rus
Issue #5/2020
V. M. Petrov, A. V. Shamrai, I. V. Il’ichev, P. M. Agruzov, V. V. Lebedev, N. D. Gerasimenko, V. S. Gerasimenko
National Microwave Integrateed Optical Modulators for Quantum Communications
National Microwave Integrateed Optical Modulators for Quantum Communications
DOI: 10.22184/1993-7296.FRos.2020.14.5.414.423
The results of studying the characteristics of integrated optical modulators of both types, amplitude and phase, developed and created at the A. F. Ioffe PTI jointly with ITMO University for quantum communication systems are presented in the article. For the first time in national practice, original technologies for the formation of optical waveguides by the method of thermal diffusion of titanium ions on crystalline substrates of X- and Z‑cuts of lithium niobate and the formation of microwave traveling wave electrodes based on galvanic silver with subsequent gilding were used to manufacture prototypes of modulators. The assessment of the main operational characteristics of the modulators is carried out. The influence of the housing design and the quality of assembly of modulators on their main parameters is revealed.
The results of studying the characteristics of integrated optical modulators of both types, amplitude and phase, developed and created at the A. F. Ioffe PTI jointly with ITMO University for quantum communication systems are presented in the article. For the first time in national practice, original technologies for the formation of optical waveguides by the method of thermal diffusion of titanium ions on crystalline substrates of X- and Z‑cuts of lithium niobate and the formation of microwave traveling wave electrodes based on galvanic silver with subsequent gilding were used to manufacture prototypes of modulators. The assessment of the main operational characteristics of the modulators is carried out. The influence of the housing design and the quality of assembly of modulators on their main parameters is revealed.
Теги: microwave integrated optical modulators modulator performance characteristics quantum communications quantum key distribution квантовая рассылка ключа квантовые коммуникации свч интегрально-оптические модуляторы эксплуатационные характеристики модуляторов
National Microwave Integrateed Optical Modulators for Quantum Communications
V. M. Petrov 1, A. V. Shamrai 2, I. V. Il’ichev 2, P. M. Agruzov 2, V. V. Lebedev 2, N. D. Gerasimenko 1, V. S. Gerasimenko 1
ITMONational Research University, St. Petersburg, Russia
A. F. Ioffe PTI of RAS, St. Petersburg, Russia
The results of studying the characteristics of integrated optical modulators of both types, amplitude and phase, developed and created at the A. F. Ioffe PTI jointly with ITMO University for quantum communication systems are presented in the article. For the first time in national practice, original technologies for the formation of optical waveguides by the method of thermal diffusion of titanium ions on crystalline substrates of X- and Z‑cuts of lithium niobate and the formation of microwave traveling wave electrodes based on galvanic silver with subsequent gilding were used to manufacture prototypes of modulators. The assessment of the main operational characteristics of the modulators is carried out. The influence of the housing design and the quality of assembly of modulators on their main parameters is revealed.
Keywords: quantum communications, quantum key distribution, microwave integrated optical modulators, modulator performance characteristics
Received on: 11.07.2020
Accepted on: 25.07.2020
INTRODUCTION
Microwave integrated optical modulators provide high-speed information input into the optical communication line. With amplitude or phase modulation in the spectrum of an optical carrier, so-called “side” frequencies. The technology of quantum key distribution (QKD) using side frequencies [1] is the base for the development and creation of quantum communication lines, including the first experimental quantum communication line Moscow – St. Petersburg [2]. The active development of national systems of quantum communication, including the quantum Internet, requires the use of an appropriate element base.
The construction of a QKD system at side frequencies implies the use of both amplitude (AM) and phase (PM) optical modulators operating in the frequency range of 3–30 GHz. As our analysis has shown, to meet the requirements of the QKD system at side frequencies, it is necessary to use electro-optical modulators based on optical waveguides on lithium niobate substrates. They have the lowest introduced noise (approximately –156 dB Vπ) compared to alternative technologies using A3B5 semiconductor materials and silicon. At the same time, their use in QKD systems puts forward special requirements for the quality of optical waveguides, which should provide a minimum level of optical losses for working with optical signals in the single photon counting mode. The required modulation bandwidth is provided by using traveling wave electrodes based on a coplanar line [3–5].
