Distributed feedback lasers in chiral media

The combined effects of chirality and gain (or loss) on wave propagation and coupling in periodic structures is investigated here. The focus is on distributed feedback (DFB) lasers in a transversely unbounded periodic slab with spatially modulated electromagnetic parameters. The analysis uses a coupled-mode approach employing a canonical physical model of chiral materials to predict the effects of modulated chirality admittance on DFB lasers. Results for DFB laser behavior in chiral media are compared and contrasted to that in achiral media. It is found that, under certain circumstances, the electric and magnetic field coupling, which is characteristic of chiral materials, results in a lower threshold gain for DFB lasers in media with a given index of refraction and characteristic impedance. It is also found that chiral index-coupled or gain-coupled DFB lasers exhibit the same spectral mode properties as achiral DFB lasers     

Image theory for chiral bodies

Image theory for a chiral body over a perfect electric or magnetic conducting ground plane is developed using the chiral volume equivalence theorem and conventional image theory for electric and magnetic currents. It is shown that the image of the chiral body has the same material parameters as the original body, except that the chirality admittance of the image is the negative of the original. In essence the mirror image of a chiral object is that object, such as a helix, with the opposite handedness. Alternatively, the same results can be obtained using tensor analysis     

Canonical sources and duality in chiral media [antenna arrays]

The authors examine the characteristics of antenna arrays embedded in unbounded chiral media using the Green's dyadic for electric sources and the Green's vector for magnetic sources. The purpose is to bring to light the new characteristics of sources, both point and extended, which interact with this medium and to examine general characteristics of sources located in a medium with handedness. Very simple quality relations are presented that are characteristic of chiral media when the results are written in terms of the circular eigenmodes. Appropriate measures of chirality such as the chirality admittance and impedance and a dimensionless chirality factor are introduced as needed. It is shown that, in the far field, both point and extended sources, whether electric or magnetic, radiate two electromagnetic eigenmodes which are of opposing handedness. Sources that access only one of the eigenmodes of the medium are demonstrated. Several applications of the results and array performance in chiral media are noted     

Periodic chiral structures

The electromagnetic properties of a structure that is both chiral and periodic are investigated using coupled-mode equations. The chirality is characterized by the constitutive relations D=εE+iξ_cB and H=iξ_cE+B/μ, where ξ_c is the chiral admittance. The periodicity is described by a sinusoidal perturbation of the permittivity, permeability, and chiral admittance. The coupled-mode equations are derived from physical considerations and used to examine bandgap structure and reflected and transmitted fields. Chirality is observed predominantly in transmission, whereas periodicity is present in both reflection and transmission     

A comprehensive study of discontinuities in chirowaveguides

We provide a comprehensive study of two- and three-dimensional discontinuities in chirowaveguides. The multimode coupled-mode method is an effective numerical approach to analyze this problem. After obtaining the coupled-mode equations, we diagonalize the coupling matrix to obtain a multimode scattering matrix rather than the usual two-mode approximation. We calculate the scattering properties of coaxial waveguides partially filled with lossy chiral media. Excellent agreement is observed between our results and those obtained by the mode-matching method. We also compare our results in the achiral case for dielectric material partially filled rectangular waveguide with experimental data and results obtained by the mode-matching method. Excellent agreement is again found. Based on our analysis, numerical and analytical results are displayed to provide physical insight into the problem. First, we discuss the effects of the chirality admittance on scattering properties and find that the sensitivity of the scattering parameters to chirality admittance increases as the chirality admittance increases. Second, we find the dielectric constant has a great influence on the scattering parameters. Third, we find the relative influence of height and width of chiral obstacles in rectangular waveguides.     

Reflection characteristics of chiral microwave absorbing coatings

The formulations of reflection coefficients for metal-backed one- and multi-layered chiral microwave absorbing coatings are derived in a much straight way in this paper. It is found that the propagation of normally incident plane waves in chiral coatings can be treated as in their achiral counterparts if the intrinsic impedance and wavenumber of the achiral structure are replaced by their associated chiral impedance and average chiral wavenumber, respectively. From a practical point of view, examples of one- and two-layered chiral microwave absorbing coatings are given, and the effects of the real and imaginary parts of the chiral admittance on the antireflection characteristics are examined for the first time, the results show that with a appropriate complex chiral admittance, the reduction in reflection can be enhanced and the minimum-reflection-frequency can be controlled.     

