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A dual-parameter fiber-optic sensor based on magnetic ionic liquids (MILs) functionalized side-hole fibers (SHFs) has been proposed and experimentally demonstrated for simultaneous measurement of temperature and magnetic field intensity. Multiple transmission dips are present in the transmission spectrum due to resonance coupling between the fundamental core mode and high-order modes in the MIL inclusion. The wavelength shifts of these resonance dips are highly sensitive to the environmental temperature and applied magnetic field intensity, providing an ideal sensing platform for simultaneous measurement of the above two physical parameters. Experimental results indicate that our proposed sensor exhibits temperature and magnetic field sensitivities up to −3.466 nm/°C and −0.0303 nm/Oe for the measurement ranges of 25 °C to 100 °C and 20 Oe to 200 Oe, respectively. The MILs-infiltrated SHFs sensor paves new way toward developing photonic devices for temperature/magnetic field dual-parameter sensing and high-precision wavelength-tuning based on functional materials.

We study the revenue-maximizing mechanism when a buyer's value evolves endogenously because of learning-by-consuming. A seller sells one unit of a divisible good, while the buyer relies on his private, rough valuation to choose his first-stage consumption level. Consuming more leads to a more precise valuation estimate, after which the buyer determines the second-stage consumption level. The optimum is a menu of try-and-decide contracts, consisting of a first-stage price-quantity pair and a second-stage per-unit price for the remaining quantity. In equilibrium, a higher first-stage valuation buyer pays more for higher first-stage consumption and enjoys a lower second-stage per-unit price. Methodologically, we deal with the difficulty that due to the failure of single-crossing condition, monotonicity in allocation plus the envelope condition is insufficient for incentive compatibility. Our results help to understand contracts about sequential consumption with the learning feature; e.g., leasing contracts for experience goods and trial sessions for certain courses., 44 pages

For many years, the number and losses of modes have restricted the large-scale application of hollow core photonic bandgap fibers (HC-PBFs) in data transmission. Researchers have successfully reduced fiber loss to an extremely low level; however, little attention has been given to the specific characteristics of the higher-order modes (HOMs) in HC-PBF. In this paper, the high-order mode characteristics of a 7-cell HC-PBF are investigated in detail, and the non-degenerate phenomenon of HE21 is observed. Through an in-depth theoretical analysis by discussing the influence of the structural deformation of the fiber near the core on the high-order mode characteristics, the cause of the phenomenon is described. Thus, an optimized 7-cell HC-PBF for supporting 6 modes is developed. Additionally, the bending losses of all the HOMs in the fiber are measured. Marked bending loss is not observed even when the bending radius is as small as 0.5 cm, which is different from a solid core four-mode fiber. These findings will provide a reference for HC-PBF as a new type of few-mode fiber for the mode division multiplexing field.

The attraction of hollow core fibers (HCF) lies in the long-distance mode retention ability and the transmission speed close to physical limit. Long-term efforts have been made to get a balance between large core and pure mode. However, the unique light guide mechanism of HCFs makes it a difficult question to decrease the number of the allowed modes. New theory of mode control in such fibers is desired. In this paper, we propose a new space for observing optical states based on the principle of representation transformation, so-called the wave vector space (k-space). The mode observation in the k-space provides a different perspective where the mechanical properties of the light are more obvious. We observe typical fiber modes in the k-space and clarify differences of their momentum characteristics, based on which a mode selection principle is proposed. As a theoretical proof of the principle, a novel 19-cell hollow-core photonic bandgap fiber (HC-PBGF) structure that only supports single pure vector mode is exhibited. The designed optical fiber supports only TE01 mode over a bandwidth of 80 nm with the lowest loss of 0.8 dB/km. This example proves the practicality of the proposed momentum selection theory and will inspire breakthroughs in other optical studies.

Trapped in the stringent adiabatic transmission condition of high-order modes, low-loss fused biconical taper mode selective coupler (FBT-MSC) has long been challenging to achieve. We identify the adiabatic predicament of high-order modes to stem from the rapid variation of the eigenmode field diameter, which is caused by the large core-cladding diameter difference of few-mode fiber (FMF). We demonstrate that introducing a positive-index inner cladding in FMF is an effective approach to address this predicament. The optimized FMF can be used as dedicated fiber for FBT-MSC fabrication, and exhibits good compatibility with the original fibers, which is critical for the wide adoption of MSC. As an example, we add inner cladding in a step-index FMF to achieve excellent adiabatic high-order mode characteristics. The optimized fiber is used to manufacture ultra-low-loss 5-LP MSC. The insertion losses of the fabricated LP01, LP11, LP21, LP02 and LP12 MSCs are 0.13 dB at 1541 nm, 0.02 dB at 1553 nm, 0.08 dB at 1538 nm, 0.20 dB at 1523 nm, and 0.15 dB at 1539 nm, respectively, with smoothly varying insertion loss across the wavelength domain. Additional loss is less than 0.20 dB from 1465.00 nm to 1639.31 nm, and the 90% conversion bandwidth exceeds 68.03 nm, 166.68 nm, 174.31 nm, 132.83 nm, and 84.17 nm, respectively. MSCs are manufactured using commercial equipment and a standardized process that takes just 15 minutes, making them a potential candidate for low-cost batch manufacturing in a space division multiplexing system.

