{"id":72263,"date":"2025-02-04T12:29:01","date_gmt":"2025-02-04T10:29:01","guid":{"rendered":"https:\/\/www.iemn.fr\/?p=72263"},"modified":"2025-02-25T11:57:32","modified_gmt":"2025-02-25T09:57:32","slug":"on-chip-photonic-guides-as-efficient-as-topological-channels","status":"publish","type":"post","link":"https:\/\/www.iemn.fr\/en\/newsletter\/on-chip-photonic-guides-as-efficient-as-topological-channels.html","title":{"rendered":"On-chip photonic guides as efficient as topological channels?"},"content":{"rendered":"<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-m6kfb4m4-5fe157acfb2922d6c407feb1ffed48f7\">\n.flex_column.av-m6kfb4m4-5fe157acfb2922d6c407feb1ffed48f7{\nbackground-color:#efefef;\n}\n<\/style>\n<div  class='flex_column av-m6kfb4m4-5fe157acfb2922d6c407feb1ffed48f7 av_one_full  avia-builder-el-0  el_before_av_hr  avia-builder-el-first  first flex_column_div'     ><section  class='av_textblock_section av-m6jedv7s-f02ac12b1e6a08b878e74e6ad2838672'   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p><a href=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/montage4.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-72154 size-full aligncenter\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/montage4.jpg\" alt=\"\" width=\"1500\" height=\"123\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/montage4.jpg 1500w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/montage4-300x25.jpg 300w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/montage4-1030x84.jpg 1030w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/montage4-768x63.jpg 768w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/montage4-18x1.jpg 18w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/montage4-705x58.jpg 705w\" sizes=\"auto, (max-width: 1500px) 100vw, 1500px\" \/><\/a><\/p>\n<\/div><\/section><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-m6kez784-1fe73fb4b3ef6c606bd74ffef34da566\">\n#top .hr.hr-invisible.av-m6kez784-1fe73fb4b3ef6c606bd74ffef34da566{\nheight:30px;\n}\n<\/style>\n<div  class='hr av-m6kez784-1fe73fb4b3ef6c606bd74ffef34da566 hr-invisible  avia-builder-el-2  el_after_av_one_full  el_before_av_textblock'><span class='hr-inner'><span class=\"hr-inner-style\"><\/span><\/span><\/div>\n<section  class='av_textblock_section av-m6jef3f8-4b1f1086f555bb536f399d768a41c089'   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><h2 style=\"text-align: center;\"><span style=\"color: #f16728;\">On-chip photonic guides as efficient as topological channels?<\/span><\/h2>\n<\/div><\/section>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-m6jek97m-829e54d364f84ac1194544dfb4ec4de2\">\n#top .hr.av-m6jek97m-829e54d364f84ac1194544dfb4ec4de2{\nmargin-top:30px;\nmargin-bottom:30px;\n}\n.hr.av-m6jek97m-829e54d364f84ac1194544dfb4ec4de2 .hr-inner{\nwidth:50px;\nborder-color:#f16728;\nmax-width:45%;\n}\n.hr.av-m6jek97m-829e54d364f84ac1194544dfb4ec4de2 .av-seperator-icon{\ncolor:#f16728;\n}\n<\/style>\n<div  class='hr av-m6jek97m-829e54d364f84ac1194544dfb4ec4de2 hr-custom  avia-builder-el-4  el_after_av_textblock  el_before_av_one_half  hr-center hr-icon-yes'><span class='hr-inner inner-border-av-border-fat'><span class=\"hr-inner-style\"><\/span><\/span><span class='av-seperator-icon' aria-hidden='true' data-av_icon='\ue883' data-av_iconfont='entypo-fontello'><\/span><span class='hr-inner inner-border-av-border-fat'><span class=\"hr-inner-style\"><\/span><\/span><\/div>\n<div  class='flex_column av-m6jdpaok-1bd26374588bb9bb424562183b62b4b8 av_one_half  avia-builder-el-5  el_after_av_hr  el_before_av_one_half  first flex_column_div'     ><style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-m6jdswo0-e63a1ab9558d0f038f3210deb76b9b3d\">\n#top .av_textblock_section.av-m6jdswo0-e63a1ab9558d0f038f3210deb76b9b3d .avia_textblock{\ntext-align:justify;\n}\n<\/style>\n<section  class='av_textblock_section av-m6jdswo0-e63a1ab9558d0f038f3210deb76b9b3d'   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><blockquote>\n<p class=\"Standard\"><strong><a href=\"https:\/\/www.nature.com\/articles\/s41598-024-53082-4\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff7b00;\"><span