Babinet-complementary structures for implementation of pseudospin-polarized waveguides.

In this work, a theorem is proved stating that in various types of waveguides with mirror reflection symmetries, the electromagnetic duality correspondence between eigenmodes of complementary structures induces counterpropagating spin-polarized states. The mirror reflection symmetries may be preserved around one or more arbitrary planes. Pseudospin-polarized waveguides supporting one-way states manifest robustness. This is similar to topologically non-trivial direction-dependent states guided by photonic topological insulators. Nevertheless, a remarkable aspect of our structures is that they can be implemented in extremely broad bandwidth by simply using complementary structures. Based on our theory, the concept of the pseudospin polarized waveguide can be realized using dual impedance surfaces ranging from microwave to optical regime. Consequently, there is no need to employ bulk electromagnetic materials to suppress backscattering in waveguiding structures. This also includes pseudospin-polarized waveguides with perfect electric conductor-perfect magnetic conductor boundaries where the boundary conditions limit the bandwidth of waveguides. We design and develop various unidirectional systems and the spin-filtered feature in the microwave regime is further investigated.

Analysis of electromagnetic scattering from array of time-modulated graphene ribbons.

An accurate and fast method is presented for the analysis of scattering of electromagnetic waves from an array of time-modulated graphene ribbons. We derive a time-domain integral equation for induced surface currents under subwavelength approximation. Using the method of harmonic balance, this equation is solved for a sinusoidal modulation. The solution of the integral equation is then used to obtain the transmission and reflection coefficients of time-modulated graphene ribbon array. The accuracy of the method was verified through comparison with results of full-wave simulations. In contrast with previously reported analysis techniques, our method is extremely fast and can analyze structures with a much higher modulation frequency. The proposed method also provides interesting physical insights useful for designing novel applications and opens up new vistas in the fast design of time-modulated graphene-based devices.

Tunable spatial fractional derivatives with graphene-based transmit arrays.

The optical implementation of mathematical spatial operators is a critical step toward achieving practical high-speed, low-energy analog optical processors. In recent years, it has been shown that using fractional derivatives in many engineering and science applications leads to more accurate results. In the case of optical spatial mathematical operators, the derivatives of the first and second orders have been investigated. But no research has been performed on fractional derivatives. On the other hand, in previous studies, each structure is dedicated to a single integer order derivative. This paper proposes a tunable structure made of graphene arrays on silica to implement fractional derivative orders smaller than two, as well as first and second orders. The approach used for derivatives implementation is based on the Fourier transform with two graded index lenses positioned at the structure's sides and three stacked periodic graphene-based transmit arrays in middle. The distance between the graded index lenses and the nearest graphene array is different for the derivatives of order smaller than one and between one and two. In fact, to implement all derivatives, we need two devices with the same structure having a slight difference in parameters. Simulation results based on the finite element method closely match the desired values. Given the tunability of the transmission coefficient of the proposed structure in the approximate amplitude range of [0,1] and phase range of [-180, 180], on top of the acceptable implementation of the derivative operator, this structure allows obtaining other spatial multi-purpose operators, which are a prelude to achieving analog optical processors and even improving the optical studies performed in image processing.

Generalized equivalent circuit model for analysis of graphene/metal-based plasmonic metasurfaces using Floquet expansion.

Due to the wide range of applications of metal/graphene-based plasmonic metasurfaces (sensors, absorbers, polarizers), it has become essential to provide an analytical method for modeling these structures. An analytical solution simplified into a circuit model, in addition to greatly reducing the simulation time, can become an essential tool for designing and predicting the behaviors of these structures. This paper presents a high-precision equivalent circuit model to study these structures in one-dimensional and two-dimensional periodic arrays. In the developed model, metallic patches similar to graphene patches are modeled as surface conductivity and with the help of current modes induced on them, the equivalent impedance related to the array is calculated. However, the proposed method has less complexity than the previous methods, is more accurate and more flexible against geometry changes and can be applied to an array of patches embedded in a layered medium with minor changes and modifications. A Metal-Insulator-Metal metasurface, as well as an array of graphene ribbons placed on two dielectric layers, are investigated as two types of widely used metasurfaces in this paper and it is shown that the proposed circuit model is a fast and efficient method to predict the behaviors of these metasurfaces.

