<?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 pub-id-type="doi">10.17586/2220-8054-2025-16-6-755-762</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-1614</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>Subwavelength LIPSS-based nanopatterning of thin titanium films</article-title><trans-title-group xml:lang="ru"><trans-title>Наноструктурирование тонких титановых пленок на основе субволновых ЛИППС</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3895-0728</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Храмов</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Khramov</surname><given-names>A. S.</given-names></name></name-alternatives><bio xml:lang="en"><p>Andrey S. Khramov</p><p>St. Petersburg, 197101</p></bio><email xlink:type="simple">askhramov@itmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0000-2686-290X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Васильев</surname><given-names>М. Д.</given-names></name><name name-style="western" xml:lang="en"><surname>Vasilev</surname><given-names>M. D.</given-names></name></name-alternatives><bio xml:lang="en"><p>Maksim D. Vasilev</p><p>St. Petersburg, 197101</p></bio><email xlink:type="simple">mdvasilev@itmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6274-1491</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Синев</surname><given-names>Д. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Sinev</surname><given-names>D. A.</given-names></name></name-alternatives><bio xml:lang="en"><p>Dmitry A. Sinev</p><p>St. Petersburg, 197101</p></bio><email xlink:type="simple">sinev@itmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8005-8410</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Шахно</surname><given-names>Е. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Shakhno</surname><given-names>E. A.</given-names></name></name-alternatives><bio xml:lang="en"><p>Elena A. Shakhno</p><p>St. Petersburg, 197101</p></bio><email xlink:type="simple">elena.shakhno@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="en">ITMO University<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>06</day><month>01</month><year>2026</year></pub-date><volume>16</volume><issue>6</issue><fpage>755</fpage><lpage>762</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Khramov A.S., Vasilev M.D., Sinev D.A., Shakhno E.A., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Храмов А.С., Васильев М.Д., Синев Д.А., Шахно Е.А.</copyright-holder><copyright-holder xml:lang="en">Khramov A.S., Vasilev M.D., Sinev D.A., Shakhno E.A.</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/1614">https://nanojournal.ifmo.ru/jour/article/view/1614</self-uri><abstract><p>Precise nanopatterning of thin films is an important task in production of modern optoelectronics and photonics elements. Direct recording of laser-induced periodic surface structures (LIPSS) is a promising tool for direct subwavelength nanopatterning. Recent studies show that the dynamics of LIPSS formation changes significantly if the film is relatively thin. Here we present a comprehensive analytical model aiming to bridge the gap between the expected dynamics of electromagnetic fields during LIPSS formation and experimentally obtainable nanopatterning results. The phenomenological model of surface electromagnetic wave (SEW) propagation at the film–substrate interface illustrates the mechanism of LIPSS formation using a periodic distribution of SEW energy concentration. SEW features are calculated depending on metal film thickness, and positive feedback between the local thickness of the growing oxide layer and the SEW energy concentration is unveiled. Changes in LIPPS formation mechanisms are confirmed experimentally on titanium films with different thickness. These findings shed light on the intrinsic physical mechanisms of LIPSS formation on thin metal films and ease the possibilities for LIPPS applications for nanopatterning.