style=\"color: #008080;\">\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-mqde7m-1524bcfe1dd544a44cfe81886c34073c\">\n.av_font_icon.av-mqde7m-1524bcfe1dd544a44cfe81886c34073c{\ncolor:#ff7b00;\nborder-color:#ff7b00;\n}\n.av_font_icon.av-mqde7m-1524bcfe1dd544a44cfe81886c34073c .av-icon-char{\nfont-size:25px;\nline-height:25px;\n}\n<\/style>\n<span  class='av_font_icon av-mqde7m-1524bcfe1dd544a44cfe81886c34073c avia_animate_when_visible av-icon-style- avia-icon-pos-left avia-icon-animate'><span class='av-icon-char' aria-hidden='true' data-av_icon='\ue885' data-av_iconfont='entypo-fontello' ><\/span><\/span><\/span><\/span><\/a><\/strong><i>Photonic topology, by proposing a particular way of creating an interface between two periodic structures of the same insulating membrane, promises to guide an electromagnetic signal with minimal losses in complex miniaturized circuits.It is thus a key element in the development of terahertz telecommunications or quantum technologies. We propose a new structuring of the membrane, enriching the possible forms of interfaces, in order to question the topological origin of the remarkable performance of photonic crystals built using the \u201cvalley\u201d approach.<\/i><\/p>\n<\/blockquote>\n<p><strong><a href=\"https:\/\/www.nature.com\/articles\/s41598-024-53082-4\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff7b00;\"><span style=\"color: #008080;\">\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-mqde7m-3-9ddbbfcf8e1204fc5bc3927ac48288f3\">\n.av_font_icon.av-mqde7m-3-9ddbbfcf8e1204fc5bc3927ac48288f3{\ncolor:#ff7b00;\nborder-color:#ff7b00;\n}\n.av_font_icon.av-mqde7m-3-9ddbbfcf8e1204fc5bc3927ac48288f3 .av-icon-char{\nfont-size:25px;\nline-height:25px;\n}\n<\/style>\n<span  class='av_font_icon av-mqde7m-3-9ddbbfcf8e1204fc5bc3927ac48288f3 avia_animate_when_visible av-icon-style- avia-icon-pos-left avia-icon-animate'><span class='av-icon-char' aria-hidden='true' data-av_icon='\ue889' data-av_iconfont='entypo-fontello' ><\/span><\/span><\/span><\/span><\/a><\/strong><\/p>\n<p>Photonic topological insulators are systems that use photons to mimic the quantum Hall effects observed in their electronic counterparts in solid-state physics, with the aim of transporting electromagnetic signals via \u201crobust\u201d interface modes, i.e. propagating without backscattering despite the presence of defects or sharp bends along their path. However, the bosonic nature of photons means that in two-dimensional systems, time-reversal symmetry must be broken (e.g. by applying a magnetic field).<\/p>\n<\/div><\/section><br \/>\n<section  class='av_textblock_section av-m6je98a0-c914cc8b53aceedf496c10fc1dab8441'   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><div id=\"attachment_72079\" style=\"width: 510px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques1.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-72079\" class=\"wp-image-72079\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques1.jpg\" alt=\"\" width=\"500\" height=\"430\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques1.jpg 800w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques1-300x258.jpg 300w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques1-768x660.jpg 768w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques1-14x12.jpg 14w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques1-705x606.jpg 705w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><p id=\"caption-attachment-72079\" class=\"wp-caption-text\">Figure 1: (a) Diagram showing the geometry of the photonic crystal, composed of three sets of diamonds of different sizes, grouped by color on the left half. The lozenges represent air holes in a silicon matrix. (b) Band diagram for the insert geometry. (c) Berry curvature distribution in the first Brillouin zone, along the lowest frequency band. (d) Interface constructed between an original grating A and an image grating B.