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Parametric resonances: from the Mathieu equation to QASER

Combination resonances produced by periodic modulation of parameters can generate substantial gains in new light amplifiers, acronymed QASER (quantum amplification by superradiant emission of radiation). Here we study such gains and investigate their parametric resonance spectral patterns. We use the Floquet theory and develop a projection method that can properly capture gains near the primary resonance and subharmonic frequencies for the Mathieu equation and QASER.