A passively mode-locked Tm3+-doped fiber laser based on the mechanism of nonlinear polarization rotation and cascading chirped long period fiber grating (LPFG) to generate ultrafast cylindrical vector (CV) mode output is proposed and demonstrated. The fiber laser output traditional soliton pulses operating at 1878.8 nm with a 3 dB bandwidth of 3.94 nm. The pulse duration of the laser is ~1.05 ps with a repetition rate of 18.766 MHz. A cascading chirped LPFG, fabricated in a few-mode fiber by a CO2 laser, serves as a broadband transverse mode converter to achieve ultrafast CV mode generation. The LPFG has a 10 dB bandwidth (corresponding to conversion efficiency of 90%) of 20 nm from 1877 nm to 1897 nm, which perfectly covers the wide mode-locked spectrum. High purity radially and azimuthally polarized modes are obtained through adjusting the polarization controllers, and the mode purity is calculated to be about 95.1% and 94.9% for TE01 and TM01. To our best knowledge, this is the first mode-locked fiber laser emitting CV modes in $2~\mu \text{m}$ waveband using a broadband LPFG as a mode converter.

The paper examines notions of incentive compatibility in an environment with ambiguity-averse agents. In particular, we propose the notion of maxmin transfer coalitional incentive compatibility, which is immune to coalitional manipulations and thus more stable than the individual incentive compatibility condition. The main result characterizes the set of allocations that satisfy the maxmin transfer coalitional incentive compatibility condition. We show that an allocation satisfies maxmin transfer coalitional incentive compatibility if and only if it is maxmin interim efficient. This result extends that of De Castro and Yannelis (J Econ Theory 177:678–707, 2018) in the sense that ambiguity not only resolves the conflict between efficiency and incentive compatibility, it also accommodates stability. Furthermore, this result is false in a finite economy where agents are subjective expected utility maximizers.

Stable generation and propagation of ultrafast high-order mode beams has become an important research direction. A core diameter not more than 10 times the wavelength is regarded as the upper limit for single mode transmission. However, a high-power laser requires a core diameter 20 to 40 times the wavelength to achieve high-power and stable output, which exceeds the design limit of the traditional fiber. In this paper, a novel 37-cell hollow core photonic bandgap fiber (HC-PBF) that only supports pure TE01 mode over a bandwidth of 50 nm with the lowest loss of 0.127 dB/km is proposed. The HC-PBF has a core diameter of more than 40 μm. Single mode guidance is achieved by adjusting the lattice size in a particular of the cladding. The best single mode performance with a loss ratio as high as 150,000 between TE01 mode and other modes with minimum loss is obtained. The fiber also has low bend-loss and thus can be coiled to a small bend radius of 1 cm having 1.6 dB/km bend loss. The tunability of the single-mode window and the manufacturing feasibility of the proposed fiber are also discussed.

A connected graph G = (V(G), E(G)) is called a quasi-unicyclic graph, if there exists u0 ∈ V(G) such that G − u0 is a unicyclic graph. Denote Q(n, d0) = {G: G is a quasi-unicyclic graph of order n with G − u0 being a unicyclic graph and dG(u0) = d0}. Let A(G) be the adjacency matrix of a graph G, and let λ1(G), λ2(G),…, λn(G) be the eigenvalues in non-increasing order of A(G). The number $$\sum\limits_{i = 1}^n {\lambda _i^k(G)} $$ (k = 0,1, …, n−1) is called the k-th spectral moment of G, denoted by Sk (G). Let S (G) = (S0(G), S1(G),…, Sn−1(G)) be the sequence of spectral moments of G. For two graphs G1, G2, we have G1 ≺SG2 if for some k(k = 1,2,…, n−1), and we have Si(G1) = Si(G2) (i = 0,1, …, k−1) and Sk(G1) < Sk(G2). In this paper, we determine the second to the fourth largest quasi-unicyclic graphs, in an S-order, in the set Q(n, d0), respectively.