<\/p><\/div>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-m6jenubk-2d51498c88dc44c60061ccabb10b1621\">\n#top .av_textblock_section.av-m6jenubk-2d51498c88dc44c60061ccabb10b1621 .avia_textblock{\ntext-align:justify;\n}\n<\/style>\n<section  class='av_textblock_section av-m6jenubk-2d51498c88dc44c60061ccabb10b1621'   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p><strong><a href=\"https:\/\/www.nature.com\/articles\/s41598-024-53082-4\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff7b00;\"><span style=\"color: #008080;\">\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-mqde7m-2-70a66f18ecee0847b59470b90592f8ca\">\n.av_font_icon.av-mqde7m-2-70a66f18ecee0847b59470b90592f8ca{\ncolor:#ff7b00;\nborder-color:#ff7b00;\n}\n.av_font_icon.av-mqde7m-2-70a66f18ecee0847b59470b90592f8ca .av-icon-char{\nfont-size:25px;\nline-height:25px;\n}\n<\/style>\n<span  class='av_font_icon av-mqde7m-2-70a66f18ecee0847b59470b90592f8ca avia_animate_when_visible av-icon-style- avia-icon-pos-left avia-icon-animate'><span class='av-icon-char' aria-hidden='true' data-av_icon='\ue889' data-av_iconfont='entypo-fontello' ><\/span><\/span><\/span><\/span><\/a><\/strong><strong>Another approach can be found in certain photonic crystals known as \u201cvalley crystals\u201d. These materials exploit a geometric property of the electromagnetic wave, called Berry curvature, which can be represented on a map in two-dimensional space of wave propagation directions (reciprocal space).\u00a0<\/strong><\/p>\n<p>To better understand this, let&rsquo;s imagine an ant trying to move \u201cas straight as possible\u201d over a bumpy surface: it will be deflected by passing over the side of a bump, which has a non-zero curvature unlike a flat surface. Similarly, Berry&rsquo;s curvature causes a rotation (phase) in the state of a photon moving in a given direction.<br \/>\nBy construction, valley photonic crystals are not symmetrical with respect to a central symmetry, which gives them a non-zero Berry curvature, concentrated around certain propagation directions (noted K and K&rsquo; in reciprocal space). When two crystals forming a mirror image of each other are placed side by side along these directions, this curvature changes sign at the interface, creating a topological transition. It is this transition that is often proposed to explain why light can propagate robustly along the interface. However, several recent works question this interpretation [1].<br \/>\nOur work introduces an original photonic crystal pattern [2], consisting of three subsets of diamonds whose size is varied independently, see Figure 1(a). For well-chosen parameters, the system exhibits a band gap between the first and second bands, Figure 1(b). In reciprocal space, the Berry curvature is concentrated around the propagation directions K and K&rsquo;, with opposite signs, Figure 1(c). The originality of our structure lies in the fact that the number of possible interfaces is greater than in conventional systems with only two asymmetric holes. Instead of just two mirror-symmetrical interfaces with topological transition in the latter case, we obtain 18 interfaces, similar to those shown in Fig. 1(d), some with topological transition and some without.<\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-pkjtzx-ae0e0864cfa130247f8f40aa1ae8dbfb av_one_half  avia-builder-el-12  el_after_av_one_half  avia-builder-el-last  flex_column_div'     ><section  class='av_textblock_section av-m6je9ub6-2b241e8a69fef25c12221b3f2c441c5c'   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><div id=\"attachment_72080\" style=\"width: 510px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques2.