Computational inverse design for cascaded systems of metasurface optics: comment.

In a recently published article by Backer [Opt. Express27(21), 30308 (2019).10.1364/OE.27.030308], a computational inverse design method is developed for designing optical systems composed of multiple metasurfaces. The forward propagation model used in this method was a discretized version of the angular spectrum propagator described by Goodman [Introduction to Fourier Optics, 1996]. However, slight modifications are necessary to increase the accuracy of this inverse design method. This comment examines the accuracy of the results obtained by the above-mentioned method by a full-wave electromagnetic solver and explains the reason of their difference. Thereafter, slight modifications to the method proposed by Backer are suggested, and the accuracy of final formulation is verified by a full-wave electromagnetic solver.

All optical divergence and gradient operators using surface plasmon polaritons.

In this paper, we propose a plasmonic structure based on Kretschmann configuration capable of performing various computational tasks, i.e. two dimensional isotropic differentiation, gradient and divergence computation. By means of two polarizers, a non-trivial topological charge can be generated in the transfer function of the structure thereby implementing a two dimensional differentiator. By using only one polarizer, on the other hand, the structure is able to compute either the gradient of the field distribution of a polarized light beam or the divergence of the field of an unpolarized light beam. The performance of the proposed structure in two dimensional differentiation has been assessed and compared with its other counterparts by a figure of merit introduced in [Opt. Express28, 898 (2020)10.1364/OE.379492]. The result proves the dominance of our two-dimensional differentiator over similar works in the literature.

Realization of optical logic gates using on-chip diffractive optical neural networks.

Optical computing is highly desired as a potential strategy for circumventing the performance limitations of semiconductor-based electronic devices and circuits. Optical logic gates are considered as fundamental building blocks for optical computation and they enable logic functions to be performed extremely quickly without the generation of heat and crosstalk. Here, we discuss the design of a multi-functional optical logic gate based on an on-chip diffractive optical neural network that can perform AND, NOT and OR logic operations at the wavelength of 1.55 µm. The wavelength-independent operation of the multi-functional logic gate at seven wavelengths (over a bandwidth of 60 nm) is also studied which paves the way for wavelength division multiplexed parallel computation. This simple, highly-integrable, low-loss, energy-efficient and broadband optical logic gate provides a path for the development of high-speed on-chip nanophotonic processors for future optical computing applications.

Analysis and design of two-dimensional compound metallic metagratings using an analytical method.

The recently proposed concept of metagrating enables wavefront manipulation of electromagnetic (EM) waves with unitary efficiency and relatively simple fabrication requirements. Herein, two-dimensional (2D) metagratings composed of a 2D periodic array of rectangular holes in a metallic medium are proposed for diffraction pattern control. We first present an analytical method for diffraction analysis of 2D compound metallic metagrating (a periodic metallic structure with more than one rectangular hole in each period). Closed-form and analytical expressions are presented for the reflection coefficients of diffracted orders for the first time. Next, we verify the proposed method's results against full-wave simulations and demonstrate their excellent agreement. As a proof of principle, two applications are presented using the proposed analytical method. The first application is a perfect out-of-plane reflector that transfers a normal transverse-magnetic (TM) polarized plane wave to an oblique transverse-electric (TE) polarized plane wave in the y - z plane. The second one is a five-channel beam splitter with an arbitrary power distribution between channels. Using the proposed analytical method, we designed these metagratings without requiring even a single optimization in a full-wave solver. The performance of the designed metagratings is better than previously reported structures in terms of power efficiency and relative distribution error. Our analytical results reveal that 2D metagratings can be used for manipulating EM waves in the plane and out of the plane of incidence with very high efficiency, thereby leading to extensive applications in a wide range of frequencies from microwave to terahertz (THz) regimes.

