Accelerating propagation properties of misplaced Hermite-Gaussian beams

A new family of finite-energy accelerating beams was constructed through misplacing the Hermite polynomial and Gaussian window function. The closed-form solution of k-space spectra and paraxial propagation of these beams are derived from the Fourier transform and the scalar angle spectra integral. These beams have similar propagation properties to finite Airy beams and parabolic beams, but the accelerating trajectory is hyperbola rather than parabola. The beam family can be experimentally generated by exponentially truncating the high-order Hermite-Gaussian beams in the spatial domain.