Transformation of a Hermite-Gaussian beam by an Airy transform optical system

Analytical expression of the Airy transform of an arbitrary Hermite-Gaussian beam is derived. The optical field in the x-direction of the Airy transform of Hermite-Gaussian beams with transverse mode number m is the sum of the zero-order derivative to mth-order derivative of the Airy function with different weight coefficients. The analytical expressions of the centre of gravity and the beam spot size of an arbitrary Hermite-Gaussian beam passing through an Airy transform optical system are also presented, which are very concise. Because the Airy transform of a Hermite-Gaussian beam has the same evolution law in the two transverse directions, only the effects of the control parameter α and the transverse mode number m on the normalized intensity distribution, the centre of gravity, and the beam spot size in the x-direction are theoretically investigated, respectively. The Airy transform of Hermite-Gaussian beams is also realized in the experiment. The influence of the control parameters on the normalized intensity distribution, the centre of gravity, and the beam spot size is experimentally investigated, respectively. The experimental results are consistent with the theoretical simulation results. When Hermite-Gaussian beams pass through an Airy transform optical system, the number of lobes may change, and the importance of lobes with the same status in the input plane may become different. By using the Airy transform of Hermite-Gaussian beams, the practical applications of Hermite-Gaussian beams can be extended.