Discrete Layer-peeling Algorithm Research Articles

Optimal Design of Short Fiber Bragg Grating Using Bat Algorithm With Adaptive Position Update

We propose a new method to optimally design short triangular-spectrum fiber Bragg gratings (TS-FBGs), using the metaheuristic bat algorithm (BA). In addition, we propose a novel modification, i.e., adaptive position update (APU), to optimize the index modulation within a predetermined range. The discrete layer-peeling algorithm is used to efficiently initialize BA. The APU improves the search performance and accuracy of the BA algorithm in fiber Bragg grating (FBG) design application. Using the proposed method, a 0.2-nm-bandwidth TS-FBG, operating in the C-band, is designed. The short-length FBG with chirp-free structure prevents complex phase modulation for practical considerations. In addition, a dual-wavelength TS-FBG of 0.75-nm bandwidth operating in the eye-safe region has been designed and provided the most accurate optimum design length. The latter is well suited for FBGs inscribed in high-birefringent fibers, which are utilized in multiwavelength fiber laser systems. For both cases, the accuracy and search performance of APU-BA are shown to be better than those of previously reported algorithms in the literature.

Design of DPSS based fiber bragg gratings and their application in all-optical encryption, OCDMA, optical steganography, and orthogonal-division multiplexing.

The future information infrastructure will be affected by limited bandwidth of optical networks, high energy consumption, heterogeneity of network segments, and security issues. As a solution to all problems, we advocate the use of both electrical basis functions (orthogonal prolate spheroidal basis functions) and optical basis functions, implemented as FBGs with orthogonal impulse response in addition to spatial modes. We design the Bragg gratings with orthogonal impulse responses by means of discrete layer peeling algorithm. The target impulse responses belong to the class of discrete prolate spheroidal sequences, which are mutually orthogonal regardless of the sequence order, while occupying the fixed bandwidth. We then design the corresponding encoders and decoders suitable for all-optical encryption, optical CDMA, optical steganography, and orthogonal-division multiplexing (ODM). Finally, we propose the spectral multiplexing-ODM-spatial multiplexing scheme enabling beyond 10 Pb/s serial optical transport networks.

RZ-OOK to NRZ-OOK format conversion based on a single fiber Bragg grating

We propose a return-to-zero on-off keying (RZ-OOK) to non-return-to-zero (NRZ) OOK conversion scheme based on a single custom-designed fiber Bragg grating (FBG). The custom-made FBG is designed and syn­thesized using discrete layer-peeling algorithm. It is shown that such a FBG can replace the combination of interferometer and the cascaded filter that are invariably employed together in the reported schemes for ­RZ-OOK to NRZ-OOK format conversion. Simulation results show that the input 20-Gb/s RZ-OOK signals with different duty cycles can be converted into NRZ-OOK signals with high Q-factor.

PPLN Poling Design Based on a Discrete Layer Peeling Algorithm Combined With a Deleted-Reversal Method

In this paper, we propose a method to design the poling pattern of periodically poled lithium niobate (PPLN) devices according to a target spectral response of the selected nonlinear interaction. This method combines a discrete layer peeling algorithm with the deleted-reversal method. The main advantages and limitations of the proposed method in terms of fabrication feasibility of the resulting poling patterns are discussed. The effectiveness of the proposed method is shown by designing PPLNs with two different types of spectral responses: quasi-rectangular bandpass filtering and multichannel filtering. We experimentally demonstrate the method by designing and producing a PPLN which allows performing wavelength conversion within a spectral response approximately given by a 400 GHz quasi-rectangular filter.

Retrieving quasi-phase-matching structure with discrete layer-peeling method

An approach to reconstruct a quasi-phase-matching grating by using a discrete layer-peeling algorithm is presented. Experimentally measured output spectra of Šolc-type filters, based on uniform and chirped QPM structures, are used in the discrete layer-peeling algorithm. The reconstructed QPM structures are in agreement with the exact structures used in the experiment and the method is verified to be accurate and efficient in quality inspection on quasi-phase-matching grating.

Optimal design of short fiber Bragg gratings with triangular spectrum

Based on the mutated adaptive quantum-behaved particle swarm optimization (MAQPSO) algorithm and the discrete layer peeling (DLP) algorithm, we propose a method to design triangular-spectrum fiber Bragg gratings (TS-FBGs). In this method, the DLP algorithm is used to generate an appropriate initial range of the index modulation, and the MAQPSO technique is applied to optimize the index modulation within this range. The quantum-behaved particle swarm optimization algorithm with mutation operation can improve the search performance of this algorithm. We purposely use a linear weighting factor for the fitness value function in view of the linear edge triangular-spectrum. This dramatically accelerates the convergence in the numerical implementation. Using the proposed method, a 0.2 nm bandwidth TS-FBG is designed and the performance is shown to be better than previously reported results in the literature. Then, a 2.5 nm bandwidth TS-FBG is reconstructed; it is indicated that a short grating length can be used to realize the TS-FBG with chirp-free structure so that complex phase modulation is avoided in fabrication. Finally, a triple-channel TS-FBG with sampled-free structure is successfully designed and optimized. We also present an analysis on the tolerance of the design method over possible fabrication error.

