important conceptual point we make concerns the sources and detectors. In the context of the controversy on perfect imaging, finding a simple, practical model for detectors has been a long-outstanding problem [9,15,17,[27][28][29][30]. Usually a source was assumed to be a predetermined current that generates electromagnetic waves, a detector was modelled as a drain.…”

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confidence: 99%

A simple model explaining super-resolution in absolute optical instruments

et al. 2015

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We develop a simple, one-dimensional model for super-resolution in absolute optical instruments that is able to describe the interplay between sources and detectors. Our model explains the subwavelength sensitivity of a point detector to a point source reported in previous computer simulations and experiments (Miñano 2011 New J. Phys.13 125009; Miñano 2014 New J. Phys.16 033015).Perfect imaging with positive refraction [1] has been subject to considerable controversy [2-17] that has given important insight into the matter. Much of the controversy has centred on the role of detection in perfect imaging-the perfect transfer of the electromagnetic field from object to image is only possible if the image is detected. Another important point was noticed in a computer simulation [18] and a subsequent experiment [19] by Miñano et al: at specific resonance frequencies of the instrument a point detector is sensitive to displacements of a point source with an accuracy that is significantly better than the diffraction limit. No physical explanation for this feature has been found yet. Here we develop a simple model that captures both issues, the role of the detection and the role of the resonance, which allows us to deduce both physical explanations and analytic expressions for the sensitivity.Perfect-imaging devices with positive refraction are absolute optical instruments [20] with closed loops of rays [21,22]. The archetype of such instruments is Maxwell's fish eye [23] where light goes in circles and where all light circles originating from any given point intersect at a corresponding image point. Luneburg [24] discovered a geometrical picture that explains the properties of Maxwell's fish eye: the refractive-index profile of Maxwell's device appears to light as the surface of a sphere in two-dimensional (2D) and hypersphere in threedimensional (3D) space; light propagates in the medium of the fish eye as if it were confined to spherical surfaces. The geodesics on the sphere appear as the circles of light (by stereographic projection), object and image correspond to antipodal points on the sphere where geodesics intersect. Let us consider the simplest case of perfect imaging, the one-dimensional (1D) sphere: the circle (figure 1). Imagine that light is confined to a circle, say a fibre loop or ring resonator. Here light can go in only two directions, to the right or to the left. An 'image' is formed when the two rays meeting have the same phase, which happens when both are antipodal. Light is coupled in and out of the circle by two 1D channels that represent the source and the detector. These 1D channels are idealizations of the cables used for injecting and extracting radiation in the simulation [18] and experiment [19]. Clearly, this 1D system represents a rather primitive model, but it is going to reproduce the findings of the experiment [19], the model is simple, but not too simple.We are going to show how a point detecter is able to sense minute displacements of a point source. Note that this is not imaging in the ...

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confidence: 99%

A simple model explaining super-resolution in absolute optical instruments

et al. 2015

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“…The pole at zero frequency, evident in the longitudinal part of the Green function (4), does not contribute, because we have assumed condition (7). Equation (9) means that the electric field reduces to a sum over the eigenmodes of the cavity after the current has been switched off ( Δ > + t t t 2 0 0 ), with each eigenmode weighted by the corresponding Fourier component of the source…”

Section: Electromagnetic Radiation From a Source In A Cavitymentioning

confidence: 99%

“…The use of an active current element to concentrate the electromagnetic field was recently the subject of debate in the context of imaging [4][5][6][7][8][9][10], where it was claimed that the sub-wavelength scale of the field around an active drain could be used to resolve small features of a distant object within the Maxwell fish-eye lens. Although it now seems unlikely that a useful imaging device can be made in this way [9], the device proposed in [4] has other interesting properties. In particular, Tyc and Danner [12] have shown that absolute optical instruments 4 tend to have a nearly uniform spacing of eigenfrequencies.…”

