The Plane-wave Expansion Approach to Characterising Optical Crystals in k-space - otherwise known as Peacock.jl - is a Julia package for solving Maxwell’s equations using the Plane Wave Expansion Method (Rumpf, 2006) in order to predict the optical properties of photonic crystals. A photonic crystal is a material whose optical properties arise from its periodic structure (John, 1987; Yablonovitch, 1987), and Peacock.jl is named for the irridescent colours of peacock feathers which arise not from pigmentation but from the scattering of light by photonic crystals (Zi et al., 2003), as shown in Figure 1. The response of a photonic crystal is strongest when the periodicity of the structure is comparable to the wavelength of light. For visible light, photonic crystals are built from components that are just a few hundred nanometers in size. Advances in nanofabrication mean that ‘designer’ photonic crystals can now be manufactured for unprecedented control over the flow of light, with applications ranging from optical fibers (Knight, 2003) to photonic circuitry (Joannopoulos, Johnson, Winn, & Meade, 2008). Photonic crystals are also a promising platform for materials known as photonic topological insulators (Blanco de Paz, Vergniory, Bercioux, Garcı́a-Etxarri, & Bradlyn, 2019; Wang, Guo, & Jiang, 2019; Wu & Hu, 2015). These are the photonic analogue of the electronic topological insulators (Bernevig, Hughes, & Zhang, 2006; Kane & Mele, 2005a, 2005b) for which the 2016 Nobel Prize in Physics was awarded, and may allow light to be guided around defects, impurities, and sharp corners without backscattering (Rider et al., 2019). S.J.P. acknowledges his studentship from the Centre for Doctoral Training on Theory and Simulation of Materials at Imperial College London funded by EPSRC Grant No. EP/L015579/1. V.G. acknowledges the Spanish Ministerio de Economia y Competitividad for financial support through the grant NANOTOPO (FIS2017-91413-EXP) and also the Ministerio de Ciencia, Innovación y Universidades through the grant MELODIA (PGC2018-095777-B-C21).