  Light with orbital angular momentum (OAM), or twisted light, is widely
investigated in the fields of optical communications, quantum information
science and nonlinear optics by harnessing its unbounded dimension. For
light-matter interacting with twisted light like quantum memory and nonlinear
frequency conversion, efficiencies in these processes are usually decreasing
exponentially with topological charges, which severely degrades the fidelity of
the output states. Here we conceive and develop a method to eliminate the
dependence of conversion efficiency on topological charges in second harmonic
generation (SHG) process by utilizing a special designed image technique. The
independence of SHG conversion efficiency on topological charge is verified for
different topological charges, this independence is valid for various pump
power. This method can be generalized to other light matter interaction
processes and will revolute the field of light matter interaction with twisted
light to achieve higher efficiency and higher fidelity.