The main characteristics of integrated optical modulators based on lithium niobate are: modulation bandwidth, half-wave voltage and optical loss. These characteristics, together with the characteristics of the optical radiation source (laser) and the photodetector, determine the resulting information characteristics of the communication system, such as throughput.
The purpose of this work is to demonstrate that the developed domestic integrated-optical modulators in their characteristics fully meet the requirements of modern QKD systems and make it possible to obtain high throughput in a fiber-optic line using a standard semiconductor laser diode as a radiation source.
ARRANGEMENT OF INTEGRATED OPTICAL MODULATORS
In this work, we investigated both types of integrated optical modulators on lithium niobate substrates (AM and PM) used in QKD systems (Fig. 1a, b).
AM is a waveguide Mach-Zehnder interferometer (MZI) and is manufactured on X‑cut lithium niobate substrates. The modulator operates with linearly polarized optical radiation lying in the plane of the substrate (TE mode). The working polarization mode was separated using a waveguide plasmon-polariton polarizer [6]. Traveling wave microwave electrodes are made on the basis of galvanic silver with surface gilding and have the configuration of a coplanar microwave line [7]. The optical waveguides of the two arms of the MZI are located in the interelectrode gap of the coplanar microwave line, providing the application of a field of opposite polarity to different arms of the MZI. The configuration of the electrodes was calculated from the condition of ensuring the matching of the phase velocity of optical radiation and the group velocity of the microwave wave with an accuracy of 0.1% (Fig. 2).
A PM is a single direct optical waveguide, which, unlike AM, is fabricated on a Z‑cut lithium niobate substrate and operates with linearly polarized optical radiation perpendicular to the plane of the substrate (TM mode). The waveguide is placed under the central, “hot” electrode of the coplanar microwave line, which provides the maximum overlap integral of the modulating microwave field and optical waveguide mode.
It is important to note that for the manufacture of optical waveguides with extremely low losses (less than 0.01 dB / mm), the original technology of diffusion of titanium ions with preliminary oxidation and special measures to suppress the reverse diffusion of lithium was developed [8].
Special attention was paid to the development of the design of the housing of microwave modulators and technical solutions for assembly into the housing. First of all, special measures were taken to suppress parasitic resonances associated with the excitation of microwave modes of the substrate [9]. Chips of integrated optical modulators were joined by pigtails based on single-mode optical fiber with polarization retention by gluing to the end. The electrical connections were made through adapter cards providing an additional function of matching with the 50 Ω microwave input path.
MODULATOR CHARACTERISTICS
The measurements of the characteristics of the modulators were carried out on two installations. The frequency characteristics of the electro-optical conversion were measured as parameters S21 and S11 using a ROHDE-SCWARZ ZNB40 vector network analyzer, which provides measurements of an electrical signal in a band up to 40 GHz (Fig.3a).
A semiconductor laser with a radiation wavelength of λ ≈ 1 552 nm, a spectrum width of <1 MHz and an output power of ≈8 mW was used as a source of coherent radiation (2). The calibrated photodetector (4) had a bandwidth of ≈50 GHz. The parameters are the transmission coefficient (S21) and the reflection coefficient (S11) of the microwave signals in the measurement system. In fig. 4 shows the dependence of the parameters S21 and S11 of the amplitude modulator on the modulation frequency F.
As can be seen from the above dependence of the gain S21 (F), the bandwidth of modulators B can be estimated at 20 GHz using the criterion for the frequency response roll-off by 3 dB. The initial section of the dependence, which has a characteristic maximum in the range of about 0–2 GHz, is usually not considered [4, 9]. Therefore, for further estimates, we will use the boundaries of the operating band from 2 to 22 GHz.
Note that the S21 (F) dependence in the 15–20 GHz interval has a “wavy” character (Fig. 4a, c). Comparing it with the dependence S11 (F), we can see that the maxima of the reflection of the power of the modulating microwave signal coincide with the minima of the transmission coefficient. This suggests that there are multiple reflections in the microwave path of the modulator. They can be associated with suboptimal configuration and insufficiently accurate installation of microwave adapter cards in the modulator case. A noticeable drop in the frequency dependence of the transmission coefficient S21 (F), starting from a frequency of 30 GHz, is due to the use of a microwave connector, for which 30 GHz is the limiting frequency according to the technical description.
