Cauchy Complete Nearness Spaces

A nearness space is Cauchy complete if every regular Cauchy filter on the space is convergent. We show that the category CCNear ₂ of Cauchy complete N ₂ spaces is reflective in the category Near ₂ C of N ₂-spaces and Cauchy maps and that the reflection of an N ₂-space is given by the strict extension associated with regular Cauchy filters on the space.     

基于长周期光纤光栅滤波器的掺铒光纤放大器理论和实验研究

从理论和实验上研究了带有高频二氧化碳激光写入的低成本长周期光纤光栅（LPFG）掺铒光纤放大器（EDFA）.结果表明,单波长和多波长EDFA的性能都可以通过在掺铒光纤（EDF）中插入长周期光纤光栅用作自发辐射噪声（ASE）滤波器或增益平坦器来提高性能.优化设计了带LPFG噪声滤波器的线放EDFA,与没有LPFG噪声滤波器相比,线放的噪声和小信号增益分别被减小和提高了约0.5 dB和7 dB。通过在多波长EDFA的EDF中插入一个LPFG增益平坦滤波器的方法,获得了1.5 dB的增益平坦度,与没有LPFG平坦器相比,EDFA的噪声被减小了0.1 dB,增益被提高了1 dB.     

Structure optimization of quasi one-dimensional acoustic filters with the use of a genetic algorithm

The paper shows how to use a genetic algorithm to design quasi one-dimensional structures with given properties. The superlattices were surrounded by water and made of epoxy resin and glass, with a layer thicknesses selected in such a way that a phononic bandgap occurs in the frequency range of acoustic waves. Multilayer transmission was calculated using the Transfer Matrix Method algorithm. In order to determine the optimal objective function for the genetic algorithm, the entire space of the possibility of the layers’ distribution for a six-layer structure was analyzed. The spread of the transmission integral values even for the 6-layer structure was significant and ranged from 11.9% to 81.5%. Minimizing the value of the transmission integral as an objective function could lead to a large number of high transmission peaks with a small half width. It allowed the determining of the optimal objective functions for minimizing transmission in a given frequency range, and another allowing for its maximization. The phase diagram of the solution space for the transmission integral from the integral of the absolute value of the transmission functions derivative was determined. Transmission of the most and the least optimal six-layer structures was shown depending on the assumed objective function. Then, the analysis of fifteen and thirty-layer structures was carried out. From the dependence of the objective function values for the best individuals for each generation, it was determined that despite carrying out a thousand iterations, the stable state was determined before reaching 250 iterations of the algorithm, and thus the optimal structure was determined. The transmissions ratio of analyzed structures in the studied frequency range (up to 20 kHz) to full transmission (without structures) in this acoustic frequency range for the analyzed optimal 6, 15 and 30-layer structures were 16.78%, 9.6% and 4.41%, respectively.     

Enhanced and restored signals as a generalized solution for shock filter models. Part II—numerical study

In Part I of this paper, we proposed a well-posed generalized model for signal enhancement and restoration based on shock filters. A theoretical study of the Cauchy problem in the framework of generalized functions algebra was developed in detail. In Part II, we investigate the numerical aspects of the model. We derive an efficient, explicit numerical scheme in both one and two dimensions, and investigate the schemes' stability and convergence. Through experimental tests, we demonstrate the effectiveness of the numerical schemes when restoring and enhancing signals in various situations with a limited number of iterations. Moreover, we show the impact of the coefficients introduced in the model on the procedure's processing time.     

olc型双折射滤波器离轴消光比的研究

提出了一种 ˇSolc型双折射滤波器的离轴消光比的一般性计算方法 ,利用所得结果模拟出了 ˇSolc型双折射滤波器的锥光干涉图以及发散光积分消光比与波长和发散角的关系曲线 ,实验结果证实了理论推算的合理性。此外本方法也适用于计算各种类型双折射滤波器的离轴消光比。     

Enhanced and restored signals as a generalized solution for shock filter models.: Part I—existence and uniqueness result of the Cauchy problem

Signal enhancement and restoration is one of the fields that make extensive use of PDE theory. More specifically, some authors have proposed successive improved shock filters based on non-linear hyperbolic equations. These models yield satisfactory results; however, a wider range of degrees of freedom when handling the model parameters (coefficients and components) would be of great interest because it would increase the model's efficiency and facilitate adaptation to specific situations. Naturally, the key challenge in proceeding thus is to ensure that the problem remains well-posed. In this paper, we propose a more general shock filter that introduces new parameters to control the shock speed. Interpreting the proposed model in a framework of generalized functions algebra, we prove existence and uniqueness solution results.     

Demonstration of high extinction ratio modal interference in a two-mode fiber and its applications for all-fiber comb filter and high-temperature sensor

We show that high extinction ratio (>20 dB) modal interference in a two-mode dispersion compensating fiber can be utilized to build a compact, easy-to-fabricate tunable all-fiber optical comb filter. Wavelength tunability over the full free spectral range of the comb filter is demonstrated with an electrical power of 115mW using an on-fiber thin film micro-heater deposited directly on the fiber. In another configuration, the comb filter is used as a temperature sensor with dynamic range of >300 °C and sensitivity of <0.1 °C. The temperature sensor is capable of measuring a temperature as high as 500 °C.     

Wavelength-selective all-fiber filter based on a single long-period fiber grating and a misaligned splicing point

A novel wavelength-selective all-fiber filter using a single long-period fiber grating (LPG) interacting with a misaligned fusion splicing point has been demonstrated. The misaligned splicing point couples a part of the core mode power into the cladding modes, which is then recoupled into the core mode by the following LPG. As an optical path difference is introduced by the differential refractive index of the fiber, an in-fiber Mach-Zehnder interferometer is therefore formed, which may function as a cost-efficient WDM filter with good isolation and low insertion loss.     

Flow of optical patterns due to small lateral wave-front shifts in a nonlinear optical feedback system

Flow of a spontaneously formed optical pattern in a nonlinear optical feedback system consisting of a liquid crystal optically addressable spatial light modulator with feedback is induced by a lateral wave-front shift of the feedback light. We demonstrate the dependency of the flow speed on the wave-front shift by tilting an optical flat inserted in the feedback loop. We also demonstrate the application to real-time, high-sensitivity detection of small tilt angles of optical components.     

Linear Separability of Positive Self-Dual Logical Filters

The threshold logic filter is an important nonlinear filter class, which is defined by a threshold logic function of binary input values. It is proved in this paper that not all positive self-dual logical functions are threshold functions if the number of input variables is 5 or more. The positive self-dual logical filter is a limited class but includes almost all filters for noise removal. Our result means that not all positive self-dual filters can be expressed by one operation of the threshold logic filters. In the sense of the filter expression by neural networks, the two-layer network cannot always optimize even this limited class.