Design of mesoscopic self-collimating photonic crystals under oblique incidence

Mesoscopic Photonic Crystals (MPhCs) are composed of alternating natural or artificial materials with compensating spatial dispersion. In their simplest form, as presented here, MPhCs are composed by the periodic repetition of a MPhC supercell made of a short slab of bulk material and a short slab of Photonic Crystal (PhCs). Therefore, MPhCs present a multiscale periodicity with a subwavelength periodicity within each PhC slab and with a few-wavelength periodicity for its supercell. Thanks to this mesoscopic structure, MPhCs allow the self-collimation of light, through a mechanism called mesoscopic self-collimation (MSC), along both directions of high symmetry and directions oblique with respect to the MPhCs slab interfaces. Here, we propose a new design method useful for conceiving MPhCs that allow MSC under oblique incidence, avoiding in-plane scattering and ensuring propagation via purely guided modes, without out-of-plane radiation losses. In addition, the proposed method allows a systematic search for optimal MSC structures, which also simultaneously satisfy the impedance matching condition at MPhC interfaces, thus reducing the effect of multiple reflections between bulk-PhC interfaces. The proposed design method has the advantage of an extreme analytical simplicity and it allows direct design of oblique-incidence MPhC structures. Its accuracy is validated through Finite Difference Time Domain simulations and the MSC performances of the designed structures are evaluated, in terms of angular direction, beam waist, overall transmittance, and through discussion of a Figure of Merit that accounts for residual beam curvature. This simple yet powerful method can pave the way for the design of advanced MSC-based photonic interconnects and circuits that are immune to crosstalk and out-of-plane losses.