Generation of optical beams with desirable orbital angular momenta by transformation media

We propose a scheme to controllably convert the wave front of an arbitrary incident beam into a helical one by compact transformation slabs, thus enabling the output beam to carry a desirable orbital angular momentum (OAM). First, based on transformation optics, a three-dimensional (3D) phase transformation between any two wave fronts by flat transformation media is established and then used to mold the wave front of a Gaussian beam into a helical one. Second, 3D finite-difference time-domain simulations are performed to confirm the spiraling evolutions of the resultant field and phase, clearly demonstrating the OAM generated. Further theoretical analyses show that the refractive index exhibiting a helical distribution leads to the oppositely spiral phase front and that it is feasible to produce a desirable OAM by generators of the unit OAM. The results not only provide an additional way to manipulate the phase and photon OAM but also reciprocally shed further light on the phase structure of helical beams, which leads to a new means of transformation by a surface.