Synthesis of long-period fiber gratings with a Lagrange multiplier optimization method

Based on the Lagrange multiplier optimization (LMO) method, a new synthesis approach for designing complex long-period fiber grating (LPG) filters is developed and demonstrated. The proposed synthesis method is a simple and direct approach. It was used to efficiently search for optimal solutions and constrain various parameters of the designed LPG filters according to practical requirements. The inverse scattering algorithm is a good tool for designing FBG filters; as well as for designing transmission-type fiber grating filters like LPGs. Compared to the results of the discrete layer-peeling (DLP) inverse scattering algorithm for LPGs, the synthesized LPGs, using the LMO approach, are more flexible and workable for the constraint conditions can be easily set in the user-defined cost functional, such as the limitation on the maximum value of the refractive index modulation and the parameters of the initial guess in LMO algorithm. Linear transmission LPG filters and EDFA gain flattening filters are synthesized and analyzed systematically by using the proposed method with different parameters. Moreover, as a variation-based method, we find that the convergence and the synthesized results of the LMO method are strongly dependent on the initial guess parameters.     

Spectral Analysis of Transmission Echelon Grating Filters for Photonic Networks

This paper describes a method of analyzing spectral behavior that allows transmission echelon grating filters to be designed for use in constructing photonic networks. These networks include dense wavelength division multiplexing systems and other such applications. First, the configuration and principle of this filter are described. Then, the transmittance spectrum of the transmission echelon grating filter is considered for incident lights with rectangular, Gaussian, and sinc electric field distributions. Next, a more realistic spectral response is considered by taking reasonable fabrication errors into account. Finally, the group delay and the transmittance of linearly chirped echelon grating filters are analyzed to access their potential for use as a wavelength dispersion equalizer. These analytical results make it possible to design practical echelon grating filters.     

Optimization of long-period grating inscribed in large mode area photonic crystal fiber for design of bandstop filter

By inscribing long period grating (LPG) in a photonic crystal fiber (PCF), optical filters for communication wavelengths can be fabricated. In this paper, by utilizing coupled-mode theory and enhanced improved vectorial effective index method, a design of bandstop filter based on optimal LPG parameters is presented where the optimized full-width half-maximum (FWHM), the number (N) and total length of gratings of LPGs (L) are determined. As a result, by the determination of optimized LPG parameters with an optimum length of L_opt=6.5 mm and optimum number of grating N_opt=27 inscribed in the PCF, a bandstop optical filter with FWHM=1 nm is designed.     

Apodized fibre Bragg grating with modulated refractive index change for transmissive gain equalization

This paper presents a new enhanced design of fibre Bragg grating for flattening the gain profile of an erbium-doped fibre amplifier in transmission configuration. This grating has modulation of refractive index change and constant chirp rate, wherein both profiles of the parameters are properly apodized. The design utilizes an alternative approach to the renowned inverse scattering method, yet produces a similar spectral response quality and conceptually simpler. Moreover, it offers precise control over all parameters of the grating structure. It is shown that the design approach could produce gain-flattening filters of satisfactory quality through simulations using the accurate transfer matrix method.     

Design of sidetap fiber Bragg grating filters

A comprehensive theoretical treatment is presented for bound-mode to radiation mode coupling loss (transmission loss) and for bound-mode to bound-mode Bragg reflection (back reflection) in a sidetap fiber phase grating. The spectra of the reflection and transmission loss in a tilt angle range useful for fiber sidetap filter design is presented for the first time. Important dependencies between the designed wavelength of operation and parameters of the fiber grating, which give a clear understanding of the process of the fiber mode to radiation mode coupling and back reflection is also discussed. A practical procedure for the design of sidetap gain flattening filter is also presented.     

Optimal design of FIR beamformer with frequency invariant patterns

Two approaches to the optimal design of FIR beamformers with frequency invariant patterns using second-order cone programming (SOCP) are proposed. The first approach is a two-step method, which is implemented via separately optimal array pattern synthesis and optimal FIR filters design. The array weights for each frequency bin within the working frequency band are designed to insure that the array patterns approximate the reference ones. And the FIR filter corresponding to each sensor is designed to insure that the frequency responses approximate the array weights. The second approach is a direct method, in which the beam response is expressed as a linear function of FIR filter tap weights and the filters are designed by jointly optimizing the spatial and frequency responses to achieve the desired array patterns. All the optimal design problems (array pattern synthesis, FIR filter design and joint optimization) are formulated as the SOCP, which can be solved efficiently using the well-developed interior-point methods. Results of computer simulations and lake experiment for a twelve-element semicircular array confirm satisfactory performance of the two approaches proposed in this paper.     

