Kazimierz Jedrzejewski

Numerical model of tapered fiber Bragg gratings for comprehensive analysis and optimization of their sensing and strain-induced tunable dispersion properties

A versatile numerical model for spectral transmission/reflection, group delay characteristic analysis, and design of tapered fiber Bragg gratings (TFBGs) is presented. This approach ensures flexibility with defining both distribution of refractive index change of the gratings (including apodization) and shape of the taper profile. Additionally, sensing and tunable dispersion properties of the TFBGs were fully examined, considering strain-induced effects. The presented numerical approach, together with Pareto optimization, were also used to design the best tanh apodization profiles of the TFBG in terms of maximizing its spectral width with simultaneous minimization of the group delay oscillations. Experimental verification of the model confirms its correctness. The combination of model versatility and possibility to define the other objective functions of Pareto optimization creates a universal tool for TFBG analysis and design.

Simultaneous Measurement of Liquid Level and Temperature Using Tilted Fiber Bragg Grating

We present a tilted fiber Bragg grating (TFBG)-based fiber optic sensor for the simultaneous measurement of liquid level and temperature. Due to different responses of cladding modes and core mode in TFBG spectrum to liquid level and temperature changes, both values can be measured independently. The examined 3.5° TFBG exhibits linear liquid level, as well as temperature, responses and sensitivities of -0.456 ± 0.009 dB/mm and 11.4 ± 0.2 pm/°C, respectively. In addition, greater sensor applicability is proposed for liquids having lower refractive indexes using TFBG with greater tilt angle. The presented system is capable of being applied in chemical, food, and automotive industries as well as, thanks to its all-fiber structure, in potentially hazardous environments where the immunity to electromagnetic fields or/and electric isolation is required.

Fiber-Optic Strain Sensors Based on Linearly Chirped Tapered Fiber Bragg Gratings With Tailored Intrinsic Chirp

In this paper, spectrally tailored tapered chirped fiber Bragg gratings (TCFBGs) are considered for use as strain sensors. Both gratings were written in fused tapered optical fiber using linearly chirped fiber Bragg gratings in co-directional and counter-directional chirp configurations. Theoretical and numerical analysis as well as experimental verification of the influence of applied strain on spectral width of both TCFBG structures were carried out. The results show that TCFBGs exhibit monotonic strain response over the wide operating range of the applied force. Compared with standard tapered FBG written using uniform phase mask, in the case of co-directionally written TCFBG with substantially larger grating chirp the monotonic operating range can be easily broadened toward the higher strain values (even above the applied force at which the optical fiber breaks). In turn, the intrinsic chirp of the counter-directionally written TCFBG can be tailored in such a way as to ensure that the monotonicity of its strain response is always satisfied when tensile force is applied. This is due to the spectral broadening of the reflected spectrum when strain increases.

Optimal design of optical fibers for electric current measurement.

The current sensitivity and bandwidth of the optical fiber current monitor are analyzed. The optimal sensitivity is proportional to the ratio of fiber attenuation to the Verdet constant at a specific fiber length. A selection of compound glasses has been investigated with a view to improving bandwidth and sensitivity over standard silica-fiber systems. A trial fiber of the most promising glass (Schott F7) has been fabricated and characterized.

Numerical analysis of double chirp effect in tapered and linearly chirped fiber Bragg gratings

In this paper, a theoretical analysis of recently developed tapered chirped fiber Bragg gratings (TCFBG) written in co-directional and counter-directional configurations is presented. In particular, the effects of the synthesis of chirps resulting from both a fused taper profile and a linearly chirped fringe pattern of the induced refractive index changes within the fiber core are extensively examined. For this purpose, a numerical model based on the transfer matrix method (TMM) and the coupled mode theory (CMT) was developed for such a grating. The impact of TCFBG parameters, such as grating length and steepness of the taper transition, as well as the effect of the fringe pattern chirp rate on the spectral properties of the resulting gratings, are presented. Results show that, by using the appropriate design process, TCFBGs with reduced or enhanced resulting chirp, and thus with widely tailored spectral responses, can be easily achieved. In turn, it reveals a great potential application of such structures. The presented numerical approach provides an excellent tool for TCFBG design.

Quasi-Uniform Fiber Bragg Gratings

A new simple and versatile method for inscribing fiber Bragg gratings with an arbitrarily chosen Bragg wavelength is presented. Owing to the optimization of the irradiation process and application of the phase mask with a properly matched chirp, the method offers the ability to adjust the FBG resonance wavelength adjustment within a range of tens of nanometer. However; the resulting grating has a chirp; its spectral properties closely resemble those of the uniform one, which explains why such gratings are called quasi-uniform fiber Bragg gratings (QUFBGs). Optimization of the inscription process involved a two parameter Pareto method. The research presented here was conducted for a 2.5 cm phase mask with a 0.35 nm/mm chirp and allowed for the modelling, optimization and inscription of QUFBGs of FWHM 0.8-0.9 nm, with a transmission minimum lower than -8 dB and Bragg wavelength adjustment range of 11.4 nm. It was estimated that if extended to a commercially available 15 cm phase mask, the method would allow a record-breaking 74.7 nm adjustment range to be obtained. Together with clear consistency of the numerical and experimental results with the design assumptions for QUFBGs inscription, this record value makes the proposed method competitive with more sophisticated and less reproducible interferometric techniques.

