Manipulating surface plasmon waves by transformation optics:Design examples of a beam squeezer,bend,and omnidirectional absorber

We present several design examples of how to apply transformation optics and curved space under coordinate transformation to manipulating the surface plasmon waves in a controlled manner.We demonstrate in detail the design procedure of the plasmonic wave squeezer,in-plane bend and omnidirectional absorber.We show that the approximation method of modifying only the dielectric material of a dielectric-metal surface of the plasmonic device could lead to acceptable performance,which facilitates the fabrication of the device.The functionality of the proposed plasmonic device is verified using three-dimensional full-wave electromagnetic simulations.Aiming at practical realization,we also show the design of a plasmonic in-plane bend and omnidirectional absorber by an alternative transformation scheme,which results in a simple device structure with a tapered isotropic dielectric cladding layer on the top of the metal surface that can be fabricated with existing nanotechnology.

Transformation optics for efficient calculation of transmembrane voltage induced on cells

We present a novel efficient approach in calculating induced transmembrane voltage（ITV） on cells based on transformation optics. As cell membrane is much thinner than the dimension of a typical cell, discretizing the membrane needs numerous meshes. Using an anisotropic medium based on transformation optics, the thickness of the membrane can be exaggerated by at least one order, which eliminates rigorous mesh refinement and reduces unknowns greatly. The accuracy and efficiency of the proposed method are verified by a cylindrical cell model. Moreover, the influence on ITV with bound water（BW） layers is also studied. The results show that when cells are exposed to nanosecond electric field, BW layers should be rigorously considered in calculating ITV.

Reflectionless spatial beam benders with arbitrary bending angle by introducing optic-null medium into transformation optics

By introducing an optic-null medium into the finite embedded transformation,a reflectionless spatial beam bender is designed,which can steer the output beam by a fixed pre-designed angleβfor an arbitrary incident angle.The bending angleβof the beam bender is determined by the geometrical angle of the device,which can be changed by simply choosing different geometrical angles.For various bending angles,the designed spatial beam bender can be realized by the same materials(i.e.,an optic-null medium),which is a homogenous anisotropic material.Numerical simulations verify the reflectionless bending effect and rotated imaging ability of the proposed beam bender.A reduction model of the optic-null medium is studied,which can also be used for a reflectionless spatial beam bender with a pre-designed bending angle.

Simultaneously realizing thermal andelectromagnetic cloaking by multi-physicalnull medium

Simultaneously manipulating multiple physical fields plays an important role in the increasingly complex integrated systems,aerospace equipment,biochemical productions,etc.For on-chip systems with high integration level,the precise and efficient control of the propagation of electromagnetic waves and heat fluxes simultaneously is particularly important.In this study,we propose a graphical designing method(i.e.,thermal-electromagnetic surface transformation)based on thermal-electromagnetic null medium to simultaneously control the propagation of electromagnetic waves and thermal fields according to the pre-designed paths.A thermal-electromagnetic cloak,which can create a cloaking effect on both electromagnetic waves and thermal fields simultaneously,is designed by thermal-electromagnetic surface transformation and verified by both numerical simulations and experimental measurements.The thermal-electromagnetic surface transformation proposed in this study provides a new methodology for simultaneous controlling on electromagnetic and temperature fields,and may have significant applications in improving thermal-electromagnetic compatibility problem,protecting of thermal-electromagnetic sensitive components,and improving efficiency of energy usage for complex onchip systems.

New decomposition of the Fresnel operator corresponding to the optical transformation in ABCD-systems

By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator, the squeezing operator, and the fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.

