title: Free space self-similar beams.
abstract: It is well known that self-similar wave dynamics can happen with the coexistence of diffraction and nonlinearity. However, things are clearly different in linear systems, since simple extrapolation by approaching the nonlinear coefficient toward zero will lead to trivial solutions. Here, we show that a broad class of self-similar beams can propagate in linear wave systems governed by a paraxial wave equation or the free particle Schrödinger equation. The linearity of free space allows us to construct these beams by superposition, and eliminates instability problems. The technique of seeking exact or approximate solutions of the wave equations in transformed coordinates presented here should be a useful avenue toward the manipulation of wave propagation in various linear systems.
authors.forename: Nan
authors.initials: N
authors.lastname: Gao
authors.forename: Changqing
authors.initials: C
authors.lastname: Xie