We introduce the new concept of "metalines" for manipulating the amplitude and phase profile of an incident wave locally and independently. Thanks to the highly confined graphene plasmons, a transmit-array of graphene-based metalines is used to realize analog computing on an ultra-compact, integrable and planar platform. By employing the general concepts of spatial Fourier transformation, a well-designed structure of such meta-transmit-array combined with graded index lenses can perform two mathematical operations; i.e. differentiation and integration, with high efficiency. The presented configuration is about 60 times shorter than the recent structure proposed by Silva et al. (Science, 2014, 343, 160-163); moreover, our simulated output responses are in more agreement with the desired analytic results. These findings may lead to remarkable achievements in light-based plasmonic signal processors at nanoscale instead of their bulky conventional dielectric lens-based counterparts.Recently, realization of analog computing has been achieved by manipulating continuous values of phase and amplitude of the transmitted and reflected waves by means of artificial engineered materials, known as metamaterials, and planar easy-to-fabricate metamaterials with periodic arrays of scaterrers, known as metasurfaces. 1-3 Both above-mentioned platforms offer the possibility of miniaturized wave-based computing systems that are several orders of magnitude thinner than conventional bulky lens-based optical processors. 1,4

We propose an unprecedented transmit-array configuration which can mold the incident beam by modulating phase and amplitude wavefronts. The transmit-array is composed of patterned graphene metasurfaces as shunt admittance sheets. Thanks to the exceptional features of graphene such as tunability, thinness, low loss, and high confinement of graphene plasmons, the proposed subwavelength structure passes strict touchstones for nano-photonic and opto-electronic applications. Two flat-optics functionalities, i.e., focusing and splitting, are realized by means of the proposed configuration.

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The concept of three-dimensional (3D) resolvability of an integral imaging system is thoroughly investigated in this research. The general concept of 3D resolution fails to describe the 3D discrimination completely. Then the concepts of the depth-resolution plane and lateral-resolution plane are introduced to show the difference between the conventional 3D spatial resolution and the newly introduced 3D resolvability. Therefore, the different properties of these planes for differentiating lateral spatial variations and axial variations are analyzed in this paper. The theoretical statements are demonstrated experimentally.

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