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-72080\" class=\"wp-image-72080\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques2.jpg\" alt=\"\" width=\"500\" height=\"412\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques2.jpg 800w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques2-300x247.jpg 300w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques2-768x633.jpg 768w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques2-15x12.jpg 15w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2025\/01\/guides_photoniques2-705x581.jpg 705w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><p id=\"caption-attachment-72080\" class=\"wp-caption-text\">Figure 2: Transmission curves and magnetic field amplitude distributions in circuits corresponding to a triangular cavity coupled to a straight guide (a-e), or to a path of arbitrary shape (f-h). The green star in figures (a) and (f) indicates the position of the source, and the dotted arrows indicate the directions of propagation without backscatter. Figures (b,c,g) (resp. d,e,h) correspond to the interface with (resp. without) topological transition. The detailed shape of the interface is shown as an insert to the transmission curves. Maps (c) and (d) are plotted for frequencies indicated by arrows.<\/p><\/div>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-qo30kd-fe4be08d43b5cba800e857057ce3aa0c\">\n#top .hr.hr-invisible.av-qo30kd-fe4be08d43b5cba800e857057ce3aa0c{\nheight:50px;\n}\n<\/style>\n<div  class='hr av-qo30kd-fe4be08d43b5cba800e857057ce3aa0c hr-invisible  avia-builder-el-14  el_after_av_textblock  el_before_av_textblock'><span class='hr-inner'><span class=\"hr-inner-style\"><\/span><\/span><\/div><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-m6jdvgw4-4e10fbe8871ac32cc0c4a990921f9217\">\n#top .av_textblock_section.av-m6jdvgw4-4e10fbe8871ac32cc0c4a990921f9217 .avia_textblock{\ntext-align:justify;\n}\n<\/style>\n<section  class='av_textblock_section av-m6jdvgw4-4e10fbe8871ac32cc0c4a990921f9217'   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p><strong><a href=\"https:\/\/www.nature.com\/articles\/s41598-024-53082-4\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff7b00;\"><span style=\"color: #008080;\">\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-mqde7m-1-177deddf30d7b619640ee9e37f2947fc\">\n.av_font_icon.av-mqde7m-1-177deddf30d7b619640ee9e37f2947fc{\ncolor:#ff7b00;\nborder-color:#ff7b00;\n}\n.av_font_icon.av-mqde7m-1-177deddf30d7b619640ee9e37f2947fc .av-icon-char{\nfont-size:25px;\nline-height:25px;\n}\n<\/style>\n<span  class='av_font_icon av-mqde7m-1-177deddf30d7b619640ee9e37f2947fc avia_animate_when_visible av-icon-style- avia-icon-pos-left avia-icon-animate'><span class='av-icon-char' aria-hidden='true' data-av_icon='\ue889' data-av_iconfont='entypo-fontello' ><\/span><\/span><\/span><\/span><\/a><\/strong><\/p>\n<div>\n<p class=\"Textbody\">We have compared the propagation of interface modes along circuits of increasing complexity (Figure 2). In the situation traditionally used as a test for topological protection, Figure 2(a), the circuit features only 120\u00b0 turns, in this case with a triangular cavity, along which the mode propagates only in the K or K&rsquo; directions, without passing from one to the other (dotted arrows in Figure 2(a)). In particular, reflection is not possible and transmission through the circuit is flat, the shape of the field is regular, whether for an interface with, (b,c), or without, (d,e), topological transition. The latter case is surprising, and is attributed to the chirality of the interface. On the other hand, simulations carried out on circuits of arbitrary shape, figure 2(f), show that the topological transition ensures much better transmission than a trivial interface, reflections distributed along the path being much less in the former case. Our study, while highlighting the possibility of transmitting a signal along a non-topological interface with virtually no backscattering, nevertheless establishes a hierarchy between topological and trivial interfaces for arbitrary-form circuits, in which the former perform better.<\/p>\n<\/div>\n<div>\n<p class=\"Textbody\"><strong><span style=\"color: #f16728;\">This study is the result of a collaboration begun in 2019 between the Physics (G. L\u00e9v\u00eaque and Y. Pennec), THz Photonics (G. Ducournau) and NAM6 (M. Faucher) groups at IEMN and the PhLAM laboratory (A. Amo and P. Szriftgiser). A first publication focused on the evaluation of topological protection in valley photonic crystals using semi-analytical and numerical methods [3], followed by a second demonstrating the applicability of valley topology to the design of terahertz telecommunication devices, notably for 5G and 6G networks [4].