Focal-space intensity distribution of an incoherent light source beam behind a focusing lens

Abstract

Based on ray-tracing technique and vectorial diffraction theory, focal-space intensity distribution of an incoherent light source (ILS) beam after a focusing lens is theoretically described. We investigated the influence of different parameters (the source size, wavelength, focusing lens type, etc.) on the focal-space intensity distribution. For a point source beam, a hyperbolic lens provides 50-fold better axial intensity concentration than a spherical lens of the same focal length (10 mm). Under a chromatic hyperbolic lens, broadening of the spectral bandwidth induces an elongation of the axial intensity distribution, which however is not obvious for spherical lens focusing since the spectral broadening-induced elongation is partly overlapped with that induced by the spherical aberration. Increasing the source size will broaden the lateral intensity distribution, which first looks like a Gaussian and then evolves into a hat top. The axial and/or lateral extension of focal-space intensity would be beneficial to applications where volume heating rather than point heating is required. For example, in an ILS-excited thermal lens microscopy, extension of the intensity distribution brings a quadratic increase of photothermal signal of an ensemble sample but a linear increase of the signal for a point-like target.