The symmetry breaking in a typical dielectric GMR-grating structure allows the coupling of the incident wave with the so-called Symmetry-Protected Modes (SPM). In this present work, the excitation conditions of such particular modes are investigated. A parametric study including the grating dimensions is carried out to exploit them for a blood refractive index sensing with higher Sensitivity (S) and Figure Of Merit (FOM). To our knowledge, the performances obtained by FDTD calculations (Q = 2.1 × 104, S = 657 nm/RIU and FOM ≃ ~9 112 RIU−1) and FMM calculations (Q = 3 × 106, S = 656 nm/RIU and FOM ≃ ~1.64 × 106 RIU−1) are the highest level reached.

We describe the implementation of the critical points model in a finite-difference-time-domain code working in oblique incidence and dealing with dispersive media through the split field method. Some tests are presented to validate our code in addition to an application devoted to plasmon resonance of a gold nanoparticles grating.

We present a proof of an exact equivalence of the two approaches that are most used in computing conductance in quantum electron and phonon transport: the wave function matching and Green's functions methods. We can obtain all the quantities defined in one method starting from those obtained in the other. This completes and illuminates the work started Ando[Ando T 1991 Phys. Rev. B 44 8017.] and continued later by Komyakov et al.[Khomyakov P A , Brocks G, Karpan V, Zwierzycki M and Kelly P J 2005 Phys. Rev. B 72 035450.]. The aim is to allow for solving the transport problem with whichever approach fits most the system at hand. One major corollary of the proven equivalence is our derivation of a generalized Fisher-Lee formula for resolving the transmission function into individual phonon mode contributions. As an illustration, we applied our method to a simple model to highlight its accuracy and simplicity.

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