Beam transformations process by active materials allows, in a controlled manner, the redistribution of the irradiance and phase of light. A material that exhibits quadratic gain or loss and refractive index profiles is regarded as active GRIN (GRadient-INdex) material. Complex refractive index is examined in order to discuss what loss or gain means in terms of the refractive index. General conditions for beam transformations by active GRIN materials are obtained in a 2D space of the complex curvature. Irradiance evolution through an active selfoc microlens is presented and it is analyzed at planes where beam shaping occurs.
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