Temperature Independent Tapered Fiber Bragg Grating-Based Inclinometer

A new concept for an optical fiber inclinometer based on tapered fiber Bragg grating (TFBG) is presented. The sensor was characterized by the experimental measurement of the dependence of inclination angle on the spectral response in fluctuating temperature conditions. The research showed that the TFBG made it possible to simultaneously measure both the inclination angle and temperature, and to operate as a temperature insensitive 0°-90° tilt sensor, in a different interrogation regime. Inscription of the FBG in the tapered optical fiber section offered not only sensor miniaturization, but also the possibility of temperature sensing by the fiber section adjacent to the inclination area. Moreover, due to the reflective mode of the TFBG, the sensor offers excellent sensitivity due to the double-loss operation.

Linearly chirped tapered fiber-Bragg-grating-based Fabry–Perot cavity and its application in simultaneous strain and temperature measurement

A novel concept of a Fabry-Perot (F-P) cavity composed of two linearly chirped fiber Bragg gratings written in a thermally fused fiber taper is presented. Both chirped gratings are written in counter-directional chirp configuration, where chirps resulting from the optical fiber taper profile and linearly increasing grating periods cancel each other out, forming a high-quality F-P resonator. A new strain-sensing mechanism is proposed in the presented structure, which is based on strain-induced detuning of the F-P resonator. Due to the different strain and temperature responses of the cavity, the resonator can be used for the simultaneous measurement of these physical quantities, or it can be used as a temperature-independent strain sensor.

Shaping the spectral characteristics of fiber Bragg gratings written in optical fiber taper using phase mask method

The paper presents the way that colour can serve solving the problem of calibration points indexing in a camera geometrical calibration process. We propose a technique in which indexes of calibration points in a black-and-white chessboard are represented as sets of colour regions in the neighbourhood of calibration points. We provide some general rules for designing a colour calibration chessboard and provide a method of calibration image analysis. We show that this approach leads to obtaining better results than in the case of widely used methods employing information about already indexed points to compute indexes. We also report constraints concerning the technique. Nowadays we are witnessing an increasing need for camera geometrical calibration systems. They are vital for such applications as 3D modelling, 3D reconstruction, assembly control systems, etc. Wherever possible, calibration objects placed in the scene are used in a camera geometrical calibration process. This approach significantly increases accuracy of calibration results and makes the calibration data extraction process easier and universal. There are many geometrical camera calibration techniques for a known calibration scene [1]. A great number of them use as an input calibration points which are localised and indexed in the scene. In this paper we propose the technique of calibration points indexing which uses a colour chessboard. The presented technique was developed by solving problems we encountered during experiments with our earlier methods of camera calibration scene analysis [2]-[3]. In particular, the proposed technique increases the number of indexed points points in case of local lack of calibration points detection. At the beginning of the paper we present a way of designing a chessboard pattern. Then we describe a calibration point indexing method, and finally we show experimental results. A black-and-white chessboard is widely used in order to obtain sub-pixel accuracy of calibration points localisation [1]. Calibration points are defined as corners of chessboard squares. Assuming the availability of rough localisation of these points, the points can be indexed. Noting that differences in distances between neighbouring points in calibration scene images differ slightly, one of the local searching methods can be employed (e.g. [2]). Methods of this type search for a calibration point to be indexed, using a window of a certain size. The position of the window is determined by a vector representing the distance between two previously indexed points in the same row or column. However, experiments show that this approach has its disadvantages, as described below. * E-mail: A.Nowakowski@ire.pw.edu.pl Firstly, there is a danger of omitting some points during indexing in case of local lack of calibration points detection in a neighbourhood (e.g. caused by the presence of non-homogeneous light in the calibration scene). A particularly unfavourable situation is when the local lack of detection effects in the appearance of separated regions of detected calibration points. It is worth saying that such situations are likely to happen for calibration points situated near image borders. Such points are very important for the analysis of optical nonlinearities, and a lack of them can significantly influence the accuracy of distortion modelling. Secondly, such methods may give wrong results in the case of optical distortion with strong nonlinearities when getting information about the neighbouring index is not an easy task. Beside this, the methods are very sensitive to a single false localisation of a calibration point. Such a single false localisation can even result in false indexing of a big set of calibration points. To avoid the above-mentioned problems, we propose using a black-and-white chessboard which contains the coded index of a calibration point in the form of colour squares situated in the nearest neighbourhood of each point. The index of a certain calibration point is determined by colours of four nearest neighbouring squares (Fig.1). An order of squares in such foursome is important. Because the size of a colour square is determined only by the possibility of correct colour detection, the size of a colour square can be smaller than the size of a black or white square. The larger size of a black or white square is determined by the requirements of the exact localisation step which follows the indexing of calibration points [3]. In this step, edge information is extracted from a blackand-white chessboard. This edge information needs larger Artur Nowakowski, Wladyslaw Skarbek Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa, A.Nowakowski@ire.pw.edu.pl Received February 10, 2009; accepted March 27, 2009; published March 31, 2009 http://www.photonics.pl/PLP

Double-clad photonic crystal fibre for laser applications

Double-clad photonic crystal fibre structure for laser applications is demonstrated. The double-clad structure of the fibre has the air-cladding with glass bridges of waists less than 500nm. The fibre was produced with phosphate glass and the core region was doped with ytterbium. The fibre was investigated and we found it to be monomode for generation wavelength of 1008nm. Whole fibre producing process including doped and undoped glass manufacturing and fibre drawing was held in Institute of Electronic Materials Technology.