  Amplification of signal intensity is essential for initiating physical
processes, diagnostics, sensing, communications, and scientific measurement.
During traditional amplification, the signal is amplified by multiplying the
signal carriers through an active gain process using an external power source.
However, for repetitive waveforms, sufficient energy for amplification often
resides in the signal itself. In such cases, the unneeded external power is
wasted, and the signal is additionally degraded by noise and distortions that
accompany active gain processes. We show noiseless, intensity amplification of
repetitive optical pulse waveforms with a gain from 2 to ~20 without using
active gain, by recycling energy already stored in the input repetitive signal.
This "green" method uses dispersion-induced self-imaging (Talbot) effects to
precisely re-distribute the original signal energy into fewer replica
waveforms. This approach simply requires a suitable manipulation of the input
signal's phase profile along the temporal and spectral domains. In addition, we
show experimentally how our passive amplifier performs a real-time average of
the wave train to reduce noise fluctuation present on the input pulse train, as
well as enhances the extinction ratio of pulses to stand above the noise floor
by approximately the passive gain factor. Finally, our technique is applicable
to repetitive waveforms in any spectral region or wave system, including
acoustic, mechanical, and quantum probability waveforms, for which active
amplification methods are challenging to implement or nonexistent.
