Abstract
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.
Highlights
Dielectric and metallic artificial structured media have allowed the tailoring of light propagation with unprecedented freedom in the conception of photonic devices
In [10], we proposed an hybrid numerical-analytical design method that conjugates mesoscopic self-collimation (MSC) condition to the control of impedance matching between the alternating layers composing the Mesoscopic Photonic Crystals (MPhCs)
Whilst the proposed technique allows to find MSC directions in a complex band-structure by an a-posteriori numerical analysis, it is not a model that allows design and parametric study of MSC below the light cone, at oblique incidence. In this manuscript we propose a novel hybrid numerical-analytical method dedicated to the design of MPhCs at oblique incidence and under the light cone
Summary
Dielectric and metallic artificial structured media have allowed the tailoring of light propagation with unprecedented freedom in the conception of photonic devices. This has the following threefold goal: (i) ensuring the simultaneous coexistence of MSC and total reflectivity control (and limiting or eliminating insertion losses due to impedance mismatch); (ii) including among the solutions those involving a direction of propagation at an oblique angle with respect to the direction of high symmetry for the crystal; (iii) limiting the solutions to those that exclude all diffraction losses, either out-of-plane losses, previously discussed, and in-plane scattering losses at the PhC interfaces This design method has the advantage of an extreme analytical simplicity and, differently from the analysis method proposed in [13], allows direct design of oblique incidence MPhC structures rather than discovering them in existing structures through a-posteriori numerical estimation of high-order derivatives of the dispersion surface, which were affected by computational noise [13]. We investigate the impact of varying the length of the homogeneous layers around the optimal value
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