Analytical method for diffraction analysis and design of perfect-electric-conductor backed graphene ribbon metagratings.

Graphene-based gratings and metagratings have attracted great interest in the last few years because they could realize various multi-functional beam manipulation, such as beam splitting, focusing, and anomalous reflection in the terahertz (THz) regime. However, most of graphene-based metagratings are designed through numerical simulations, which are very time-consuming. In this paper, an accurate analytical method is proposed for diffraction analysis of a perfect electric conductor (PEC)-backed array of graphene ribbons. In contrast to previous analytical treatments, the proposed method can predict the electromagnetic performance of graphene ribbons not only in the subwavelength regime, but also for wavelengths shorter than the array constant. Results are obtained by first deriving the surface current density induced on graphene ribbons by an obliquely incident transverse-magnetic (TM) polarized plane wave. Closed-form expressions for reflection coefficients of diffracted orders are then obtained using the surface current distribution. We validate the proposed method through comparison with full-wave simulation results. Finally, a tunable beam splitter and a tunable retroreflector in the THz regime are designed using the method proposed. The designed structures have good power efficiency (80% for beam splitter and 90% for retroreflector). Moreover, their operating frequency and angle may be controlled by changing the bias voltage of graphene ribbons. The proposed method paves the path for analytical design of tunable metagratings with widespread potential for THz and optical beam-manipulation applications.

Integrated photonic neural network based on silicon metalines.

An integrated photonic neural network is proposed based on on-chip cascaded one-dimensional (1D) metasurfaces. High-contrast transmitarray metasurfaces, termed as metalines in this paper, are defined sequentially in the silicon-on-insulator substrate with a distance much larger than the operation wavelength. Matrix-vector multiplications can be accomplished in parallel and with low energy consumption due to intrinsic parallelism and low-loss of silicon metalines. The proposed on-chip whole-passive fully-optical meta-neural-network is very compact and works at the speed of light, with very low energy consumption. Various complex functions that are performed by digital neural networks can be implemented by our proposal at the wavelength of 1.55 µm. As an example, the performance of our optical neural network is benchmarked on the prototypical machine learning task of classification of handwritten digits images from the Modified National Institute of Standards and Technology (MNIST) dataset, and an accuracy comparable to the state of the art is achieved.

On-chip second-order spatial derivative of an optical beam by a periodic ridge.

In this paper, a very simple periodic ridge on a symmetric slab waveguide is used for implementing an on-chip CMOS-compatible second-order spatial differentiator. The reflection and transmission coefficients of this structure show that the second derivative is performed in the transmission when the optical beam normally incidents on the periodic ridge. Simulations confirm that the reason behind the second-order spatial differentiation of the incoming beam is the excitation of the guided mode of the periodic ridge. A Maxwell's equation solver that utilizes the finite element method (FEM) is used to simulate this structure, and an eigenmode solver is utilized for the validation. The results of both methods have a very good agreement with each other.

Spin-polarized unidirectional cylindrical waveguide in bianisotropic media.

In this paper, we analyze a cylindrical waveguide consisting of two layers of bianisotropic material with anti-symmetric magnetoelectric coupling tensors. The analysis is carried out in terms of pseudo-electric and pseudo-magnetic fields which satisfy Maxwells' equations with gyrotropic permittivity and permeability tensors. We show that the rotationally symmetric modes of the waveguide are unidirectional with transverse pseudo-electric and transverse pseudo-magnetic modes propagating in opposite directions. These modes are surface waves whose electromagnetic field is concentrated near the interface between the two anisotropic materials. They follow the contour of the interface even in the case of sharp discontinuities and pass through an obstacle without backscattering if the obstacle does not change the polarization of the wave. Higher-order modes of the waveguide are also investigated. Although these modes are hybrid modes and not, strictly speaking, unidirectional, they practically behave as the rotationally symmetric mode.

