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We propose a new class of localized solutions of the paraxial wave equation. They have a form of a product of a Gaussian term and an amplitude which contains only elementary coordinate functions. Solutions are obtained by summing of the quadratic Bessel–Gauss beams with odd indices. Due to the configuration of the obtained solutions, we named them quadratic cosine-Gauss beams.

Quadratic cosine-Gauss beams – the new family of localized solutions of the paraxial wave equation