Abstract
We introduce the concept of the envelope dyadic Green’s function (EDGF) and 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 EDGFs 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 EMFSVA passing through active and passive media with the Lorentz and the Drude type dispersions, demonstrating beam focusing in hyperbolic media and superluminal propagation in media with inverted population. The results of this paper are applicable to the propagation of modulated electromagnetic fields and slowly varying amplitude fluctuations of such fields through frequency dispersive and dissipative (or active) anisotropic metamaterials. The developed approach can be also used for the analysis of metamaterial-based waveguides, filters, and delay lines.
Highlights
We introduce the concept of the envelope dyadic Green’s function (EDGF) and 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
Here we introduce the concept of the envelope dyadic Green’s function (EDGF) and develop a related formalism to deal with the electromagnetic fields with slowly varying amplitude (EMFSVA) in dispersive anisotropic MMs with known dyadics of permittivity (ε) and permeability (μ)
We have presented the EDGF concept and the related formalism which are applicable for studying the propagation of the amplitude fluctuations of quasi-monochromatic electromagnetic field in anisotropic dispersive media
Summary
We introduce the concept of the envelope dyadic Green’s function (EDGF) and 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. When dealing with the amplitude and phase fluctuations of the electromagnetic fields in such MMs, it is appealing to construct a framework in which the generation and propagation of such excitations is described by linear operators acting directly on the slowly varying envelope of the excitations In pursuing this goal, here we introduce the concept of the envelope dyadic Green’s function (EDGF) and develop a related formalism to deal with the electromagnetic fields with slowly varying amplitude (EMFSVA) in dispersive anisotropic MMs with known dyadics of permittivity (ε) and permeability (μ). Besides the RHT problems, the EDGF approach is well suited for dealing with spatio-temporally modulated signals in dispersive uniaxial MMs, e.g. when studying the spatio-temporal transformations (refraction, deflection, focusing, etc.) of modulated Gaussian beams in flat lenses and hyperlenses based on such media Having these applications in mind, here we derive the paraxial approximation of the EDGF method applicable to the uniaxial MM layers, in particular, MMs with extreme anisotropy and wire media. In extremely anisotropic uniaxial MMs the beam diffraction effects can be suppressed, which creates new opportunities for the flexible control of the RHT in MMs
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