Focusing a Gaussian laser beam without focal shift

Abstract It is shown for the first time that the focal shift of a Gaussian laser beam can be offset with the use of the spherical aberration of a focusing lens. The diffraction integral, in the presence of aberrations, which is applicable to a low Fresnel number focusing system is derived. A new approximate formula is proposed for the normalized axial intensity in the presence of aberrations. This formula reduces to an exact formula for a nontruncated, aberration-free Gaussian beam. The expression for the coefficient of spherical aberration required to offset the focal shift is given as a function of the Fresnel number of the beam. The axial intensity distributions of Gaussian beams with the spherical aberration are presented, predicting the focusing without the focal shift.

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