</p></abstract><trans-abstract xml:lang="ru"><p>Прецизионное наноструктурирование тонких пленок является важной задачей в производстве современных элементов оптоэлектроники и фотоники. Прямая запись лазерно-индуцированных периодических поверхностных структур (ЛИППС) является перспективным инструментом для прямого субволнового наноструктурирования. Недавние исследования показывают, что динамика формирования ЛИППС существенно изменяется, если пленка является оптически тонкой. В этой работе представлена комплексная аналитическая модель, призванная сократить разрыв между ожидаемой динамикой электромагнитных полей во время формирования ЛИППС и экспериментально получаемыми результатами наноструктурирования. Феноменологическая модель распространения поверхностной электромагнитной волны (ПЭВ) на границе раздела пленка–подложка иллюстрирует механизм формирования ЛИППС с использованием периодического распределения концентрации энергии ПЭВ. Рассчитаны характеристики ПЭВ в зависимости от толщины металлической пленки, а также показана положительная обратная связь между локальной толщиной растущего оксидного слоя и концентрацией энергии ПЭВ. Изменения в механизмах формирования ЛИППС подтверждены экспериментально на пленках титана различной толщины. Эти результаты проясняют внутренние физические механизмы формирования ЛИППС на тонких металлических пленках и расширяют возможности применения ЛИППС для наноструктурирования.</p><p> </p></trans-abstract><kwd-group xml:lang="ru"><kwd>лазерно-индуцированные периодические поверхностные структуры</kwd><kwd>ЛИППС</kwd><kwd>наноструктурирование</kwd><kwd>тонкие пленки</kwd><kwd>прямая лазерная запись</kwd></kwd-group><kwd-group xml:lang="en"><kwd>laser-induced periodic surface structures</kwd><kwd>LIPSS</kwd><kwd>nanopatterning</kwd><kwd>thin films</kwd><kwd>direct laser writing</kwd></kwd-group><funding-group xml:lang="en"><funding-statement>Dmitry A. Sinev acknowledges the financial support of the Ministry of Science and Higher Education of the Russian Federation (No. FSER-2025–0007). Film deposition was conducted in the Interdisciplinary Resource Center for Nanotechnology of St. Petersburg State University within the framework of research project SPbSU: 125021702335-5. Andrey S. Khramov and Maksim D. Vasilev thank the ITMO University NIRMA project No 624128 for the support of students’ research.</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">Feng E., Zhang C., Chang J., Han Y., Li H., Luo Q., Ma C.Q., Yip H.L., Ding L., Yang J. A 16.10 % efficiency organic solar module with ultra-narrow interconnections fabricated via nanosecond ultraviolet laser processing. Cell Reports Physical Science, 2024, 5 (3), 101883.</mixed-citation><mixed-citation xml:lang="en">Feng E., Zhang C., Chang J., Han Y., Li H., Luo Q., Ma C.Q., Yip H.L., Ding L., Yang J. A 16.10 % efficiency organic solar module with ultra-narrow interconnections fabricated via nanosecond ultraviolet laser processing. Cell Reports Physical Science, 2024, 5 (3), 101883.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Nirmal A., Kyaw A.K.K., Jianxiong W., Dev K., Sun X., Demir H.V. Light Trapping in Inverted Organic Photovoltaics with Nanoimprinted ZnO Photonic Crystals. IEEE J. of Photovoltaics, 2017, 7 (2), P. 545–549.</mixed-citation><mixed-citation xml:lang="en">Nirmal A., Kyaw A.K.K., Jianxiong W., Dev K., Sun X., Demir H.V. Light Trapping in Inverted Organic Photovoltaics with Nanoimprinted ZnO Photonic Crystals. IEEE J. of Photovoltaics, 2017, 7 (2), P. 545–549.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Dang S., Ye H. A visible-infrared-compatible camouflage photonic crystal with heat dissipation by radiation in 5–8 µm. Cell Reports Physical Science, 2021, 2 (11), 100617.</mixed-citation><mixed-citation xml:lang="en">Dang S., Ye H. A visible-infrared-compatible camouflage photonic crystal with heat dissipation by radiation in 5–8 µm. Cell Reports Physical Science, 2021, 2 (11), 100617.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Bronnikov K., Terentyev V., Simonov V., Fedyaj V., Simanchuk A., Babin S.A., Lapidas V., Mitsai E., Cherepakhin A., Zhang J., Zhizhchenko A. Highly Regular Laser-Induced Periodic Surface Structures on Titanium Thin Films for Photonics and Fiber Optics. ACS Applied Materials &amp; Interfaces, 2024, 16 (50), P. 70047–70056.