Perfect anomalous reflection using a compound metallic metagrating.

Metagrating is a new concept for wavefront manipulation that, unlike phase gradient metasurfaces, does not suffer from low efficiency and also has a less complicated fabrication process. In this paper, a compound metallic grating (a periodic metallic structure with more than one slit in each period) is proposed for anomalous reflection. We propose an analytical method for analyzing the electromagnetic response of this grating. Closed-form and analytical expressions are presented for the reflection coefficients of zeroth diffracted order and also higher diffracted orders. The proposed method is verified against full-wave simulations and the results are in excellent agreement. Thanks to the geometrical asymmetry of compound metallic grating, it can be used for designing anomalous reflection at the normal incidence. Given analytical expressions for reflection coefficients, we design a perfect anomalous reflector for a TM polarized plane wave via transferring all the incident power to ( - 1) diffraction order . The structure designed in this study has an unprecedented near-to-unitary efficiency of 99.9%. Finally, a multi-element compound metallic grating is proposed for reflecting the normal incidence to angles of below 30°, which is a challenging accomplishment. This excellent performance of compound metallic grating shows its high potential for microwave and terahertz wavefront manipulation applications.

Reconfigurable Meta-Coupler Employing Hybrid Metal-Graphene Metasurfaces.

Efficient excitation of surface wave (SW) remains one of the most challenging considerations in the photonics and plasmonics areas. Inspired by recent investigations of metasurfaces, we propose a hybrid metal-graphene transmitarray converting incident propagating wave (PW) to SW, as a solution for SW excitations-a meta-coupler. The structure comprises ultra-thin four-layer transparent metasurfaces in which H-shaped etched metal films together with graphene patches are employed, and also all four layers are identical. Full-wave simulations demonstrate that the suggested meta-coupler possesses an efficiency of 46% and a directivity of 19 dB, which is promising in the terahertz (THz) range. At the same time, in light of unique graphene characteristics, the proposed device is tunable and easily reconfigurable, i.e., the direction of converted SWs can be electrically switched from right to left and vice versa. We believe that this system responds to emerging applications such as THz communications and sensing, and furthermore the employed architecture introduce electrostatically tunable building blocks being able to develop graphene plasmonic components effectively.

Fundamental limit for gain and resolution in analog optical edge detection.

In this paper, the relation between gain and resolution of an ideal analog optical differentiator in two different cases and their fundamental limits are investigated. Based on this relation, a figure of merit for comparison of the designed differentiators in recent papers is proposed. The differentiators are optimized using this figure of merit, and they are compared with each other to determine the best one. Also, a new differentiator is presented based on the dielectric slab waveguide in which the trade-off between its gain and resolution is easily controllable, and its best operating point is determined.

Analytical and rigorous method for analysis of an array of magnetically-biased graphene ribbons.

A sheet of graphene under magnetic bias attains anisotropic surface conductivity, opening the door for realizing compact devices such as Faraday rotators, isolators and circulators. In this paper, an accurate and analytical method is proposed for a periodic array of graphene ribbons under magnetic bias. The method is based on integral equations governing the induced surface currents on the coplanar array of graphene ribbons. For subwavelength size ribbons subjected to an incident plane wave, the current distribution is derived leading to analytical expressions for the reflection/transmission coefficients. The results obtained are in excellent agreement with full-wave simulations and predict resonant spectral effects that cannot be accounted for by existing semi-analytical methods. Finally, we extract an analytical, closed form solution for the Faraday rotation of magnetically-biased graphene ribbons. In contrast to previous studies, this paper presents a fast, precise and reliable technique for analyzing magnetically-biased array of graphene ribbons, which are one of the most popular graphene-based structures.

