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The intensity of a superoscillatory Airy beam (solid line) with a=1.5, N=5, compared to the intensity of a single Airy beam (dashed line) with the highest oscillation frequency of the sum.
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It is now well-appreciated that a bandlimited wave can possess oscillations much more rapidly than those predicted by the bandlimit itself, in a phenomenon known as superoscillation. Such superoscillations are required to be of dramatically smaller amplitude than the signal they are embedded in, and this has initially led researchers to consider th...
Citations
... Superoscillation is the phenomenon in which a band-limited function can contain local oscillations that are faster than those of the fastest Fourier components and can be used for superresolution and imaging. Although these oscillations have a much smaller amplitude than the signal they are embedded in, superoscillations have nonetheless been used in a number of systems to overcome the limitations of traditional diffraction theory (Rayleigh limit [11]), see, for example, the reviews [12,13]. The inherent phase structure of the vortex beams is ideal for applications in highresolution phase contrast imaging, as required for biological samples with low absorption contrast [14]. ...
A major application of the inverse scattering and tomography methods is imaging all types of structural, physical, chemical and biological features of matter. The term vortex beam refers to a beam of electromagnetic radiation, electrons, photons or others—whose phase changes in corkscrew-like manner along the direction of propagation. The paper is devoted to the use of scalar Bessel beams of integer and fractional mode for the reconstruction of scattering potential. In practical applications, one naturally deals with Bessel beams truncated in the radial direction. The inversion formula for truncated Bessel beams is also obtained. Instead of the conventional Fourier diffraction theorem (Kak and Slaney in Principles of computerized tomographic imaging, SIAM, New York, 2001), the relations connecting the scattered field and the scattering potential in the Fourier space are obtained in the explicit form.
... Another reason why the rotation of the array beams occurs is that the energy of the cross section flows differently in all directions and the energy distribution is non-uniform, so that a redistribution of energy can occur [43,60]. The phase distribution shown in Fig. 3b5 is similar to the phase diagram of superimposed Bessel beams with super-oscillations, which can propagate over a long distance without changing and can be used to improve super-resolution imaging techniques [61]. The above content studies the case of a = 0. ...
The propagation dynamics of the complex variable cosine-Gaussian cross-phase (CVCGCP) array beams in strongly nonlocal nonlinear media are researched based on the nonlocal nonlinear Schrödinger equation. Under the effect of cross-phase, the transverse mode of CVCGCP array beams changes periodically and rotates during propagation. Compared with higher-order temporal solitons in nonlinear optical fibers, CVCGCP array beams can be considered as a new form of higher-order spatial solitons. The expression of the optical field distribution for the propagation evolution of CVCGCP array beams is presented. According to the different parameters, three cases are studied in detail. The light intensity pattern, phase and statistical width of CVCGCP array beams are discussed and analyzed. The results show that CVCGCP array beams have rich transmission characteristics and can form a linear shape distribution, which has the practical application value. By selecting the parameters, the light intensity patterns can be repeated and controlled, so as to achieve the purpose of controlling the light intensity patterns. The results of this paper enrich the types of higher-order spatial solitons, and also provide theoretical references for beam control and information transmission, etc.
... Over the course of the last two decades, a plethora of methods was developed to overcome the limitations of direct imaging and achieve super resolution. This includes photoactivated localization microscopy [4,5], optical reconstruction microscopy [6], the use of superoscillations [7,8] and inversion of coherence along an edge [9,10], among others [11,12]. In the particular case of estimating the distance between two incoherent light sources, such as a planet orbiting around a distant star [13], the optimal measurement is given by spatial demultiplexing (SPADE) in Hermite-Gauss modes [14,15]. ...
Superresolution is one of the key issues at the crossroads of contemporary quantum optics and metrology. Recently, it was shown that for an idealized case of two balanced sources, spatial mode demultiplexing (SPADE) achieves resolution better than direct imaging even in the presence of measurement crosstalk [Phys. Rev. Lett. 125, 100501 (2020)]. In this work, we consider arbitrarily unbalanced sources and provide a systematic analysis of the impact of crosstalk on the resolution obtained from SPADE. As we dissect, in this generalized scenario, SPADE's effectiveness depends non-trivially on the strength of crosstalk, relative brightness and the separation between the sources. In particular, for any source imbalance, SPADE performs worse than ideal direct imaging in the asymptotic limit of vanishing source separations. Nonetheless, for realistic values of crosstalk strength, SPADE is still the superior method for several orders of magnitude of source separations.
... Although backflow in quantum systems has not yet been experimentally realized, it has been demonstrated with optical beams [13,14] in one dimension, by exploiting its connection to the concept of superoscillations in waves, as established by Berry et al. [15,16]. In a superoscillatory function, local Fourier components are not contained in the global Fourier spectrum [17,18]. For example, in classical electromagnetism, this manifests as follows: the local Poynting vector of a superposition state can point in directions not contained between those of the constituent plane waves, leading to counter-flow or backflow of the energy density [19,20]. ...
M. V. Berry’s work [J. Phys. A 43, 415302 (2010)1751-811310.1088/1751-8113/43/41/415302] highlighted the correspondence between backflow in quantum mechanics and superoscillations in waves. Superoscillations refer to situations where the local oscillation of a superposition is faster than its fastest Fourier component. This concept has been used to experimentally demonstrate backflow in transverse linear momentum for optical waves. In the present work, we examine the interference of classical light carrying only negative orbital angular momenta, and in the dark fringes of such an interference, we observe positive local orbital angular momentum. This finding has implications for the studies of light–matter interaction and represents a step towards observing quantum backflow in two dimensions.
