Differential Form Valued Forms and Distributional Electromagnetic Sources

Properties of a fundamental double-form of bi-degree $(p,p)$ for $p\ge 0$ are reviewed in order to establish a distributional framework for analysing equations of the form $$\Delta \Phi + \lambda^2 \Phi = {\cal S}$$ where $\Delta$ is the Hodge-de Rham operator on $p-$forms $\Phi$ on ${\bf R}^3$. Particular attention is devoted to singular distributional solutions that arise when the source ${\cal S}$ is a singular $p-$form distribution. A constructive approach to Dirac distributions on (moving) submanifolds embedded in ${\bf R}^3$ is developed in terms of (Leray) forms generated by the geometry of the embedding. This framework offers a useful tool in electromagnetic modeling where the possibly time dependent sources of certain physical attributes, such as electric charge, electric current and polarization or magnetization, are concentrated on localized regions in space.Comment: 40 page

Electrodynamics of balanced charges

In this work we modify the wave-corpuscle mechanics for elementary charges introduced by us recently. This modification is designed to better describe electromagnetic (EM) phenomena at atomic scales. It includes a modification of the concept of the classical EM field and a new model for the elementary charge which we call a balanced charge (b-charge). A b-charge does not interact with itself electromagnetically, and every b-charge possesses its own elementary EM field. The EM energy is naturally partitioned as the interaction energy between pairs of different b-charges. We construct EM theory of b-charges (BEM) based on a relativistic Lagrangian with the following properties: (i) b-charges interact only through their elementary EM potentials and fields; (ii) the field equations for the elementary EM fields are exactly the Maxwell equations with proper currents; (iii) a free charge moves uniformly preserving up to the Lorentz contraction its shape; (iv) the Newton equations with the Lorentz forces hold approximately when charges are well separated and move with non-relativistic velocities. The BEM theory can be characterized as neoclassical one which covers the macroscopic as well as the atomic spatial scales, it describes EM phenomena at atomic scale differently than the classical EM theory. It yields in macroscopic regimes the Newton equations with Lorentz forces for centers of well separated charges moving with nonrelativistic velocities. Applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the same for the Schrodinger model with any desired accuracy.Comment: Manuscript was edited to improve the exposition and to remove noticed typo

General Relativity in Electrical Engineering

In electrical engineering metamaterials have been developed that offer unprecedented control over electromagnetic fields. Here we show that general relativity lends the theoretical tools for designing devices made of such versatile materials. Given a desired device function, the theory describes the electromagnetic properties that turn this function into fact. We consider media that facilitate space-time transformations and include negative refraction. Our theory unifies the concepts operating behind the scenes of perfect invisibility devices, perfect lenses, the optical Aharonov-Bohm effect and electromagnetic analogs of the event horizon, and may lead to further applications

A rigorous analysis of high order electromagnetic invisibility cloaks

There is currently a great deal of interest in the invisibility cloaks recently proposed by Pendry et al. that are based in the transformation approach. They obtained their results using first order transformations. In recent papers Hendi et al. and Cai et al. considered invisibility cloaks with high order transformations. In this paper we study high order electromagnetic invisibility cloaks in transformation media obtained by high order transformations from general anisotropic media. We consider the case where there is a finite number of spherical cloaks located in different points in space. We prove that for any incident plane wave, at any frequency, the scattered wave is identically zero. We also consider the scattering of finite energy wave packets. We prove that the scattering matrix is the identity, i.e., that for any incoming wave packet the outgoing wave packet is the same as the incoming one. This proves that the invisibility cloaks can not be detected in any scattering experiment with electromagnetic waves in high order transformation media, and in particular in the first order transformation media of Pendry et al. We also prove that the high order invisibility cloaks, as well as the first order ones, cloak passive and active devices. The cloaked objects completely decouple from the exterior. Actually, the cloaking outside is independent of what is inside the cloaked objects. The electromagnetic waves inside the cloaked objects can not leave the concealed regions and viceversa, the electromagnetic waves outside the cloaked objects can not go inside the concealed regions. As we prove our results for media that are obtained by transformation from general anisotropic materials, we prove that it is possible to cloak objects inside general crystals.Comment: The final version is now published in Journal of Physics A: Mathematical and Theoretical, vol 41 (2008) 065207 (21 pp). Included in IOP-Selec

The Boundary Conditions for Point Transformed Electromagnetic Invisibility Cloaks

