ҚазККА Хабаршысы - Вестник КазАТК

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ҚазККА Хабаршысы № 2 (121), 2022 ISSN 1609-1817 (Print) The Bulletin of KazATC Вестник КазАТК № 2 (121), 2022 ISSN 2790-5802 (Online) DOI 10.52167/1609-1817 vestnik.alt.edu.kz

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UDC 004.9 DOI 10.52167/1609-1817-2022-121-2-503-510

A.Kalizhanova ^1,2, A.Kozbakova^1,3 , M.Kunelbayev¹, Zh. Aitkulov^1,4, Zh.Amirgaliyeva¹

1Institute of Information and Computation Technologies CS MES RK, Almaty, Kazakhstan

2Almaty University of Energy and Communications, Almaty, Kazakhstan

3Almaty Technological University, Almaty, Kazakhstan

4Academy of Logistics and Transport Almaty, Kazakhstan Е-mail: [email protected]

NUMERICAL ANALYSIS OF FORMING UNIFORM FIBER BRAGG GRATINGS, USING PHASE MASK

Abstract. In the work herein there was developed numerical analysis of forming uniform fiber Bragg gratings, using phase mask. There was developed method of recording Bragg grating, using uniform phase mask, which is characterized with a fact, that it consists of ultraviolet excimer laser, output laser light beam, directed to the system of mobile diaphragms with regulated gap between them and located behind the system of mobile diaphragms of uniform phase mask, after which there is a photosensitive multimode optical fiber with tilted Bragg grating. In the research there was applied diffraction theory to analyze intensity distribution in the fiber core during fabricating fiber Bragg grating (FBG), using uniform phase mask. There was calculated averaged distribution of diffraction field in the fiber core as a function of optic fiber position. Outcomes show, that in case of fabricating uniform FBG, averaged intensity field profile, as well, refraction index of optical fiber position behind phase mask is decreased for average intensity distribution in the fiber core along with increase of its diameter.

Keywords. Fiber optic sensors, fiber Bragg gratings, numerical analysis.

Introduction.

In the articles [1,2] there were developed fiber Bragg gratings, which in the recent years become popular in telecommunication and sensor-based systems. In some applications it is necessary to have FBG with sufficiently decreased side lobes of their spectral characteristics. For that aim there fabricated apodized Bragg gratings with decreased amplitude of index changing at both ends of FBG. One of recording methods for apodized fiber Bragg gratings is the phase mask with variable diffraction effectiveness – the method, providing the highest reproducibility. In the articles [3,4] there were developed fiber Bragg gratings, applying diffraction method, where is the main advantage is maintaining constant effective refraction index along the whole Bragg grating. In the works [3,6] there was developed diffraction grating, where diffraction effectiveness of phase mask is implemented by changing its operating cycle [5] and/or groove depth.

The work [7] researched coherent ultraviolent laser beam, which illuminates the phase mask, In the fiber core there is formed interference picture, which is set directly behind

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diffraction optic element (DOE) and causes periodical changes of refraction index. Thus, there is formed fiber Bragg grating. Thanks to closeness of optic fiber to the phase mask, the method operates even in case of sources with low consistency. The works [8,9] show, that interference happens only between diffraction orders ±1. In the article [10] there was minimized diffractions influence, having selected corresponding parameters of uniform phase mask. In turn, in case of phase mask with variable diffraction effectiveness, to obtain constant effective refraction index, in anodized Bragg grating there is required 0-order diffraction. Moreover, intensity distribution behind the phase mask changes dependent on distribution distance (and, consequently, depends on phase mask – segregation of optic fiber) [11]. Therefore, while forming FBG, it is more feasible to consider the average intensity inside fiber core, but not distribution in one plane.

The article herein considers average intensity distribution inside the fiber. Main data was obtained from diffraction field behind the uniform phase mask. There is researched the influence of optic fiber position at averaged intensity distribution.

Materials and methods.

Theoretical model.

The given research’s novelty is the technique of recording Bragg grating, using uniform phase mask, which is characterized with the fact, that it consists of ultraviolet excimer laser, output laser light beam, directed to mobile diaphragms system with regulated gap between them, located behind mobile diaphragms system of uniform phase mask, behind which there is photosensitive multimode optic fiber with tilted Bragg grating.

Technique of recording Bragg gratings is fulfilled in compliance with the invention.

