  Mode conversion of transverse electromagnetic waves into longitudinal
oscillations and the associated resonant absorption of wave energy in
inhomogeneous plasmas is a phenomenon that has been studied extensively in
plasma physics. We show that precisely analogous phenomena occur generically in
electronic and photonic systems where dispersionless flat bands and dispersive
bands coexist in the presence of an inhomogeneous potential or medium
parameter. We demonstrate that the systems described by the pseudospin-1 Dirac
equation with two dispersive bands and one flat band display mode conversion
and resonant absorption in a very similar manner to $p$-polarized
electromagnetic waves in an unmagnetized plasma by calculating the mode
conversion coefficient explicitly using the invariant imbedding method. We also
show that a similar mode conversion process takes place in many other systems
with a flat band such as pseudospin-2 Dirac systems, continuum models obtained
for one-dimensional stub and sawtooth lattices, and two-dimensional electron
systems with a quadratic band and a nearly flat band. We discuss some
experimental implications of mode conversion in flat-band materials and
metamaterials.
