Final Report Summary - TEMESAMA (New production technology development for most efficient and more stable application of electro-optic and nonlinear optical crystalline materials)
The main objective of No.272715 project and No.910715 its return phase (see web-site: http://tk-lab.lp.edu.ua/eng/projects.html) was development of new production technology for highly efficient and stable crystalline materials applicable as sensitive elements of electro-optic and nonlinear optical cells. Relevant devices have in principle a broad range of optoelectronic applications and particularly may be used for control and conversion of laser radiation.
For achievement of the project's objectives and its return phase such work have been carried out. In the first steps it was created the interferometric setup for electro-optic measurements as well as modernized the nonlinear optical setup available at the Czestochowa University of Technology [7,10] (see references list below). It was also elaborated the interferometric technique applicable to the wedge angle and surface flatness measurements of optical slabs, which lets to provide a quality control of relevant optical elements while their manufacturing [3]. In the next steps, it was developed relevant fundamental methodologies suitable for precise determination of complete sets of electro-optic tensor coefficients in crystal materials of any symmetry [7]. Particularly, by using available laboratory setups the electro-optic and nonlinear optical characteristics of langasite, pure and MgO doped lithium niobate crystals were investigated [9-12]. For these anisotropic materials, a complete tensor sets of electro-optic and nonlinear optical coefficients were determined. Notice that a complete sets of such tensor constants represent requiring input parameters [1,2,13] for further 3D-analysis of the spatial anisotropy of parametrical effects. Accordingly, in the final steps there was calculated the indicative surfaces and corresponding stereographic projections of the effective electro-optic [1,13] and acousto-optic [4] coefficients as well as obtained the indicative surfaces composed from maximal values of relevant effects [4,8]. On their basis the global directional maxima of the electro-optic and acousto-optic effects for the crystal materials mentioned above were determined and for these directional maxima an angular stability analysis has been performed using improved our own software [2]. The main technological solutions and approaches were protected by Ukrainian patent [5] and by Polish patent [6].
During the return phase, which is the final stage of No.272715 project, the main objective was further development of new production technology for most efficient and more stable application of the crystalline materials. For this the working elements samples with highest magnitude of electro-optic and nonlinear optical effects were manufactured and the experimental verification of the electro-optic parameters on manufactured samples with different orientations was performed [16, 18-19]. It was also fabricated the prototype of electro-optic cell made of mentioned above crystalline materials for highly efficient control of superpowerful laser radiation and its technical characteristics were investigated. Besides, it was developed and approved our tech¬nology also for nanostructures with aim of their using as sensitive elements for electro-optic or nonlinear optical cells [14-17].
During execution of the project and its return phase the main results obtained are the following:
1) Creation of the laboratory interferometric setup for the electro-optic measurements [7,10] and modernization of the nonlinear optical setup;
2) Creation of the laboratory interferometric setup applicable to the control of samples quality while their preparation [3];
3) Elaboration of the methodology for measurements and calculations of all electro-optic coefficients in the crystalline materials of any symmetry [7];
4) Electro-optic and piezo-optic investigations of langasite, pure and MgO doped lithium niobate crystals [9-12] providing determination of the full set of electro-optic and/or piezo-optic tensor constants;
5) Exploration of the spatial anisotropy 3D-analysis of electro-optic and acousto-optic effects for selected crystal materials that provides directional maxima related with the most efficient geometries of relevant electro-optic or acousto-optic interactions. It was shown theoretically and in several cases proved also experimentally that for the interaction geometries being optimized relevant effects rise from about 1.5 to 2.7 times [1,4,8,9,11,12,15] comparing to standard geometries (usually the direct crystal cuts) widely used in most applications. This, in fact, opens hidden possibilities for further increase of the application efficiency of electro-optic and/or acousto-optic crystal materials in relevant optoelectronic devices;
6) Exploration of the directional stability of electro-optic and piezoelectrical devices against uncontrolled deviations of material parameters. For this purpose basing on full sets of electro-optic and piezo-electrical constants we have performed the spatial stability analysis [2]. Amazingly, it turns out that parametrical effects along the directional maxima characterize by enhanced stability of their effective characteristics as well. Obviously, it appears to be very important from the practical point of view;
7) Demonstration of the experimental verification of analytical approaches used for evaluation of the spatial anisotropy of linear electro-optic effect in crystal materials [16, 18-19]. For this the electro-optic measurements have been performed on a series of crystal X/-cuts (0o < < 90o) of LiNbO3 crystals to get a cross section of the indicative surfaces. A fairly good agreement was found between the experiment and calculations for the effective electro-optic coefficients describing both electro-induced optical pathlength and birefringence in investigated crystalline materials;
8) Fabrication of the prototype of electro-optic cell made of investigated materials of MgO doped lithium niobate crystals for highly efficient control of superpowerful laser radiation and investigation of its technical characteristics. It confirms the validity and prospects developed in this project the production technology for the most efficient and more stable application of crystalline materials (see: http://tk-lab.lp.edu.ua/eng/research.html) which give a possible to reveal the large hidden reserves of their application efficiency improvement as working elements for electro-, piezo-, acousto- or nonlinear optical devices in industry.
