arXiv subjects

Gengkai Hu

Publications and source records attributed to Gengkai Hu.

30 records · Page 2Linked to original sources

arXiv2011

Constraint condition on transformed relation for generalized acoustics

Contrary to transformation optics (TO), there exist many possibilities for transformed relations of material property and field variable in case of transformation acoustics (TA). To investigate the underlining mechanism and develop a general method that can obtain the full transformed relations, an alternative interpretation to the form-invariance is explored. We consider a spatial transformation, with which a physical phenomenon described in an initial space is transformed to a deformed space, and interpret the mapping by local affine transformation point-by-point. Further, we postulate that the transformed material property and field must rebuild the same physical process, and that the energy must be conserved at each point during the transformation. These conditions impose the constraint on the transformed relation for material property and field. By establishing two local Cartesian frames defined uniquely by the spatial transformation, any physical quantity is shown to first experience a rigid rotation and then a stretch operation during the transformation. We show that the constraint conditions are not enough to determine completely the transformed relation for TA, leaving a possibility to define them differently as found in the literature. New acoustic transformations with constant density or modulus are also proposed and verified by constructing a two-dimensional acoustic cloak. Finally, we show that the transformed relation is uniquely determined for transformation optics, and discuss how this method can be extended to other transformation physics.

physics.optics↗

arXiv2011

Transformation Ray Method: Controlling High Frequency Elastic Waves

A transformation method based on elastic ray theory is proposed to control high frequency elastic waves. We show that ray path can be controlled in an exact manner, however energy distribution along the ray is only approximately controlled. A numerical example of an elastic rotator is provided to illustrate the method and to access the approximation. The proposed theory may be found potential applications in seismic wave protection and structure health monitoring.

physics.class-ph↗

arXiv2011

An approximate method for controlling solid elastic waves by transformation media

By idealizing a general mapping as a series of local affine ones, we derive approximately transformed material parameters necessary to control solid elastic waves within classical elasticity theory. The transformed elastic moduli are symmetric, and can be used with Navier's equation to manipulate elastic waves. It is shown numerically that the method can provide a powerful tool to control elastic waves in solids in case of high frequency or small material gradient. Potential applications can be anticipated in nondestructive testing, structure impact protection, petroleum exploration and seismology.

physics.class-ph↗

arXiv2011

Superlensing effect of an anisotropic metamaterial slab with near-zero dynamic mass

A metamaterial slab of anisotropic mass with one diagonal component being infinity and the other being zero is demonstrated to behave as a superlens for acoustic imaging beyond the diffraction limit. The underlying mechanism for extraordinary transmission of evanescent waves is attributed to the zero mass effect. Microstructure design for such anisotropic lens is also presented. In contrast to the anisotropic superlens based on Fabry-Pérot resonant mechanism, the proposed lens operates without the limitation on lens thickness, thus more flexible in practical applications. Numerical modeling is performed to validate the proposed ideas.

cond-mat.mtrl-sci↗

arXiv2010

Controlling elastic wave with isotropic transformation materials

There are great demands to design functional devices with isotropic materials, however the transformation method usually leads to anisotropic material parameters difficult to be realized in practice. In this letter, we derive the isotropic transformed material parameters in case of elastodynamic under local conformal transformation, they are subsequently used to design a beam bender, a four-beam antenna and an approximate carpet cloak for elastic wave with isotropic materials, the simulation results validate the derived transformed material parameters. The obtained materials are isotropic and greatly simplify subsequent experimental implementation.

physics.class-ph↗

arXiv2010

Negative effective mass below a cut-off frequency

Negative mass phenomena occurring below a cut-off frequency is examined by both theoretical and experimental methods. The paper begins with the investigation on a mass-spring structure, the effective mass of which is shown to be negative below a specific frequency. Due to the decaying nature of lattice waves in the negative-mass system, the transmission drop induced by negative effective mass is demonstrated experimentally. Further investigation is conducted for a rectangular solid waveguide with clamped boundary conditions. It is shown that the lowest bandgap mode of the clamped waveguide can be attributed to negative effective mass below a cut-off frequency. Based on this observation, elastic metamaterials made of the steel grid filled by styrene butadiene rubber are designed and fabricated. Both simulation and experimental analyses demonstrate that the designed metamaterial have negative effective mass below a cut-off frequency.

physics.class-ph↗

arXiv2010

Theory and experiment of isotropic electromagnetic beam bender made of dielectric materials