Fiber Grating Based Optical Recirculating Filter with an Optimized Response

A novel optical recirculating filter for RF applications is described, which exploits a specially designed fiber grating with a ramped spectral profile to enable optimization of the filter response. The design overcomes the limitations imposed by loss in conventional fiber recirculating filters. Additionally, a tunable free spectral range is demonstrated by using the device in a grating array. Both theoretical and experimental results are presented and discussed.     

Fiber Grating Based Optical Recirculating Filter with an Optimized Response

A novel optical recirculating filter for RF applications is described, which exploits a specially designed fiber grating with a ramped spectral profile to enable optimization of the filter response. The design overcomes the limitations imposed by loss in conventional fiber recirculating filters. Additionally, a tunable free spectral range is demonstrated by using the device in a grating array. Both theoretical and experimental results are presented and discussed.     

Design and characterization of guided mode resonance filters with the improved structure for facile fabrication

In this study, a guided mode resonance filter with the improved structure for facile fabrication is designed; the properties of the designed filters are simulated by rigorous coupled wave analysis. It is found that the resonance wavelength and spectral linewidth are slightly increased with the increasing of the grating thickness, and seldom changed with the thickness of the grating filling factor, as the parameter error of the grating thickness and the grating filling factor are deviated from the designed value by ±10%, respectively, which are very favorable for simplifying preparation process of the GMR filter.     

Long-Period Fiber Grating Filter Synthesis Using Evolutionary Programming

An innovative algorithm based on the evolutionary programming (EP) method is developed for the synthesis of long-period fiber gratings (LPGs). The proposed method exhibits a number of attractive features that prove to be effective for solving the inverse design problems of LPGs. The basics of EP are reviewed and the detailed programming procedures of the proposed algorithm are presented. A new mutation process using the concepts of leveled adjustment and adaptive weighting factor is proposed and verified. Comprehensive numerical results on designing practical LPG filters are presented to demonstrate the feasibility and the effectiveness of the proposed algorithm.     

Several mechanically-induced long-period gratings by a grooved plate

A simple method to mechanically induce a long-period fiber grating (LPFG) by a grooved plate is improved. The transmission spectra of a grating under different pressures and other types of gratings are experimentally investigated. This method is simple and reconfigurable and offers large spectra tunability. This type of LPFG has potential applications in gain flattening in erbium-doped fiber amplifiers (EDFA) and will be of particular use in filter design.     

A comparison of filter design structures for multi-channel acoustic communication systems

The application of inverse filter designs as a means of providing improved communication performance in acoustic environments is investigated. Tikhonov regularized inverse filters of channel transfer functions calculated in the frequency domain are used as a means of obtaining multi-channel filters. Three classifications of inverse filter structures have been considered using time-domain simulations. The performance of Tikhonov regularized inverse filters designed according to each of these classifications is compared with each other and against a filter design developed by Stojanovic [Stojanovic, M. (2005). "Retrofocusing techniques for high rate acoustic communications," J. Acoust. Soc. Am. 117, 1173-1185]. It is shown that the filter design developed by Stojanovic requires less regularization and outperforms the Tikhonov regularized inverse filter designs when communicating over a single channel. While the filter developed by Stojanovic is designed to use multiple transmitters to transmit to a single receiver, the filter was implemented in a multi-channel system and proposed to have a focusing similar to that obtained using time-reversal. It was found that for the scenario used in the simulation, the Tikhonov regularized inverse design for full multi-channel inversion achieved better focusing than the design by Stojanovic, where simulation results show 20 dB less cross-talk at the expense of around 2 dB loss in signal strength.     

Theory and practice of long-period gratings: when a loss becomes a gain

Losses of cladding modes are part of the mechanism of operation of a long-period grating (LPG) when it is used as an optical filter. We present a LPG computer simulation that accounts for these losses. On the basis of this simulation, we show that losses result in qualitatively different LPG spectral behavior. There is an optimal loss value that provides sidelobe-free, 100% power transfer from the core to the cladding mode for a uniform LPG. We obtained a simple equation that relates this optimum lose value to the LPG length and the cross-coupling coefficient. Based on the results, we propose new approaches to LPG design in a fiber as well as in waveguide platforms for fiber-optic communication and sensor applications. A design of a LPG reconfigurable filter is suggested.     

Loop-mirror filters based on saturable-gain or-absorber gratings

We present a novel all-fiber narrow-band filter based on pump-induced saturable-gain or-absorber gratings in a loop mirror. Our design provides built-in interferometric phase alignment of the signal to the grating for optimal filtering. Notch or bandpass functionality is determined by the choice of gain or absorption and the input ports selected for the pump and signal. The loop-mirror filter has potential bandwidths from the submegahertz to beyond the gigahertz regimes, and one can tune it optically by changing the wavelength of the pump light that establishes the grating. Such filters have potential applications to wavelength-division-multiplexed optical networks and optical rf signal processing.     