Shielding effect of hollow chiral sphere

The low-frequency shielding effect of a spherical layer is studied. The layer is made of a chiral material and it is electromagnetically characterized with three material parameters: permittivity, permeability, and chirality. Due to chirality, there is magnetoelectric coupling. The electric and magnetic shielding effects are derived and are shown to be functions of the three material parameters and also the relative thickness of the layer. Illustrations display the effects of the various parameters on the shielding, which is different for the magnetic and electric fields. Among the special effects is that the shielding increases rapidly as the chirality parameter approaches the refractive index of the shell. This makes chiral shells in principle effective shields, and in the future they may offer an alternative to conducting materials for novel shielding applications     

Calculation and measurement of the effective chirality parameter ofa composite chiral material over a wide frequency band

Materials that are effectively chiral at microwave frequencies can be fabricated by embedding identical, randomly oriented chiral inclusions, often metal helices, in a continuous matrix. We show that the chirality parameter can be calculated in the dilute limit using single scattering theory. The required tumble-averaged forward scattering by an individual inclusion is determined by the method of moments. Values of the effective chirality parameter are determined directly from the constitutive parameters of the matrix and the geometry and concentration of the inclusions. Comparisons are made with measurements previously reported in the literature. In addition, a chiral composite material was fabricated specifically to validate the calculations over frequencies including resonance. The measurements agree well with the calculations, providing quantitative values of the chirality parameter over a wide frequency band. It appears that the chirality parameter is appreciable only near the resonant frequencies of the inclusion. Finally, it is clear that an oscillator model can be used to describe the frequency dependence of the complex chirality parameter, and that therefore our results are consistent with the Kramers-Kronig relation     

A finite element analysis on electromagnetic waves in rectangular dielectric chirowaveguide

A finite element algorithm on eigenvalue problem of the dielectric waveguide with chiral material is presented. The chiral material is defined by the constitution relations which make the electromagnetic coupling between the electric and magnetic fields by means of the chirality admittance. The chiral material has potential applications in the areas of infrared and mm-wave band. For different chirality admittance, the computation is developed for different structure of waveguides which are difficult for analytical calculation. From the eigenvalues and the eigenvectors, the dispersion curves, the modes and the field patterns are obtained. The maximum value of dispersion curves is obvious greater than that without chiral material. The main points of the results of finite element calculation are consistent with those of analytical approach.     

A general expression of dyadic Green's functions in radiallymultilayered chiral media

A general expression of spectral-domain dyadic Green's function (DGF) is presented for defining the electromagnetic radiation fields in spherically arbitrary multilayered and chiral media. Without any loss of the generality, each of the radial multilayers could be the chiral layer with different permittivity, permeability, and chirality admittance, while both distribution and location of current sources are assumed to be arbitrary. The DGF is composed of the unbounded DGF and the scattering DGF, based on the method of scattering superposition. The scattering DGF in each layer is constructed in terms of the modified and normalized spherical vector wave functions. The coefficients of the scattering DGFs are derived and expressed in terms of the equivalent reflection and transmission coefficients, by applying boundary conditions satisfied by the coefficient matrices     

任意分层手征介质球域中并矢格林函数理论和应用

本文首先应用散射迭加法，给出了含源任意分层手征介质球域中的并矢格林函数，以手征介质球壳为例，分析了位于球中心处点偶极天线的辐射特性，以及归一化辐射阻抗随球壳厚度的变化规律，在平板近似条件下，研究了手征导纳对手征介质球壳传输特性的影响，并且讨论了手征介质球壳内、外表面与空气之间阻抗匹配时，点偶极天线远区辐射场的极化特性。结果表明，通过改变球壳的归一化厚度，可以调节辐射场的极化状态。     

双层手征介质板中电偶极天线的辐射特性

本文首先给出了电流源激励下双层手征介质中的并矢格林函数表达式。应用鞍点积分法,导出了有金属板衬底的双层手征介质中电偶极天线的辐射场表达式。分析了有、无空气隙时手征导纳对电偶极天线的方向图,＝0方向的最大场强和谐振频率的影响程度。结果表明,通过改变手征导纳参数,可以有效地调节电偶极天线的辐射特性。     

Field analysis of a general chiral planar waveguide

The propagation characteristics of general chiral planar waveguides are presented. This is the first time the eigen equation is given in a simple formulation. The results indicate that there are two types of field distribution which is related to the working wavelength and chiral admittance. When the chiral admittance is larger than a certain value, the fields of one kind of circularly polarized wave in the core become exponentially damping in the transverse direction.     

