Evidence for subwavelength imaging with positive refraction

Gui, Yang; Sahebdivan, Sahar; Ong, C. K.; Tyc, Tomáš; Leónhardt, Ulf

doi:10.1088/1367-2630/13/3/033016

Cited by 62 publications

(124 citation statements)

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“…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.…”

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confidence: 77%

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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confidence: 77%

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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“…Despite the limitations of the superlens restricting its effect to the near field, the excitement generated by Pendry's paper led to extensive work on subwavelength focusing and imaging, and in the ensuing years multiple groups reported 'breaking' the diffraction limit in the far field in both optics and acoustics: sub-diffraction-limited focusing or imaging was observed with metamaterials and without metamaterials, with negative refraction and without negative refraction, with Helmholtz resonators in acoustics and with Maxwell's fish eye lenses in optics [12][13][14][15][16][17]. The general mood was expressed by a commentary in Nature Materials entitled "What diffraction limit?"…”

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confidence: 99%

Upholding the diffraction limit in the focusing of light and sound

Maznev

Wright

2017

Wave Motion

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The concept of the diffraction limit put forth by Ernst Abbe and others has been an important guiding principle limiting our ability to tightly focus classical waves, such as light and sound, in the far field. In the past decade, numerous reports have described focusing or imaging with light and sound 'below the diffraction limit'. We argue that the diffraction limit defined in a reasonable way, for example in terms of the upper bound on the wave numbers corresponding to the spatial Fourier components of the intensity profile, or in terms of the spot size into which at least 50% of the incident power can be focused, still stands unbroken to this day. We review experimental observations of 'subwavelength' or 'sub-diffraction-limit' focusing, which can be principally broken down into three broad categories: (i) 'super-resolution', i.e. the technique based on the modification of the pupil of the optical system to reduce the width of the central maximum in the intensity distribution at the expense of increasing side bands; (ii) solid immersion lenses, making use of metamaterials with a high effective index; (iii) concentration of intensity by a subwavelength structure such as an antenna. Even though a lot of interesting work has been done along these lines, none of the hitherto performed experiments violated the sensibly defined diffraction limit.

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“…The mirror serves as a simple model that resembles the fish eye, but this model is too simple: Maxwell's fish eye has imaging properties different from mirrors [9]. Furthermore, his reasoning is in conflict with experimental evidence [10]. Let us briefly explain how perfect imaging is achieved in Maxwell's fish eye and what the role of the drain is.…”

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confidence: 99%

“…give the wave an outlet at the image such that it is not reflected there [10]. In this case the series (10) of reflections is truncated at the first term:…”

mentioning

confidence: 99%

“…In practice, of course, detectors are not ideal and have finite cross section and finite efficiency. The cross section of detectors does indeed limit the imaging resolution [10], whereas the finite efficiency simply reduces the amplitude of the perfectly focused wave: the total wave becomes a superposition of the diffraction-limited wave (6) and the perfectly imaged component (12). Maxwell's fish eye thus makes a perfect lens with point-like resolution for electromagnetic waves, but only when such waves are detected by perfect point detectors.…”

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confidence: 99%

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Reply to “Comment on ‘Perfect imaging with positive refraction in three dimensions’ ”

Leónhardt

Philbin

2010

Phys. Rev. A

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Exact time-dependent solutions of Maxwell's equations in Maxwell's fish eye show that perfect imaging is not an artifact of a drain at the image, although a drain is required for subwavelength resolution.PACS numbers: 42.30. Va, 77.84.Lf Perfect imaging with positive refraction [1][2][3] challenges some of the accepted wisdom of subwavelength imaging [4][5][6][7]. In particular, it requires a drain for perfect resolution [8]. Merlin [7] argues that the perfect focusing is an artifact of the drain. However, instead of discussing Maxwell's fish eye, he considers the focusing of light in a spherical mirror. The mirror serves as a simple model that resembles the fish eye, but this model is too simple: Maxwell's fish eye has imaging properties different from mirrors [9]. Furthermore, his reasoning is in conflict with experimental evidence [10]. Let us briefly explain how perfect imaging is achieved in Maxwell's fish eye and what the role of the drain is. Further details can be found in Ref. [9].In Ref.[2] we solved Maxwell's equations for electromagnetic radiation in Maxwell's fish eye (with ε = µ = n) by reducing the problem to the propagation of a scalar wave D; the electromagnetic field can be calculated from D by certain differentiations [11]. We thus only need to discuss the imaging properties of D, which does not constitute a simple model, but an exact representation of the electromagnetic Green tensor [2, 11] in Maxwell's fish eye.The fish eye is characterized in terms of a length R that defines the scale of the refractive index profile. For simplicity of notation, we measure space in units of R and time in units of R/c; in these units the speed of light in vacuum is 1. In our units the index profile of Maxwell's fish eye is given by n = 2 1 + r 2 .(The scalar wave D satisfies the equationwhere we include a source term on the right-hand side that corresponds to a point source at position r 0 acting in one moment of time that we set to t 0 = 0 without loss of generality. The wave equation thus describes a flash of light emitted at an arbitrary position and we can shift the time of emission to an arbitrary t 0 . Note that any light field can be thought of as a continuous superposition of such light flashes, and so our case is sufficiently general. Consider the Fourier transformation of the light flashNote that we can read the Fourier integral (3) as the amplitude of the wavethat is created by the continuous emission of light flashes at times t 0 with phases ωt 0 . The Fourier amplitude D thus plays a double role: it describes the frequency components of a single flash of light emitted at r 0 but also the amplitude of a stationary wave generated at the source point r 0 with frequency ω.To proceed, we write the wave equation (2) in the frequency domainthat has the solution [9]in terms of the Möbius-transformed radius [2, 11]We see that the source point r 0 corresponds to r ′ = 0. We also see that the image point of light rays in Maxwell's fish eye [11],corresponds to r ′ = ∞. The Möbius-transformed radius thus ...

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Evidence for subwavelength imaging with positive refraction

Cited by 62 publications

References 40 publications

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

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

Upholding the diffraction limit in the focusing of light and sound

Reply to “Comment on ‘Perfect imaging with positive refraction in three dimensions’ ”

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