Efficient second-harmonic generation in a lithium niobate metasurface governed by high-Q magnetic toroidal dipole resonances.

Lithium niobate (LN) is an excellent nonlinear optical material due to its large nonlinear coefficient, low loss, and broad optical transparency window. So, it is widely used in the generation of nonlinear harmonics. Magnetic toroidal dipole (MTD) resonance is a special optical resonance mode, which can effectively localize the light field inside the device, thus enhancing the nonlinear effects of the materials. In this work, we numerically study the second-harmonic generation (SHG) effect of the LN metasurface based on the MTD mode with a high quality factor (Q-factor). The designed LN nanorod dimer metasurface supports high Q-factor MTD guided mode resonances (GMRs), which are excited by varying the center spacing of the two nanorods, and the Q-factor can be controlled by the offset distance. The excited MTD can effectively confine the electric field within the device, which enables the LN metasurface SHG conversion efficiency to reach 1.15 × 10-2. In addition, by adjusting the structural parameters, it is possible to effectively modulate the wavelength and conversion efficiency of the SHG. Our results provide a new route for high-quality nonlinear light sources.

Quantification of degeneracy in biological systems for characterization of functional interactions between modules.

There is an evolutionary advantage in having multiple components with overlapping functionality (i.e degeneracy) in organisms. While theoretical considerations of degeneracy have been well established in neural networks using information theory, the same concepts have not been developed for differential systems, which form the basis of many biochemical reaction network descriptions in systems biology. Here we establish mathematical definitions of degeneracy, complexity and robustness that allow for the quantification of these properties in a system. By exciting a dynamical system with noise, the mutual information associated with a selected observable output and the interacting subspaces of input components can be used to define both complexity and degeneracy. The calculation of degeneracy in a biological network is a useful metric for evaluating features such as the sensitivity of a biological network to environmental evolutionary pressure. Using a two-receptor signal transduction network, we find that redundant components will not yield high degeneracy whereas compensatory mechanisms established by pathway crosstalk will. This form of analysis permits interrogation of large-scale differential systems for non-identical, functionally equivalent features that have evolved to maintain homeostasis during disruption of individual components.

Oscillations and multiscale dynamics in a closed chemical reaction system: second law of thermodynamics and temporal complexity.

We investigate the oscillatory reaction dynamics in a closed isothermal chemical system: the reversible Lotka-Volterra model. The second law of thermodynamics dictates that the system ultimately reaches an equilibrium. Quasistationary oscillations are analyzed while the free energy of the system serves as a global Lyapunov function of the dissipative dynamics. A natural distinction between regions near and far from equilibrium in terms of the free energy can be established. The dynamics is analogous to a nonlinear mechanical system with time-dependent increasing damping. Near equilibrium, no oscillation is possible as dictated by Onsager's reciprocal symmetry relation. We observe that while the free energy decreases in the closed system's dynamics, it does not follow the steepest descending path.

Coexistence in a metapopulation model with explicit local dynamics.

Many patch-based metapopulation models assume that the local population within each patch is at its equilibrium and independent of changes in patch occupancy. We studied a metapopulation model that explicitly incorporates the local population dynamics of two competing species. The singular perturbation method is used to separate the fast dynamics of the local competition and the slow process of patch colonization and extinction. Our results show that the coupled system leads to more complex outcomes than simple patch models which do not include explicit local dynamics. We also discuss implications of the model for ecological systems in fragmented landscapes.