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Dive into the research topics where Konrad Markowski is active.

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Featured researches published by Konrad Markowski.


Applied Optics | 2015

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

Tomasz Osuch; Konrad Markowski; Kazimierz Jedrzejewski

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.


IEEE Sensors Journal | 2016

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

Tomasz Osuch; Tomasz Jurek; Konrad Markowski; Kazimierz Jedrzejewski

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.


IEEE Sensors Journal | 2016

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

Tomasz Osuch; Konrad Markowski; Kazimierz Jedrzejewski

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.


Progress in Automation, Robotics and Measuring Techniques | 2015

Digraphs minimal realisations of state matrices for fractional positive systems

Krzysztof Hryniów; Konrad Markowski

This paper presents a method of the determination of characteristic polynomial realisations of the fractional positive system. The algorithm finds a complete set of all possible realisations instead of only a few realisations. In addition, all realisations in the set are minimal. The proposed method uses a parallel computing algorithm based on a digraphs theory which is used to gain much needed speed and computational power for a numeric solution. The presented procedure has been illustrated with a numerical example.


Applied Optics | 2016

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

Konrad Markowski; Kazimierz Jedrzejewski; Tomasz Osuch

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.


Journal of Lightwave Technology | 2015

Quasi-Uniform Fiber Bragg Gratings

Tomasz Osuch; Konrad Markowski; Pawel Gasior; Kazimierz Jedrzejewski

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.


international conference on methods and models in automation and robotics | 2014

Reachability Index Calculation by Parallel Digraphs-Building

Krzysztof Hryniów; Konrad Markowski

In this paper the alternative method for determination of all possible lower reachability indices has been proposed. Method is based on the extension of parallel digraphs creation algorithm presented previously. As a solution of problem of determination of lower reachability index, method finds all possible finite paths in the digraphs - each of them representing one of the indices. By performing complete traversal of the digraphs we are able to reach all the possible lower reachability indices for any number of variables at once. Proposed method is illustrated by a numerical example.


Archive | 2016

Digraphs Minimal Positive Stable Realisations for Fractional One-Dimensional Systems

Konrad Markowski; Krzysztof Hryniów

This paper presents a method of the determination of positive stable realisation of the fractional continuous-time positive system. The algorithm finds a complete set of all possible realisations instead of only a few realisations. In addition, all realisations in the set are minimal and stable. The proposed method uses a parallel computing algorithm based on a digraphs theory which is used to gain much needed speed and computational power for a numeric solution. The presented procedure has been illustrated with a numerical example.


international conference on methods and models in automation and robotics | 2015

Optimisation of digraphs creation for parallel algorithm for finding a complete set of solutions of characteristic polynomial

Krzysztof Hryniów; Konrad Markowski

This paper presents a series of further modifications to the parallel algorithm used for finding digraphs realisations of the characteristic polynomial. What distinguishes the mentioned algorithm from other state-of-the-art solutions is the ability to find a complete set of existing solutions, not just a few of them. Moreover, solutions found tend to be minimal in terms of a rank of matrices created. Due to a of large number of solutions tested and an NP-hard complexity of the problem, the parallel algorithm is incapable of finding solutions for more complicated problems in reasonable time. To address this problem additional modifications of the algorithm structure are proposed and explained. Modifications presented in this paper contribute to a reduction of a number of improper solutions that are created, and later tested and rejected, by the algorithm making it work in all cases, except the most trivial ones, at least by an order of magnitude faster.


Progress in Automation, Robotics and Measuring Techniques | 2015

Optimisation of digraphs-based realisations for polynomials of one and two variables

Krzysztof Hryniów; Konrad Markowski

This paper proposes a set of modifications to the algorithm proposed earlier, that finds a complete set of minimal solutions for the characteristic polynomial on basis of digraphs theory and parallel computation. Changes proposed allow for parallelisation of previously sequential part of the algorithm, accurate estimation of number of solutions created and speed-up of both parts of the algorithm. Reduction of algorithm’s complexity is greatest for monomials consisting of only one variable and for one-variable polynomial a complete set of minimal solutions can be found as fast as in linearithmic time.

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Tomasz Osuch

Warsaw University of Technology

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Kazimierz Jedrzejewski

Warsaw University of Technology

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Krzysztof Hryniów

Warsaw University of Technology

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J.P. Turkiewicz

Warsaw University of Technology

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Paweł Gąsior

Warsaw University of Technology

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Anna Duzynska

Warsaw University of Technology

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Anna Wróblewska

Warsaw University of Technology

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Piotr Lesiak

Warsaw University of Technology

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Piotr Sobotka

Warsaw University of Technology

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Tomasz Jurek

Warsaw University of Technology

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