Narrow Results

A double U-shaped PCF-SPR sensor is proposed for the detection of analytes with low refractive indexes (RI). The U-shaped structure facilitates the penetration of analytes. Compared with a single formant sensor, the sensor exhibits double formant characteristics. Therefore, the analytes to be measured can be identified more accurately. This study employs the finite element method (FEM) to analyze the sensor. The findings suggest that the sensor is capable of detecting analytes with low RI ranging from 1.15 to 1.33 over an ultra-wide wavelength range of 800–6400nm. The maximum wavelength sensitivities of the first and second peaks of the sensor are 54,300nm/RIU and 60,000nm/RIU, respectively. In addition, this paper introduces double peak shift sensitivity (DPSS), the highest DPSS value is 55,700nm/RIU. Owing to these distinct characteristics, the sensor has great application prospects in the field of biosensing, especially in drug detection.

The tools of normal forms and recurrence are used to analyze the interaction of low and higher order resonances in Hamiltonian systems. The resonance zones where the short-periodic solutions of the low order resonances exist are characterized by small variations of the corresponding actions that match the variations of the higher order resonance; this yields cases of embedded double resonance. The resulting interaction produces periodic solutions that in some cases destabilize a resonance zone. Applications are given to the three dof $1:1:4$ resonance and to periodic FPU-chains producing unexpected nonlinear stability results and quasi-trapping phenomena.