We consider single-layer arrays of electrically small lossy bi-anisotropic particles that completely absorb electromagnetic waves at normal incidence. Required conditions for electromagnetic properties of bi-anisotropic particles have been identified in the most general case of uniaxial reciprocal and nonreciprocal particles. We consider the design possibilities offered by the particles of all four fundamental classes of bianisotropic inclusions: reciprocal chiral and omega particles and nonreciprocal Tellegen and moving particles. We also study the reflection/transmission properties of asymmetric structures with different properties when illuminated from the opposite sides of the sheet. It has been found that it is possible to realize single-layer grids which exhibit the total absorption property when illuminated from one side but are totally transparent when illuminated from the other side (an ultimately thin isolator). Other possible properties are co-polarized or twist polarized reflection from the side opposite to the absorbing one. Finally, we discuss possible approaches to practical realization of particles with the properties required for single-layer perfect absorbers and other proposed devices.
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