Section: Introductionmentioning

confidence: 99%

Active absorption of electromagnetic pulses in a cavity

et al. 2015

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We show that a pulse of electromagnetic radiation launched into a cavity can be completely absorbed into an infinitesimal region of space, provided one has a high degree of control over the current flowing through this region. We work out explicit examples of this effect in a cubic cavity and a cylindrical one, and experimentally demonstrate the effect in the microwave regime. OPEN ACCESS RECEIVED

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“…The subwavelength focusing is due to the drain in MFEL/MFEM but not the medium itself [4,5,10]; if there are some additional passive drains around the imaging point, they will greatly influence the imaging effect (e.g., we may also get a focused spot at other drains that are not located at the image point) and an MFEM cannot give a super-resolution imaging if there are some other drains around the imaging points [9,11,17].…”

Section: Introductionmentioning

confidence: 99%

“…Leonhardt claimed that Maxwell's fish eye lens (MFEL), which can provide ideal imaging from the perspective of geometric optics, can also provide perfect imaging from the perspective of wave optics (i.e., the resolution can be infinite theoretically). He also proposed that a 2D Maxwell's fish eye mirror (i.e., a Maxwell's fish eye lens enclosed by a mirror) could theoretically provide perfect imaging, which has been an intense subject of controversy [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Blaikie commented that the super-resolution is due to the active drain at the image point but not the property of the lens [4], and hence many other types of imaging system can also achieve such subwavelength focusing with the help of a drain, e.g., we can obtain a sub-wavelength focused spot at the image point if there is only one drain exactly located at the image point in any absolute image system (such as a mirror-enclosed elliptical cavity filled with air when a line current is at one focus and a drain is exactly located at the other focus [5]).…”

Section: Introductionmentioning

confidence: 99%

Can Maxwell's Fish Eye Lens Really Give Perfect Imaging? Part Iii. A Careful Reconsideration of the ``Evidence for Subwavelength Imaging With Positive Refraction''

He¹,

Sun²,

Guo³

et al. 2015

PIER

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Abstract-Many scientists do not believe that Maxwell's fish eye mirror (MFEM) can provide perfect imaging even if there is a drain array around the imaging points. However, one microwave experiment found a case where a 0.2λ resolution could be achieved in an MFEM experiment [1]. In this paper, we show that the MFEM cannot resolve two imaging points at such a subwavelength resolution in most cases even in the presence of a drain array, and an extraordinary case of subwavelength imaging requires a particular phase difference between two coherent sources. Both numerical simulations and experimental results show that the phase difference of two subwavelength-distanced coherent sources greatly influences the field distribution around the drain array. In very few cases (when the phase difference of the two sources is chosen to be a very specific value), we might resolve the image points in the drain array under the assumption that the power absorbed by the scanning cable on the left side of the drain array should be symmetric to that on the right side of the drain array [1]. However, in most cases, we cannot obtain a super-resolution imaging, as other drains around the image points will greatly influence the imaging. We also note that the experiment assumed that the power absorbed by the scanning cable on the left and the right sides of the drain array is symmetric is not correct for the experiment reported in [1], as the drain array itself is not symmetric. The highly non-symmetric distribution of the absorbed power is also verified by our simulation and experimental results. The experimental "result" of resolving two image peaks could potentially be recovered using only a single image peak, which demonstrates the wrong assumption of mirror symmetry. Comparisons and comments on perfect passive drains, "super-resolution" in a spherical geodesic waveguide, and time reverse imaging are also given.

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Frequency dependence and passive drains in fish-eye lenses

Cited by 18 publications

References 31 publications

A simple model explaining super-resolution in absolute optical instruments

A simple model explaining super-resolution in absolute optical instruments

Active absorption of electromagnetic pulses in a cavity

Can Maxwell's Fish Eye Lens Really Give Perfect Imaging? Part Iii. A Careful Reconsideration of the ``Evidence for Subwavelength Imaging With Positive Refraction''

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