The compact cookbook of structured modes of light

Abstract This concise tutorial serves as a guide to the generation and characterisation of higher-order optical mode bases, such as HG, LG, OAM, IG, MG, BG, and various vector modes. It succinctly outlines the creation methods and practicalities for these structured light forms using liquid crystal spatial light modulators and digital micro-mirror devices. An overview of measurement and characterisation using modal decomposition, and approaches to measure and characterise vector beams is also given (\bp{S}tokes polarimetry and vector quality factor). The tutorial concludes with a brief discussion on the effects of varying coherence on these complex light structures, providing essential insights for anyone starting out in the field of photonics.