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In this work we consider polarization dynamics of a class A vector laser subject to new kind of vector modulation which drives the eigenmode ellipticity. Such a modulation can be accomplished by an intracavity device consisting of two crossed quarterwave plates with Faraday element between them. It is found that sinusoidal modulation of the eigenmode ellipticity is directly transferred to the polarization parameters of the emitted field only at small amplitude of modulation. Among interesting features in the laser dynamic behaviour we report on resonant and quasiperiodic behaviours in the vicinity of the polarization relaxation frequency.

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