Transverse-optical Josephson plasmons: Equations of motion

A detailed calculation is presented of the dielectric function in superconductors consisting of two Josephson coupled superconducting layers per unit cell, taking into account the effect of finite compressibility of the electron fluid. From the model, it follows that two longitudinal and one transverse-optical Josephson plasma resonance exist in these materials for electric-field polarization perpendicular to the planes. The latter mode appears as a resonance in the transverse dielectric function, and it couples directly to the electrical-held vector of infrared radiation. A shift of all plasma frequencies and a reduction of the intensity of the transverse-optical Josephson plasmon is shown to result from the finite compressibility of the electron fluid.