[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-283271-105":53,"doc-detail-283271-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","controlling-electromagnetic-fields","Controlling Electromagnetic Fields","","Using metamaterial design freedom, the work shows how electromagnetic fields can be redirected at will through consistent displacement of conserved quantities: electric displacement, magnetic induction, and the Poynting vector. A cloaking example demonstrates excluding electromagnetic fields from a prohibited spatial region. The approach is connected to exact manipulations of Maxwell’s equations, not limited to ray approximations, and applies across frequencies and length scales. It begins with a target field topology and implements a coordinate-transformation viewpoint.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/controlling-electromagnetic-fields/283271/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/controlling-electromagnetic-fields/283271.png","ImageObject",442,249,{"name":88,"@type":89},"Đào","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-11-04","2026-09-16",true,{"@type":98,"interactionType":99,"userInteractionCount":8},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What conserved electromagnetic quantities are displaced in a consistent manner?","Question",{"text":108,"@type":109},"The electric displacement field, the magnetic induction field, and the Poynting vector are all displaced consistently according to the proposed design strategy.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How does the cloak example relate to electromagnetic field control?",{"text":113,"@type":109},"The illustration shows cloaking of a prohibited volume of space so that all electromagnetic fields are completely excluded from that region.",{"name":115,"@type":106,"acceptedAnswer":116},"Why are the conclusions not limited to ray approximations?",{"text":117,"@type":109},"The results follow from exact manipulations of Maxwell’s equations, which in principle encompass all electromagnetic phenomena on all length scales.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},283271,1791740738,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":8,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":76,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":9},1374402968488,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","REPORTS  \nControlling Electromagnetic Fields  \nJ. B. Pendry1, D. Schurig2 and D. R. Smith2  \n1 Department of Physics, The Blackett Laboratory, Imperial College London, London SW7 2AZ, UK, 2 Department of Electrical and Computer Engineering, Duke University, Box 90291, Durham, NC 27708 , USA.  \nUsing the freedom of design which metamaterials provide, we show how electromagnetic fields can be redirected at will and propose a design strategy. The conserved fields: electric displacement field, ! , magnetic induction field, ! , and Poynting vector, ! , are all displaced in a consistent manner. A simple illustration is given of the cloaking of a proscribed volume of space to exclude completely all electromagnetic fields. Our work has relevance to exotic lens design and to the cloaking of objects from electromagnetic fields.  \nTo exploit electromagnetism we use materials to control and direct the fields: a glass lens in a camera to produce an image, a metal cage to screen sensitive equipment,‘black bodies’ of various forms to prevent unwanted reflections. With homogeneous materials, optical design is largely a matter of choosing the interface between two materials. For example, the lens of a camera is optimized by altering its shape so as to minimize geometrical aberrations. Electromagnetically inhomogeneous  \nmaterials offer a different approach to control light; the introduction of specific gradients in the refractive index of a material can be used to form lenses and other optical elements, although the types and ranges of such gradients tend to be limited.  \nA new class of electromagnetic materials (1,2) is currently under study: metamaterials, which owe their properties to subwavelength details of structure rather than to their chemical composition, can be designed to have properties difficult or impossible to find in nature. In this report we show how the design flexibility of metamaterials can be  \nexploited to achieve new and remarkable electromagnetic devices. The message of this paper is that metamaterials enable a new paradigm for the design of electromagnetic structures at all frequencies from optical down to DC.  \nProgress in the design of metamaterials has been impressive. A negative index of refraction (3) is an example of a material property that does not exist in nature, but has been enabled using metamaterial concepts. As a result, negative refraction has been much studied in recent years (4) and realizations have been reported at both GHz and optical frequencies (5-8) . Novel magnetic properties have also been reported over a wide spectrum of frequencies. Further information on the design and construction of metamaterials may be found in (9-13) . Infact, it is now conceivable that a material can be constructed whose permittivity and permeability values may be designed to vary independently and arbitrarily throughout a material, taking positive or negative values as desired  \nIf we take this unprecedented control over the material properties and form inhomogeneous composites, we enable anew and powerful form of electromagnetic design. Asan example of this design methodology, we show how the conserved quantities of  \nelectromagnetism: the electric displacement field,  \nFig. 1 Left: a field line in free space with the background Cartesian coordinate grid shown. Right: the distorted field line with the background coordinates distorted in the same fashion. The field in question may be the electric displacement or magnetic induction fields !! \" , or the Poynting vector, ! , which is equivalent to a ray of light.  \n! , the magnetic field intensity, ! , and the Poynting vector, ! , can all be directed at will, given access to the appropriate metamaterials. In particular these fields can be focused  \nas required or made to avoid objects and flow around them like a fluid, returning undisturbed to their original trajectories. These conclusions follow from exact manipulations of Maxwell’s equations and are not confined to a ra","cbCaigURAxRIMvjq","https://ap.wps.com/l/cbCaigURAxRIMvjq","pdf",1724911,"English","# Controlling Electromagnetic Fields\n## Metamaterial design strategy\n## Examples: cloaking and field redirection\n## Coordinate transformations and Maxwell’s equations","[{\"question\":\"What conserved electromagnetic quantities are displaced in a consistent manner?\",\"answer\":\"The electric displacement field, the magnetic induction field, and the Poynting vector are all displaced consistently according to the proposed design strategy.\"},{\"question\":\"How does the cloak example relate to electromagnetic field control?\",\"answer\":\"The illustration shows cloaking of a prohibited volume of space so that all electromagnetic fields are completely excluded from that region.\"},{\"question\":\"Why are the conclusions not limited to ray approximations?\",\"answer\":\"The results follow from exact manipulations of Maxwell’s equations, which in principle encompass all electromagnetic phenomena on all length scales.\"}]","Controlling Electromagnetic Fields | PDF",1789595599]