</mixed-citation><mixed-citation xml:lang="en">Bronnikov K., Terentyev V., Simonov V., Fedyaj V., Simanchuk A., Babin S.A., Lapidas V., Mitsai E., Cherepakhin A., Zhang J., Zhizhchenko A. Highly Regular Laser-Induced Periodic Surface Structures on Titanium Thin Films for Photonics and Fiber Optics. ACS Applied Materials &amp; Interfaces, 2024, 16 (50), P. 70047–70056.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Dostovalov A., Bronnikov K., Korolkov V., Babin S., Mitsai E., Mironenko A., Tutov M., Zhang D., Sugioka K., Maksimovic J., Katkus T. Hierarchical anti-reflective laser-induced periodic surface structures (LIPSSs) on amorphous Si films for sensing applications. Nanoscale, 2020, 12 (25), P. 13431–13441.</mixed-citation><mixed-citation xml:lang="en">Dostovalov A., Bronnikov K., Korolkov V., Babin S., Mitsai E., Mironenko A., Tutov M., Zhang D., Sugioka K., Maksimovic J., Katkus T. Hierarchical anti-reflective laser-induced periodic surface structures (LIPSSs) on amorphous Si films for sensing applications. Nanoscale, 2020, 12 (25), P. 13431–13441.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Banerjee D., Akkanaboina M., Kanaka R.K., Soma V.R. Femtosecond Bessel beam induced ladder-like LIPSS on trimetallic surface for SERSbased sensing of Tetryl and PETN. Applied Surface Science, 2023, 616, 156561.</mixed-citation><mixed-citation xml:lang="en">Banerjee D., Akkanaboina M., Kanaka R.K., Soma V.R. Femtosecond Bessel beam induced ladder-like LIPSS on trimetallic surface for SERSbased sensing of Tetryl and PETN. Applied Surface Science, 2023, 616, 156561.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Pan X., Zhou L., Hu D., He W., Liu P., Yu Z., Liang X. Superior wear resistance in cast aluminum alloy via femtosecond laser induced periodic surface structures and surface hardening layer. Applied Surface Science, 2023, 636, 157866.</mixed-citation><mixed-citation xml:lang="en">Pan X., Zhou L., Hu D., He W., Liu P., Yu Z., Liang X. Superior wear resistance in cast aluminum alloy via femtosecond laser induced periodic surface structures and surface hardening layer. Applied Surface Science, 2023, 636, 157866.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Sotelo L., Fontanot T., Vig S., Herre P., Yousefi P., Fernandes M.H., Sarau G., Leuchs G., Christiansen S. Influence of initial surface roughness on LIPSS formation and its consecutive impact on cell/bacteria attachment for TiAl6V4 surfaces. Advanced Materials Technologies, 2023, 8 (12), 2201802.</mixed-citation><mixed-citation xml:lang="en">Sotelo L., Fontanot T., Vig S., Herre P., Yousefi P., Fernandes M.H., Sarau G., Leuchs G., Christiansen S. Influence of initial surface roughness on LIPSS formation and its consecutive impact on cell/bacteria attachment for TiAl6V4 surfaces. Advanced Materials Technologies, 2023, 8 (12), 2201802.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Andreeva Y.M., Luong V.C., Lutoshina D.S., Medvedev O.S., Mikhailovskii V.Y., Moskvin M.K., Odintsova G.V., Romanov V.V., Shchedrina N.N., Veiko V.P. Laser coloration of metals in visual art and design. Optical Materials Express, 2019, 9 (3), P. 1310–1319.</mixed-citation><mixed-citation xml:lang="en">Andreeva Y.M., Luong V.C., Lutoshina D.S., Medvedev O.S., Mikhailovskii V.Y., Moskvin M.K., Odintsova G.V., Romanov V.V., Shchedrina N.N., Veiko V.P. Laser coloration of metals in visual art and design. Optical Materials Express, 2019, 9 (3), P. 1310–1319.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Ibrahim Q., Andreeva Y., Suvorov A., Khmelenin D., Grigoryev E., Shcherbakov A.A., Sinev D. Laser fabrication of 1D and 2D periodic subwavelength gratings on titanium films. Optics &amp; Laser Technology, 2024, 174, 110642.</mixed-citation><mixed-citation xml:lang="en">Ibrahim Q., Andreeva Y., Suvorov A., Khmelenin D., Grigoryev E., Shcherbakov A.A., Sinev D. Laser fabrication of 1D and 2D periodic subwavelength gratings on titanium films. Optics &amp; Laser Technology, 2024, 174, 110642.