Design and applicability analysis of independent double acquisition circuit of all-fiber optical current transformer

The advantages of the all-fiber optical current transformer include but are not limited to being small in size,having no magnetic saturation,exhibiting high measurement accuracy,and boasting strong electromagnetic interference resistance.However,the high cost of the all-fiber optical transformer limits its promotion and application in engineering.This paper proposes a design scheme of an independent double acquisition loop for the all-fiber optical current transformer based on the single optical path.Firstly,based on the closed-loop control mode and open-loop control mode,the twochannel sampling signal demand for relay protection,and the independent dual-acquisition loop design scheme of the all-fiber optical current transformer are proposed.Secondly,the reliability and economic feasibility of the scheme are demonstrated by an analysis of system failure and cost.The results show that the scheme can actualize the acquisition function of two independent all-fiber optical current transformer products on a single all-fiber current transformer in an integrated manner,which greatly reduces the cost of the all-fiber optical current transformer in engineering applications.

Unitary transformation of general nonoverlapping-image multimode interference couplers with any input and output ports

An explanation of optical unitary transformation is presented for general nonoverlapping-image multimode interference(MMI)couplers with any number of input and output ports.The light transformation in the MMI coupler can be considered as an optical field matrix acting on an input light column vector.We investigate the general phase principle of output light image.The complete proof of nonoverlapping-image MMI coupler’s optical unitarity along with the phase analysis of matrix element is provided.Based on a two-dimensional finite-difference time-domain(2 D-FDTD)simulation,the unitary transformation is obtained for a 4×4 nonoverlapping-image MMI coupler within a deviation of 4×10-2 for orthogonal invariance and 8×10-2 for transvection invariance in the C-band spectral range.A compact 1×4 splitter based on cascaded MMI coupler is proposed,showing a phase deviation less than 5.4°while maintaining a low-loss performance in C-band spectra.

Integrated photonic systems based on transformation optics enabled gradient index devices

Integrated photonics is expected to play an increasingly important role in optical communications,imaging,computing and sensing with the promise for significant reduction in the cost and weight of these systems.Future advancement of this technology is critically dependent on an ability to develop compact and reliable optical components and facilitate their integration on a common substrate.Here we reveal,with the utility of the emerging transformation optics technique,that functional components composed of planar gradient index materials can be designed and readily integrated into photonic circuits.The unprecedented design flexibility of transformation optics allows for the creation of a number of novel devices,such as a light source collimator,waveguide adapters and a waveguide crossing,which have broad applications in integrated photonic chips and are compatible with current fabrication technology.Using the finite-difference time-domain method,we perform full-wave numerical simulations to demonstrate their superior optical performance and efficient integration with other components in an on-chip photonic system.These components only require spatially-varying dielectric materials with no magnetic properties,facilitating low-loss,broadband operation in an integrated photonic environment.

Concealing arbitrary objects remotely with multi-folded transformation optics

An invisibility cloak that can hide an arbitrary object external to the cloak itself has not been devised before.In this Letter,we introduce a novel way to design a remote cloaking device that makes any object located at a certain distance invisible.This is accomplished using multi-folded transformation optics to remotely generate a hidden region around the object that no field can penetrate and that does not disturb the far-field scattering electromagnetic field.As a result,any object in the hidden region can stay in position or move freely within that region and remain invisible.Our idea is further extended in order to design a remote illusion optics that can transform any arbitrary object into another one.Unlike other cloaking methods,this method would require no knowledge of the details of the object itself.The proposed multi-folded transformation optics will be crucial in the design of remote devices in a variety of contexts.

Transformation optics from macroscopic to nanoscale regimes:a review

Transformation optics is a mathematical method that is based on the geometric interpretation of Maxwell’s equations.This technique enables a direct link between a desired electromagnetic(EM)phenomenon and the material response required for its occurrence,providing a powerful and intuitive design tool for the control of EM fields on all length scales.With the unprecedented design flexibility offered by transformation optics(TO),researchers have demonstrated a host of interesting devices,such as invisibility cloaks,field concentrators,and optical illusion devices.Recently,the applications of TO have been extended to the subwavelength scale to study surface plasmon-assisted phenomena,where a general strategy has been suggested to design and study analytically various plasmonic devices and investigate the associated phenomena,such as nonlocal effects,Casimir interactions,and compact dimensions.We review the basic concept of TO and its advances from macroscopic to the nanoscale regimes.