<\/span><\/strong><\/p>\n<\/div>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-m6kg6dp4-cdb16a1ca5241aeac82523099100c8d2\">\n#top .hr.av-m6kg6dp4-cdb16a1ca5241aeac82523099100c8d2{\nmargin-top:30px;\nmargin-bottom:30px;\n}\n.hr.av-m6kg6dp4-cdb16a1ca5241aeac82523099100c8d2 .hr-inner{\nwidth:50px;\nmax-width:45%;\n}\n<\/style>\n<div  class='hr av-m6kg6dp4-cdb16a1ca5241aeac82523099100c8d2 hr-custom  avia-builder-el-17  el_after_av_textblock  el_before_av_textblock  hr-center hr-icon-yes'><span class='hr-inner inner-border-av-border-thin'><span class=\"hr-inner-style\"><\/span><\/span><span class='av-seperator-icon' aria-hidden='true' data-av_icon='\ue84e' data-av_iconfont='entypo-fontello'><\/span><span class='hr-inner inner-border-av-border-thin'><span class=\"hr-inner-style\"><\/span><\/span><\/div><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-m6kg42zo-457e19a1b4d7d7d31dc338d29c09f353\">\n#top .av_textblock_section.av-m6kg42zo-457e19a1b4d7d7d31dc338d29c09f353 .avia_textblock{\ntext-align:justify;\n}\n<\/style>\n<section  class='av_textblock_section av-m6kg42zo-457e19a1b4d7d7d31dc338d29c09f353'   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p><em>1] Impact of Transforming Interface Geometry on Edge States in Valley Photonic Crystals, D. Yu, S. Arora, L. Kuipers, Phys. Rev. Lett. 132, 116901 (2024) ; Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend, T. Torres, C. Bellis, R. Cottereau, A. Coutant, Proc. R. Soc. A 480, 20230905 (2024).<\/em><\/p>\n<p><em>[2] Relation between interface symmetry and propagation robustness along domain walls based on valley topological photonic crystals, G. L\u00e9v\u00eaque, P. Szriftgiser, A. Amo, Y. Pennec, APL Photonics 9, 126107 (2024). <a href=\"https:\/\/hal.science\/hal-04850762v1\" target=\"_blank\" rel=\"noopener\">https:\/\/hal.science\/hal-04850762v1<\/a><\/em><\/p>\n<p><em>[3] Scattering matrix approach for a quantitative evaluation of the topological protection in valley photonic crystals, G. L\u00e9v\u00eaque, Y. Pennec, P. Szriftgiser, A. Amo, and A. Mart\u00ednez, Phys. Rev. A 108, 043505 (2023). <a href=\"https:\/\/hal.science\/hal-04274279v1\" target=\"_blank\" rel=\"noopener\">https:\/\/hal.science\/hal-04274279v1<\/a><\/em><\/p>\n<p><em>[4] Engineering the breaking of topological protection in valley photonic crystals enables to design chip level functions for THz 6G communications and beyond, A. S. Mohammed, G. L\u00e9v\u00eaque, E. Lebouvier, Y. Pennec, M. Faucher, A. Amo, P. Szriftgiser, and G. Ducournau, J. Lightwave Technol. 42(23), 8323\u20138335 (2024).\u00a0 <a href=\"https:\/\/hal.science\/hal-04664538v1\" target=\"_blank\" rel=\"noopener\">https:\/\/hal.science\/hal-04664538v1<\/a><\/em><\/p>\n<div  class='avia-button-wrap av-rpqvoq-541f5de2fe706c01b67e0748dd16b3c5-wrap avia-button-left  avia-builder-el-19  avia-builder-el-no-sibling'><a href='mailto:gaetan.leveque@univ-lille.fr'  class='avia-button av-rpqvoq-541f5de2fe706c01b67e0748dd16b3c5 av-link-btn avia-icon_select-yes-left-icon avia-size-light avia-position-left avia-color-silver'   aria-label=\"Ga\u00ebtan Lev\u00eaque\"><span class='avia_button_icon avia_button_icon_left' aria-hidden='true' data-av_icon='\ue805' data-av_iconfont='entypo-fontello'><\/span><span class='avia_iconbox_title' >Ga\u00ebtan Lev\u00eaque<\/span><\/a><\/div>\n<\/div><\/section><\/p><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[297],"tags":[],"class_list":["post-72263","post","type-post","status-publish","format-standard","hentry","category-newsletter"],"_links":{"self":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/posts\/72263","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/comments?post=72263"}],"version-history":[{"count":0,"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/posts\/72263\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/media?parent=72263"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/categories?post=72263"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/tags?post=72263"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}