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Coherent perfect absorbers for transient, periodic or chaotic optical fields: time-reversed lasers beyond threshold

Recent works [Y.D. Chong {\it et al.}, Phys. Rev. Lett. {\bf 105}, 053901 (2010); W. Wan {\it et al.}, Science {\bf 331}, 889 (2011)] have shown that the time-reversed process of lasing at threshold realizes a coherent perfect absorber (CPA). In a CPA, a lossy medium in an optical cavity with a specific degree of dissipation, equal in modulus to the gain of the lasing medium, can perfectly absorb coherent optical waves at discrete frequencies that are the time-reversed counterpart of the lasing modes. Here the concepts of time-reversal of lasing and CPA are extended for optical radiation emitted by a laser operated in an arbitrary (and generally highly-nonlinear) regime, i.e. for transient, chaotic or periodic coherent optical fields. We prove that any electromagnetic signal $E(t)$ generated by a laser system \textbf{S} operated in an arbitrary regime can be perfectly absorbed by a CPA device $\bf{S'}$ which is simply realized by placing inside \textbf{S} a broadband linear absorber (attenuator) of appropriate transmittance. As examples, we discuss CPA devices that perfectly absorb a chaotic laser signal and a frequency-modulated optical wave.