Accelerating nondiffracting beams

•A set of beams having arbitrary trajectories of accelerating and nondiffracting behaviors are generalized and presented.•Bessel-like accelerating beams are generalized to the higher-order (hollow) version.•Mathieu-like accelerating beams and parabolic-nondiffracting-like accelerating beams are presented.•A possible application of these beams may be found in optical trapping and guiding of particles.

We present a set of beams which combine the properties of accelerating beams and (conventional) diffraction-free beams. These beams can travel along a desired trajectory while keeping an approximately invariant transverse profile, which may be (higher-order) Bessel-, Mathieu- or parabolic-nondiffracting-like beams, depending on the initial complex amplitude distribution. A possible application of these beams presented here may be found in optical trapping field. For example, a higher-order Bessel-like beam, which has a hollow (transverse) pattern, is suitable for guiding low-refractive-index or metal particles along a curve.