Multichannel Arbitrary-Order Photonic Temporal Differentiator for Wavelength-Division-Multiplexed Signal Processing Using a Single Fiber Bragg Grating

A multichannel photonic temporal differentiator implemented based on a single multichannel fiber Bragg grating (FBG) for wavelength-division-multiplexed (WDM) signal processing is proposed for the first time to our knowledge. The multichannel FBG is designed using the discrete layer peeling (DLP) algorithm together with the spatial sampling technique. Specifically, the DLP algorithm is used to design the spectral response of an individual channel, while the spatial sampling is employed to generate a multichannel response. The key feature of the proposed temporal differentiator is that WDM signals at multiple optical wavelengths can be simultaneously processed. Two sampling techniques, the phase-only and the amplitude-only, are employed. The use of the phase-only sampling technique to design a 45-channel first-order and second-order temporal differentiator is performed, and the use of the amplitude sampling technique to design a 3-channel first-order and second-order temporal differentiator is also performed. A proof-of-concept experiment is then carried out. A 3-channel first-order differentiator with a bandwidth of 33.75 GHz and a channel spacing of 100 GHz is fabricated. The use of the fabricated 3-channel FBG to perform first-order temporal differentiation of a 13.2-GHz Gaussian-like optical pulse with different optical carrier wavelength is demonstrated.

Simple index modulation profile with fast-converging design optimization for multichannel fiber Bragg grating filters

In this paper, a novel hybrid algorithm featuring a simple index modulation profile with fast-converging optimization is proposed towards the design of dense wavelength-division-multiplexing systems (DWDM) multichannel fiber Bragg grating (FBG) filters. The approach is based on utilizing one of other FBG design approaches that may suffer from spectral distortion as the first step, then performing Lagrange multiplier optimization (LMO) for optimized correction of the spectral distortion. In our design examples, the superposition method is employed as the first design step for its merits of easy fabrication, and the discrete layer-peeling (DLP) algorithm is used to rapidly obtain the initial index modulation profiles for the superposition method. On account of the initially near-optimum index modulation profiles from the first step, the LMO optimization algorithm shows fast convergence to the target reflection spectra in the second step and the design outcome still retains the advantage of easy fabrication.

Numerically extrapolated discrete layer-peeling algorithm for synthesis of nonuniform fiber Bragg gratings

The discrete layer-peeling algorithm (DLPA) requires to discretize the continuous medium into discrete reflectors to synthesize nonuniform fiber Bragg gratings (FBG), and the discretization step of this discrete model should be sufficiently small for synthesis with high accuracy. However, the discretization step cannot be made arbitrarily small to decrease the discretization error, because the number of multiplications needed with the DLPA is proportional to the inverse square of the layer thickness. We propose a numerically extrapolated time domain DLPA (ETDLPA) to resolve this tradeoff between the numerical accuracy and the computational complexity. The accuracy of the proposed ETDLPA is higher than the conventional time domain DLPA (TDLPA) by an order of magnitude or more, with little computational overhead. To be specific, the computational efficiency of the ETDLPA is achieved through numerical extrapolation, and each addition of the extrapolation depth improves the order of accuracy by one. Therefore, the ETDLPA provides us with computationally more efficient and accurate methodology for the nonuniform FBG synthesis than the TDLPA.

Optimal Design of Multichannel Fiber Bragg Grating Filters With Small Dispersion and Low Index Modulation

We have proposed an effective method to synthesize and optimize multichannel fiber Bragg grating filters (MCFBGFs). The novel method contains two steps, i.e., the discrete layer peeling algorithm generates the excellent initial guess values and, successively, the nonlinear least squares method reconstructs and optimizes the expected fiber Bragg grating parameters from the initial guess in the previous step. Design examples demonstrate that the proposed method has unique merits to optimize the reflectivity and dispersion of MCFBGFs and effectively reduce their index modulation simultaneously.

Optimal method of designing triangular-spectrum fiber Bragg gratings with low index modulation and chirp-free structure

Combining the traditional nonlinear least squares (NLLS) method with a discrete layer peeling (DLP) algorithm, we propose a new method (for the first time to our knowledge) to synthesize triangular-spectrum fiber Bragg gratings (TS-FBGs) with chirp-free structures. In this method, the DLP algorithm is used to generate an appropriate initial value, and the NLLS method is successfully used to optimize the design parameters from the initial value in the previous step. Numerical results show that our method can design both single- and multiple-channel TS-FBGs with their maximum index modulations being effectively suppressed to a feasible level. These novel TS-FBGs thus designed can act as wavelength readout devices and provide potential applications to wavelength interrogation in optical sensor systems.

Direct design of multichannel fiber Bragg grating with discrete layer-peeling algorithm

The conventional sampling approach fails when the seed grating contains phase shifts because this approach is based on the resonant coupling principle, which explains the multichannel spectrum formation but does not provide an accurate solution. We use the discrete layer-peeling algorithm for directly synthesizing the multichannel grating. The new method restores the channel distortion in the sampled grating, resulting in uniform reflection and dispersion spectrum channels. We introduce further an optimized set of channel phases, such that the maximum reflective index modulation required for N channels is only /spl radic/N times that for the single channel.

On the synthesis of fiber Bragg gratings by layer peeling

Two methods for grating synthesis which have appeared in the literature recently are compared directly. In particular, we point out the similarity between the two; both algorithms are based on propagation of the fields through the structure with simultaneous evaluation of the coupling coefficient according to simple causality arguments (layer-peeling algorithms). The first published method (the discrete layer-peeling algorithm) is reformulated in a simpler, more efficient way, and it is shown that its implementation can be made exact. For mathematical comparison, a derivation of the second method (the continuous layer-peeling algorithm) is presented. The methods are compared both mathematically and numerically. We find that the discrete layer-peeling algorithm is significantly faster and can be more stable than its continuous counterpart, whereas the continuous algorithm offers some advantages in flexibility.