Broadband continuous supersymmetric transformation:a new paradigm for transformation optics

Transformation optics has formulated a versatile framework to mold the flow of light and tailor its spatial characteristics at will.Despite its huge success in bringing scientific fiction(such as invisibility cloaking)into reality,the coordinate transformation often yields extreme material parameters unfeasible even with metamaterials.Here,we demonstrate a new transformation paradigm based upon the invariance of the eigenspectra of the Hamiltonian of a physical system,enabled by supersymmetry.By creating a gradient-index metamaterial to control the local index variation in a family of isospectral optical potentials,we demonstrate broadband continuous supersymmetric transformation in optics,on a silicon chip,to simultaneously transform the transverse spatial characteristics of multiple optical states for arbitrary steering and switching of light flows.Through a novel synergy of symmetry physics and metamaterials,our work provides an adaptable strategy to conveniently tame the flow of light with full exploitation of its spatial degree of freedom.

Homogeneous transparent device and its layered realization

Arbitrarily shaped electromagnetic transparent devices with homogeneous, non-negative, anisotropic and generic constitutive parameters are proposed based on linear transformation optics, which provides the flexibility for device design that is applicable for the practical fabrication. To remove the anisotropic property, a layered structure is developed based on effective medium theory. Simulation results show that with sufficient layers, the performance of the layered transparent device is nearly as perfect as an ideal device, and it is able to protect an antenna without sacrificing its performance. The feasibility of designing a transparent device by using natural isotropic materials instead of metamaterials would dramatically reduce the difficulty of fabrication and further promote the practicality of the device.

Design method of reusable reciprocal invisibility and phantom device

Reusable reciprocal invisibility and phantom device is proposed and designed based on multi-folded transformation optics and equivalent components. In comparison with the reported reciprocal invisibility cloaks, the material parameters of the device presented here are homogeneous, and the hiding of the target object does not require any “anti-object” at all,which dramatically breaks through the limitations of the “anti-object” design in previous reciprocal cloak design. Perfectly illusion effect is also found by reasonably setting the material parameters of the restored medium of the device, which can be used to confuse detection radars while hiding target objects. Last but not least, the proposed device has an open structure,which enables the target object enclosed by the device to perform material exchange and simplex transfer of information with the outside world through open channels. In other words, the proposed device has a reusable function, enabling stealth or phantom of new target objects without changing any parameters of the device.

Exact transformation optics by using electrostatics

We present a novel method for designing transformation optical devices based on electrostatics.An arbi-trary transformation of electrostatic field can lead to a new refractive index distribution,where wave-fronts and energy flux lines correspond to equipotential surfaces and electrostatic flux lines,respectively.Owing to scalar wave propagating exactly following an eikonal equation,wave optics and geometric optics share the same solutions in the devices.The method is utilized to design multipole lenses derived from multipoles in electrostatics.The source and drain in optics are considered as corre-sponding to positive charge and negative charge in the static field.By defining winding numbers in vir-tual and physical spaces,we explain the reason for some multipole lenses with illusion effects.Besides,we introduce an equipotential absorber to replace the drain to correspond to a negative charge with a grounded conductor.Therefore,it is a very general platform to design intriguing devices based on the combination of electrostatics and transformation optics.

Near-field multiple super-resolution imaging from Mikaelian lens to generalized Maxwell's fish-eye lens

Super-resolution imaging is vital for optical applications, such as high capacity information transmission, real-time bio-molecular imaging, and nanolithography. In recent years, technologies and methods of super-resolution imaging have attracted much attention. Different kinds of novel lenses, from the superlens to the super-oscillatory lens, have been designed and fabricated to break through the diffraction limit. However, the effect of the super-resolution imaging in these lenses is not satisfactory due to intrinsic loss, aberration, large sidebands, and so on. Moreover, these lenses also cannot realize multiple super-resolution imaging. In this research, we introduce the solid immersion mechanism to Mikaelian lens(ML) for multiple super-resolution imaging. The effect is robust and valid for broadband frequencies. Based on conformal transformation optics as a bridge linking the solid immersion ML and generalized Maxwell's fish-eye lens(GMFEL), we also discovered the effect of multiple super-resolution imaging in the solid immersion GMFEL.

