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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2022-13-6-615-620</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-274</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Investigation of the method of current thermal modulation of the wavelength VCSEL</article-title><trans-title-group xml:lang="ru"><trans-title>Исследование метода токовой тепловой модуляции длины волны VCSEL</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-4265-8818</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мирошниченко</surname><given-names>Г. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Miroshnichenko</surname><given-names>G. P.</given-names></name></name-alternatives><email xlink:type="simple">gpmirosh@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-4869-2838</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Аржаненкова</surname><given-names>А. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Arzhanenkova</surname><given-names>A. N.</given-names></name></name-alternatives><email xlink:type="simple">11arzh11@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-2506-0379</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Плотников</surname><given-names>М. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Plotnikov</surname><given-names>M. Yu.</given-names></name></name-alternatives><email xlink:type="simple">plotnikov-michael@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Университет ИТМО</institution></aff><aff xml:lang="en"><institution>ITMO University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>06</day><month>06</month><year>2025</year></pub-date><volume>13</volume><issue>6</issue><fpage>615</fpage><lpage>620</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Miroshnichenko G.P., Arzhanenkova A.N., Plotnikov M.Y., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Мирошниченко Г.П., Аржаненкова А.Н., Плотников М.Ю.</copyright-holder><copyright-holder xml:lang="en">Miroshnichenko G.P., Arzhanenkova A.N., Plotnikov M.Y.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/274">https://nanojournal.ifmo.ru/jour/article/view/274</self-uri><abstract><p>Subject of investigation. In this paper, we analyzed in detail the thermal mode of the operation of a vertical-cavity surface-emitting laser (VCSEL) used in the experiment. Method. As a part of the work, we carried out a theoretical study of the recurrence relation describing the change in the VCSEL wavelength under the action of specially selected modulation current pulses. The high speed of the device working is determined by the optical demodulation scheme, which is based on using a phase-modulated carrier (the demodulation method used is arctangent demodulation: Phase Generated Carrier (PGC-ATAN)). Main results. Formulas were obtained that determine the frequency, phase, and modulation depth which leads to calculation of the principle of change in the modulated VCSEL wavelength at sampling points. Comparison with experimental data showed that the obtained formulas allow one to choose the optimal thermal mode of VCSEL operation and reliably calculate the characteristics of the modulation process in terms of the carrier phase. Practical significance. The obtained formulas make it possible to calculate the exact characteristics of the modulation process, and the precisely calculated phase of the modulation source. As a result, one can compensate it more effectively when demodulating phase of the interferometer.</p></abstract><trans-abstract xml:lang="ru"><p>Предмет исследования. В работе детально проанализирован применяемый в экперименте тепловой режим работы вертикально-излучающего лазера (Vertical-cavity surface-emitting laser-VCSEL). Метод. В рамках работы было проведено теоретическое исследование рекуррентного соотношения, описывающего изменение длины волны VCSEL под действием специально выбранных импульсов тока модуляции. Высокоскоростные свойства прибора определяются оптической схемой демодуляции, в которой использована промодулированная по фазе несущая (используемый метод демодуляции - демодуляция на основе вычислений функции арктангенса: Phase Generated Carrier (PGC-ATAN)). Основные результаты. В рамках данной работы были получены формулы, определяющие частоту, фазу и глубину модуляции, для расчёта закона изменения промодулированной длины волны VCSEL в точках дискретизации. Сравнение с экспериментальными данными показало, что полученные формулы позволяют выбрать оптимальный тепловой режим работы VCSEL и надёжно рассчитать характеристики процесса модуляции по фазе несущей. Практическая значимость. Полученные формулы позволяют рассчитать точные характеристики процесса модуляции, а точно рассчитанная фаза источника модуляции позволит эффективнее её компенсировать в процессе демодуляции фазы сигнала интерферометра.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>VCSEL</kwd><kwd>модуляция</kwd><kwd>интерферометрические измерения</kwd><kwd>PGC</kwd></kwd-group><kwd-group xml:lang="en"><kwd>VCSEL</kwd><kwd>modulation</kwd><kwd>interferometric measurements</kwd><kwd>PGC-demodulation</kwd><kwd>PGC-ATAN</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Kivshar Yu.S. From metamaterials to metasurfaces and metadevices. Nanosystems: physics, chemistry, mathematics, 2015, 6(3), P. 346-352.</mixed-citation><mixed-citation xml:lang="en">Kivshar Yu.S. From metamaterials to metasurfaces and metadevices. 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