Akhlesh Lakhtakia, Tom G. Mackay
Dyadic Green functions for time-harmonic fields in a homogeneous, isotropic, dielectric-magnetic medium, moving with constant velocity, are derived by first implementing a simple transformation and then using the dyadic Green functions available for uniaxial dielectric-magnetic mediums.
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The relative permittivity dyadic of a dielectric structurally chiral material (SCM) varies helicoidally along a fixed direction; in consequence, the SCM exhibits the circular Bragg phenomenon, which is the circular-polarization-selective reflection of light. The introduction of hyperbolicity in an SCM---by making either one or two but not all three eigenvalues of the relative permittivity dyadic acquire negative real parts---does not eliminate the circular Bragg phenomenon, but significantly alters the regime for its exhibition. Physical vapor deposition techniques appear to be suitable to fab…
Vector spherical wavefunctions were derived in closed-form to represent time-harmonic electromagnetic fields in an orthorhombic dielectric-magnetic material with gyrotropic-like magnetoelectric properties. These wavefunctions were used to formulate the T matrix for scattering by a three-dimensional object composed of the chosen material. Furthermore, a closed-form, coordinate-free expression of the dyadic Green function for the chosen material was derived. Expressions ascertained for the singularity behavior will be useful for formulating volume integral equations for scattering inside the cho…
The dyadic Green functions for a uniaxial dielectric-magnetic medium, together with a reversible field transformation, were implemented to derive a formulation of the Huygens principle appropriate to a uniaxial dielectric-magnetic medium with gyrotropic-like magnetoelectric properties.
A random mixture of two isotropic dielectric materials, one composed of oriented spheroidal particles of relative permittivity $ε_a$ and the other composed of oriented spheroidal particles of relative permittivity $ε_b$, was considered in the long wavelength regime. The permittivity dyadic of the resulting homogenized composite material (HCM) was estimated using the Bruggeman homogenization formalism. The HCM was an orthorhombic biaxial material if the symmetry axes of the two populations of spheroids were mutually perpendicular and a uniaxial material if these two axes were mutually aligned. …
The extended boundary condition method can be used to study planewave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative permeability dyadic. The scattered and internal field phasors can be expanded in terms of appropriate vector spherical wavefunctions with unknown expansion coefficients, whereas the incident field phasors can be similarly expanded but with known expansion coefficients. The scattered-field coefficients are related to the incident-field coefficients through a matrix. The sc…
An ambichiral structure comprising sheets of an anisotropic dielectric material rejects normally incident plane waves of one circular polarization (CP) state but not of the other CP state, in its fundamental Bragg regime. However, if the same structure is made of an dielectric--magnetic material with indefinite permittivity and permeability dyadics, it may function as a polarization--universal rejection filter because two of the four planewave components of the electromagnetic field phasors in each sheet are of the positive--phase--velocity type and two are of the negative--phase--velocity typ…
A general analytic form of the full 6x6 dyadic Green's function of a spherically symmetric open optical system is presented, with an explicit solution provided for a homogeneous sphere in vacuum. Different spectral representations of the Green's function are derived using the Mittag-Leffler theorem, and their convergence to the exact solution is analyzed, allowing us to select optimal representations. Based on them, more efficient versions of the resonant-state expansion (RSE) are formulated, with a particular focus on the static mode contribution, including versions of the RSE with a complete…
A dielectric columnar thin film (CTF), characterized macroscopically by a relative permittivity dyadic, was investigated theoretically with the assumption that, on the nanoscale, it is an assembly of parallel, identical, elongated ellipsoidal inclusions made of an isotropic dielectric material that has a different refractive index from the bulk material that was evaporated to fabricate the CTF. The inverse Bruggeman homogenization formalism was developed in order to estimate the refractive index of the deposited material, one of the two shape factors of the ellipsoidal inclusions, and the volu…
Based on the dyadic Green's function (DGF) method, we present a formalism to study the propagation of electromagnetic fields with slowly varying amplitude (EMFSVA) in dispersive anisotropic media with two dyadic constitutive parameters, the dielectric permittivity and the magnetic permeability. We find the matrix elements of the envelope DGFs by applying the formalism for uniaxial anisotropic metamaterials. We present the relations for the velocity of the EMFSVA envelopes which agree with the known definition of the group velocity in dispersive media. We consider examples of propagation of the…
The extended boundary condition method can be formulated to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative permeability dyadic, when the constitutive principal axes are arbitrarily oriented with respect to the shape principal axes. Known vector spherical wavefunctions are used to represent the fields in the surrounding matter-free space. After deriving closed-form expressions for the vector spherical wavefunctions for the scattering material, the internal fields are rep…
We design planar silicon antennas for controlling the emission rate of magnetic or electric dipolar emitters. Evolutionary algorithms coupled to the Green Dyadic Method lead to different optimized geometries which depend on the nature and orientation of the dipoles. We discuss the physical origin of the obtained configurations thanks to modal analysis but also emphasize the role of nanoscale design of the LDOS. We complete our study using finite element method and demonstrate an enhancement up to 2000 of the magnetic Purcell factor in europium ions. Our work brings together random optimization…
An effective cylindrical cloak may be conceptualized as an assembly of adjacent local neighbourhoods, each of which is made from a homogenized composite material (HCM). The HCM is required to be a certain uniaxial dielectric-magnetic material, characterized by positive-definite constitutive dyadics. It can arise from the homogenization of remarkably simple component materials, such as two isotropic dielectric-magnetic materials, randomly distributed as oriented spheroidal particles. By carefully controlling the spheroidal shape of the component particles, a high degree of HCM anisotropy may be…
Dyadic Greens function for a topological insulator stratified sphere
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Planewave propagation in a simply moving, dielectric-magnetic medium that is isotropic in the co-moving reference frame, is classified into three different categories: positive-, negative-, and orthogonal-phase-velocity (PPV, NPV, and OPV). Calculations from the perspective of an observer located in a non-co-moving reference frame show that, whether the nature of planewave propagation is PPV or NPV (or OPV in the case of nondissipative mediums) depends strongly upon the magnitude and direction of that observer's velocity relative to the medium. PPV propagation is characterized by a positive re…
Hyperbolic phonon polaritons (HPhPs) are generated when infrared photons couple to polar optic phonons in anisotropic media, confining long-wavelength light to nanoscale volumes. However, to realize the full potential of HPhPs for infrared optics, it is crucial to understand propagation and loss mechanisms on substrates suitable for applications from waveguiding to infrared sensing. In this paper, we employ scattering-type scanning near-field optical microscopy (s-SNOM) and nano-Fourier transform infrared (FTIR) spectroscopy, in concert with analytical and numerical calculations, to elucidate …
Coupled Dipole Oscillation Enabled Scintillation Compensation in Turbulence-Impacted Laser Beam
本工作扩展洛伦兹模型至非线性恢复力，结合并矢格林函数建立非局域介质框架，通过简正模式微扰展开获得有效非线性磁化率核，并利用标量格林函数推导输出场，桥接微观偶极动力学与宏观光学传播，为湍流影响下的激光闪烁补偿提供理论支撑。
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