This paper introduces ambiguous transfers to the problems of full surplus extraction and implementation in finite dimensional naive type spaces. The mechanism designer commits to one transfer rule but informs agents of a set of potential ones. Without knowing the adopted transfer rule, agents are assumed to make decisions based on the worst-case expected payoffs. A key condition in this paper is the Beliefs Determine Preferences (BDP) property, which requires an agent to hold distinct beliefs about others' information under different types. We show that full surplus extraction can be guaranteed via ambiguous transfers if and only if the BDP property is satisfied by all agents. When agents' beliefs can be generated by a common prior, all efficient allocations are implementable via individually rational and budget-balanced mechanisms with ambiguous transfers if and only if the BDP property holds for all agents. This necessary and sufficient condition is weaker than those for full surplus extraction and implementation via Bayesian mechanisms. Therefore, ambiguous transfers may achieve first-best outcomes that are impossible under the standard approach. In particular, with ambiguous transfers, efficient allocations become implementable generically in two-agent problems, a result that does not hold under a Bayesian framework.

A few mode wavelength division multiplexing coupler (WDMC) based on a five-core fiber is proposed to couple pump light with the wavelength of 980 nm into few-mode fiber amplifiers supporting four LP modes at 1550 nm. The WDMC is composed of a few-mode core and four single mode cores surrounding it. The pump light is coupled into LP 01 , LP 11 , LP 21 , LP 02 mode, respectively. Numerical simulation results show that the coupling efficiency for pump light is 99.6%, 99.3%, 99.9%, and 99.9%, and the power loss of the signal light in the LP 01 , LP 11 , LP 21 , and LP 02 modes in few mode core is 0 , 0 . 01 , 0 . 03 , 0 . 10 , and 0 . 18 dB , respectively. The proposed few-mode WDMC with lower insertion loss and easier fabrication, which can provide four LP modes of pump light in the few mode fiber, is an ideal candidate for pump scheme for the few-mode fiber amplifier.

High order modes in a six-mode fiber are separately observed and characterized using an Optical Frequency Domain Reflectometry (OFDR) method. Due to the difference in group refractive index between fundamental mode and the high order modes, Fresnel reflection peaks for each mode can be separated in beat frequency domain with their corresponding time delay. In the experiment, the fundamental mode and high order modes are excited in turn and observed at a 6.6 m six-mode fiber end, which agree with their beat frequency difference in theoretical simulation. The demonstration provides a flexible and feasible method for mode identification and characterization of all kinds of fibers.

A single-resonator, stable dual-longitudinal-mode optofluidic microcavity laser based on a hollow-core microstructured optical fiber is proposed and experimentally demonstrated. The resonator and microfluidic channel are integrated in the hollow-core region of the fiber, inside which a hexagonal silica ring is used as the only resonator of the laser. Experimental results show that with mixing a small amount of Rhodamine B into a 1 mM Rhodamine 6G solution to form a dual-dye solution as a gain medium, the laser obtained by the method of lateral pumping can operate at dual longitudinal modes, with a threshold of 90 nJ/mm2. By adjusting the concentration of Rhodamine B, the lasing wavelength of the laser and the power ratio of the two wavelengths can be controlled. And because the laser emission is co-excited by different kinds of dye molecules, the mode competition is diminished, enabling the simultaneously efficient optical gain and therefore lasing at dual longitudinal modes stably with a maximum lasing intensity fluctuation of 3.2% within 30 minutes even if the dual longitudinal modes have the same linear polarization states. This work can open up promising opportunities for diverse applications in biosensing and medical diagnosis with high sensitivity and integrated photonics with compact structure.

We propose a low-loss broadband symmetric mode multiplexing coupler. By studying the influence of polarization on the coupler, multiplexing of LP11 and LP21 modes in the range of 990-1570 nm is realized.

In this paper, a novel full vector numerical simulation method based on the finite element method (FEM) and local coupled mode theory (LCMT) for analyzing the mode transmission characteristics of photonic lantern (PL) with arbitrary input mode field is proposed. Compared with the traditional numerical simulation methods for PL, our method can greatly reduce the computational complexity and ensure high precision. Taking a three-core PL as an example, we verify the validity of our method. The advantages and properties of our method are also discussed in detail and found instructive for optimization design of PL. Through specifically optimizing the geometric parameters of the PL according to the properties, mode selectivity of LP01 and LP11 can be respectively improved up to 44.5 dB and 54.7 dB with more than 95% coupling efficiency.