The final result of project and its return phase is elaborated new production technology applicable both for a search of new prospective electro-, piezo-, acousto-optic or nonlinear optical crystals likewise an improvement of application efficiency and/or parameter stability of already existing crystal materials being used as sensitive elements in respective high performance devices including the systems for control and/or conversion of the superpowerful laser radiation, which in many aspects appear to be a key problem of the optoelectronic industry in the European Union. No doubt that relevant devices represent high technology and knowledge based products provided by scientific innovations and technological advances of European Union. The innovations implemented here may appear to be very useful and important for many branches of practically whole optoelectronic industry starting from different kinds of high performance light modulators and deflectors, applicable in modern communication systems, to specialized highly efficient sensor techniques, the working principle of which are based on parametrical or nonlinear optical phenomena. In addition, the technological solutions drawn within this project may be characterized as market competitive taking into account that, on the one hand, they appear to be much cheaper comparing to existing other solutions and, on the other hand, they are time saving and more accurate since there is no need to prepare a large number of different crystal samples (cuts) likewise perform relevant measurements on different samples which usually rises considerably errors in evaluation of actual material parameters. The competitiveness of our technology is caused also by the fact that its implementation in practice does not require any serious reorganization of technological process while manufacturing of electro-optic, acousto-optic or nonlinear optical cells.
The final results of this project have a social effect too. Project elaborations, which are generally based on optimized applicability of existing or new crystal materials, including nanostructures, inevitably bring us to material and power saving technologies since the geometry optimization of electro-, acousto-optic and nonlinear optical interactions leads in each case to a reduction of cell size likewise a decreasing of operational power.
The elaborated methodological and technological solutions may be interesting for companies producing devices which use crystal materials as working elements, namely
Germany: Landwehr Electronic GmbH, APE GmbH, IPAG-Innovative Processing AG, GTU LaserTechnic GmbH; France: FASTLITE, A.A. Opto-Electronique; Great Britain: AG Electro-Optics, Leysop Ltd., Lambda Photometrics, Gooch & Housego PLC; Sweden: Hamamatsu Photonics Norden AB; USA: IntraAction Corp., Quanta Tech. Inc., Electro-Optical Products Corp., AOTF Technology Inc., Aurora Photonics Inc., Isomet Corp., NEOS Technologies Inc., Crystal Technology Inc., Photonic System Inc. (PSI), SOCC Optoelectronics Inc., Boulder Nonlinear Systems, Inc., IMRA America Inc.; China: Dayoptics Inc., Castech-Phoenix Inc. (CASIX). As potentially interesting ones there may be considered also any other companies which deal with optical crystal materials requiring express measurements of optical parameters in crystalline materials.
Contact details
Dr. Sci., Prof. Anatoliy S. Andrushchak
Laboratory of Optical and Quasioptical Investigation
and Optoelectronic Devices Design
Lviv Polytechnic National University
5/620 Knyazya Romana Str., Lviv, 79005, Ukraine
Phone/Fax: +38 032 2582103
E-mail: anat@polynet.lviv.ua
Web-site: http://tk-lab.lp.edu.ua/
Dr. Sci., Prof. Myhaylo Klymash
Department of Telecommunication
Lviv Polytechnic National University
12/11 St. Bandera Str., Lviv, 79013, Ukraine
Phone/Fax: +38 032 2582103
E-mail: mklimash@polynet.lviv.ua
Web-site: http://tk-lab.lp.edu.ua/
List of the references (published or submitted during the realization of No.272715 project ([1]-[13]) and No.910715 its return phase ([14]-[19])):
1. Andrushchak A.S. et al. Electric-field-induced optical path length change in LiNbO3:MgO crystals: spatial anisotropy analysis // Applied Optics.– 2013.– V.52 No.16. – P.3757–3763.
