Spectral and temporal properties of optical signals with multiple sinusoidal phase modulations

Optical signals generated by multiple sinusoidal temporal phase modulations (multi-FMs) applied to a monochromatic field are studied from the viewpoint of their optical spectrum and temporal modulations arising from spectral impairments. Statistical analysis based on the central limit theorem shows that the signals' optical spectrum converges to a normal distribution as the number of modulations increases, allowing one to predict the frequency range containing a given fraction of the total energy with the associated cumulative density function. The conversion of frequency modulation to amplitude modulation is analyzed and simulated for arbitrary multi-FM signals. These developments are of theoretical and practical importance for high-energy laser systems, where optical pulses are phase modulated in the front end to smooth out the on-target beam profile and prevent potentially catastrophic damage to optical components.