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A search for laser light from the directions of Alpha Centauri A and B was performed by examining 15362 optical, high-resolution spectra obtained between 2004 and 2018. None of the spectra exhibit laser emission lines. The threshold was 10% of the continuum intensity of the spectra of both stars at all wavelengths between 3850 and 6900 Å. This search would have revealed optical laser light from the directions of Alpha Cen B if the laser had a power at least 1.4 to 5.4 MW (depending on wavelength) and was positioned within the 1 arcsecond field of view (projecting to 1.3 AU), for a benchmark 10-meter laser launcher. For Alpha Cen A, the laser power must be 3 times greater for detection. Lasers of smaller aperture would also have been detected but would require more power. Considering all optical surveys, a growing desert is emerging in the search for extraterrestrial technology.