具有任意方向的扇形滤波器及其在图像方向检测中的应用

扇形滤波器在图像的方向检测中是非常重要的.本文基于极傅里叶变换和一个楔形滤波器,设计出具有任意方向的二维扇形滤波器.首先,楔形滤波器被变换到极傅里叶域,再利用极傅里叶变换的旋转特性,楔形滤波器可以通过将其极傅里叶变换沿着水平方向进行移动来实现旋转,得到一系列具有任意方向导向的扇形滤波器,它们能够检测图像中所包含的任意方向信息.由于整个设计过程不涉及二维优化,因此所提出的设计方法具有设计简单的优点.为了验证扇形滤波器的方向敏感性,将所设计的扇形滤波器应用于图像的纹理方向检测,结果表明,具有任意方向的扇形滤波器在图像纹理方向检测中具有很大的潜能.     

Numerical analysis of plasmon polarition refractive index fiber sensors with hollow core and a long period grating

The main principle of this design is based on the efficient energy transfer between the waveguide mode (WM) and the co-directional SPP provided by a properly designed fiber long period grating (LPG). This LPG is imprinted into a waveguide fiber layer of a specially designed hollow core optical fiber. The simulations are based on the finite element method (FEM) algorithm in electromagnetics and coupled mode theory for gratings. Compared to the previous proposed structure using a fiber Bragg grating (FBG), this novel kind of sensor can greatly enhance the refractive index sensitivity, e.g., from 5.93 nm/RIU (with FBG) to 817 nm/RIU (with LPG) at the sensing refractive index of 1.40. The other advantage is that the working conditions can be performed for the well-developed telecom wavelength windows 1500-1600 nm.     

级联长周期光栅光谱特性

利用传输矩阵法分析了级联长周期光栅的光谱特性,讨论了级联处光纤的长度、位置以及包层模损耗系数对级联长周期光栅光谱的影响,并对级联长周期光栅和相移长周期光栅的光谱进行了比较。结果表明两者光谱存级联光纤长度较小或级联位置靠近光栅两端时具有较强的一致性,而在级联处光纤较长并且级联位置在中间时,两者表现出截然不同的光谱特性;在不考虑其他损耗的情况下,如果只改变级联处光纤长度,级联长周期光栅总量守恒;此外,当级联长周期光栅在级联处光纤包层模损耗系数较大时,级联长周期光栅的光谱等效于两个长周期光栅光谱的非相干叠加,从而为长周期光栅增益均衡器的优化设计和制作提供了一个简便有效的方法。     

基于长周期光纤光栅的可变体机翼翼表温度测试系统研究

为实现可变体机翼翼表温度的高精度的实时检测,设计了一种基于长周期光纤光栅(LPG)的温度测试系统.该系统采用长周期光纤光栅作为温度传感元件,高双折射光纤环镜作为边缘滤波器件.在边缘滤波理论研究的基础上,提出了一种降噪增敏的算法.实验中将LPG粘贴在可变体机翼翼表材料的表面,当外界温度发生变化时,LPG的谐振波长发生偏移...     

A quantitative analysis of an athermal design for a long period grating based tunable filter

In this paper, a quantitative analysis of an athermal design for a unique all-fiber tunable filter based on the combination of a single resonant band long period grating (LPG) with an electro-optic polymer second cladding layer is presented. The single resonant band LPG is used to select the resonant wavelength, which can be tuned by changing the refractive index of an electro-optic polymer second cladding layer via external electric field. Although the basic operational principle and implementation of this unique tunable filter have been previously reported, this paper is focused on the quantitative analysis of the athermal design, which may significantly enhance the practicability of the proposed tunable filter.     

Fabrication of ultrathin color filters for three primary colors using guided-mode resonance in silicon subwavelength gratings

We fabricate reflection color filters for three primary colors using silicon two-dimensional triangular-lattice subwavelength gratings on the same quartz substrate. The grating periods are 480, 390, and 300 nm for red, green, and blue filters, respectively. All of the color filters have the same thickness of 100 nm, which enables the simple fabrication of a color filter array. Maximum reflectances of 75 and 46% are obtained at wavelengths of 647.1 and 522.1 nm for the red and green filters, respectively. The blue filter has a double-peaked spectrum with a reflectance of 30% at the peak wavelengths of 450.0 and 502.7 nm. By rigorous coupled-wave analysis, the dimensions of each color filter are designed, and the calculated theoretical reflectance is compared with the measured one.