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Based on transformation optics (TO), this paper uses geometric divisions and linear coordinate transformations to design shrinking-shifting - and reshaping, and amplifying-shifting - and reshaping devices. The proposed devices can reshape the sizes and locations of the wrapped-objects inside the core-region. The shrinking-shifting device shrinks the larger object into a smaller one and shifts it to different location, whereas the shrinking-reshaping device can generate a smaller-size image with different shape located at different location. In contrast to previously designed shrinking devices, the real object wrapped inside the proposed core-region and the transformed object contains the same material properties, and the location-shifting is another feature. Here, the shifting-region is located inside the physical-space boundaries to achieve the non-negative, homogeneous, and anisotropic material properties of the proposed device, which are easier for real implementations. Thus, we further verified this concept with the amplifying-shifting and -reshaping devices for visually transformation of smaller object into bigger one placed at different location and position. We also applied active scatterer to further validate the working functionality of proposed devices. In addition, the proposed devices behave like the concentrator and or rotator effect in the absence of any scatterer. Our findings highlight the role of TO, suggesting directions for future research on bi-functional devices that will be useful for shrinking and amplifying devices, illusion optics, camouflage, and object protection etc. Keywords: amplifying, reshaping, shrinking, transformation optics, invisibility cloaks

In the quest to realize analog signal processing using sub-wavelength metasurfaces, in this paper, we demonstrate the first experimental demonstration of programmable time-modulated metasurface processors based on the key properties of spatial Fourier transformation. Exploiting space-time coding strategy enables local, independent, and real-time engineering of not only amplitude but also phase profile of the contributing reflective digital meta-atoms at both central and harmonic frequencies. Several illustrative examples are demonstrated to show that the proposed multifunctional calculus metasurface is capable of implementing a large class of useful mathematical operators, including 1st- and 2nd-order spatial differentiation, 1st-order spatial integration, and integro-differential equation solving accompanied by frequency conversions. Unlike the recent proposals, the designed time-modulated signal processor effectively operates for input signals containing wide spatial frequency bandwidths with an acceptable gain level. Proof-of-principle simulations are also reported along with the successful realization of image processing functions like edge detection. This time-varying wave-based computing system can set the direction for future developments of programmable metasurfaces with highly promising applications in ultrafast equation solving, real-time and continuous signal processing, and imaging., Comment: 24 pages, 9 figures

This paper addresses a reflection-type dual-band 2-bit coding metasurface (CM) design to achieve the dual-band functionalities in two different operating bands, independently. We are particularly interested to control linearly-polarized incident waves by encoding the propagation / dynamic phase in order to realize and fully control the orbital angular momentum (OAM) vortex beam (VB) for dual-band, independently. In this regard, we perform digital addition operations to combine the coding sequences of traditional OAM and phase-gradient to construct the proposed CM. The proposed CM generates and steers the OAM-VB with different topological charges in both lower and higher bands, independently. Similarly, the proposed CM is further extended for OAM-VB shaping by combining the coding sequences of traditional OAM and splitting phase unit-cells, and, we discuss two different scenarios. Firstly, OAM-VB splitting is performed to achieve different topological charges in both lower and higher bands, independently. Secondly, quad-beam shaping is realized to verify the proposed concept of this paper. Finally yet importantly, we also examine that the reflected beam directions can be further independently controlled to achieve anomalous, negative and retro-reflection at two different operating bands. The proposed concept will open up possibilities of multi-functional meta-devices and will be useful in many applications such as optical spanners, quantum optics, spatial mode multiplexing for telecommunications, and astronomy etc.

Conventional concentrators with inhomogeneous coating materials that fully enclose the destined region pose great challenges for fabrication. In this paper, we propose to design an EM concentrator with homogeneous materials. Distinguished from conventional ones, the elaborately designed EM concentrator features a concentrator region that is open to the outer-world, which is achieved with multi-folded transformation optics method by compressing and folding the coating materials to create window(s). Based on this concept, we also investigate open-rotator and open rotational-concentrator devices, which could simultaneously rotate and store the EM waves in the central destined region. Due to the open nature of our proposed designs, we believe they will find potential applications in remote controlling with impressive new functionalities.

