Characteristic matrix operation for finding global solution of one-time ray-tracing optimization method.

The one-time ray-tracing optimization method is a fast way to design LED illumination systems [Opt. Express22, 5357 (2014)10.1364/OE.22.005357]. The method optimizes the performance of LED illumination systems by modifying the LEDs' luminous intensity distribution curve (LIDC) with a freeform lens, instead of modifying the illumination system structure. In finding the LEDs' LIDC for optimizing the illumination system's performance, the LEDs' LIDC found by means of a general gradient descent method can be trapped in a local solution. This study develops a matrix operation method to directly find the global solution of the LEDs' LIDC for the optimization of the illumination system's performance for any initial design of an illumination system structure. As compared with the gradient descent method, using the proposed characteristic matrix operation method to find the best LEDs' LIDC reduces the cost in time by several orders of magnitude. The proposed characteristic matrix operation method ensures that the one-time ray-tracing optimization method is an efficient and reliable method for designing LED illumination systems.

Generation of high-order Hermite-Gaussian modes in end-pumped solid-state lasers for square vortex array laser beam generation.

This study reports the first systematic approach to the excitation of all high-order Hermite-Gaussian modes (HGMs) in end-pumped solid-state lasers. This study uses a metal-wire-inserted laser resonator accompanied with the "off axis pumping" approach. This study presents numerical analysis of the excitation of HGMs in end-pumped solid-state lasers and experimentally generated HGM patterns. This study also experimentally demonstrates the generation of an square vortex array laser beams by passing specific high-order HGMs (HGn,n + 1 or HGn + 1,n modes) through a Dove prism-embedded unbalanced Mach-Zehnder interferometer [Optics Express 16, 19934-19949]. The resulting square vortex array laser beams with embedded vortexes aligned in a square array can be applied to multi-spot dark optical traps in the future.

Numerical study for selective excitation of Mathieu-Gauss modes in end-pumped solid-state laser systems.

This study reports a possible first systematic approach to the selective excitations of all Mathieu-Gauss modes (MGMs) in end-pumped solid-state lasers with a new kind of axicon-based stable laser resonator. The study classifies MGMs into two categories, and explores and verifies the approach to excite each MGM category using numerical simulations. Controlling both the "cavity mode gain" and the "cavity conical asymmetry" of the axicon-based stable laser resonator achieves the proposed selective MGM-excitation approach.