<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<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 custom-type="elpub" pub-id-type="custom">najo-1286</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="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>Ultrashort optical pulse propagation in a double layer of graphene boron nitride with accounting the material dispersion</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Pak</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="en"><p>400062, Volgograd</p></bio><email xlink:type="simple">pak.anastasia@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Belonenko</surname><given-names>M. B.</given-names></name></name-alternatives><bio xml:lang="en"><p>400048, Volgograd</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Tuzalina</surname><given-names>O. Y.</given-names></name></name-alternatives><bio xml:lang="en"><p>400002,Volgograd</p></bio><xref ref-type="aff" rid="aff-3"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="en">Volgograd State University<country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="en">Laboratory of Nanotechnologies, Volgograd Institute of Business<country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="en">Volgograd State Agricultural University<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2013</year></pub-date><pub-date pub-type="epub"><day>21</day><month>08</month><year>2025</year></pub-date><volume>4</volume><issue>3</issue><fpage>329</fpage><lpage>335</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Pak A.V., Belonenko M.B., Tuzalina O.Y., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Pak A.V., Belonenko M.B., Tuzalina O.Y.</copyright-holder><copyright-holder xml:lang="en">Pak A.V., Belonenko M.B., Tuzalina O.Y.</copyright-holder><license 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/1286">https://nanojournal.ifmo.ru/jour/article/view/1286</self-uri><abstract><p>The propagation of ultra-short optical pulses in a thin film created by graphene grown on a boron nitride base will be considered, taking into account the environment’s dispersion characteristics, electron conduction in such a system described by the framework of an effective long-wave Hamiltonian for low-temperature media. The electromagnetic field is taken as classical Maxwell’s. We reveal the dependence of the electric field on the maximum amplitude of ultra-short optical pulses, as well as on empirical dispersion constants.</p></abstract><kwd-group xml:lang="en"><kwd>graphene</kwd><kwd>propagation of ultra-short optical pulses</kwd><kwd>boron nitride base</kwd></kwd-group><funding-group xml:lang="en"><funding-statement>This work was was supported by the Russian Foundation for Basic Research under Project No. 11-02-97054, 12-02-31654.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Ci L., Song L., Jin C., Jariwala D., Wu D., Li Y.J., Srivastava A., Wang Z.F., Storr K., Balicas L., Liu F., and Ajayan P.M. Atomic layers of hybridized boron nitride and graphene domains. Nature Materials, 9, P. 430–435 (2010). doi:10.1038/nmat2711.</mixed-citation><mixed-citation xml:lang="en">Ci L., Song L., Jin C., Jariwala D., Wu D., Li Y.J., Srivastava A., Wang Z.F., Storr K., Balicas L., Liu F., and Ajayan P.M. Atomic layers of hybridized boron nitride and graphene domains. Nature Materials, 9, P. 430–435 (2010). doi:10.1038/nmat2711.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Giovannetti G., Khomyakov P.A., Brocks G., Kelly P.J., and Van den Brink J., Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations. Physics Review, B 76, P. 073103 (2007).</mixed-citation><mixed-citation xml:lang="en">Giovannetti G., Khomyakov P.A., Brocks G., Kelly P.J., and Van den Brink J., Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations. Physics Review, B 76, P. 073103 (2007).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Greber T. Graphene and boron nitride single layers. In: Sattler K., editor. The Handbook of Nanophysics. Taylor and Francis Books, Inc, Oxfordshire (2010).</mixed-citation><mixed-citation xml:lang="en">Greber T. Graphene and boron nitride single layers. In: Sattler K., editor. The Handbook of Nanophysics. Taylor and Francis Books, Inc, Oxfordshire (2010).</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Partoens B., Peeters F. M. From graphene to graphite: electronic structure around the K point. Physical Review, B 74, P. 075404-11 (2006).</mixed-citation><mixed-citation xml:lang="en">Partoens B., Peeters F. M. From graphene to graphite: electronic structure around the K point. Physical Review, B 74, P. 075404-11 (2006).</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Avetisyan A. A., Partoens B., and Peeters F. M. Stacking order dependent electric field tuning of the band gap in graphene multilayers. Physical Review, B 79, P. 035421 (2009).</mixed-citation><mixed-citation xml:lang="en">Avetisyan A. A., Partoens B., and Peeters F. M. Stacking order dependent electric field tuning of the band gap in graphene multilayers. Physical Review, B 79, P. 035421 (2009).