Abstract |
| This detailed write-up reviews very nature of negative refraction vis-à-vis existing physical thoughts. Why this project is called as “Left Handed Maxwell Systems” is due to counterintuitive nature of the cross product we need to take in the Maxwell equations, to satisfy that wave vector as opposite to the Poynting vector when the dielectric permittivity and magnetic permeability are both negatives; that is giving us a media of refractive index negative. This detailed note explains these phenomena, with mathematical and possible physical explanations via thought experiment; elaborating concepts of ‘backward wave’, ‘hidden momentum’, ‘negative root’, and several counterintuitive topics. Though several approaches to explain these counterintuitive phenomena have been evolving, yet it is interesting if in the meta-material parlance particle-wave theory be founded! Here we give possible classical explanations to these counterintuitive phenomena and also a new explanation regarding (quantized) energy momentum, wave equation if applied to this negative indexed material: how shall they look, vis-à-vis positive indexed systems. Here, we propose the concept of reactive energy and expression for new wave-momentum for pulse of electromagnetic energy inside a medium (negative refractive indexed), with suitable derivation along with possible new wave equation. We have started to explain some basics which otherwise we all take as granted as though the concept are very simple, for instance, we have spent considerable effort here to bring out dispersion concept of refractive index via classical electrodynamics principles. Also, we tried to give clear simple concept of radiation pressure via kinetic theory of gases, and as to if the volume is with negative refraction the pressure formula gives negative answer, which needs attention. We tried to elaborate via simple thought experiments the meaning of energy momentum of a single radiation pulse - a photon; and proceeded for quantizing the same. We have tried to give visual picture of a single photon and then its mathematical representation. We also have included simple thought experiments to elucidate the principle of the mechanical, and wave momentum and need to have new wave momentum; along with an interpretation of constant multiplier, i.e., C2, as equivalent (and not always equal to) as product of group and phase velocities. In this detailed note, we have tried to generalize the classical wave equation and proposed a new one so that wave propagation of negative indexed materials is covered. Before concluding, we have tried to evolve the basic discussion on why shall a negative root be taken for product of two negative numbers (negative epsilon and negative mu)! This note may be taken as some sort or review paper, and/or thought provoking popular science article; the details are difficult to find elsewhere; as enquired by several researchers across the globe. |
Keywords and phrases
Negative Indexed Material (NRM), meta-material, group refractive index, phase refractive index, phase momentum, wave momentum, pseudo-momentum, hidden momentum, left handed cross product, group and phase velocity, mechanical momentum, reactive energy, polariton, phonon, nihility.
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