We numerically study the entanglement dynamics of free fermions on a cubic lattice with potential disorder following a quantum quench. We focus, in particular, on the metal-insulator transition at a critical disorder strength and compare the results to the putative many-body localization (MBL) transition in interacting one-dimensional systems. We find that at the transition point the entanglement entropy grows logarithmically with time $t$ while the number entropy grows $\sim lnlnt$. This is exactly the same scaling recently found in the MBL phase of the Heisenberg chain with random magnetic fields, suggesting that the MBL phase might be more akin to an extended critical regime with both localized and delocalized states rather than a fully localized phase. We also show that the experimentally easily accessible number entropy can be used to bound the full entanglement entropy of the Anderson model and that the critical properties at the metal-insulator transition obtained from entanglement measures are consistent with those obtained by other probes.

The lower order cladding mode resonances of a fiber Bragg grating (FBG) are sensitive to fiber bending but their spectral density makes their response to bending very complex. In this work we present a simple method to reduce and control the number of low order cladding mode resonances via FBGs written in a two-mode fiber (TMF) with an ultrafast laser. Owing to the larger core size of the TMF, a slight break of the cylindrical asymmetry of the grating patterns can be induced when using femtosecond side-irradiation with a small change in the writing condition. This allows us to control the mode families coupled by the grating, and in particular to those modes that have positive or negative bending responses along certain bend directions. Experimental results demonstrate that several lower-order neighboring-cladding mode pairs coupled by the asymmetric TMFBG have antagonistic loss responses (by several dB) for different bending directions, thus allowing full 2D bending measurements with many applications in shape sensing. Finally, this device has similar advantages as tilted FBGs, i.e. temperature de-correlation and the possibility of increasing the signal to noise ratio by averaging simultaneous measurements on several pairs of resonances.

An optical fiber directional-bend sensor based on an inline Mach–Zehnder interferometer is proposed and demonstrated. The device consists of a piece of a multimode fiber (MMF) splicing with a polarization-maintaining photonic crystal fiber (PMPCF) and sandwiched by lead in/out single-mode fibers (SMFs). Owing to the larger diameter of the MMF, some high-order modes in fiber are efficiently coupled and transmitted through the PMPCF, and finally interfere with each other in the output SMFs. The experimental results show that a well-defined interference fringe envelope can be obtained in the transmitted spectrum and, when the fiber is bent, both the intensity and the fringe visibility of the interference pattern are changed with the bending curvature. Meanwhile, the bend sensitivities are varied with different bending directions, and the maximum sensitivity is achieved up to − 8.33 d B / m − 1 within the bend range from 0 to 1.7 m − 1 . The proposed device also demonstrates a very low-intensity cross-talk of environment temperature.

We propose and experimentally demonstrate a hybrid grating, in which an excessively tilted fiber grating (Ex-TFG) and a fiber Bragg grating (FBG) were co-inscribed in a reduced-diameter fiber (RDF). The hybrid grating showed strong resonances due to coupling among core mode and a set of polarization-dependent cladding modes. This coupling showed enhanced evanescent fields by the reduced cladding size, thus allowing stronger interaction with the surrounding medium. Moreover, the FBG’s Bragg resonance confined by the thick cladding was exempt from the change of the surrounding medium’s refractive index (RI), and then the FBG can work as a temperature compensator. As a result, the Ex-TFG in RDF promised a highly sensitive RI measurement, with a sensitivity up to ~1224 nm/RIU near the RI of 1.38. Through simultaneous measurement of temperature and RI, the temperature dependence of water’s RI is then determined. Therefore, the proposed hybrid grating with a spectrum of multi-peaks embedded with a sharp Bragg resonance is a promising alternative for the simultaneous measurement of multi-parameters for many RI-based sensing applications.

A 10 mm-long three-dimensional shape sensor in a single-mode fiber is described and demonstrated experimentally. The sensor is based on a pair of fiber Bragg gratings inscribed at the same location along the fiber axis but offset along different radial directions away from the fiber center. Each offset grating generates cladding mode resonances over a ∼ 20 n m -wide spectral bandwidth, and the two gratings are also offset in period so that their transmission spectra are separated by 40 nm, and thus non-overlapping and fully distinguishable. Directional bending sensitivity results from the differential amplitude response of the cladding mode resonances from the two gratings, depending on the relative orientation of the bend with the azimuthal direction of the grating offsets. It is further demonstrated that both axial deformation and temperature have no influence on the shape measurement as they both only cause a global wavelength shift of the spectra without amplitude change. The experimental results demonstrate that the shape orientation of an object can be unambiguously determined for bend directions covering the full 360° range around the fiber axis with sensitivities of the order of 1 d B / m − 1 and small curvatures between 0 and 1 m − 1 .