2. Kushnir O.S. Yurkevych O. V., Andrushchak A.S. Angular stability of electric field-induced effects in crystalline materials // Cryst. Res. Technol. – 2013. – V.48 No.6. – P.387–399.
3. Andrushchak A.S. et al. Interferometric technique for controlling wedge angle and surface flatness of optical slabs // Optics & Lasers in Engineering. – 2013. – V.51 No.4. – P.342–347.
4. Buryy O.A. Andrushchak A.S. et al. Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: Example of LiNbO3 crystals // J. Appl. Phys. – 2013. – V.113. –P.083103(1-12).
5. Demyanyshyn N.M. Mytsyk B.G. Andrushchak A.S. Manufacturing method of sensitive element from anisotropical crystalline material for electro-optic and photo-elastic cells. Patent of Ukraine No. 73511 from 25.09.2012 Bul. No.18.
6. Andrushchak A.S. et al. Manufacturing method of most efficient sensitive element from crystalline material for electro-optic cell. Patent of Poland (submitted).
7. Andrushchak A.S. et al. // Proc. 11th Internat. Conf. on modern problems of radioengineering, telecommunications and computer science, 21-24 February 2012, Lviv-Slavske (Ukraine). – P. 492–494.
8. Buryy O.A. Ubizskii S.B. Andrushchak A.S. // Proc. 11th Internat. Conf. on modern problems of radioengineering, telecommunications and computer science, 21-24 February 2012, Lviv-Slavske (Ukraine). – P.495–497.
9. Andrushchak A.S. et al. // Proc. of SIXTH INTERNATIONAL WORKSHOP “Relaxed, nonlinear and acoustic optical processes and materials”. – May 25-29, 2012, Lutsk (Ukraine). – P. 71–73.
10. Andrushchak A.S. et al. // Proc. of XIIIth International scientific-practical conference ”Modern Information and Electronic Technologies”. – June 4-8, 2012, Odesa (Ukraine). – P. 294.
11. Andrushchak A.S. et al. // Proc. of the Internat. Conf. “Nanomaterials: Applications and Properties”. – September 17-22, 2012, Alushta, Crimea (Ukraine). – 2012. – V. 1, No. 4. 04NMEEo8 (4pp).
12. Andrushchak A.S. et al. // Proc. of the Ist International Conference “Actual Problems of Applied Physics”. – September 24-28, 2012, Sevastopol, Crimea (Ukraine). – P. 208–210.
13. Andrushchak A.S. et al. // Proc. of 6-th International Conference on Advanced Optoelectronics and Lasers (CAOL’2013). – Sudak, Crimea (Ukraine). – September 9-13, 2013. – P.307-308.
14. Andrushchak A. et al. // Proc. 12th Internat. Сonf. on modern problems of radio engineering, telecommunications and computer science TCSET’2014. – February 21 - March 1, 2014, Lviv-Slavske (Ukraine). – P. 347–350.
15. Demyanyshyn N.M. Mytsyk B.G. Andrushchak A.S. // Proc. XIII Internat. Сonf.: Physics of Dielectrics (Dielectrics – 2014). – June 2-6, 2014, St. Petersburg (Russia). – P. 67–70.
16. Andrushchak A.S. et al. // Proc. of SEVEN INTERNATIONAL WORKSHOP “Relaxed, nonlinear and acoustic optical processes and materials”. – June 8-12, 2014, Lutsk (Ukraine). – P. 7–9.
17. Andrushchak N.A. Yashchyshyn Ye.M. Andrushchak A.S. et al. // Proc. of Nanotechnologies: from fundamental research to innovations. – August 23-30, 2014, Lviv (Ukraine) – P.443-444.
18. Yurkevych O.V. Andrushchak V.S. Solskii I.M. Kityk A.V. Andrushchak A.S. Experimental investigations of electro-optical effect anisotropy for example of LiNbO3 crystals // Herald Nation. Univ. “Lvivs’ka Politechnika” (Electronics). – 2014. – No.798. – P.61–68 (in Ukrainian).
