Synthesis Of Fiber Bragg Gratings Research Articles

Synthesis of Fiber Bragg Gratings With Arbitrary Stationary Power/Field Distribution

A method to synthesize a fiber Bragg grating (FBG) providing a desired, arbitrary stationary power/field distribution along the grating length is proposed and numerically demonstrated. In the proposed method, starting from the desired stationary power/field distribution or its differential at the Bragg wavelength, the forward and the backward propagation modes are derived for a uniform-period FBG consisting of a prescribed number of grating sections. Using the transfer matrix method, the local reflection coefficient (i.e., ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ) is calculated from the two derived propagation modes, and this information is subsequently employed to obtain the corresponding local coupling coefficient (i.e., q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ) and the associated refractive index modulation (i.e., FBG profile) along the grating length. The proposed synthesis method is first numerically verified when two stationary power distributions from a uniform and a Gaussian-apodized FBGs are chosen as the target, showing an excellent agreement between the reconstructed refractive index modulations and those of the original FBGs. Next, several FBG profiles providing user-defined stationary power distributions, including a flat-top shape, a sharp peak, a saddle shape, or multiple peaks in the power distribution differential, are successfully synthesized. In addition, the proposed method is also shown to be suitable for the synthesis of integrated-waveguide Bragg gratings with arbitrary stationary power/field distributions.

&lt;bold&gt;Optimized synthesis of fiber Bragg gratings with triangular spectrum for wavelength-interrogation application&lt;/bold&gt;

A novel method for synthesizing arbitrary-shape triangular-spectrum fiber Bragg gratings (TS-FBGs) is proposed. It involves the use of a discrete layer peeling method for exploiting initial guess and a simulated annealing method for optimizing the desired grating parameter. By comparing it to the reported TS-FBGs synthesis methods, the proposed method has advantages of reducing the maximum index modulation and smoothing index modulation profile simultaneously. We employ the proposed method to synthesize FBGs with symmetric, asymmetric, and right-angled triangular spectrum, all of which have the low and smooth index modulation profiles. The synthesized gratings can act simple and cost-effective wavelength-interrogation devices in optical sensor systems.

Synthesis of Fiber Bragg Gratings with Right-Angled Triangular Spectrum

The spectrum shape of conventional fiber Bragg gratings is near-rectangular. By means of a discrete layer peeling method we numerically study fiber Bragg gratings with right-angled triangular spectrum. Fiber Bragg grating structures with single- and multi-channel right-angled triangular spectra are synthesized. These kinds of devices provide potential applications in wavelength interrogation in optical sensor systems.

The Fractional Fourier Transform in the Analysis and Synthesis of Fiber Bragg Gratings

An approach based on the fractional Fourier transform is proposed for both analysis and synthesis of fiber Bragg gratings. The method is shown to be simple and accurate. A comparison is made with the results of the numerical integration of the full Riccati equation, which are valid for arbitrary reflectivities. The method being very efficient, processing times can be short enough for a real-time control of the writing process, during grating manufacturing. The effects of profile random irregularities on FBG performance are studied, and several examples, useful for design purposes, are given.

Two-stage hybrid optimization of fiber Bragg gratings for design of linear phase filters

We present a new hybrid optimization method for the synthesis of fiber Bragg gratings (FBGs) with complex characteristics. The hybrid optimization method is a two-tier search that employs a global optimization algorithm [i.e., the tabu search (TS) algorithm] and a local optimization method (i.e., the quasi-Netwon method). First the TS global optimization algorithm is used to find a "promising" FBG structure that has a spectral response as close as possible to the targeted spectral response. Then the quasi-Newton local optimization method is applied to further optimize the FBG structure obtained from the TS algorithm to arrive at a targeted spectral response. A dynamic mechanism for weighting of different requirements of the spectral response is employed to enhance the optimization efficiency. To demonstrate the effectiveness of the method, the synthesis of three linear-phase optical filters based on FBGs with different grating lengths is described.

Synthesis of fiber Bragg gratings for use in transmission

A method for designing fiber Bragg gratings with desired complex transmission coefficients is proposed. The transmission coefficient of a fiber grating satisfies the minimum-phase condition when the linear phase from the pure propagation is ignored. Therefore only a finite bandwidth is considered for the synthesis. The algorithm is based on a result of Krein and Nudel’man [Prob. Peredachi Inf.11, 37 (1975)]. A numerical algorithm is developed, and by numerical examples it is demonstrated that it is possible to realize gratings with specified complex transmission responses inside the considered bandwidth. The method is also applicable for thin-film filters.

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.