{"id":25999,"date":"2018-10-12T12:03:22","date_gmt":"2018-10-12T10:03:22","guid":{"rendered":"https:\/\/www.iemn.fr\/?page_id=25999"},"modified":"2019-02-11T17:29:58","modified_gmt":"2019-02-11T15:29:58","slug":"modeling-of-thz-sources","status":"publish","type":"page","link":"https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/research\/modeling-of-thz-sources","title":{"rendered":"Modeling of THz sources based on Quantum Cascade Lasers"},"content":{"rendered":"<div id='layer_slider_1'  class='avia-layerslider main_color avia-shadow  avia-builder-el-0  el_before_av_submenu  avia-builder-el-first  container_wrap sidebar_right'  style='height: 261px;'  ><div id=\"layerslider_3_9gw6e1ao3p4r\" data-ls-slug=\"homepageslider\" class=\"ls-wp-container fitvidsignore ls-selectable\" style=\"width:100%;height:260px;margin:0 auto;margin-bottom: 0px;\"><div class=\"ls-slide\" data-ls=\"duration:4000;transition2d:5;\"><\/div><div class=\"ls-slide\" data-ls=\"duration:4000;transition2d:5;\"><\/div><div class=\"ls-slide\" data-ls=\"duration:4000;transition2d:5;\"><\/div><div class=\"ls-slide\" data-ls=\"duration:4000;transition2d:5;\"><div style=\"width:;height:;padding-top:;padding-right:;padding-bottom:;padding-left:;border-top:;border-right:;border-bottom:;border-left:;font-family:;font-size:;line-height:;color:;background:;border-radius:;top:0px;left:0px;\" class=\"ls-l ls-post-layer\" data-ls=\"offsetxin:80;easingin:linear;offsetxout:-80;durationout:400;easingout:linear;parallaxlevel:0;\"><\/div><\/div><\/div><\/div>\n<div id='sub_menu1'  class='av-submenu-container av-jrqfadqy-807d5a51dd3616f0d00a06e9b2d077f0 footer_color  avia-builder-el-1  el_after_av_layerslider  el_before_av_heading  submenu-not-first container_wrap sidebar_right' style='z-index:301' ><div class='container av-menu-mobile-disabled av-submenu-pos-left'><ul id='av-custom-submenu-1' class='av-subnav-menu' role='menu'>\n<li class='menu-item av-av_submenu_item-8cfdaa9ad07fd6a0ccb509a50dffc6f6 menu-item-top-level menu-item-top-level-1' role='menuitem'><a href='https:\/\/www.iemn.fr\/en\/?page_id=25957'  ><span class='avia-bullet'><\/span><span class='avia-menu-text'>Introduction<\/span><\/a><\/li>\n<li class='menu-item av-av_submenu_item-b4f170efd399a2be0e3448b0ed0e8486 menu-item-top-level menu-item-top-level-2' role='menuitem'><a href='https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/members'  ><span class='avia-bullet'><\/span><span class='avia-menu-text'>Members<\/span><\/a><\/li>\n<li class='menu-item av-av_submenu_item-8e1a366b5289a4655e340360bb600c95 menu-item-top-level menu-item-top-level-3' role='menuitem'><a href='https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/research'  ><span class='avia-bullet'><\/span><span class='avia-menu-text'>Research<\/span><\/a><\/li>\n<li class='menu-item av-kbk05k-5c5944fac313107f26dddee0ba9e2d5b menu-item-top-level menu-item-top-level-4' role='menuitem'><a href='https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes'  ><span class='avia-bullet'><\/span><span class='avia-menu-text'>Other groups<\/span><\/a><\/li>\n<\/ul><\/div><\/div><div id='after_submenu_1'  class='main_color av_default_container_wrap container_wrap sidebar_right'  ><div class='container av-section-cont-open' ><div class='template-page content  av-content-small alpha units'><div class='post-entry post-entry-type-page post-entry-25999'><div class='entry-content-wrapper clearfix'>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-av_heading-5d26c73b5eb29f795410bc2174d633c2\">\n#top .av-special-heading.av-av_heading-5d26c73b5eb29f795410bc2174d633c2{\npadding-bottom:10px;\n}\nbody .av-special-heading.av-av_heading-5d26c73b5eb29f795410bc2174d633c2 .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-av_heading-5d26c73b5eb29f795410bc2174d633c2 .av-subheading{\nfont-size:15px;\n}\n<\/style>\n<div  class='av-special-heading av-av_heading-5d26c73b5eb29f795410bc2174d633c2 av-special-heading-h3  avia-builder-el-2  el_after_av_submenu  el_before_av_hr  avia-builder-el-first'><h3 class='av-special-heading-tag'  itemprop=\"headline\"  >Modeling of THz sources based on Quantum Cascade Lasers<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div>\n<section  class='av_textblock_section av-jn5ul7i7-07ada957a1f2e7568310c23a698981be'   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>In our team, we have developed several kinds of simulators of QCLs, ranging from the most detailed and most computer consuming Monte Carlo method to simplified rate equation models which allow fast systematic computation for engineering purpose and from which one can derive analytic expressions for compact models or equivalent circuit modeling. In recent years, we mainly worked on such simplified models, in collaboration with our colleagues from S\u00e9tif University in Algeria and applied them to systems derived from QCLs and aimed at room temperature THz emission.<\/p>\n<p>Quantum Cascade Lasers (QCLs) have proven as extremely valuable compact sources, especially in the terahertz range. Unfortunately, in this range of frequency, the need of cryogenic cooling severely limits practical applications. Room temperature operation at terahertz frequencies seems beyond reach for 'standard' QCLs. However, several systems derived from QCLs have been proposed to overcome this limitation.