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Bonse J., Graf S. Maxwell meets Marangoni – a review of theories on laser-induced periodic surface structures. ¨ Laser &amp; Photonics Reviews, 2020, 14 (10), 2000215.</mixed-citation><mixed-citation xml:lang="en">Bonse J., Graf S. Maxwell meets Marangoni – a review of theories on laser-induced periodic surface structures. ¨ Laser &amp; Photonics Reviews, 2020, 14 (10), 2000215.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Oktem B., Pavlov I., Ilday S., Kalaycıo ¨ glu H., Rybak A., Yavas¸ S., Erdo ˘ gan M., Ilday F. ˘ O. Nonlinear laser lithography for indefinitely large-area ¨ nanostructuring with femtosecond pulses. Nature Photonics, 2013, 7 (11), P. 897–901.</mixed-citation><mixed-citation xml:lang="en">Oktem B., Pavlov I., Ilday S., Kalaycıo ¨ glu H., Rybak A., Yavas¸ S., Erdo ˘ gan M., Ilday F. ˘ O. Nonlinear laser lithography for indefinitely large-area ¨ nanostructuring with femtosecond pulses. Nature Photonics, 2013, 7 (11), P. 897–901.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Sinev D.A., Yuzhakova D.S., Moskvin M.K., Veiko V.P. Formation of the submicron oxidative LIPSS on thin titanium films during nanosecond laser recording. Nanomaterials, 2020, 10 (11), 2161.</mixed-citation><mixed-citation xml:lang="en">Sinev D.A., Yuzhakova D.S., Moskvin M.K., Veiko V.P. Formation of the submicron oxidative LIPSS on thin titanium films during nanosecond laser recording. Nanomaterials, 2020, 10 (11), 2161.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Belousov D.A., Bronnikov K.A., Okotrub K.A., Mikerin S.L., Korolkov V.P., Terentyev V.S., Dostovalov A.V. Thermochemical laser-induced periodic surface structures formation by femtosecond laser on Hf thin films in air and vacuum. Materials, 2021, 14 (21), 6714.</mixed-citation><mixed-citation xml:lang="en">Belousov D.A., Bronnikov K.A., Okotrub K.A., Mikerin S.L., Korolkov V.P., Terentyev V.S., Dostovalov A.V. Thermochemical laser-induced periodic surface structures formation by femtosecond laser on Hf thin films in air and vacuum. Materials, 2021, 14 (21), 6714.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Yang H.Z., Jiang G.D., Wang W.J., Mei X.S., Pan A.F., Zhai Z.Y. Picosecond laser fabrication of nanostructures on ITO film surface assisted by pre-deposited Au film. Applied Physics B, 2017, 123 (10), 251.</mixed-citation><mixed-citation xml:lang="en">Yang H.Z., Jiang G.D., Wang W.J., Mei X.S., Pan A.F., Zhai Z.Y. Picosecond laser fabrication of nanostructures on ITO film surface assisted by pre-deposited Au film. Applied Physics B, 2017, 123 (10), 251.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Dostovalov A.V., Derrien T.J.-Y., Lizunov S.A., Pˇreucil F., Okotrub K.A., Mocek T., Korolkov V.P., Babin S.A., Bulgakova N.M. LIPSS on thin ˇ metallic films: New insights from multiplicity of laser-excited electromagnetic modes and efficiency of metal oxidation. Applied Surface Science, 2019, 491, P. 650–658.</mixed-citation><mixed-citation xml:lang="en">Dostovalov A.V., Derrien T.J.-Y., Lizunov S.A., Pˇreucil F., Okotrub K.A., Mocek T., Korolkov V.P., Babin S.A., Bulgakova N.M. LIPSS on thin ˇ metallic films: New insights from multiplicity of laser-excited electromagnetic modes and efficiency of metal oxidation. Applied Surface Science, 2019, 491, P. 650–658.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Dostovalov A.V., Korolkov V.P., Okotrub K.A., Bronnikov K.A., Babin S.A. Oxide composition and period variation of thermochemical LIPSS on chromium films with different thickness. Optics Express, 2018, 26 (6), P. 7712–7723.</mixed-citation><mixed-citation xml:lang="en">Dostovalov A.V., Korolkov V.P., Okotrub K.A., Bronnikov K.A., Babin S.A. Oxide composition and period variation of thermochemical LIPSS on chromium films with different thickness. Optics Express, 2018, 26 (6), P. 7712–7723.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Bronnikov K., Gladkikh S., Okotrub K., Simanchuk A., Zhizhchenko A., Kuchmizhak A., Dostovalov A. Regulating morphology and composition of laser-induced periodic structures on titanium films with femtosecond laser wavelength and ambient environment. Nanomaterials, 2022, 12 (3), 306.