19. Andrushchak A.S. et al. Spatial anisotropy of the linear electro-optic effect in lithium niobate crystals: Analytical calculations and their experimental verification // Optical Materials (to be published in 2015).
For achievement of the project's objectives and its return phase such work have been carried out. In the first steps it was created the interferometric setup for electro-optic measurements as well as modernized the nonlinear optical setup available at the Czestochowa University of Technology [7,10] (see references list below). It was also elaborated the interferometric technique applicable to the wedge angle and surface flatness measurements of optical slabs, which lets to provide a quality control of relevant optical elements while their manufacturing [3]. In the next steps, it was developed relevant fundamental methodologies suitable for precise determination of complete sets of electro-optic tensor coefficients in crystal materials of any symmetry [7]. Particularly, by using available laboratory setups the electro-optic and nonlinear optical characteristics of langasite, pure and MgO doped lithium niobate crystals were investigated [9-12]. For these anisotropic materials, a complete tensor sets of electro-optic and nonlinear optical coefficients were determined. Notice that a complete sets of such tensor constants represent requiring input parameters [1,2,13] for further 3D-analysis of the spatial anisotropy of parametrical effects. Accordingly, in the final steps there was calculated the indicative surfaces and corresponding stereographic projections of the effective electro-optic [1,13] and acousto-optic [4] coefficients as well as obtained the indicative surfaces composed from maximal values of relevant effects [4,8]. On their basis the global directional maxima of the electro-optic and acousto-optic effects for the crystal materials mentioned above were determined and for these directional maxima an angular stability analysis has been performed using improved our own software [2]. The main technological solutions and approaches were protected by Ukrainian patent [5] and by Polish patent [6].
During the return phase, which is the final stage of No.272715 project, the main objective was further development of new production technology for most efficient and more stable application of the crystalline materials. For this the working elements samples with highest magnitude of electro-optic and nonlinear optical effects were manufactured and the experimental verification of the electro-optic parameters on manufactured samples with different orientations was performed [16, 18-19]. It was also fabricated the prototype of electro-optic cell made of mentioned above crystalline materials for highly efficient control of superpowerful laser radiation and its technical characteristics were investigated. Besides, it was developed and approved our tech¬nology also for nanostructures with aim of their using as sensitive elements for electro-optic or nonlinear optical cells [14-17].
During execution of the project and its return phase the main results obtained are the following:
1) Creation of the laboratory interferometric setup for the electro-optic measurements [7,10] and modernization of the nonlinear optical setup;
2) Creation of the laboratory interferometric setup applicable to the control of samples quality while their preparation [3];
3) Elaboration of the methodology for measurements and calculations of all electro-optic coefficients in the crystalline materials of any symmetry [7];
4) Electro-optic and piezo-optic investigations of langasite, pure and MgO doped lithium niobate crystals [9-12] providing determination of the full set of electro-optic and/or piezo-optic tensor constants;
5) Exploration of the spatial anisotropy 3D-analysis of electro-optic and acousto-optic effects for selected crystal materials that provides directional maxima related with the most efficient geometries of relevant electro-optic or acousto-optic interactions. It was shown theoretically and in several cases proved also experimentally that for the interaction geometries being optimized relevant effects rise from about 1.5 to 2.7 times [1,4,8,9,11,12,15] comparing to standard geometries (usually the direct crystal cuts) widely used in most applications. This, in fact, opens hidden possibilities for further increase of the application efficiency of electro-optic and/or acousto-optic crystal materials in relevant optoelectronic devices;
6) Exploration of the directional stability of electro-optic and piezoelectrical devices against uncontrolled deviations of material parameters. For this purpose basing on full sets of electro-optic and piezo-electrical constants we have performed the spatial stability analysis [2]. Amazingly, it turns out that parametrical effects along the directional maxima characterize by enhanced stability of their effective characteristics as well. Obviously, it appears to be very important from the practical point of view;
7) Demonstration of the experimental verification of analytical approaches used for evaluation of the spatial anisotropy of linear electro-optic effect in crystal materials [16, 18-19]. For this the electro-optic measurements have been performed on a series of crystal X/-cuts (0o < < 90o) of LiNbO3 crystals to get a cross section of the indicative surfaces. A fairly good agreement was found between the experiment and calculations for the effective electro-optic coefficients describing both electro-induced optical pathlength and birefringence in investigated crystalline materials;
8) Fabrication of the prototype of electro-optic cell made of investigated materials of MgO doped lithium niobate crystals for highly efficient control of superpowerful laser radiation and investigation of its technical characteristics. It confirms the validity and prospects developed in this project the production technology for the most efficient and more stable application of crystalline materials (see: http://tk-lab.lp.edu.ua/eng/research.html) which give a possible to reveal the large hidden reserves of their application efficiency improvement as working elements for electro-, piezo-, acousto- or nonlinear optical devices in industry.
