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The Xe(L) system is an amplifier with fundamentally different dynamic characteristics from all previously developed laser amplifiers; it represents the conceptual ideal through full utilization of the Kramers-Kronig relations that fundamentally couple the dispersive and absorptive components.The dispersive response of the system, through optimal governance of the power compression, rules the amplification and establishes a minimum gain for the amplifier.Accordingly, the amplification requires a minimum value of the dispersion to be surpassed; the corresponding gain follows automatically.As a leading consequence, since this minimum gain is sufficiently high, the key experimental observation is the uniform presence of saturated amplification signaled by strong spectral hole burning on all transitions exhibiting amplification, including double-vacancy lines.This cardinal signature demonstrates that the amplification is legislated by the saturated gain gs, not the corresponding small signal value go.The chief outcome is that explosive dispersion yields perforce explosive amplification and the efficient generation of maximally bright coherent power.