Unidimensional photonic crystal-based biosensors have gained much attention in the area of blood glucose measurement. In this paper, we propose two novel designs based on two-dimensional (2D) Van der Waals materials. The first 1D photonic crystal design consists of multilayers of 2D gallium sulfide and 2D muscovite mica [GaS/Mica]^ND[GaS/Mica]^N, and the second design consists of multilayers of 2D gallium sulfide [GaS/G]^ND[GaS/G]^N. We conducted a numerical analysis using the transfer matrix method to investigate the properties of photonic crystals, both with and without defect layers, in order to assess their suitability for biosensing applications. The biosensors’ performances were investigated as a function of glucose concentration, revealing a high sensitivity of 832 nm/RIU, a notable figure-of-merit of 1.46 × 10⁵ RIU⁻¹, a Q-factor exceeding 10⁵, and a minimum limit of detection of 3.4 × 10⁻⁷ RIU. Finally, we modified the [GaS/G]^ND[GaS/G]^Nstructure in order to enhance the sensitivity nearly 5-fold. The proposed biosensors offer the advantage of being label-free, making them promising platforms for the sensitive and reliable detection of blood glucose levels.

A simple Kronig-Penney model is used to study the effect of nonlinear interactions on the electronic properties of ordered and disordered electrified chains. In the case of ordered potentials, we found that the nonlinearity suppresses the Wannier-Stark effect caused by the electric field. In the case of disordered potentials, the nonlinearity gives rise to a transition from superlocalized to weakly localized states.

The Kronig-Penney model is used to study the effect of non-linear interaction on the transmissive properties of both ordered and disordered chains. In the ordered case, the non-linearity can either localize or delocalize the electronic states depending on both its sign and strength, but there is a critical strength above which all states are localized. In the disordered case, however, we found that the transmission decays as around the band edge of the corresponding periodic system. The exponent is independent of the strength of the non-linearity in the case of disordered barrier potentials, while it varies with this strength for mixed potentials.

A simple Kronig-Penney model for one-dimensional (1D) mesoscopic systems with $\delta$ peak potentials is used to study numerically the influence of a constant electric field on the conductance fluctuations and distribution at the metal-insulator transition. We use the Levy laws to investigate the statistical properties of the eigenstates. We found at this transition that the conductance probability distribution has a system-size independent shape with large fluctuations in good agreement with previous works in 2D and 3D systems.

We investigate numerically the effect of weak Kerr nonlinearity on the transmission spectrum of a one-dimensional (1D) $\delta$-function photonic crystal. A new and interesting phenomenon is observed. It is found that, for weak defocusing nonlinearity, a defect-mode-like (DML) resonance peak is obtained inside the photonic band gap (PBG). That means that a weak nonlinearity acts as a defect introduced in a 1D perfect photonic crystal. A total transmission of this peak is found for a critical value of nonlinearity strength $|{\alpha }_c|$, while above this value a splitting of the DML resonance peak is observed. Calculations of the spatial dependence of the electric-field intensity reveal that DML resonance peaks have a similar origin as the well-known gap solitons appearing in nonlinear systems. The influences of nonlinearity strength, refractive index, incident angle, number of periods, and polarization on this DML resonance peak are analyzed.