In this paper we study point transformed electromagnetic invisibility cloaks in transformation media that are obtained by transformation from general anisotropic media. We assume that there are several cloaks located in different points in space. Our results apply in particular to the first order invisibility cloaks introduced by Pendry et al. and to the high order invisibility cloaks introduced by Hendi et al. and by Cai et al.. We identify the appropriate {\it cloaking boundary conditions} that the solutions of Maxwell equations have to satisfy at the outside, $\partial K_+$, and at the inside, $\partial K_-$, of the boundary of the cloaked object $K$. Namely, that the tangential components of the electric and the magnetic fields have to vanish at $\partial K_+$ -what is always true- and that the normal components of the curl of the electric and the magnetic fields have to vanish at $\partial K_-$. These results are proven requiring that energy be conserved. In the case of one spherical cloak with a spherically stratified $K$ and a radial current at $\partial K$ we verify by an explicit calculation that our {\it cloaking boundary conditions} are satisfied and that cloaking of active devices holds even if the current is at the boundary of the cloaked object. As we prove our results for media that are obtained by transformation from general anisotropic media, our results apply to the cloaking of objects with active and passive devices contained in general anisotropic media, in particular to objects with active and passive devices contained inside general crystals.Comment: This final, published, version has been edited, comments have been adde

Theory of quantum radiation observed as sonoluminescence

Sonoluminescence is explained in terms of quantum radiation by moving interfaces between media of different polarizability. In a stationary dielectric the zero-point fluctuations of the electromagnetic field excite virtual two-photon states which become real under perturbation due to motion of the dielectric. The sonoluminescent bubble is modelled as an optically empty cavity in a homogeneous dielectric. The problem of the photon emission by a cavity of time-dependent radius is handled in a Hamiltonian formalism which is dealt with perturbatively up to first order in the velocity of the bubble surface over the speed of light. A parameter-dependence of the zero-order Hamiltonian in addition to the first-order perturbation calls for a new perturbative method combining standard perturbation theory with an adiabatic approximation. In this way the transition amplitude from the vacuum into a two-photon state is obtained, and expressions for the single-photon spectrum and the total energy radiated during one flash are given both in full and in the short-wavelengths approximation when the bubble is larger than the wavelengths of the emitted light. It is shown analytically that the spectral density has the same frequency-dependence as black-body radiation; this is purely an effect of correlated quantum fluctuations at zero temperature. The present theory clarifies a number of hitherto unsolved problems and suggests explanations for several more. Possible experiments that discriminate this from other theories of sonoluminescence are proposed.Comment: Latex file, 28 pages, postscript file with 3 figs. attache

Plasmonic nanoparticle monomers and dimers: From nano-antennas to chiral metamaterials

We review the basic physics behind light interaction with plasmonic nanoparticles. The theoretical foundations of light scattering on one metallic particle (a plasmonic monomer) and two interacting particles (a plasmonic dimer) are systematically investigated. Expressions for effective particle susceptibility (polarizability) are derived, and applications of these results to plasmonic nanoantennas are outlined. In the long-wavelength limit, the effective macroscopic parameters of an array of plasmonic dimers are calculated. These parameters are attributable to an effective medium corresponding to a dilute arrangement of nanoparticles, i.e., a metamaterial where plasmonic monomers or dimers have the function of "meta-atoms". It is shown that planar dimers consisting of rod-like particles generally possess elliptical dichroism and function as atoms for planar chiral metamaterials. The fabricational simplicity of the proposed rod-dimer geometry can be used in the design of more cost-effective chiral metamaterials in the optical domain.Comment: submitted to Appl. Phys.

A significant proportion of classic Hodgkin lymphoma recurrences represents clonally unrelated second primary lymphoma

