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We present a comprehensive theory of the one-dimensional plasmonic crystalformed in the grating gated two-dimensional electron gas (2DEG) insemiconductor heterostructures. To describe collective plasma excitations inthe 2DEG, we develop a generalized transmission line theoretical formalismconsistent with the plasma hydrodynamic model. We then apply this formalism toanalyze the plasmonic spectra of 2DEG systems with step-like periodic changesof electron density and/or gate screening. We show that in a periodicallymodulated 2DEG, a plasmonic crystal is formed and derive closed-form analyticalexpressions describing its energy band spectrum for both infinite and finitesize crystals. Our results demonstrate a non-monotonic dependence of theplasmonic band gap width on the electron density modulation. At so-calledtransparency points where the plasmon propagates through the periodic 2DEG in aresonant manner, the plasmonic band gaps vanish. In semi-infinite plasmoniccrystals, we demonstrate the formation of plasmonic Tamm states andanalytically derive their energy dispersion and spatial localization. Finally,we present detailed numerical analysis of the plasmonic band structure of afinite four-period plasmonic crystal terminated either by an Ohmic contact orby an infinite barrier on each side. We trace the evolution of the plasmonicband spectrum, including the Tamm states, with changing electron densitymodulation and analyze the boundary conditions necessary for formation of theTamm states. We also analyze interaction between the Tamm states formed at theopposite edges of the short length plasmonic crystal. The validity of ourtheoretical approach was confirmed in experimental studies of plasmoniccrystals in short modulated plasmonic cavities which demonstrated excellentquantitative agreement between theory and experiment.

Transmission Line Theory of Collective Plasma Excitations in Periodic Two-Dimensional Electron Systems: Finite Plasmonic Crystals and Tamm States