Focal shift of a focused partially coherent Laguerre-Gaussian beam of all orders

Abstract

We explore the focusing properties of a partially coherent Laguerre–Gaussian (LG) beam of all orders, particularly the focal shift (i.e. the shift of the actual focal plane away from the geometrical focal plane). We derive the analytical expressions for the average intensity and the effective beam width of a focused partially coherent LG beam, and we adopt the minimum effective beam width instead of the conventional maximum on-axis intensity to determine the actual focal plane. It is found that the focused beam shape, minimum effective beam width and the focal shift of a focused partially coherent LG beam are determined by its initial coherence width, radial mode order and azimuthal mode order (i.e. topological charge) together. Our results may be useful for optical trapping and micro-fabrication, where precise focal position and prescribed beam shape are required.

Keywords:

• Partially coherent Laguerre–Gaussian beam
• effective beam width
• focal shift