<\/p>\n<p>An example of such systems is the 'optically-pumped electrically-driven QCL', which retains the cascade scheme in a periodic structure under the action of an applied electric field, but uses optical (rather electrical) pumping to ensure population inversion. We developed a simplified 4-level rate equations model of such systems and obtained closed-form expressions for steady-state characteristics (populations, mid infra-red pump threshold, external optical efficiency) which bring into light the dependencies on device parameters. On the same premises we also investigated the dynamical behavior of this device, which depends on pump intensity but appears in general faster than conventional QCLs.<\/p>\n<p>However, to date, the most successful compact sources for THz generation at RT are based on difference frequency generation. We applied our 'simplified rate equations approach' to the study of static and transient dynamics of such systems and get analytic expressions for time dependence of important characteristics such as levels populations and generated THz power.<\/p>\n<h4 style=\"text-align: center;\">Dynamic modeling of optically pumped electrically driven terahertz QCLs<\/h4>\n<div id=\"attachment_26002\" style=\"width: 446px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde04_dynamic_modelling.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-26002\" class=\"wp-image-26002\" title=\"Schematic conduction band energy diagram of two stages of a THz QC laser based on the optically pumped electrically driven scheme. Solid arrow: Pump absorption, dashed arrow: Pump recovery.\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde04_dynamic_modelling.jpg\" alt=\"Schematic conduction band energy diagram of two stages of a THz QC laser based on the optically pumped electrically driven scheme. Solid arrow: Pump absorption, dashed arrow: Pump recovery.\" width=\"436\" height=\"277\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde04_dynamic_modelling.jpg 728w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde04_dynamic_modelling-300x191.jpg 300w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde04_dynamic_modelling-705x448.jpg 705w\" sizes=\"auto, (max-width: 436px) 100vw, 436px\" \/><\/a><p id=\"caption-attachment-26002\" class=\"wp-caption-text\">Schematic conduction band energy diagram of two stages of a THz QC laser based on the optically pumped electrically driven scheme. Solid arrow: Pump absorption, dashed arrow: Pump recovery.<\/p><\/div>\n<div id=\"attachment_26005\" style=\"width: 690px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde05_time_evolution.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-26005\" class=\"wp-image-26005\" title=\"Time evolution of the THz QC laser intensity (blue solid line) and population inversion density (red dashed line) under different pump intensity above threshold. Calculated by means of our rate equation model... A. Hamadou, J.-L. Thobel, S. Lamari, Infrared Physics &amp; Technology 81 (2017) 195-200 http:\/\/dx.doi.org\/10.1016\/j.infrared.2016.12.019\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde05_time_evolution.png\" alt=\"Time evolution of the THz QC laser intensity (blue solid line) and population inversion density (red dashed line) under different pump intensity above threshold. Calculated by means of our rate equation model... A. Hamadou, J.-L. Thobel, S. Lamari, Infrared Physics &amp; Technology 81 (2017) 195-200 http:\/\/dx.doi.org\/10.1016\/j.infrared.2016.12.019\" width=\"680\" height=\"620\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde05_time_evolution.png 928w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde05_time_evolution-300x273.png 300w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde05_time_evolution-768x700.png 768w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde05_time_evolution-705x643.png 705w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/a><p id=\"caption-attachment-26005\" class=\"wp-caption-text\">Time evolution of the THz QC laser intensity (blue solid line) and population inversion density (red dashed line) under different pump intensity above threshold. Calculated by means of our rate equation model... A. Hamadou, J.-L. Thobel, S. Lamari, Infrared Physics &amp; Technology 81 (2017) 195-200 http:\/\/dx.doi.org\/10.1016\/j.infrared.2016.12.019<\/p><\/div>\n<h4 style=\"text-align: center;\">QCL-Difference Frequency Generation structure<\/h4>\n<div id=\"attachment_26007\" style=\"width: 690px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde06_qcl.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-26007\" class=\"wp-image-26007\" title=\"(a) Cross sectional view of the THz DFG device showing schematically the two parts of the active region. (b) Four-level model of one stage of the bound-to-continuum active region in a dual-wavelength QC laser as used in our work. Lasing takes place simultaneously through transitions from 4 onto 3 on one hand and from 4 onto 2 on the other. The THz frequency (60 \u00b5m wavelength) is generated via DFG process between levels 3 and 2.\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde06_qcl.jpg\" alt=\"(a) Cross sectional view of the THz DFG device showing schematically the two parts of the active region. (b) Four-level model of one stage of the bound-to-continuum active region in a dual-wavelength QC laser as used in our work. Lasing takes place simultaneously through transitions from 4 onto 3 on one hand and from 4 onto 2 on the other. The THz frequency (60 \u00b5m wavelength) is generated via DFG process between levels 3 and 2.