Abstract
The ability to control electromagnetic fields, heat currents, electric currents, and other physical phenomena by coordinate transformation methods has resulted in novel functionalities, such as cloaking, field rotations, and concentration effects. Transformation optics, as the underlying mathematical tool, has proven to be a versatile approach to achieve such unusual outcomes relying on materials with highly anisotropic and inhomogeneous properties. Most applications and designs thus far have been limited to functionalities within a single physical domain. Here we present transformation optics applied to thermoelectric phenomena, where thermal and electric flows are coupled via the Seebeck coefficient. Using laminates, we describe a thermoelectric cloak capable of hiding objects from thermoelectric flow. Our calculations show that such a cloak does not depend on the particular boundary conditions and can also operate in different single domain regimes. These proof-of-principle results constitute a significant step forward towards finding unexplored ways to control and manipulate coupled transport.
Highlights
Designing metamaterials (MMs), artificial systems with functionalities unattainable with naturally occurring materials, is a promising direction with far reaching consequences[1,2,3,4,5]
transformation optics (TO) techniques have been indispensable in the design of MMs for bifunctional cloaks, which can operate in the simultaneous presence of temperature and voltage gradients
In this work the following fundamental question is addressed: Can the versatility of TO techniques be used to mold thermoelectric flow and achieve effects not possible to observe with natural materials? This problem requires generalizing the diffusive nature of thermodynamic flows by taking into account the coupling between heat and electricity via the Seebeck coefficient
Summary
Designing metamaterials (MMs), artificial systems with functionalities unattainable with naturally occurring materials, is a promising direction with far reaching consequences[1,2,3,4,5]. Optical devices, including invisibility cloaks, field concentrators, and rotators have been designed based on a medium with a spatially changing refractive index that alters light propagation pathways[7,8,9,10,11,12,13] Some of this progress has relied on transformation optics (TO), a powerful mathematical tool that enables molding the electromagnetic energy flow in desired ways by using fictitious spatial distortions mapped into material composites capable of guiding light[14,15,16,17]. Electromagnetic flow is associated with the wave-like electromagnetic nature of charge density propagation while heat and particle diffusion propagation are not mediated by waves, the physical behavior of this stationary transport is the same This point has been explored recently by constructing bifunctional cloaks capable of guiding both, heat and electric currents[38,39,40,41]. Since such materials are not readily available in nature, using bilayer composites we construct laminate MMs by finding the specific properties necessary to achieve a cloaking effect
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