Silicon sub-wavelength structures have become a versatile design tool for practical, high-performance integrated optical devices, ranging from highly efficient grating couplers to ultra-broadband beam-splitters. Recently, some of the basic anisotropic properties of these structures have been proposed for advance device design. Here we explore these properties in detail, from the underlying physics to emerging applications in on-chip polarization management.Ministerio de Economía y Competitividad, Programa Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad (cofinanciado FEDER), Proyectos TEC2016-80718-R, TEC2015-71127-C2-1-R (FPI scholarship BES-2016-077798), and IJCI-2016-30484, the Community of Madrid (S2013/MIT-2790), the Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech, the EMPIR program (JRP-i22 14IND13 Photind), co-financed by the participating countries and the European Union’s 2020 research and innovation program, and the Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant No. 734331