\" width=\"680\" height=\"290\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde06_qcl.jpg 1100w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde06_qcl-300x128.jpg 300w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde06_qcl-768x327.jpg 768w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde06_qcl-1030x439.jpg 1030w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde06_qcl-705x301.jpg 705w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/a><p id=\"caption-attachment-26007\" class=\"wp-caption-text\">(a) Cross sectional view of the THz DFG device showing schematically the two parts of the active region. (b) Four-level model of one stage of the bound-to-continuum active region in a dual-wavelength QC laser as used in our work. Lasing takes place simultaneously through transitions from 4 onto 3 on one hand and from 4 onto 2 on the other. The THz frequency (60 \u00b5m wavelength) is generated via DFG process between levels 3 and 2.<\/p><\/div>\n<div id=\"attachment_26011\" style=\"width: 691px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde07_rate_equation.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-26011\" class=\"wp-image-26011\" title=\"Example of use of our rate equation model for studying dynamical behavior: Time evolution of the normalized powers of the two mid-IR pumps and the THz DFG under different bias currents above the second QC laser threshold. The blue solid, red dashed and purple dotted lines are for 10.5 \u00b5m, 8.9 \u00b5m and 60 \u00b5m respectively. The build-up time \uf044t of the THz radiation can be explicitly obtained from our rate equations model. A. Hamadou, J.-L. Thobel, S. Lamari, Optik 156 (2018) 596-605 https:\/\/doi.org\/10.1016\/j.ijleo.2017.11.126\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde07_rate_equation.png\" alt=\"Example of use of our rate equation model for studying dynamical behavior: Time evolution of the normalized powers of the two mid-IR pumps and the THz DFG under different bias currents above the second QC laser threshold. The blue solid, red dashed and purple dotted lines are for 10.5 \u00b5m, 8.9 \u00b5m and 60 \u00b5m respectively. The build-up time \uf044t of the THz radiation can be explicitly obtained from our rate equations model. A. Hamadou, J.-L. Thobel, S. Lamari, Optik 156 (2018) 596-605 https:\/\/doi.org\/10.1016\/j.ijleo.2017.11.126\" width=\"681\" height=\"655\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde07_rate_equation.png 820w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde07_rate_equation-300x288.png 300w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde07_rate_equation-768x738.png 768w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde07_rate_equation-36x36.png 36w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde07_rate_equation-705x677.png 705w\" sizes=\"auto, (max-width: 681px) 100vw, 681px\" \/><\/a><p id=\"caption-attachment-26011\" class=\"wp-caption-text\">Example of use of our rate equation model for studying dynamical behavior: Time evolution of the normalized powers of the two mid-IR pumps and the THz DFG under different bias currents above the second QC laser threshold. The blue solid, red dashed and purple dotted lines are for 10.5 \u00b5m, 8.9 \u00b5m and 60 \u00b5m respectively. The build-up time \uf044t of the THz radiation can be explicitly obtained from our rate equations model. A. Hamadou, J.-L. Thobel, S. Lamari, Optik 156 (2018) 596-605 https:\/\/doi.org\/10.1016\/j.ijleo.2017.11.126<\/p><\/div>\n<\/div><\/section>\n<div  class='av_promobox av-js09a3uo-95c6a6ac9fb24e9e4d24e2dec1561c1b avia-button-no'><div class='avia-promocontent'><p>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-w73dns-418873852a2a8329b913b5be35537f92\">\n.av_font_icon.av-w73dns-418873852a2a8329b913b5be35537f92 .av-icon-char{\nfont-size:25px;\nline-height:25px;\n}\n<\/style>\n<span  class='av_font_icon av-w73dns-418873852a2a8329b913b5be35537f92 avia_animate_when_visible av-icon-style- avia-icon-pos-left av-no-color avia-icon-animate'><span class='av-icon-char' aria-hidden='true' data-av_icon='\ue87f' data-av_iconfont='entypo-fontello' ><\/span><\/span><\/p>\n<p><strong>SILPHYDE Group : OTHER ACTIVITIES<\/strong><\/p>\n<ul>\n<li class=\"page_item page-item-25984\"><a href=\"https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/research\/simulation-of-nitride-based-electronic-devices\/\">Simulation of nitride-based electronic devices<\/a><\/li>\n<li class=\"page_item page-item-25984\"><a href=\"https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/research\/study-nanostructures\/\">Study of ferroelectric nanostructures<\/a><\/li>\n<li class=\"page_item page-item-25984\"><a href=\"https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/research\/monte-carlo-simulation\/\">Monte Carlo simulation of 2D materials for electronic and spintronic applications<\/a><\/li>\n<\/ul>\n<p>\n<\/div><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"parent":25981,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-25999","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/pages\/25999","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/types\/page"}],"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=25999"}],"version-history":[{"count":0,"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/pages\/25999\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/pages\/25981"}],"wp:attachment":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/media?parent=25999"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}