</mixed-citation><mixed-citation xml:lang="en">Bronnikov K., Gladkikh S., Okotrub K., Simanchuk A., Zhizhchenko A., Kuchmizhak A., Dostovalov A. Regulating morphology and composition of laser-induced periodic structures on titanium films with femtosecond laser wavelength and ambient environment. Nanomaterials, 2022, 12 (3), 306.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Bad´ıa-Majos A., Mart ´ ´ınez E., Angurel L.A., de la Fuente G.F., Fourneau E., Marinkovic S., Silhanek A.V. Laser nanostructured metasurfaces in ´ Nb superconducting thin films. Applied Surface Science, 2024, 649, 159164.</mixed-citation><mixed-citation xml:lang="en">Bad´ıa-Majos A., Mart ´ ´ınez E., Angurel L.A., de la Fuente G.F., Fourneau E., Marinkovic S., Silhanek A.V. Laser nanostructured metasurfaces in ´ Nb superconducting thin films. Applied Surface Science, 2024, 649, 159164.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Xu L., Geng J., Shi L., Cui W., Qiu M. Impact of film thickness in laser-induced periodic structures on amorphous Si films. Frontiers of Optoelectronics, 2023, 16 (1), 16.</mixed-citation><mixed-citation xml:lang="en">Xu L., Geng J., Shi L., Cui W., Qiu M. Impact of film thickness in laser-induced periodic structures on amorphous Si films. Frontiers of Optoelectronics, 2023, 16 (1), 16.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Fraggelakis F., Lingos P., Tsibidis G.D., Cusworth E., Kay N., Fumagalli L., Kravets V.G., Grigorenko A.N., Kabashin A.V., Stratakis E. Double-Pulse Femtosecond Laser Fabrication of Highly Ordered Periodic Structures on Au Thin Films Enabling Low-Cost Plasmonic Applications. ACS Nano, 2025, 19 (25), P. 23258–23275.</mixed-citation><mixed-citation xml:lang="en">Fraggelakis F., Lingos P., Tsibidis G.D., Cusworth E., Kay N., Fumagalli L., Kravets V.G., Grigorenko A.N., Kabashin A.V., Stratakis E. Double-Pulse Femtosecond Laser Fabrication of Highly Ordered Periodic Structures on Au Thin Films Enabling Low-Cost Plasmonic Applications. ACS Nano, 2025, 19 (25), P. 23258–23275.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Derrien T.J.-Y., Kruger J., Bonse J. Properties of surface plasmon polaritons on lossy materials: lifetimes, periods and excitation conditions. ¨ J. of Optics, 2016, 18 (11), 115007.</mixed-citation><mixed-citation xml:lang="en">Derrien T.J.-Y., Kruger J., Bonse J. Properties of surface plasmon polaritons on lossy materials: lifetimes, periods and excitation conditions. ¨ J. of Optics, 2016, 18 (11), 115007.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Johnson P.B., Christy R.W. Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd. Physical Review B, 1974, 9 (12), P. 5056–5070.</mixed-citation><mixed-citation xml:lang="en">Johnson P.B., Christy R.W. Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd. Physical Review B, 1974, 9 (12), P. 5056–5070.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Libenson M.N. Laser-induced optical and thermal processes in condensed matter and their mutual influence. Nauka Publisher, St. Petersburg, 2007. 423 p. (in Russian).</mixed-citation><mixed-citation xml:lang="en">Libenson M.N. Laser-induced optical and thermal processes in condensed matter and their mutual influence. Nauka Publisher, St. Petersburg, 2007. 423 p. (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Malitson X.I.H. Interspecimen comparison of the refractive index of fused silica. J. of the Optical Society of America, 1965, 55 (10), P. 1205–1209.</mixed-citation><mixed-citation xml:lang="en">Malitson X.I.H. Interspecimen comparison of the refractive index of fused silica. J. of the Optical Society of America, 1965, 55 (10), P. 1205–1209.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Devore J.R. Refractive indices of rutile and sphalerite. J. of the Optical Society of America, 1951, 41 (6), P. 416–419.</mixed-citation><mixed-citation xml:lang="en">Devore J.R. Refractive indices of rutile and sphalerite. J. of the Optical Society of America, 1951, 41 (6), P. 416–419.</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>
