Three-component zoom systems for transformation of Gaussian laser beams

The paper presents a theoretical analysis of paraxial properties of the three-element zoom systems for the transformation of circular Gaussian beams. It is required from the optical system that the distance between a beam waist of the incoming Gaussian beam (object waist) and beam waist of the output Gaussian beam (image waist) does not change during the change of the magnification of the system. Relations enabling the computation of the paraxial parameters of a three-element zoom optical system are derived and applied on an example of a zoom optical system with a continuously adjustable magnification. It is shown that the kinematics of the optical system for the transformation of a Gaussian beam differs from the kinematics of the optical system for the transformation of a classical beam and the direct application of the theory of classical zoom systems for the transformation of laser beams is thus not possible. With lasers generating Gaussian beams with different parameters, it would be necessary to design a special zoom system for each type of laser. However, practically it is possible to design a zoom system for Gaussian beams with specific parameters and the adjustment to another Gaussian beam is achieved by a suitable optical system. Using the derived equations it is further possible to solve a number of other issues of transforming the Gaussian beam such as beam expansion etc.

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