The final result of project and its return phase is elaborated new production technology applicable both for a search of new prospective electro-, piezo-, acousto-optic or nonlinear optical crystals likewise an improvement of application efficiency and/or parameter stability of already existing crystal materials being used as sensitive elements in respective high performance devices including the systems for control and/or conversion of the superpowerful laser radiation, which in many aspects appear to be a key problem of the optoelectronic industry in the European Union. No doubt that relevant devices represent high technology and knowledge based products provided by scientific innovations and technological advances of European Union. The innovations implemented here may appear to be very useful and important for many branches of practically whole optoelectronic industry starting from different kinds of high performance light modulators and deflectors, applicable in modern communication systems, to specialized highly efficient sensor techniques, the working principle of which are based on parametrical or nonlinear optical phenomena. In addition, the technological solutions drawn within this project may be characterized as market competitive taking into account that, on the one hand, they appear to be much cheaper comparing to existing other solutions and, on the other hand, they are time saving and more accurate since there is no need to prepare a large number of different crystal samples (cuts) likewise perform relevant measurements on different samples which usually rises considerably errors in evaluation of actual material parameters. The competitiveness of our technology is caused also by the fact that its implementation in practice does not require any serious reorganization of technological process while manufacturing of electro-optic, acousto-optic or nonlinear optical cells.
The final results of this project have a social effect too. Project elaborations, which are generally based on optimized applicability of existing or new crystal materials, including nanostructures, inevitably bring us to material and power saving technologies since the geometry optimization of electro-, acousto-optic and nonlinear optical interactions leads in each case to a reduction of cell size likewise a decreasing of operational power.
The elaborated methodological and technological solutions may be interesting for companies producing devices which use crystal materials as working elements, namely
Germany: Landwehr Electronic GmbH, APE GmbH, IPAG-Innovative Processing AG, GTU LaserTechnic GmbH; France: FASTLITE, A.A. Opto-Electronique; Great Britain: AG Electro-Optics, Leysop Ltd., Lambda Photometrics, Gooch & Housego PLC; Sweden: Hamamatsu Photonics Norden AB; USA: IntraAction Corp., Quanta Tech. Inc., Electro-Optical Products Corp., AOTF Technology Inc., Aurora Photonics Inc., Isomet Corp., NEOS Technologies Inc., Crystal Technology Inc., Photonic System Inc. (PSI), SOCC Optoelectronics Inc., Boulder Nonlinear Systems, Inc., IMRA America Inc.; China: Dayoptics Inc., Castech-Phoenix Inc. (CASIX). As potentially interesting ones there may be considered also any other companies which deal with optical crystal materials requiring express measurements of optical parameters in crystalline materials.
Contact details
Dr. Sci., Prof. Anatoliy S. Andrushchak
Laboratory of Optical and Quasioptical Investigation
and Optoelectronic Devices Design
Lviv Polytechnic National University
5/620 Knyazya Romana Str., Lviv, 79005, Ukraine
Phone/Fax: +38 032 2582103
E-mail: anat@polynet.lviv.ua
Web-site: http://tk-lab.lp.edu.ua/
Dr. Sci., Prof. Myhaylo Klymash
Department of Telecommunication
Lviv Polytechnic National University
12/11 St. Bandera Str., Lviv, 79013, Ukraine
Phone/Fax: +38 032 2582103
E-mail: mklimash@polynet.lviv.ua
Web-site: http://tk-lab.lp.edu.ua/
List of the references (published or submitted during the realization of No.272715 project ([1]-[13]) and No.910715 its return phase ([14]-[19])):
1. Andrushchak A.S. et al. Electric-field-induced optical path length change in LiNbO3:MgO crystals: spatial anisotropy analysis // Applied Optics.– 2013.– V.52 No.16. – P.3757–3763.
