[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-157013-105":59,"doc-detail-157013-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","zero-index-bound-states-in-the-continuum-physrevlett-121-263901","Zero-Index Bound States in the Continuum - PhysRevLett 121 263901","","Zero-effective-refractive-index metamaterials are attractive for communications and nonlinear optics, but prior all-dielectric photonic-crystal implementations suffer strong intrinsic radiative losses because zero-index modes fall into the light cone and couple to external plane waves. This work proposes a photonic crystal slab whose zero-index modes are simultaneously symmetry-protected bound states in the continuum. The symmetry protection removes the associated radiation loss, enabling practical, scalable integration of zero-index materials into photonic devices.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/zero-index-bound-states-in-the-continuum-physrevlett-121-263901/157013/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/zero-index-bound-states-in-the-continuum-physrevlett-121-263901/157013.png","ImageObject",300,407,{"name":92,"@type":93},"Clementine","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-08-29",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"Why do conventional zero-index photonic-crystal slab modes radiate strongly?","Question",{"text":113,"@type":114},"In the slab geometry the Γ-point modes lie in the surrounding medium’s radiation continuum, so modes in the relevant symmetry representation necessarily couple to external plane waves, producing intrinsic radiative loss.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is the key idea behind the proposed PhC slab design?",{"text":118,"@type":114},"The design uses effectively zero-index modes that are also symmetry-protected bound states in the continuum, preventing coupling to radiation channels and thus suppressing radiation loss.",{"name":120,"@type":111,"acceptedAnswer":121},"How is an effective zero-index response related to the band structure near the Γ point?",{"text":122,"@type":114},"By introducing an accidental degeneracy at the Γ point between symmetry-related bands, the k·p description yields Dirac-like linear dispersion plus a flat band, which corresponds to the same band-structure characteristics as a zero-index material.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},157013,1787971192,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144,"preview_page_count":4},1374391974564,"https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002","Zero-Index Bound States in the Continuum  \nMomchil Minkov,* Ian A. D. Williamson, Meng Xiao, and Shanhui Fan†  \nDepartment of Electrical Engineering, and Ginzton Laboratory, Stanford University, Stanford, California 94305, USA  \n (Received 24 August 2018; published 27 December 2018)  \nMetamaterials with an effective zero refractive index associated with their electromagnetic response are sought for a number of applications in communications and nonlinear optics. A promising way that this can be achieved in all-dielectric photonic crystals is through the design of a Dirac cone at zero Bloch wavevector in the photonic band structure. In the optical frequency range, the natural way to implement this design is through the use of a photonic crystal slab. In the existing implementation, however, the zero-index photonic modes also radiate strongly into the environment due to intrinsic symmetry properties. This has resulted in large losses in recent experimental realizations of this zero-index paradigm. Here, we propose aphotonic crystal slab with zero-index modes which are also symmetry-protected bound states in the continuum. Our approach thus eliminates the associated radiation loss. This could enable, for the first time, large-scale integration of zero-index materials in photonic devices.  \nDOI: 10.1103/PhysRevLett.121.263901  \nRecently, there has been a lot of interest in photonic metamaterials with a zero (effective) refractive index [1–4] . In such materials, all fields oscillate in spatial unison regardless of the shape and size of the sample, and the wavelength oflight appears tobe effectively infinite. This has been demonstrated to lead to a variety of interesting effects and possible applications, including tailoring the radiation phase[2], developing enhanced and directional light emitters [5–7], enhanced and directional transmission through bends, disorder, and subwavelength channels [8–12], cloaking [13], and enhanced optical nonlinearities [14–16] .  \nIn the visible or near-infrared wavelength range, zeroindex response can be achieved starting from the plasmonic effects from free carriers [4], which, however, also come with a substantial material loss. Alternatively, Ref. [17] has shown that a zero-index effect can be achieved in a twodimensional all-dielectric photonic crystal, whose band structure is designed to exhibit a Dirac-like dispersion in the vicinity of the Γ point at the Brillouin zone center. However, while a purely two-dimensional implementation of the idea of Ref. [17] has intrinsically zero loss, in the optical frequency the most natural way to implement the same concept is through the use of a photonic crystal slab structure consisting of a patterned dielectric slab surrounded by low-dielectric-constant materials. In this case, the Γ point lies in the light cone of the surrounding medium, which leads to substantial radiative losses. For example, the implementation of this concept in Ref. [18] reported a very large propagation loss of the order of 1 dB=μm. In Ref. [19], gold mirrors on each side of the slab were introduced to avoid that radiation, but this resulted in absorption losses of comparable magnitude. Finally, it has also been proposed that this issue could be mitigated through a dielectric reflector on one side of the slab [20],  \nbut this significantly increases the complexity and footprint of the structure.  \nIn this Letter, we overcome the problem of radiative losses by designing a PhC slab with effectively zero-index modes, which are also symmetry-protected bound states in the continuum (BIC) [21] . Consider a photonic crystal structure with two-dimensional periodicity, with a pointgroup symmetry that supports at least one two-dimensional irreducible representation. At the Γ point, suppose the crystal supports a singly degenerate state jsi at a frequency ω 1 , and a pair of doubly degenerate states jpxi and jpyi belonging to the two-dimensional irreducible representation at a frequency ω2. ","cbCaifgUEafBsDsF","https://ap.wps.com/l/cbCaifgUEafBsDsF","pdf",1286237,"English","# Introduction\n## Zero effective refractive index and application motivation\n## Limitations of photonic crystal slabs: radiation losses\n# Theory and design principle\n## Accidental degeneracy at the Γ point\n## Effective Hamiltonian and Dirac-like dispersion with a flat band\n## Symmetry protection and bound states in the continuum\n# Proposed approach and expected impact\n## Eliminating radiative loss for zero-index modes\n## Enabling large-scale integration in photonic devices","[{\"question\":\"Why do conventional zero-index photonic-crystal slab modes radiate strongly?\",\"answer\":\"In the slab geometry the Γ-point modes lie in the surrounding medium’s radiation continuum, so modes in the relevant symmetry representation necessarily couple to external plane waves, producing intrinsic radiative loss.\"},{\"question\":\"What is the key idea behind the proposed PhC slab design?\",\"answer\":\"The design uses effectively zero-index modes that are also symmetry-protected bound states in the continuum, preventing coupling to radiation channels and thus suppressing radiation loss.\"},{\"question\":\"How is an effective zero-index response related to the band structure near the Γ point?\",\"answer\":\"By introducing an accidental degeneracy at the Γ point between symmetry-related bands, the k·p description yields Dirac-like linear dispersion plus a flat band, which corresponds to the same band-structure characteristics as a zero-index material.\"}]","Zero-Index Bound States in the Continuum - PhysRevLett 121 263901 | PDF",13]