This Letter builds upon a recent concept [Phys. Rev. Lett. 113, 104801 (2014)] for producing ultrashort optical pulses through the coherent radiation of electrons in an undulator. Each pulse contains only a single oscillation cycle, and has a controlled waveform (and hence a stable carrier-envelope phase). While the concept had been demonstrated numerically, this Letter provides an analytical model for the radiation mechanism, thereby revealing three key observations: (i) the correlation between the waveforms of the optical and undulator fields; (ii) the free-space dispersion of transversely confined light; and (iii) the dependence of the optical pulse shape on the undulator field strength. (C) 2018 Optical Society of America
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