Despite high cure rates in classic Hodgkin lymphoma (cHL), relapses are observed. Whether relapsed cHL represents second primary lymphoma or an underlying T-cell lymphoma (TCL) mimicking cHL is under-investigated. To analyze the nature of cHL recurrences, in-depth clonality testing of immunoglobulin (IG) and T-cell receptor (TR) rearrangements was performed in paired cHL diagnosis and recurrences of 60 patients, supported by targeted mutation analysis of lymphoma-associated genes. Clonal IG rearrangements were detected by next-generation sequencing (NGS) in 69/120 (58%) diagnosis and recurrence samples. The clonal relationship could be established in 34 cases, identifying clonally related relapsed cHL in 24/34 patients (71%). Clonally unrelated cHL was observed in 10/34 patients (29%) as determined by IG-NGS clonality assessment, and confirmed by the identification of predominantly mutually exclusive gene mutations in the paired cHL samples. In recurrences of &gt;2 years, ~60% of cHL patients for which the clonal relationship could be established showed a second primary cHL. Clonal TR gene rearrangements were identified in 14/125 samples (11%), and TCL-associated gene mutations were detected in 7/14 samples. Retrospective pathology review with integration of the molecular findings were consistent with an underlying TCL in 5 patients aged &gt;50 years. This study shows that cHL recurrences, especially after 2 years, sometimes represent a new primary cHL or TCL mimicking cHL, as uncovered by NGS-based IG/TR clonality testing and gene mutation analysis. Given the significant therapeutic consequences, molecular testing of a presumed relapse in cHL is crucial for subsequent appropriate treatment strategies adapted to the specific lymphoma presentation.</p

A significant proportion of classic Hodgkin lymphoma recurrences represents clonally unrelated second primary lymphoma

Despite high cure rates in classic Hodgkin lymphoma (cHL), relapses are observed. Whether relapsed cHL represents second primary lymphoma or an underlying T-cell lymphoma (TCL) mimicking cHL is under-investigated. To analyze the nature of cHL recurrences, in-depth clonality testing of immunoglobulin (IG) and T-cell receptor (TR) rearrangements was performed in paired cHL diagnosis and recurrences of 60 patients, supported by targeted mutation analysis of lymphoma-associated genes. Clonal IG rearrangements were detected by next-generation sequencing (NGS) in 69/120 (58%) diagnosis and recurrence samples. The clonal relationship could be established in 34 cases, identifying clonally related relapsed cHL in 24/34 patients (71%). Clonally unrelated cHL was observed in 10/34 patients (29%) as determined by IG-NGS clonality assessment, and confirmed by the identification of predominantly mutually exclusive gene mutations in the paired cHL samples. In recurrences of &gt;2 years, ~60% of cHL patients for which the clonal relationship could be established showed a second primary cHL. Clonal TR gene rearrangements were identified in 14/125 samples (11%), and TCL-associated gene mutations were detected in 7/14 samples. Retrospective pathology review with integration of the molecular findings were consistent with an underlying TCL in 5 patients aged &gt;50 years. This study shows that cHL recurrences, especially after 2 years, sometimes represent a new primary cHL or TCL mimicking cHL, as uncovered by NGS-based IG/TR clonality testing and gene mutation analysis. Given the significant therapeutic consequences, molecular testing of a presumed relapse in cHL is crucial for subsequent appropriate treatment strategies adapted to the specific lymphoma presentation.</p

A significant proportion of classic Hodgkin lymphoma recurrences represents clonally unrelated second primary lymphoma

Despite high cure rates in classic Hodgkin lymphoma (cHL), relapses are observed. Whether relapsed cHL represents second primary lymphoma or an underlying T-cell lymphoma (TCL) mimicking cHL is under-investigated. To analyze the nature of cHL recurrences, in-depth clonality testing of immunoglobulin (IG) and T-cell receptor (TR) rearrangements was performed in paired cHL diagnosis and recurrences of 60 patients, supported by targeted mutation analysis of lymphoma-associated genes. Clonal IG rearrangements were detected by next-generation sequencing (NGS) in 69/120 (58%) diagnosis and recurrence samples. The clonal relationship could be established in 34 cases, identifying clonally related relapsed cHL in 24/34 patients (71%). Clonally unrelated cHL was observed in 10/34 patients (29%) as determined by IG-NGS clonality assessment, and confirmed by the identification of predominantly mutually exclusive gene mutations in the paired cHL samples. In recurrences of &gt;2 years, ~60% of cHL patients for which the clonal relationship could be established showed a second primary cHL. Clonal TR gene rearrangements were identified in 14/125 samples (11%), and TCL-associated gene mutations were detected in 7/14 samples. Retrospective pathology review with integration of the molecular findings were consistent with an underlying TCL in 5 patients aged &gt;50 years. This study shows that cHL recurrences, especially after 2 years, sometimes represent a new primary cHL or TCL mimicking cHL, as uncovered by NGS-based IG/TR clonality testing and gene mutation analysis. Given the significant therapeutic consequences, molecular testing of a presumed relapse in cHL is crucial for subsequent appropriate treatment strategies adapted to the specific lymphoma presentation.</p