Fig. 4c, d shows the dependences S21 (F) for modulators equipped with microwave connectors having an operating frequency band above 40 GHz. An example of inaccurate installation of riser cards is illustrated in Fig. 4c (undulating is observed). Fig. 4d shows an example of the exact installation of risers – the waviness is smoothed, and the line looks almost even. The presence of a narrow minimum in the 36 GHz frequency region (see Fig. 4c, d) is associated with resonance phenomena, when a part of the input microwave radiation can penetrate into the lithium niobate plate.
The value of the transmission coefficient G [dB] at a fixed power of the laser source is directly related to the half-wave voltage [9]:
,
where Idc [mA] is the constant component of the current at the output of the calibrated photodetector, Vπ [V] is the half-wave voltage. The estimated 5.4 V half-wave voltage from the spectral dependence is consistent with the results of direct measurements at a frequency of 1 kHz.
Since the modulators are intended for use in QKD systems at side frequencies, in addition to standard measurements of the frequency band and half-wave voltage, measurements of the optical spectra at the output of the modulators were carried out with modulation with a sinusoidal microwave signal. An APEX AR2060 optical spectrum analyzer was used for measurements (Fig. 3b). Fig. 5 shows the optical spectra of the carrier after a single-frequency semiconductor laser and the spectra after the amplitude and phase modulators. In the optical spectrum after AM, at the quadrature operating point, two side harmonics are visible, corresponding to the modulation of the optical signal amplitude. The appearance of higher harmonics with significantly lower amplitudes is associated with nonlinear distortions. The optical spectrum at the output of the phase modulator is richer and contains a full set of higher harmonics.
From measurements of the optical spectrum at the output of integrated-optical modulators at different amplitudes of the modulating signal, varying in the range from –40 dBm to 25 dBm, the dependences of the signal-to-noise ratio were constructed for different frequency harmonics of the modulating signal (Fig. 6).
For the first harmonic of the baseband signal, the (S / N)MAX ratio is greater than 60 dB, mainly determined by the averaging time of the optical spectrum analyzer, at a baseband power of 25 dBm. Similar measurements were carried out for three frequencies of the modulating signal F = 4.8; 7.8 and 12.0 GHz. It should be noted that, within the accuracy of these measurements, the value of the (S / N)MAX ratio for all three values did not differ and amounted to ≈60 dB (Fig. 7). Due to the peculiarities of the technical characteristics of the microwave generator, measurements at frequencies above 12 GHz were not performed. Nevertheless, using the measured frequency dependences of the gain S21 (F), it can be estimated that the value (S / N) for the first harmonic is at least 57 dB for F = 20 GHz. This indicates the possibility of effective use of modulators in QKD systems at side frequencies in the entire available operating frequency range of 20 GHz.
CONCLUSION
The developed and manufactured integrated optical amplitude and phase microwave modulators have a working frequency bandwidth of at least 20 GHz (according to the criterion of 3 dB decay). The 5.4 V half-wave voltage provides efficient sideband generation. The achieved parameters fully meet the requirements for modulators both for “conventional” optical communication systems with amplitude and phase modulation, and for communication systems using the principle of quantum key distribution at side frequencies.
REFERENCES
Gleĭm A. V., Chistyakov V. V., Bannik O. I., et al. Sideband quantum communication at 1 Mbit / s on a metropolitan area network. Journal of Optical Technology. 2017; 84(6): 362–367. DOI: 10.1364/JOT.84.000362.
URL: https://digital.ac.gov.ru/news/4761/https://drive.google.com/file/d/1nDQLGTIfnW7suHANdXQyms-kxbc_hl3P/view?usp=s
Mahapatra A., Murphy E. J. Electrooptic Modulators. Optical Fiber Telecommunications IV A: Components, edited by I. P. Caminov and T. Li, Academic Press, San-Diego, USA. 2002; 258–294. DOI: 10.1016/B978-012395172-4/50006-1.
Chen A., Murphy E., Raton B. (ed.). Broadband Optical Modulators: Science, Technology, and Applications. – CRC Press. 2011. 568 p. ISBN 978-1-4398-2506-8.
Petrov V. M., Shamrai A. V. Interferenciya i difrakciya dlya informacionnoj fotoniki. – S.-Pb.: Lan’. 2019. 460 pp. ISBN 978-5-8114-3567-8.
