For as widely used a tool as nonlinear optical frequency conversion is for both science and industry, it remains widely limited in efficiency and bandwidth (and ultimately also in cost) due to the fundamental problem of backconversion in the nonlinear evolution dynamics. This review paper covers new developments and capabilities in frequency conversion devices, including optical up- and down-converters and amplifiers, based on nonlinear evolution dynamics in which back-conversion is suppressed. One such approach is adiabatic frequency conversion, in which the dynamics of rapid adiabatic passage replace the regular cyclic conversion evolution in phase-matched sum- and difference-frequency generation. This approach has enabled devices far surpassing the conventional efficiency-bandwidth trade-off. For example, in chirped quasi-phase matched quadratic crystals, microjouleenergy single-cycle mid-infrared pulses were generated with arbitrary pulse shaping capability, presenting a source with unique features for nonlinear spectroscopy and strong-field physics applications. We review new developments in the use of optical fibers as a cubic nonlinear platform for the same concept, utilizing a tapered core diameter or a pressure gradient to allow up- and down-conversion with ultra-wide bandwidth and high efficiency. We also review a newly introduced concept for high efficiency optical parametric amplification, via a novel approach for suppressing back-conversion in optical parametric amplification by simultaneously phasematching the idler wave for second harmonic generation.
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