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Mode conversion of transverse electromagnetic waves into longitudinaloscillations and the associated resonant absorption of wave energy ininhomogeneous plasmas is a phenomenon that has been studied extensively inplasma physics. We show that precisely analogous phenomena occur generically inelectronic and photonic systems where dispersionless flat bands and dispersivebands coexist in the presence of an inhomogeneous potential or mediumparameter. We demonstrate that the systems described by the pseudospin-1 Diracequation with two dispersive bands and one flat band display mode conversionand resonant absorption in a very similar manner to $p$-polarizedelectromagnetic waves in an unmagnetized plasma by calculating the modeconversion coefficient explicitly using the invariant imbedding method. We alsoshow that a similar mode conversion process takes place in many other systemswith a flat band such as pseudospin-2 Dirac systems, continuum models obtainedfor one-dimensional stub and sawtooth lattices, and two-dimensional electronsystems with a quadratic band and a nearly flat band. We discuss someexperimental implications of mode conversion in flat-band materials andmetamaterials.

Mode conversion and resonant absorption in inhomogeneous materials with flat bands