Il’ichev I. V., Toguzov N. V., Shamrai A. V. Plazmon-polyaritonnyj polyarizator na poverhnosti kanal’nyh odnomodovyh volnovodov v niobate litiya. Pis’ma v zhurnal tekhnicheskoj fiziki (Technical Physics Letters). 2009; 35(17): 97–103.
Lebedev V. V., Il’ichev I.V., Agruzov P. M., Shamrai A. V. Vliyanie materiala tokovedushchih chastej elektrodov na harakteristiki integral’no-opticheskih Microwave-modulyatorov. Pis’ma v zhurnal tekhnicheskoj fiziki (Technical Physics Letters). 2014; 40(17): 39–46.
Patent RU187990U1 Optical modulator / Lebedev V. V., Il’ichev I.V., Agruzov P. M., Tronev A. V., Shamrai A. V.
Urick Jr., Vincent J. et al. Fundamentals of microwave photonics [New York]: Wiley, cop. 2015. – M.: Technosphera. 2016. 375 pp. ISBN978-5-94836-445-2.
V. M. Petrov 1, A. V. Shamrai 2, I. V. Il’ichev 2, P. M. Agruzov 2, V. V. Lebedev 2, N. D. Gerasimenko 1, V. S. Gerasimenko 1
ITMONational Research University, St. Petersburg, Russia
A. F. Ioffe PTI of RAS, St. Petersburg, Russia
The results of studying the characteristics of integrated optical modulators of both types, amplitude and phase, developed and created at the A. F. Ioffe PTI jointly with ITMO University for quantum communication systems are presented in the article. For the first time in national practice, original technologies for the formation of optical waveguides by the method of thermal diffusion of titanium ions on crystalline substrates of X- and Z‑cuts of lithium niobate and the formation of microwave traveling wave electrodes based on galvanic silver with subsequent gilding were used to manufacture prototypes of modulators. The assessment of the main operational characteristics of the modulators is carried out. The influence of the housing design and the quality of assembly of modulators on their main parameters is revealed.
Keywords: quantum communications, quantum key distribution, microwave integrated optical modulators, modulator performance characteristics
Received on: 11.07.2020
Accepted on: 25.07.2020
INTRODUCTION
Microwave integrated optical modulators provide high-speed information input into the optical communication line. With amplitude or phase modulation in the spectrum of an optical carrier, so-called “side” frequencies. The technology of quantum key distribution (QKD) using side frequencies [1] is the base for the development and creation of quantum communication lines, including the first experimental quantum communication line Moscow – St. Petersburg [2]. The active development of national systems of quantum communication, including the quantum Internet, requires the use of an appropriate element base.
The construction of a QKD system at side frequencies implies the use of both amplitude (AM) and phase (PM) optical modulators operating in the frequency range of 3–30 GHz. As our analysis has shown, to meet the requirements of the QKD system at side frequencies, it is necessary to use electro-optical modulators based on optical waveguides on lithium niobate substrates. They have the lowest introduced noise (approximately –156 dB Vπ) compared to alternative technologies using A3B5 semiconductor materials and silicon. At the same time, their use in QKD systems puts forward special requirements for the quality of optical waveguides, which should provide a minimum level of optical losses for working with optical signals in the single photon counting mode. The required modulation bandwidth is provided by using traveling wave electrodes based on a coplanar line [3–5].
The main characteristics of integrated optical modulators based on lithium niobate are: modulation bandwidth, half-wave voltage and optical loss. These characteristics, together with the characteristics of the optical radiation source (laser) and the photodetector, determine the resulting information characteristics of the communication system, such as throughput.
The purpose of this work is to demonstrate that the developed domestic integrated-optical modulators in their characteristics fully meet the requirements of modern QKD systems and make it possible to obtain high throughput in a fiber-optic line using a standard semiconductor laser diode as a radiation source.
ARRANGEMENT OF INTEGRATED OPTICAL MODULATORS
In this work, we investigated both types of integrated optical modulators on lithium niobate substrates (AM and PM) used in QKD systems (Fig. 1a, b).
