The transmission of terahertz radiation through a two-dimensional electron gas with a lattice gate placed in a perpendicular magnetic field B was studied. It is shown that a voltage applied to the gate creates a lateral plasma crystal with a band structure that can be controlled by both the gate voltage and the magnetic field. It has been demonstrated that only part of the lateral plasma crystal plasmonic modes is present in the transmission spectrum of homogeneous excitation, while the other half-dark modes-appear only in the case of inhomogeneous excitation. The transition between weak coupling and strong coupling regimes, as the density modulation depth changes, is theoretically described. Two excitation regimes are predicted, resonant and "super-resonant" and the transition between them is described as the quality factor of the structure increases. The main focus are the effects associated with the presence of a magnetic field. In particular, it is shown that plasmon resonances, which are visible in the transmission spectrum, approach each other with increasing of magnetic field and in the presence of a finite momentum relaxation rate can merge. Keywords: two-dimensional electron liquid, plasma waves, dark modes, homogeneous excitation, band structure, plasmonic crystal, magnetic field, weak and strong coupling.

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