Using multiple temporally-overlapped, frequency offset and phase-tuned, linear frequency chirps, a new method of multi-GHz optical coherent transient optical pulse shaping and processing in inhomogeneously broadened rare-earth doped crystals is proposed. Using this technique with properly chirped laser sources, multi-GHz processing can be controlled with conventional low-bandwidth electronics and optical modulators. Specifically, this technique enables pulse shaping in the MHz to THz frequency regime with time-bandwidth-products exceeding 100,000, filling the gap between the operating regimes of femtosecond pulse shaping and analog electronics. The low bandwidth (~20 MHz) proof-of-concept demonstrations presented in this paper include pulse train creation, self-convolution, auto-correlation, and chirped pulse compression.
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