We have developed an analytic theory of the nonlinear resonant absorption of electromagnetic radiation in an inhomogeneous plasma with account for the relativistic nonlinearity of the plasma field being excited near the critical density of the plasma, which considerably shifts the boundary of the theoretical description of resonant absorption by the laser plasma to the region of high laser radiation intensities. The nonlinear resonant absorption coefficient as a function of four laser-plasma control parameters (laser radiation intensity, plasma inhomogeneity scale, plasma temperature, and the angle of incidence of laser radiation on the plasma) is obtained. We have demonstrated the nonlinear effect of suppression of the plasma resonance field amplitude and "switching-off" of the resonant absorption with increasing laser radiation intensity, which is a consequence of the relativistic nonlinearity of the electron plasma in the region of a critical density.
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