Means of recording apodized Bragg gratings, using uniform phase mask is characterized with the fact, that there is set the gap width between mobile diaphragms system 3 in the range from 0,1 to 0,2 mm. Afterwards, from ultraviolet excimer laser 1 there is radiated the laser beam 2, appropriate to create Bragg grating, at mobile diaphragms 3 and after passing through the mobile system, the diaphragm 4 radiates constricted laser beam at uniform phase mask 5, behind which there is the photosensitive multimode optic fiber with tilted Bragg grating 6, and part of Bragg grating burns down at photosensitive multimode optic fiber with tilted grating. Afterwards, mobile diaphragms system 3 moves along the photosensitive multimode optic fiber with tilted Bragg grating 6 for the gap depth, maintaining fixed gap width, following which, the cycle occurs again till Bragg fixed grating recording.

Figure 1 - Technique of Bragg grating recording, using uniform phase mask

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Further there will be considered, how FBG is recorded by means of ultraviolet excimer laser with continuous wav. Uniform phase mask with optic fiber displaces perpendicular to the falling beam, creating scanning effect. Thus, illuminating wave might be considered as a plane wave. Induced changes of refraction index are the same, as in case of lighting the whole phase mask by plane wave.

Fig. 1 shows the method of uniform phase mask for fabricating fiber Bragg grating. As a rule, the period of fiber Bragg grating constitutes a half of phase mask period (Λ =ΛPM/2).

Figure 2 - FBG recording, using uniform phase mask, where: ZF—phase mask distance along optic fiber, ZT — Talbot distance

Fig.2 shows FBG recording, using uniform phase mask. Upon modeling, there were accepted following parameters: fiber core refraction index nCO= 1,50, phase mask period ΛPM= 1055 Nm, falling plane wave length λUV= 256 Nm, and d denotes fiber core diameter. Difference between refraction indices of core and cladding is small enough to assume, that nCL=nCO=n. In practice, ideal (continuous) phase mask profile is approximated with ladder function due to discreet values of electrons or ions doses in fabrication process [3].

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Figure 3 -Profile of phase step in uniform phase mask, L—phase mask length

Fig.3 demonstrates the phase step profile in uniform phase mask. In the analysis herein the uniform phase mask consists of eight sections with grooves depth, corresponding to phase displacement (phase steps) ϕ=k⋅ π/8, where k = 1,..., 8. Sections width was selected for maximum possible approximation of mask profile according to Gausse (see Fig. 3).

The given profile cannot be directly transferred to diffraction field (due to nonlinear function of intensity distribution dependent on the phase step [12]), it does not influence at definition clarity of uniform FBG recording. It was supposed, that intensity distribution, which participates in FBG forming, might be presented as simple average IAV(z) of intensities I(zi) in discreet planes in fiber core area. Therefore, distance between phase mask and optical fiber zF,

IAV(z) is computed according to the following formulae:

, (1)

, (2)

where i= 1, 2,..., N and I(zi) – intensity distribution in planes zi in fiber core area, while cl – difference between radii of fiber and cladding cores.

According to Talbot effect, the diffraction field behind uniform phase mask in z direction is periodical and repeats itself every ZT= 2⋅ n⋅ Λ² PM/λUV=13,47 micrometer [11]. Consequently, in order to get complete information about interrelation between averaged intensity distribution IAV and distance between optical fiber and phase mask, it is enough to study characteristics IAV=f (z) for z∈(zF; zF+zT). Computations were prepared for M=101 planes between adjacent self- visual displays in fiber core area. Numerical algorithms are based on the theory of scalar diffraction [13] and convolution method [14,15].

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507 Results and discussion.

Numerical results.

Initially, distribution of the field behind the uniform phase mask in the fiber core area was computed for the distance ZF=315 micrometers, which means, that region of interest equals to z∈〈z_F+zCL;zF+zCL+2zT). It consists of eight segments with 5⋅ΛPM width, each of which conforms to corresponding phase stages (phase mask sections).

In the article [16] in the distribution of the field behind uniform phase mask in fiber core area there is occurred the problem of existing perturbations, though it is not essential in the analysis herein.

а) b) c)

Figure 4 - Cross sections of IAV averaged intensity distribution IAV along z axis

Fig. 4-5 present cross sections of averaged distribution intensity. Fig. 4 illustrates cross sections along “lateral z” – line for different fiber core diameters and for every section of the phase mask.

