Synthesizing optical spectra using computer-generated holography techniques

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Experimental control and detection of atoms and molecules often rely on optical transitions between different electronic states. In many cases, substructure such as hyperfine or spin-rotation structure leads to the need for multiple optical frequencies spaced by MHz to GHz. The task of creating multiple optical frequencies—optical spectral engineering—becomes challenging when the number of frequencies becomes large, a situation that one could encounter in complex molecules and atoms in large magnetic fields. In this work, we point out a novel mapping between computer-generated holography (CGH) and spectrum generation via phase modulation, which is an established technique. Using this mapping, we synthesize arbitrary optical spectra by modulating a monochromatic light field with a time-dependent phase generated through CGH techniques. Our method is compatible with non-linear optical processes such as sum frequency generation and second harmonic generation. Additional requirements that arise from the finite lifetimes of excited states can also be satisfied in our approach. As a proof-of-principle demonstration, we generate spectra suitable for cycling photons on the X–B transition in CaF, and verify via optical Bloch equation simulations that one can achieve high photon scattering rates, which are important for fluorescent detection and laser cooling. Our method could offer significant simplifications in future experiments that would otherwise be prohibitively complex.