AM is a waveguide Mach-Zehnder interferometer (MZI) and is manufactured on X‑cut lithium niobate substrates. The modulator operates with linearly polarized optical radiation lying in the plane of the substrate (TE mode). The working polarization mode was separated using a waveguide plasmon-polariton polarizer [6]. Traveling wave microwave electrodes are made on the basis of galvanic silver with surface gilding and have the configuration of a coplanar microwave line [7]. The optical waveguides of the two arms of the MZI are located in the interelectrode gap of the coplanar microwave line, providing the application of a field of opposite polarity to different arms of the MZI. The configuration of the electrodes was calculated from the condition of ensuring the matching of the phase velocity of optical radiation and the group velocity of the microwave wave with an accuracy of 0.1% (Fig. 2).
A PM is a single direct optical waveguide, which, unlike AM, is fabricated on a Z‑cut lithium niobate substrate and operates with linearly polarized optical radiation perpendicular to the plane of the substrate (TM mode). The waveguide is placed under the central, “hot” electrode of the coplanar microwave line, which provides the maximum overlap integral of the modulating microwave field and optical waveguide mode.
It is important to note that for the manufacture of optical waveguides with extremely low losses (less than 0.01 dB / mm), the original technology of diffusion of titanium ions with preliminary oxidation and special measures to suppress the reverse diffusion of lithium was developed [8].
Special attention was paid to the development of the design of the housing of microwave modulators and technical solutions for assembly into the housing. First of all, special measures were taken to suppress parasitic resonances associated with the excitation of microwave modes of the substrate [9]. Chips of integrated optical modulators were joined by pigtails based on single-mode optical fiber with polarization retention by gluing to the end. The electrical connections were made through adapter cards providing an additional function of matching with the 50 Ω microwave input path.
MODULATOR CHARACTERISTICS
The measurements of the characteristics of the modulators were carried out on two installations. The frequency characteristics of the electro-optical conversion were measured as parameters S21 and S11 using a ROHDE-SCWARZ ZNB40 vector network analyzer, which provides measurements of an electrical signal in a band up to 40 GHz (Fig.3a).
A semiconductor laser with a radiation wavelength of λ ≈ 1 552 nm, a spectrum width of <1 MHz and an output power of ≈8 mW was used as a source of coherent radiation (2). The calibrated photodetector (4) had a bandwidth of ≈50 GHz. The parameters are the transmission coefficient (S21) and the reflection coefficient (S11) of the microwave signals in the measurement system. In fig. 4 shows the dependence of the parameters S21 and S11 of the amplitude modulator on the modulation frequency F.
As can be seen from the above dependence of the gain S21 (F), the bandwidth of modulators B can be estimated at 20 GHz using the criterion for the frequency response roll-off by 3 dB. The initial section of the dependence, which has a characteristic maximum in the range of about 0–2 GHz, is usually not considered [4, 9]. Therefore, for further estimates, we will use the boundaries of the operating band from 2 to 22 GHz.
Note that the S21 (F) dependence in the 15–20 GHz interval has a “wavy” character (Fig. 4a, c). Comparing it with the dependence S11 (F), we can see that the maxima of the reflection of the power of the modulating microwave signal coincide with the minima of the transmission coefficient. This suggests that there are multiple reflections in the microwave path of the modulator. They can be associated with suboptimal configuration and insufficiently accurate installation of microwave adapter cards in the modulator case. A noticeable drop in the frequency dependence of the transmission coefficient S21 (F), starting from a frequency of 30 GHz, is due to the use of a microwave connector, for which 30 GHz is the limiting frequency according to the technical description.
Fig. 4c, d shows the dependences S21 (F) for modulators equipped with microwave connectors having an operating frequency band above 40 GHz. An example of inaccurate installation of riser cards is illustrated in Fig. 4c (undulating is observed). Fig. 4d shows an example of the exact installation of risers – the waviness is smoothed, and the line looks almost even. The presence of a narrow minimum in the 36 GHz frequency region (see Fig. 4c, d) is associated with resonance phenomena, when a part of the input microwave radiation can penetrate into the lithium niobate plate.
The value of the transmission coefficient G [dB] at a fixed power of the laser source is directly related to the half-wave voltage [9]:
,
where Idc [mA] is the constant component of the current at the output of the calibrated photodetector, Vπ [V] is the half-wave voltage. The estimated 5.4 V half-wave voltage from the spectral dependence is consistent with the results of direct measurements at a frequency of 1 kHz.