... In recent years, a number of imaging systems have been developed based on the principle of superoscillations [4][5][6][7][8][9]. A superoscillation is an oscillation of a band limited signal with a local frequency higher than the highest frequency (bandlimit) of the signal, and can manifest in the temporal or spatial oscillations of a signal. ...
Superoscillations are oscillations of a band limited waveform with a local frequency higher than the bandlimit. Spatial superoscillations show great potential for performing super-resolution imaging. However, these superoscillatory waveforms are inevitably surrounded by high intensity sidelobes which severely limit the usable super-resolved area of an image. In this study, we demonstrate how polarization engineering can be used in some circumstances to suppress superoscillation sidelobes, taking advantage of the transverse wave nature of light. We illustrate the principle by a model super-resolution imaging system that can image Rayleigh scatterers with separations smaller than the classic Rayleigh criterion.
... Single-shot SO imaging leverages the engineered SO pointspread function (PSF) that has a main lobe oscillating faster than the highest Fourier component 19,[22][23][24] to convert such sub-diffraction information into a human-readable format. This sub-diffraction main lobe enhances optical resolution through convolution with the objects. ...
A point-spread function (PSF) that locally oscillates faster than its highest Fourier component can reconstruct the sub-diffraction information of objects in the far field without any near-field placements to break the diffraction limit. However, the spatial capacity of such super-oscillatory (SO) PSFs for carrying sub-diffraction information is restricted by high sidelobes surrounding a desired region of interest (ROI). Here, we propose generalized periodic SO masks without optimization to push the ROI borders away for imaging extended objects. Our imaging experiments without any image post-processing demonstrate single-shot extended-object SO imaging with extended ROIs more than ten times the size of some typical ROIs (around 2λ/NA) and a sub-wavelength resolution of 0.49λ. The SO sub-wavelength resolution (0.7 times the diffraction limit) remains robust to additive noise with a signal-to-noise ratio above 13 dB. Our method is applicable to lifting the ROI size restrictions for various SO applications such as high-density data storage, acoustic SO imaging, super-narrow frequency conversion, and temporal SO pulses.
... It is now widely recognized that band-limited signals can possess regions where the local frequency is arbitrarily larger than the fastest oscillating Fourier component in the function. The oscillations in these regions are known as superoscillations [1][2][3]. Superoscillations have been rigorously mathematically discussed with their relation to quantum mechanics and the Schrödinger equation in [4]. In a real-valued spatial wavefunction, the local rate of oscillation is dictated by the separation of its zeros, with the space between two zeros representing one half of an oscillation; when the space is less than one half of a wavelength, the field in the region is said to be superoscillatory. ...
Oscillations of a wavefield that are locally higher than the bandlimit of the field are known as superoscillations. Superoscillations have to date been studied primarily in coherent wavefields; here we look at superoscillations that appear in the phase of the correlation function in partially coherent Talbot carpets. Utilizing the Talbot effect, it is shown that superoscillations can be propagated into the far field, even under a decrease in spatial coherence. It is also shown that this decrease in spatial coherence can strengthen the superoscillatory behavior at the primary and secondary Talbot images.
... Accepted Fourier thinking indicates that the signal has no fluctuations with a period less than 2π/ . However, a signal can have superoscillations or places where the local frequency is higher, in principle arbitrarily higher, than the highest nonzero frequency in the bandwidth [15]. There are several techniques exist for producing superoscillations in optics [16,17]. ...
Diffraction of a spherical wave through various types of 2D aperiodic hollow masks is investigated computationally. Unlike a periodic transmissive grating, an aperiodic hollow mask can focus light into a hotspot with sub-wavelength diameter. In this work, several types of 2D aperiodic hollow masks are investigated in the framework of sub-diffraction focusing of light and generating superoscillations at the hotspot region.
... In 2019, this method was modified to design a superoscillatory filter for imaging [13], in which zero rings are used to generate a superoscillatory spot and to adjust the position of the sidelobes. Additional discussions of superoscillation techniques can be found in a number of review articles [14][15][16]. ...
In recent years, superoscillations have become a new method for creating super-resolution imaging systems. The design of superoscillatory wavefronts and their corresponding lenses can, however, be a complicated process. In this study, we extend a recently developed method for designing complex superoscillatory filters to the creation of phase- and amplitude-only filters and compare their performance. These three types of filters can generate nearly identical superoscillatory fields at the image plane.
... Over the course of the last two decades, a plethora of methods was developed to overcome the limitations of direct imaging and achieve superresolution. This includes photoactivated localization microscopy (PALM) [4,5], optical reconstruction microscopy (STORM) [6], the use of superoscillations [7,8] and inversion of coherence along an edge (SPLICE) [9,10], among others [11,12]. In the particular case of estimating the distance between two incoherent light sources, such as a planet orbiting around a distant star [13], the optimal measurement is given by spatial demultiplexing (SPADE) in Hermite-Gauss modes [14,15]. ...
... We begin our analysis with the asymptotic limit of vanishing distances, x → 0, for which we obtain exact analytical results. From the definition of light intensity (8), making use of eqs (4-6), we calculate that ...
Superresolution is one of the key issues at the crossroads of contemporary quantum optics and metrology. Recently, it was shown that for an idealized case of two balanced sources, spatial mode demultiplexing (SPADE) achieves resolution better than direct imaging even in the presence of measurement crosstalk [Phys. Rev. Lett. 125, 100501 (2020)]. In this work, we consider the more general case of unbalanced sources and provide a systematic analysis of the impact of crosstalk on the resolution obtained from SPADE depending on the strength of crosstalk, relative brightness and the separation between the sources. We find that, in contrast to the original findings for perfectly balanced sources, SPADE performs worse than ideal direct imaging in the asymptotic limit of vanishing source separations. Nonetheless, for realistic values of crosstalk strength, SPADE is still the superior method for several orders of magnitude of source separations.
