Bifurcation phenomenon in the energy-angular correlation spectrum of the vacuum laser acceleration has been observed with computer simulation. Concerning a focused laser pulse, the classical single-valued energy-angular correlation spectrum for a plane wave is, besides broadened to a band, bifurcated with the classical value in between the two branches. Analytic expression to describe the correlation has been derived and physical explanations based on the ponderomotive potential model and Lorentz-Newton force analyses are presented. The theoretical results are supported by numerical simulations which have been compared with the experimental results. This study is helpful in designing vacuum laser acceleration experiments.