Measurement and prediction of helix-loaded chiral composites

A method is described for the extraction of the permittivity, permeability, and chirality of composite chiral materials, using measurements of reflection and transmission in a circular waveguide. This has been applied to a number of helix-loaded composites, in the frequency band 8-12 GHz. The properties of these composites have also been computed from the helix geometry and other basic information. The theory correctly predicts the frequency of the half-wavelength resonance observed, the relative magnitude of the constitutive parameters, and the low-frequency dielectric constant. But it has been found necessary to adjust the host-medium loss to obtain the correct absolute magnitudes. This agreement provides a confirmation that the theory is basically sound and so assists in discovering what chiral parameters are practically obtainable and in exploring applications of chiral materials     

Reflection and transmission of guided electromagnetic waves at anair-chiral interface and at a chiral slab in a parallel-plate waveguide

Recently, the concept of chirowaveguides, which exhibit some novel and interesting properties due to electromagnetic chirality, was introduced and studied elsewhere. In this paper, the authors analyze theoretically another problem associated with chirowaveguides, namely, the problem of reflection and transmission of guided waves at an air-chiral interface and at a chiral slab located transversely in a parallel-plate waveguide. The notable features and the role of chirality of the medium on the reflected and transmitted guided waves are discussed, and physical insights into these results are provided. It is found that since the guided modes inside the chiral region of the waveguide are hybrid, in order to satisfy the boundary conditions at interfaces, the reflected and transmitted guided modes in the air regions of the waveguides need to be of TE and TM modes. The motivation behind this study is the potential applications of this problem to the design of novel measurement techniques for determining material parameters of chiral composites     

Modeling effective properties of chiral composites

After a brief overview of the concepts of electromagnetic chirality and wave propagation in chiral media, this paper deals with the field of microwave-chiral-material modeling. First, studies regarding the scattering of single-chiral or non-chiral elements with different shapes (various designs of helices, Ω-shaped scatterers, wires, and loops) are presented. Results of the backscattered field given by different computer codes are compared. Comparisons among analytical, numerical, and experimental results are also reported. Second, the case of a collection of chiral inclusions is treated. A review of different methods, developed to estimate average properties of helix-loaded materials, is given. Modeling of the effective properties of a chiral slab, such as the rotation angle, ellipticity, permittivity, and permeability, is explored. Reflection and transmission coefficients, evaluated by various methods, are compared with each other, and with measurements. Limitations of the models, possible improvements, and new directions for research are also described. Finally, applications of such composites to the design of radar-absorbing materials are addressed     

Electromagnetic waves in Faraday chiral media

Plane wave propagation in two kinds of Faraday chiral media, where Faraday rotation is combined with optical activity, is studied to examine methods of controlling chirality. The two types of media studied are magnetically biased chiroplasmas and chiroferrites. For propagation along the biasing magnetic field, four wavenumbers and two wave impedances are found which are dependent on the strength of the biasing field. Dispersion diagrams for the chiroplasma case are plotted. Propagation at the plasma frequency of the chiroplasma is also investigated     

Analysis of Circular Dielectric Waveguide with Chiral Cladding

The propagation characteristics of a circular dielectric waveguide with chiral media filled in the cladding are investigated. The relation between the cutoff frequency and the chiral admittance, the dispersion curves for some modes with different angular mode numbers and the transverse distribution of fields are presented. Some new features different from the ordinary circular dielectric waveguide are resulted. The results show that the cladding chirality may lead to a single-mode operation in the circular dielectric waveguide.     

手征光纤中导模的色散特性

从手征介质中的电磁场本构关系出发，利用麦克斯韦方程组，对纤芯和包层都是手征介质构成的阶跃型手征光纤进行了解析求解，导出了模式场解和特征方程。用数值方法研究了纤芯和包层的手征导纳对手征光纤中导模的归一化传播常数、群延迟、波导色散等特性的影响。     

The electric quadrupole contribution to the circular birefringenceof nonmagnetic anisotropic chiral media: a circular waveguide experiment

Constitutive relations which include electric quadrupole terms, in addition to electric and magnetic dipole terms, are used to describe the “optical activity”, in particular the circular birefringence, of an anisotropic chiral medium which is nonmagnetic. The resulting permittivity and chirality tensors are then used to predict the rotation of the polarization plane of a linearly polarized wave propagating in a circular waveguide filled with the medium. The numerical predictions were tested by measurements between 2.4 and 4 GHz on a 2 m long artificial crystal in a circular waveguide and it was found that the rotation of the polarization was within 13% of the predicted value-good agreement after considering the possible sources of error. It is thus established that the effect of electric quadrupoles must be included when modeling the optical activity of anisotropic chiral media in the long wavelength regime. The anisotropic chiral media which are dealt with here can be classified according to the crystallographic point groups to which they belong, and they may therefore also be considered to be artificial crystals