Lithography-free, manganese-based ultrabroadband absorption through annealing-based deformation of thin layers into metal-air composites.

Fabrication, characterization, and analysis of an ultrabroadband lithography-free absorber is presented. An over 94% average absorption is experimentally achieved in the wavelength range of 450-1400 nm. This ultrabroadband absorption is obtained by a simple annealed trilayer metal-insulator-metal (MIM) configuration. The metal used in the structure is manganese (Mn), which also makes the structure cost-effective. It is shown that the structure retains its high absorption for TM polarization, up to 70 deg, and, for TE polarization, up to 50 deg. Moreover, the physical mechanism behind this broadband absorption is explained. Being both lithography-free and cost-effective, the structure is a perfect candidate for large-area and mass production purposes.

Tunable leaky-wave radiation by graphene-covered corrugated surfaces.

In this paper, we propose a graphene-covered subwavelength metallic grating where the Fermi level of graphene is sinusoidally modulated as a leaky-wave antenna at terahertz frequencies. This structure can convert spoof surface plasmon guided waves to free-space radiation due to the tunability of graphene. Analysis and design of the proposed leaky-wave antenna are discussed based on sinusoidally modulated surface impedance. The surface impedance is obtained by an analytical circuit model. The sinusoidal surface impedance is realized using modulation of the conductivity of graphene by applying a bias voltage. The proposed leaky-wave antenna is capable of electronic beam scanning with an almost constant gain and low sidelobe level by tuning the graphene Fermi level. In addition, a mode-converting section is proposed that drastically improves the return loss of the antenna.

Toward Electrically Tunable, Lithography-Free, Ultra-Thin Color Filters Covering the Whole Visible Spectrum.

The possibility of real-time tuning of optical devices has attracted a lot of interest over the last decade. At the same time, coming up with simple lithography-free structures has always been a challenge in the design of large-area compatible devices. In this work, we present the concept and the sample design of an electrically tunable, lithography-free, ultra-thin transmission-mode color filter, the spectrum of which continuously covers the whole visible region. A simple Metal-Insulator-Metal (MIM) cavity configuration is used. It is shown that using the electro-optic dielectric material of 4-dimethyl-amino-N-methyl-4-stilbazoliumtosylate (DAST) as the dielectric layer in this configuration enables efficient electrical tuning of the color filter. The total thickness of the structure is 120 nm, so it is ultra-thin. The output color gets tuned from violet to red by sweeping the applied voltage from -12 to +12 Volts (V). We present an in-detail optimization procedure along with a simple calculation method for the resonance wavelength of the MIM cavity that is based on circuit theory. Such power-efficient structures have a large variety of potential applications ranging from optical communication and switching to displays and color-tunable windows.

Large-Area, Cost-Effective, Ultra-Broadband Perfect Absorber Utilizing Manganese in Metal-Insulator-Metal Structure.

Achieving broadband absorption has been a topic of intensive research over the last decade. However, the costly and time consuming stage of lithography has always been a barrier for the large-area and mass production of absorbers. In this work, we designed, fabricated, and characterized a lithography-free, large-area compatible, omni-directional, ultra-broadband absorber that consists of the simplest geometrical configuration for absorbers: Metal-Insulator-Metal (MIM). We introduced and utilized Manganese (Mn) for the first time as a very promising metal for broadband absorption applications. We optimized the structure step-by-step and compared Mn against the other best candidates introduced so far in broadband absorption structures and showed the better performance of Mn compared to them. It also has the advantage of being cheaper compared to metals like gold that has been utilized in many patterned broadband absorbers. We also presented the circuit model of the structure. We experimentally achieved over 94 percent average absorption in the range of 400-900 nm (visible and above) and we obtained absorption as high as 99.6 percent at the wavelength of 626.4 nm. We also experimentally demonstrated that this structure retains broadband absorption for large angles up to 70 degrees.