As it is seen from the Figure, when the center of fiber core is in the plane of self-image, cross section IAV is almost identical to such in case of z2. For the central part of uniform phase mask (ϕ=π), mentioned above ΛPM/ 2 displacement is imperceptible, as the main period of intensity distribution (and, consequently, average intensity) constitutes a half of phase mask period [11]. Modeling results show, that in case of uniform phase mask (ϕ=π) period of distributing the average intensity Λ =ΛPM /2 and it does not depend on the distance between optical fibers. Magnitude of optic fiber core diameter (i.e., averaging intensity distribution area) does not sufficiently influence at averaged intensity distribution. IAV permanence reason as functions zF and d is periodicity of intensity distribution behind uniform phase mask, where for ϕ=π the main period in distribution direction (axis z) equals to zT/ 8.

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a) b) c)

Figure 5 - Presents IAV changes periodicity in direction z in two cases: z1 — when cladding border of optic fiber-core is located in the plane of self-image, and z2 center of fiber core is

located in the plane between adjacent self-images

As it is seen from Figure 4, when fiber Bragg grating fits with lighting of the uniform phase mask, for the phase steps ϕ<π the averaged intensity distribution in fiber core area depends on position of optical fiber behind uniform phase mask (averaging area). Thus, according to Fig.

5, for ϕ∈〈2π/8;7π/8〉 influence zF at IAV is sufficient. When ϕ is small, zF dependence on IAV is not sufficient due to low contrast between maximum and minimum magnitudes of the averaged intensity distribution. Also it might be said, that regularity of averaged intensity distribution IAV

comprises a half of phase mask period (Λ =ΛPM/2) and it does not depend on the diameter of optic fiber core.

Conclusions.

In the work herein there was carried out analysis of forming the uniform FBG, using the phase mask. Outcomes show, that the averaged intensity distribution in the fiber core area and, consequently, refraction index perturbation have shaped form. When the phase step equals to π, the main period of uniform FBG direction diagram comprises a half of the phase mask period.

Considering other areas, it can be observed, that the phase step has decreased, every second maximum in the distribution IAV decreases and Λ = ΛPM. In the numerical results the averaged intensity distribution becomes substantial, when the diameter of the optic fiber core is small comparing with Talbot distance.

This work is supported by grant from the Ministry of Education and Science of the Republic of Kazakhstan within the framework of the Project № AP09259547 «Development of a system of distributed fiber-optic sensors based on fiber Bragg gratings for monitoring the state of building structures», Institute Information and Computational Technologies CS MES RK.

Experimental researches have been carried out in the laboratories of optoelectronics at the Electric engineering and computer sciences faculty of Lublin Technical University.

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509 REFERENCES

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[9] P.E. Dyer, R.J. Farley, R. Gidle, Opt. Commun. 115 (1995) 327–334.

[10] Y. Qiu, Y. Sheng, C. Beaulieu, J. Lightwave, Technology 17 (1999) 2366–2370.

[11] T. Osuch, Z. Jaroszewicz, Phot. Lett. Pol. 1 (2009) 190–192.

[12] Z. Jaroszewicz, A. Kolodziejczyk, A. Kowalik, R. Restrepo, Optik 111 (2000) 207–

210. [13] J.W. Goodman, Introduction to Fourier Optics, second. McGraw-Hill, 1996.

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[15] M. Sypek, C. Prokopowicz, M. Gorecki, Opt. Eng. 42 (2003) 3158–3164.

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61871G-9).

Әлия Қалижанова, ф.-м.ғ.к., ҚР БҒМ ҒК Ақпараттық және есептеуіш технологиялар институты, Алматы энергетика және байланыс университеті, Алматы, Қазақстан, [email protected]

Айнұр Козбакова, PhD, ҚР БҒМ ҒК Ақпараттық және есептеуіш технологиялар институты, Алматы технологиялық университеті, Алматы, Қазақстан, [email protected]

Мұрат Кунелбаев, PhD, ҚР БҒМ ҒК Ақпараттық және есептеуіш технологиялар институты, Алматы, Қазақстан, [email protected]

Жалау Айтқұлов, ҚР БҒМ ҒК Ақпараттық және есептеуіш технологиялар институты, Алматы логистика және көлік Академиясы, Қазақстан, [email protected]

Жазира Амиргалиева, PhD, ҚР БҒМ ҒК Ақпараттық және есептеуіш технологиялар институты, Алматы, Қазақстан, [email protected]