2. Kushnir O.S. Yurkevych O. V., Andrushchak A.S. Angular stability of electric field-induced effects in crystalline materials // Cryst. Res. Technol. – 2013. – V.48 No.6. – P.387–399.
3. Andrushchak A.S. et al. Interferometric technique for controlling wedge angle and surface flatness of optical slabs // Optics & Lasers in Engineering. – 2013. – V.51 No.4. – P.342–347.
4. Buryy O.A. Andrushchak A.S. et al. Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: Example of LiNbO3 crystals // J. Appl. Phys. – 2013. – V.113. –P.083103(1-12).
5. Demyanyshyn N.M. Mytsyk B.G. Andrushchak A.S. Manufacturing method of sensitive element from anisotropical crystalline material for electro-optic and photo-elastic cells. Patent of Ukraine No. 73511 from 25.09.2012 Bul. No.18.
6. Andrushchak A.S. et al. Manufacturing method of most efficient sensitive element from crystalline material for electro-optic cell. Patent of Poland (submitted).
7. Andrushchak A.S. et al. // Proc. 11th Internat. Conf. on modern problems of radioengineering, telecommunications and computer science, 21-24 February 2012, Lviv-Slavske (Ukraine). – P. 492–494.
8. Buryy O.A. Ubizskii S.B. Andrushchak A.S. // Proc. 11th Internat. Conf. on modern problems of radioengineering, telecommunications and computer science, 21-24 February 2012, Lviv-Slavske (Ukraine). – P.495–497.
9. Andrushchak A.S. et al. // Proc. of SIXTH INTERNATIONAL WORKSHOP “Relaxed, nonlinear and acoustic optical processes and materials”. – May 25-29, 2012, Lutsk (Ukraine). – P. 71–73.
10. Andrushchak A.S. et al. // Proc. of XIIIth International scientific-practical conference ”Modern Information and Electronic Technologies”. – June 4-8, 2012, Odesa (Ukraine). – P. 294.
11. Andrushchak A.S. et al. // Proc. of the Internat. Conf. “Nanomaterials: Applications and Properties”. – September 17-22, 2012, Alushta, Crimea (Ukraine). – 2012. – V. 1, No. 4. 04NMEEo8 (4pp).
12. Andrushchak A.S. et al. // Proc. of the Ist International Conference “Actual Problems of Applied Physics”. – September 24-28, 2012, Sevastopol, Crimea (Ukraine). – P. 208–210.
13. Andrushchak A.S. et al. // Proc. of 6-th International Conference on Advanced Optoelectronics and Lasers (CAOL’2013). – Sudak, Crimea (Ukraine). – September 9-13, 2013. – P.307-308.
14. Andrushchak A. et al. // Proc. 12th Internat. Сonf. on modern problems of radio engineering, telecommunications and computer science TCSET’2014. – February 21 - March 1, 2014, Lviv-Slavske (Ukraine). – P. 347–350.
15. Demyanyshyn N.M. Mytsyk B.G. Andrushchak A.S. // Proc. XIII Internat. Сonf.: Physics of Dielectrics (Dielectrics – 2014). – June 2-6, 2014, St. Petersburg (Russia). – P. 67–70.
16. Andrushchak A.S. et al. // Proc. of SEVEN INTERNATIONAL WORKSHOP “Relaxed, nonlinear and acoustic optical processes and materials”. – June 8-12, 2014, Lutsk (Ukraine). – P. 7–9.
17. Andrushchak N.A. Yashchyshyn Ye.M. Andrushchak A.S. et al. // Proc. of Nanotechnologies: from fundamental research to innovations. – August 23-30, 2014, Lviv (Ukraine) – P.443-444.
18. Yurkevych O.V. Andrushchak V.S. Solskii I.M. Kityk A.V. Andrushchak A.S. Experimental investigations of electro-optical effect anisotropy for example of LiNbO3 crystals // Herald Nation. Univ. “Lvivs’ka Politechnika” (Electronics). – 2014. – No.798. – P.61–68 (in Ukrainian).
19. Andrushchak A.S. et al. Spatial anisotropy of the linear electro-optic effect in lithium niobate crystals: Analytical calculations and their experimental verification // Optical Materials (to be published in 2015).