Multi-window invisible cloaks

This paper reports that a general method of designing invisible cloaks is using variant constitutive material parameters to realize the space transformation. A hollow region can be hidden after this transformation. It was recently shown （Ma H, Qu S B, Xu Z and Wang J F 2009 Appl. Phys. Lett. 94 103501） that when the original point moves to the boundary of a cloak, the cloak can be designed to be open. Based on this theory, we propose multi-window invisible cloaks which can conceal a group of objects. Full wave simulations for invisible cloaks with regular and irregular shapes verified this method.

Design of two-dimensional elliptically cylindrical invisible cloaks with multiple regions

Two-dimensional （2D） elliptically cylindrical invisible cloaks with multiple regions are designed based on the trans-formation optics and the complementary media theory. Multiple invisible cloak regions can be obtained by properly using the compressed or folded transformation in each space layer. The constitutive parameter tensor expressions for each re- gion have been obtained. The results of full wave simulations by using finite element software confirm the validity of the constitutive parameter tensor expressions. In addition, the parameters are relatively easier to realize.

Revealing the Transformation Invariance of Full-Parameter Omnidirectional Invisibility Cloaks

Searching for an optimal solution among many nonunique answers provided by transformation optics is critical for many branches of research,such as the burgeoning research on invisibility cloaks.The past decades have witnessed rapid development of transformation optics,and different kinds of invisibility cloaks have been designed and implemented.However,the available cloaks realized thus far have been mostly demonstrated with reduced parameters,which greatly impact the predefined cloaking performance.Here,we report a general design strategy to realize full-parameter omnidirectional cloaks that can hide arbitrarily shaped objects in free space.Our approach combines a singular transformation with transformation-invariant metamaterials.The cloaking device with extreme parameters is implemented using a metallic array structure.In the experiment,two cloak samples are designed and fabricated,one with nondiscrete cloaking regions and the other with separated hidden regions.Near-unit transmission of electromagnetic waves with arbitrary incident angles is experimentally demonstrated along with significantly suppressed scattering.Our work challenges the prevailing paradigms of invisibility cloaks and provides deep insight into how transformation optics could be harnessed to obtain easily-accessible metadevices.

Arbitrarily shaped retro-reflector by optics surface transformation

A novel way to design arbitrarily shaped retro-reflectors by optics surface transformation is proposed. The entire design process consists of filling an optic-null medium between the input and output surfaces of the retroreflector, on which the points have 180 deg reverse corresponding relations. The retro-reflector can be designed to be very thin(a planar structure) with high efficiency. The effective working angles of our retro-reflector are very large(from-80 deg to +80 deg), which can, in principle, be further extended. Layered metal plates and zero refractive index materials are designed to realize the proposed retro-reflector for a TM polarized beam.

Optimization of loss and gain multilayers for reducing the scattering of a perfect conducting cylinder

Reduction of electromagnetic scattering from a conducting cylinder could be achieved by covering it with optimized multilayers of normal dielectric and plasmonic material. The plasmonic material with intrinsic losses could degrade the cloaking effect. Using a genetic algorithm, we present the optimized design of loss and gain multilayers for reduction of the scattering from a perfect conducting cylinder. This multilayered structure is theoretically and numerically analyzed when the plasmonic material with low loss and high loss respectively is considered. We demonstrate by full-wave simulation that the optimized nonmagnetic gain-loss design can greatly compensate the decreased cloaking effect caused by loss material,which facilitates the realization of practical electromagnetic cloaking, especially in the optical range.