In this paper, we utilize the deformation transformation optics (DTO) method to design electromagnetic beam bender, which can change the direction of electromagnetic wave propagation as desire. According to DTO, the transformed material parameters can be expressed by deformation tensor of the spatial transformation. For a beam bender, since the three principal stretches at each point induced by the spatial transformation are independent to each other, there are many possibilities to simplify the transformed material parameters of the bender by adjusting the stretches independently. With the DTO method, we show that the reported reduced parameters of the bender obtained by equivalent dispersion relation can be derived as a special case. An isotropic bender is also proposed according to this method, and it is fabricated by stacking dielectric materials in layered form. Experiments validate the function of the designed isotropic bender for a TE wave; it is also shown that the isotropic bender has a broadband with low loss, compared with the metamaterial bender. The isotropic bender has much easier design and fabrication procedures than the metamaterial bender.

physics.optics↗

arXiv2010

Design method for quasi-isotropic transformation materials based on inverse Laplace's equation with sliding boundaries

The deformation method of transformation optics has been demonstrated to be a useful tool, especially in designing arbitrary and nonsingular transformation materials. Recently, there are emerging demands for isotropic material parameters, arising from the broadband requirement of the designed devices. In this work, the deformation method is further developed to design quasi-isotropic/isotropic transformation materials. The variational functional of the inverse Laplace's equation is investigated and found to involve the smooth and quasi-conformal nature of coordinate transformation. Together with the sliding boundary conditions, the inverse Laplace's equation can be utilized to give transformations which are conformal or quasi-conformal, depending on functionalities of interest. Examples of designing an arbitrary carpet cloak and a waveguide with arbitrary cross sections are given to validate the proposed idea. Compared with other quasi-conformal methods based on grid generation tools, the proposed method unifies the design and validation of transformation devices, and thus is much convenient.

physics.class-ph↗

arXiv2009

Design Arbitrary Shaped 2D Acoustic Cloak without Singularity

A method is proposed to design arbitrary shaped two dimensional (2D) isotropic-inertia acoustic cloaks without singularity. The method is based on the deformation view of the transformation method, where the transformation tensor A is identified as the deformation gradient tensor and the transformed material parameters can be expressed by the principal stretches in the principal system of the deformation. The infinite material parameters of a perfect 2D cloak is induced by an infinite principal stretch in one direction while the other two remains finite at the inner boundary during the transformation. To circumvent this difficulty, for a 2D cloak we can choose the principal stretch perpendicular to the cloak plane to be also infinite but in the same order as the infinite principal stretch in the cloak plane during the transformation, so the transformed material parameters may keep finite. To illustrate this idea, the analytical expressions of nonsingular material parameters for a cylindrical acoustic cloak are given. For the acoustic cloaks with irregular shapes, the numerical method is proposed to evaluate the principal stretches and in turn the nonsingular material parameters. The designed 2D cloaks are validated by numerical simulation.

physics.class-ph↗

arXiv2009

Nonsingular two dimensional cloak of arbitrary shape

We propose a general method to circumvent the singularity of arbitrary 2D cloaks, which arises from infinitely large values of material parameters at inner boundaries. The presented method is based on the deformation view of the transformation design method. It is shown that by adjusting the principle stretch out of the cloaking plane, 2D cloaks of arbitrary shapes without singularity can be constructed. It is also demonstrated that the method based on the equivalent dispersion relation and the design method for nonsingular 2D cloak from mirror-symmetric cross section of 3D cloak can be derived from the proposed theory. Examples of a cylindrical electromagnetic cloak and an arbitrary shaped 2D electromagnetic cloak without singularity are provided to illustrate the method.

physics.optics↗

arXiv2008

Design Method for Electromagnetic Cloak with Arbitrary Shapes Based on Laplace's Equation

In transformation optics, the space transformation is viewed as the deformation of a material. The permittivity and permeability tensors in the transformed space are found to correlate with the deformation field of the material. By solving the Laplace's equation, which describes how the material will deform during a transformation, we can design electromagnetic cloaks with arbitrary shapes if the boundary conditions of the cloak are considered. As examples, the material parameters of the spherical and elliptical cylindrical cloaks are derived based on the analytical solutions of the Laplace's equation. For cloaks with irregular shapes, the material parameters of the transformation medium are determined numerically by solving the Laplace's equation. Full-wave simulations based on the Maxwell's equations validate the designed cloaks. The proposed method can be easily extended to design other transformation materials for electromagnetic and acoustic wave phenomena.

physics.class-ph↗

arXiv2008

Calculation of material properties for arbitrary shape transformation media

We propose a general method to evaluate the material parameters for arbitrary shape transformation media. By solving the original coordinates in the transformed region via Laplace's equations, we can obtain the deformation field numerically, in turn the material properties of the devices to be designed such as cloaks, rotators or concentrators with arbitrary shape. Devices which have non-fixed outer boundaries, such as beam guider, can also be designed by the proposed method. Examples with full wave simulation are given for illustration. In the end, wave velocity and energy change in the transformation media are discussed with help of the deformation view.

physics.optics↗