一种通过梯形PPMgLN波导倍频实现带宽可调谐光源的理论研究

本文设计了一种梯形的周期极化掺镁铌酸锂(PPMgLN)波导,并通过在传播方向上引入温度梯度来拓宽其倍频(SHG)过程的泵浦光源可接收带宽。通过有限差分的光束传输法,计算波导的有效折射率,并进行波导尺寸的设计。结果表明,通过改变梯形波导不同位置的温度,使其形成一个温度梯度,可拓宽泵浦光源的波长可接收带宽。本文所设计的PPMgLN波导最大泵浦光源可接收带宽为C波段,即1 530~1 565 nm,该波导可倍频C波段,得到输出波段带宽为765~782.5 nm,温度调谐范围为30~150 ℃。     

Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres

Applied Mathematics and Mechanics - Mechanical models of residually stressed fibre-reinforced solids, which do not resist bending, have been developed in the literature. However, in some residually...     

Asymmetric nonlinear-mode-conversion in an optical waveguide withPT symmetry

Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this work, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics.     

The Scattering Problem in PT‐Symmetric Periodic Structures of 1D Two‐Material Waveguide Networks

A PT‐symmetric periodic structure with two‐material waveguide networks is constructed. In this study, how changing the number of cells affects the transmission properties is investigated. The results show that the PT‐unbroken (broken) region of the system is only determined by the cell structure, regardless of the number of unit cells. This means that any system has the same exceptional points (EPs), regardless of the number of cells and as long as the cell structure is consistent. In addition, it is confirmed that the coherent perfect absorbers and lasers (CPA lasers) occur in our model. The transfer matrix method is used to derive a sufficient condition for achieving the CPA laser point. A simple, effective formula for predicting the CPA laser state in an N unit cell system is derived.     

Generation of NOON States in Waveguide Arrays

A method to generate NOON states with three photons by injecting photons in an array of three waveguides is presented. Conditional measurements project the wave function in a given (desired) state. In passing, it is shown how the array of three waveguides, that effectively reproduces the interaction of three fields, may be reduced to the interaction of two fields.     

Nanoscale C‐Rich SixC1−x Bus/Ring Waveguide Based Cross‐Wavelength Data Converter

The carbon‐rich silicon carbide (C‐rich Si_xC_1?x) micro‐ring channel waveguide with asymmetric core aspect is demonstrated for all‐optical cross‐wavelength pulsed return‐to‐zero on‐off keying (PRZ‐OOK) data conversion. Enhanced nonlinear optical Kerr switching enables 12‐Gbit per second data processing with optimized modulation depth. The inverse tapered waveguide at end‐face further enlarges the edge‐coupling efficiency, and the asymmetric channel waveguide distinguishes the polarization modes. To prevent data shape distortion, the bus/ring gap spacing is adjusted to control the quality factor (Q‐factor) of the micro‐ring. Designing the waveguide cross section at 500 × 350 nm² provides the C‐rich Si_xC_1?x channel waveguide to induce strong transverse electric mode (TE‐mode) confinement with a large Kerr nonlinearity of 2.44 × 10^?12 cm² W^?1. Owing to the trade‐off between the Q‐factor and the on/off extinction ratio, the optimized bus/ring gap spacing of 1400 nm is selected to provide a coupling ratio at 5–6% for compromising the modulation depth and the switching throughput. Such a C‐rich Si_xC_1?x micro‐ring with asymmetric channel waveguide greatly enhances the cross‐wavelength data conversion efficiency to favor its on‐chip all‐optical data processing applications for future optoelectronic interconnect circuits.     

Multi-physics dynamics of a mechanical oscillator coupled to an electro-magnetic circuit

The dynamics of a non-linear electro-magneto-mechanical coupled system is addressed. The non-linear behavior arises from the involved coupling quadratic non-linearities and it is explored by relying on both analytical and numerical tools. When the linear frequency of the circuit is larger than that of the mechanical oscillator, the dynamics exhibits slow and fast time scales. Therefore the mechanical oscillator forced (actuated) via harmonic voltage excitation of the electric circuit is analyzed; when the forcing frequency is close to that of the mechanical oscillator, the long term damped dynamics evolves in a purely slow timescale with no interaction with the fast time scale. We show this by assuming the existence of a slow invariant manifold (SIM), computing it analytically, and verifying its existence via numerical experiments on both full- and reduced-order systems. In specific regions of the space of forcing parameters, the SIM is a complicated geometric object as it undergoes folding giving rise to hysteresis mechanisms which create a pronounced non-linear resonance phenomenon. Eventually, the roles played by the electro-magnetic and mechanical components in the resulting complex response, encompassing bifurcations as well as possible transitions from regular to chaotic motion, are highlighted by means of Poincaré sections.     

Geometrical methods for analyzing the optimal management of tipping point dynamics

Natural resources are not infinitely resilient and should not be modeled as being such. Finitely resilient resources feature tipping points and history dependence. This paper provides a didactical discussion of mathematical methods that are needed to understand the optimal management of such resources: viscosity solutions of Hamilton–Jacobi–Bellman equations, the costate equation and the associated canonical equations, exact root counting, and geometrical methods to analyze the geometry of the invariant manifolds of the canonical equations. Recommendations for Resource Managers

• Management of natural resources has to take into account the possible breakdown of resilience and induced regime shifts.
• Depending on the characteristics of the resource and on its present and future economic importance, either for all initial states the same kind of management policy is optimal, or the type of the optimal management policy depends on the initial state.
• Modeling should reflect the finiteness of the data.