Since the modulators are intended for use in QKD systems at side frequencies, in addition to standard measurements of the frequency band and half-wave voltage, measurements of the optical spectra at the output of the modulators were carried out with modulation with a sinusoidal microwave signal. An APEX AR2060 optical spectrum analyzer was used for measurements (Fig. 3b). Fig. 5 shows the optical spectra of the carrier after a single-frequency semiconductor laser and the spectra after the amplitude and phase modulators. In the optical spectrum after AM, at the quadrature operating point, two side harmonics are visible, corresponding to the modulation of the optical signal amplitude. The appearance of higher harmonics with significantly lower amplitudes is associated with nonlinear distortions. The optical spectrum at the output of the phase modulator is richer and contains a full set of higher harmonics.
From measurements of the optical spectrum at the output of integrated-optical modulators at different amplitudes of the modulating signal, varying in the range from –40 dBm to 25 dBm, the dependences of the signal-to-noise ratio were constructed for different frequency harmonics of the modulating signal (Fig. 6).
For the first harmonic of the baseband signal, the (S / N)MAX ratio is greater than 60 dB, mainly determined by the averaging time of the optical spectrum analyzer, at a baseband power of 25 dBm. Similar measurements were carried out for three frequencies of the modulating signal F = 4.8; 7.8 and 12.0 GHz. It should be noted that, within the accuracy of these measurements, the value of the (S / N)MAX ratio for all three values did not differ and amounted to ≈60 dB (Fig. 7). Due to the peculiarities of the technical characteristics of the microwave generator, measurements at frequencies above 12 GHz were not performed. Nevertheless, using the measured frequency dependences of the gain S21 (F), it can be estimated that the value (S / N) for the first harmonic is at least 57 dB for F = 20 GHz. This indicates the possibility of effective use of modulators in QKD systems at side frequencies in the entire available operating frequency range of 20 GHz.
CONCLUSION
The developed and manufactured integrated optical amplitude and phase microwave modulators have a working frequency bandwidth of at least 20 GHz (according to the criterion of 3 dB decay). The 5.4 V half-wave voltage provides efficient sideband generation. The achieved parameters fully meet the requirements for modulators both for “conventional” optical communication systems with amplitude and phase modulation, and for communication systems using the principle of quantum key distribution at side frequencies.
REFERENCES
Gleĭm A. V., Chistyakov V. V., Bannik O. I., et al. Sideband quantum communication at 1 Mbit / s on a metropolitan area network. Journal of Optical Technology. 2017; 84(6): 362–367. DOI: 10.1364/JOT.84.000362.
URL: https://digital.ac.gov.ru/news/4761/https://drive.google.com/file/d/1nDQLGTIfnW7suHANdXQyms-kxbc_hl3P/view?usp=s
Mahapatra A., Murphy E. J. Electrooptic Modulators. Optical Fiber Telecommunications IV A: Components, edited by I. P. Caminov and T. Li, Academic Press, San-Diego, USA. 2002; 258–294. DOI: 10.1016/B978-012395172-4/50006-1.
Chen A., Murphy E., Raton B. (ed.). Broadband Optical Modulators: Science, Technology, and Applications. – CRC Press. 2011. 568 p. ISBN 978-1-4398-2506-8.
Petrov V. M., Shamrai A. V. Interferenciya i difrakciya dlya informacionnoj fotoniki. – S.-Pb.: Lan’. 2019. 460 pp. ISBN 978-5-8114-3567-8.
Il’ichev I. V., Toguzov N. V., Shamrai A. V. Plazmon-polyaritonnyj polyarizator na poverhnosti kanal’nyh odnomodovyh volnovodov v niobate litiya. Pis’ma v zhurnal tekhnicheskoj fiziki (Technical Physics Letters). 2009; 35(17): 97–103.
Lebedev V. V., Il’ichev I.V., Agruzov P. M., Shamrai A. V. Vliyanie materiala tokovedushchih chastej elektrodov na harakteristiki integral’no-opticheskih Microwave-modulyatorov. Pis’ma v zhurnal tekhnicheskoj fiziki (Technical Physics Letters). 2014; 40(17): 39–46.
Patent RU187990U1 Optical modulator / Lebedev V. V., Il’ichev I.V., Agruzov P. M., Tronev A. V., Shamrai A. V.
Urick Jr., Vincent J. et al. Fundamentals of microwave photonics [New York]: Wiley, cop. 2015. – M.: Technosphera. 2016. 375 pp. ISBN978-5-94836-445-2.
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