</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Avetisyan A. A., Partoens B., and Peeters F. M. Electric field control of the band gap and Fermi energy in graphene multilayers by top end back gates. Phys. Rev., B 80, P. 195401 (2009).</mixed-citation><mixed-citation xml:lang="en">Avetisyan A. A., Partoens B., and Peeters F. M. Electric field control of the band gap and Fermi energy in graphene multilayers by top end back gates. Phys. Rev., B 80, P. 195401 (2009).</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Wakabayashi K., Takane Y., Sigrist M. Perfectly conducting channel and universality crossover in disordered graphene nanoribbons. Physical Review Letters, 99, P. 036601 (2007).</mixed-citation><mixed-citation xml:lang="en">Wakabayashi K., Takane Y., Sigrist M. Perfectly conducting channel and universality crossover in disordered graphene nanoribbons. Physical Review Letters, 99, P. 036601 (2007).</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Blase X., Rubio A., Louie S.G., and Cohen M.L. Stability and band-gap constancy of boron-nitride nanotubes. Europhys Letters, 28(6), P. 355–340 (1994).</mixed-citation><mixed-citation xml:lang="en">Blase X., Rubio A., Louie S.G., and Cohen M.L. Stability and band-gap constancy of boron-nitride nanotubes. Europhys Letters, 28(6), P. 355–340 (1994).</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Hern´ andez E., Goze C., Bernier P., and Rubio A. Elastic properties of C and BxCyNz composite nanotubes. Physical Review Letters, 80(20), P. 4502–4505 (1998).</mixed-citation><mixed-citation xml:lang="en">Hern´ andez E., Goze C., Bernier P., and Rubio A. Elastic properties of C and BxCyNz composite nanotubes. Physical Review Letters, 80(20), P. 4502–4505 (1998).</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Chen Y., Zou J., Campbell S.J., and Le Caer G. Boron nitride nanotubes: Pronounced resistance to oxidation. Applied Physics Lettes, 84, P. 2430–2432 (2004).</mixed-citation><mixed-citation xml:lang="en">Chen Y., Zou J., Campbell S.J., and Le Caer G. Boron nitride nanotubes: Pronounced resistance to oxidation. Applied Physics Lettes, 84, P. 2430–2432 (2004).</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Suryavanshi A. P., Yu M., Wen J., Tang C., and Bando Y. Elastic modulus and resonance behavior of boron nitride nanotubes. Applied Physics Letters, 84, P. 2527–2529 (2004).</mixed-citation><mixed-citation xml:lang="en">Suryavanshi A. P., Yu M., Wen J., Tang C., and Bando Y. Elastic modulus and resonance behavior of boron nitride nanotubes. Applied Physics Letters, 84, P. 2527–2529 (2004).</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Breshenan M.S., Hollander M.J., Wetherington M. and al. Integration of hexagonal boron nitride with quasi-freestanding epitaxial graphene: toward wafer-scale, high-perfomance devices. ACS Nano, 6(6), P. 5234-5241 (2012). DOI: 10.1021/nn300996t.</mixed-citation><mixed-citation xml:lang="en">Breshenan M.S., Hollander M.J., Wetherington M. and al. Integration of hexagonal boron nitride with quasi-freestanding epitaxial graphene: toward wafer-scale, high-perfomance devices. ACS Nano, 6(6), P. 5234-5241 (2012). DOI: 10.1021/nn300996t.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Xue J., Sanchez-Yamagishi J., Bulmash D., Jacquod Ph., Deshpande A., Watanabe K., Taniguchi T., Jarillo-Herrero P., LeRoy B. J. Scanning tunneling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride. Nature Materials, 10, P. 282–285 (2011).</mixed-citation><mixed-citation xml:lang="en">Xue J., Sanchez-Yamagishi J., Bulmash D., Jacquod Ph., Deshpande A., Watanabe K., Taniguchi T., Jarillo-Herrero P., LeRoy B. J. Scanning tunneling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride. Nature Materials, 10, P. 282–285 (2011).</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Cortijo A., Guinea F., Vozmediano M.A.H., Geometrical and topological aspects of graphene and related materials. arXiv: 1112.2054v1 (2011).</mixed-citation><mixed-citation xml:lang="en">Cortijo A., Guinea F., Vozmediano M.A.H., Geometrical and topological aspects of graphene and related materials. arXiv: 1112.2054v1 (2011).</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Landau L. D., Lifshitz E. M. Theoretical physics, T. II. Field theory, Science, Moscow, 512 p. (1988).</mixed-citation><mixed-citation xml:lang="en">Landau L. D., Lifshitz E. M. Theoretical physics, T. II. Field theory, Science, Moscow, 512 p. (1988).</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Bakhvalov N.S. Calculus of approximations (analysis, algebra, ordinary differential equations). Science, Moscow, 632 p. (1975).</mixed-citation><mixed-citation xml:lang="en">Bakhvalov N.S. Calculus of approximations (analysis, algebra, ordinary differential equations). Science, Moscow, 632 p. (1975).</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