ФАЗАЛЫҚ МАСКАНЫ ҚОЛДАНА ОТЫРЫП, БІРТЕКТІ ТАЛШЫҚТЫ БРЭГГ ТОРЛАРЫНЫҢ ПАЙДА БОЛУЫН САНДЫҚ ТАЛДАУ

Аңдатпа: Бұл жұмыста фазалық масканы қолдана отырып, біртекті талшықты Брэгг торларының пайда болуына сандық талдау жасалды. Біртекті фазалық масканы қолдана отырып, Брэгг торын жазу әдісі жасалды, ол ультрафиолет эксимерлі лазерден, олардың арасындағы реттелетін саңылауы бар жылжымалы диафрагмалар жүйесіне бағытталған лазерлік жарықтың шығу сәулесінен және жылжымалы диафрагмалар жүйесінің артында орналасқан біртекті фазалық маскадан тұрады, оның артында көлбеу Брэгг торы бар фотосезімтал көп режимді оптикалық талшық бар. Зерттеуде біртекті фазалық масканы қолдана отырып, талшықты Брэгг торын (VBR) жасау кезінде талшықтың өзегіндегі қарқындылықтың таралуын талдау үшін дифракция теориясы

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қолданылды. Оптикалық талшықтың орналасу функциясы ретінде талшық өзегіндегі дифракциялық өрістің орташа таралуы есептелді. Нәтижелер біртекті VBR өндірісі жағдайында өрістің қарқындылығының орташа профилі, сондай-ақ талшықтың өзегіндегі сыну көрсеткішінің өзгеруі күрделі пішінге ие екенін көрсетеді. Сондай-ақ, фазалық маскадан кейінгі оптикалық талшықтың орналасуының орташа қарқындылыққа әсері есептелген талшықтың өзегіндегі таралу диаметрі жоғарылаған сайын төмендейді.

Түйінді сөздер. Талшықты-оптикалық датчиктер, Брэгг талшықты торлары, сандық талдау.

Алия Калижанова, к.ф.-м.н, профессор, Институт информационных и вычислительных технологий КН МОН РК, Алматинский университет энергетики и связи, Алматы, Казахстан; [email protected]

Айнур Козбакова, PhD, Институт информационных и вычислительных технологий КН МОН РК, Алматинский технологический университет, Алматы, Казахстан, [email protected]

Мурат Кунелбаев, Институт информационных и вычислительных технологий КН МОН РК, Алматы, Казахстан, [email protected]

Жалау Айткулов, Институт информационных и вычислительных технологий КН МОН РК, Академия логистики и транспорта, Алматы, Казахстан, [email protected]

Жазира Амиргалиева, PhD, Институт информационных и вычислительных технологий КН МОН РК, Алматы, Казахстан, [email protected]

ЧИСЛЕННЫЙ АНАЛИЗ ФОРМИРОВАНИЯ ОДНОРОДНЫХ ВОЛОКОННЫХ БРЭГГОВСКИХ РЕШЕТОК С ИСПОЛЬЗОВАНИЕМ ФАЗОВОЙ МАСКИ

Аннотация. В данной работе разработан численный анализ формирования однородных волоконных брэгговских решеток с использованием фазовой маски. Был разработан способ записи брэгговской решетки с использованием однородной фазовой маски, которая характеризуется тем, что она состоит из ультрафиолетового эксимерного лазера, выходного луча лазерного света, направленного на систему подвижных диафрагм с регулируемым зазором между ними и расположенным за системой подвижных диафрагм однородной фазовой маской, за которой находится фоточувствительное многомодовое оптическое волокно с наклонной решеткой Брэгга. В исследовании применена теория дифракции для анализа распределения интенсивности в сердцевине волокна во время изготовления волоконной брэгговской решетки (ВБР) с использованием однородной фазовой маски. Было рассчитано усредненное распределение дифракционного поля в сердцевине волокна как функция положения оптического волокна. Результаты показывают, что в случае изготовления однородных ВБР усредненный профиль интенсивности поля, а также изменения показателя преломления в сердцевине волокна имеют сложную форму. Также было рассчитано, что влияние положения оптического волокна за фазовой маской на среднюю интенсивность распределение в сердцевине волокна уменьшается с увеличением его диаметра.

Ключевые слова. Волоконно-оптические датчики, волоконные решетки Брэгга, численный анализ.

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