Beam splitter mediated entanglement of nonlinear photon-added coherent states was studied by Honarasa, Bagheri and Gharaati [1]. We believe that this work contains errors in numerical computations of linear entropy and Mandel parameter which lead to wrong conclusions. We point out the possible errors and describe the necessary corrections. The conclusions based on our arguments are in complete agreement with previously published literature., Comment: 8 pages

We develop generalized coherent states for a class of nonlinear oscillators with position-dependent effective mass in the context of the Gazeau-Klauder formalism and discuss some of their properties. In order to investigate the temporal evolution we first explore the statistical properties by means of weighting distribution and the Mandel parameter. It is found that the temporal evolution of the coherent states may exhibit the phenomena of quantum revivals and fractional revivals for a particular choice of position-dependent mass oscillator., Comment: 14 pages, 6 figures (22 plots); accepted for publication in "Communications in Theoretical Physics"

Quantum carpets- in position and momentum space- woven by the self-interference of de Broglie wave of an atom or an electron, trapped in an infinitely deep potential well, are explained. The recurrence of self-similar structures in designs of these carpets mimics the phenomena of quantum revivals and fractional revivals. We identify fractional revivals of various order by means of these space-time and momentum-time interference patterns., Comment: 9 pages, 6 Figures

Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with position-dependent effective mass is discussed. We quantize the Hamiltonian of the pertaining system by using symmetric ordering of the operators concerning momentum and the spatially varying mass, initially proposed by von Roos and Levy-Leblond. The algebraic method, used to obtain the solutions, is based on the concepts of supersymmetric quantum mechanics and shape invariance. In order to exemplify the general formalism a class of non-linear oscillators has been considered. This class includes the particular example of a one-dimensional oscillator with different position-dependent effective mass profiles. Explicit expressions for the eigenenergies and eigenfunctions in terms of generalized Hermite polynomials are presented. Moreover, properties of these modified Hermite polynomials, like existence of generating function and recurrence relations among the polynomials have also been studied. Furthermore, it has been shown that in the harmonic limit, all the results for the linear harmonic oscillator are recovered., Comment: 27 pages, 2 figures, to appear in Journal of Mathematical Physics

A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are obtained using the concepts of supersymmetric quantum mechanics and the property of shape-invariance. In order to exemplify the general results and to analyzed the properties of the coherent states, several examples have been considered., Comment: 6 pages and 2 figures

Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut-Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass., Comment: 12 pages and 4 figures

We argue that the statistical features of generalized coherent states for power-law potentials based on Heisenberg algebra, presented in a recent paper by Berrada et al (Phys. Lett. A, 375, 298 (2011)) are incorrect., Comment: 9 pages, 1 figure

We propose a simple way to determine the periodicities of wave packets in quantum systems directly from the energy differences of the states involved. The resulting classical periods and revival times are more accurate than those obtained with the traditional expansion of the energies about the central quantum number n, especially when n is low. The latter type of wave packet motion occurs upon excitation of highly charged ions with short XUV or X-ray pulses. Moreover, we formulate the wave packet dynamics in such a form that it directly reveals the origin of phase shifts in the maxima of the autocorrelation function. This phenomenon, so far poorly understood since it is not prominent in the high n regime, becomes a dominant feature in low n wave packet dynamics., Comment: 10 pages, 8 figures

The recurrence phenomena of an initially well localized wave packet are studied in periodically driven power-law potentials. For our general study we divide the potentials in two kinds, namely tightly binding and loosely binding potentials. In the presence of an external periodically modulating force, these potentials may exhibit classical and quantum chaos. The dynamics of a quantum wave packet in the modulated potentials displays recurrences at various time scales. We develop general analytical relations for these times and discuss their parametric dependence.

As part of the project to universalize primary education in Pakistan by the mid-1980's, 1977 participation rates of boys and girls in rural primary schools in the Federal Capitol Territory have been determined through school mapping procedures. In three of four Territorial headquarters areas about 35% of boys and between 7% and 16% of girls attend primary school. In the fourth area, 17% of boys and 28% of girls attend. For the four rural areas combined, 35% of boys and 13% of girls go to school, as compared to attendance rates of 51% for boys and 49% for girls in the city of Islamabad. Among all Territorial primary aged children, only 39% of boys and 23% of girls attend school. Many rural children, especially those in remote areas and girls in general, are denied educational opportunities because of lack of schools or inefficient organization and operation of existing schools. All districts in Pakistan should initiate a similar mapping study in order to describe the present situation and determine what has to be done to improve the educational opportunities for rural children. These studies should be the basis for all educational development in Pakistan. (SB)