Lateral plasmonic crystals: Tunability, dark modes, and weak-to-strong coupling transition

We study transmission of the terahertz radiation through a two-dimensional electron gas with a concentration controlled by grating gate electrodes. Voltage applied to these electrodes creates a lateral plasmonic crystal with a gate-tunable band structure. We find that only a part of plasmonic modes of such a crystal is seen in the transmission spectrum for the case of homogeneous excitation (so-called bright modes), while there also exist dark modes which show up only in a case of inhomogeneous excitation. We develop a theory that describes both weak-to-strong coupling transition in the crystal with increasing depth of the density modulation and a transition from resonant to super-resonant regime with increasing quality factor of the structure. We discuss very recent experiments, where transmission of the terahertz radiation through GaN/AlGaN-based grating-gate periodic structures was studied. We argue that this experiment represents an evidence of formation of the lateral plasmonic crystal with the band structure fully controlled by the gate electrodes, in a full agreement with developed theory.