We demonstrated a wavelength-tunable, ultra-wideband, biconical, long-period fiber grating (BLPFG) mode converter in a two-mode fiber based on fusion taper technology and CO2 laser writing technology. Theoretical and experimental results show that after changing the diameter of the two-mode fiber by fusing and tapering, the dispersion turning point of the fiber is adjusted and wavelength-tunable broadband mode conversion is achieved efficiently. Theoretical simulation shows that the mode conversion bandwidth can cover the O + E + S + C band. In the experiment, we fabricated adiabatic tapers with cladding diameters of 113 μm and 121 μm and wrote gratings on these tapers to achieve dual-resonance coupling, thus realizing mode conversion from LP01 to LP11, with a 15 dB bandwidth of 148.8 nm from 1229.0 nm to 1377.8 nm and of 168.5 nm from 1319.7 nm to 1488.2 nm, respectively. As far as we know, this is the first time that fusion taper technology has been used to adjust the window of the dual-resonant coupling of an optical fiber. This work broadens the scope of application of the dual-resonance effect and proposes a general method for widening the bandwidth of a fiber grating with tunable wavelength.

A multi-sample analysis method with spatial resolution based on a single-longitudinal-mode fiber optofluidic microring laser is proposed and experimentally demonstrated. Spatial resolution is introduced into micro-fluid control system of the single-longitudinal-mode optofluidic laser, in which a hexagonal silica ring inside a simplified hollow-core microstructured optical fiber is used as the resonator. By monitoring the power change of the single longitudinal mode lasing generated by the side pumping, continuous detection and analysis for multiple samples can be realized quickly and efficiently. With this method, the influence of Rhodamine B solution with different concentration on the single-longitudinal-mode fiber optofluidic laser designed by mixing 1 mM Rhodamine 6G is investigated experimentally. The experimental results show that the proposed multi-sample analysis method can clearly distinguish the Rhodamine B solution from 0.08 mM to 0.13 mM, with a high lasing intensity sensitivity of 303 a.u./μM. Moreover, due to the introduction of energy resonance transfer effect, the minimum excitation concentration of Rhodamine B is reduced from 270 µM to 45 µM. Increase the concentration of Rhodamine 6G to 2 mM, laser-based sensing for the concentration of Rhodamine B can still be achieved, and the minimum excitation concentration can be further reduced to 15 µM. This work provides possibilities for laser-based biochemical analysis with multi-sample, high throughput and high sensitivity.

As a high-throughput data analysis technique, photon time stretching (PTS) is widely used in the monitoring of rare events such as cancer cells, rough waves, and the study of electronic and optical transient dynamics. The PTS technology relies on high-speed data collection, and the large amount of data generated poses a challenge to data storage and real-time processing. Therefore, how to use compatible optical methods to filter and process data in advance is particularly important. The time-lens proposed, based on the duality of time and space as an important data processing method derived from PTS, achieves imaging of time signals by controlling the phase information of the timing signals. In this paper, an optical neural network based on the time-lens (TL-ONN) is proposed, which applies the time-lens to the layer algorithm of the neural network to realize the forward transmission of one-dimensional data. The recognition function of this optical neural network for speech information is verified by simulation, and the test recognition accuracy reaches 95.35%. This architecture can be applied to feature extraction and classification, and is expected to be a breakthrough in detecting rare events such as cancer cell identification and screening.

Ferroelectric aging behavior was investigated in Na0.5Bi0.5(Ti0.99Zr0.01)O3 thin film on FTO/glass substrate by the dielectric constant (dissipation factor)-electric field (er–E and tan δ–E) curves. The aged sample can be gained by keeping the fresh film for two months at room temperature. Compared with the typical single butterfly er (tan δ)–E of the fresh sample, an abnormal loop has been exhibited in the aged one. Furthermore, with the increase of the measuring electric field or decrease of applied frequency, the aging phenomenon becomes weak and even disappeared. These present results are analyzed based on defect chemistry by the symmetry-conforming principle of defect dipoles.

As a fundamental issue, determining the proportions of spatial modes in multimode fibers has been continuously discussed over the past few years. People have successfully measured the components of spatial modes with different orders but have rarely addressed the measurement of degenerated modes under these spatial modes. In this article, we propose an interference method to measure the proportions of these degenerated modes. This method is based on the discussion of coherent superposition of degenerated modes in multimode fibers. In the experiment, we randomly generate spatial states in two-mode fibers and simulate these phenomena according to the proposed method, which agrees well with the experiment. This measuring method improves the accuracy of mode measurement from mode groups to degenerated modes and may provide a unique perspective for the field of multimode fibers.

Real-time detection of the ultrafast dynamics in complex nonlinear optical systems provides novel insights into pulse interactions and dynamic patterns, especially for soliton molecules. Herein, the concept of soliton molecule is extended to the pulsating regime, revealing the dynamical diversity of soliton molecule and the universality of pulsating behavior. By virtue of the dispersive Fourier transform (DFT) technique, we present the first experimental observation of the dissociation dynamics within a pulsating soliton molecule generated in an L-band normal-dispersion mode-locked fiber laser. The results provide valuable references for resolving the interactions in complex dissipative systems.