  Shaping the light emission characteristics of laser systems is of great
importance in various areas of science and technology. In a typical lasing
arrangement, the spatial profile of the mode tends to remain self-similar
throughout the cavity. Here, we introduce a paradigm shift where a spatially
evolving mode is faithfully settled into a pair of bi-orthogonal states at the
two facets of a laser cavity. This is achieved by deliberately eliminating
non-adiabatic jumps in a purposely designed structure that features a dynamic
encirclement of a non-Hermitian exceptional point. The resulting state transfer
reflects the unique topology of the associated Riemann surfaces. Our approach
provides a route to develop versatile mode selective active
