A baya a cikin 1887, masanin kimiyya dan Scotland William Thomson ya ba da shawarar tsarinsa na geometric na tsarin ether, wanda ake zaton matsakaici ne mai ko'ina, girgizar da ke bayyana mana kansu a matsayin igiyoyin lantarki, ciki har da haske. Duk da rashin gazawar ka'idar ether, ƙirar lissafi ta ci gaba da wanzuwa, kuma a cikin 1993, Denis Ware da Robert Phelan sun ba da shawarar ingantaccen tsarin tsarin da zai iya cika sararin samaniya gwargwadon yiwuwa. Tun daga wannan lokacin, wannan samfurin ya kasance mai ban sha'awa ga masu ilmin lissafi ko masu fasaha, amma bincike na baya-bayan nan ya nuna cewa zai iya zama tushen fasahar zamani da ke amfani da haske maimakon wutar lantarki. Menene Ware-Phelan kumfa, menene ya sa ya zama sabon abu, kuma ta yaya za a yi amfani da shi don kama haske? Za mu sami amsoshin waɗannan da sauran tambayoyi a cikin rahoton ƙungiyar bincike. Tafi
Tushen bincike
A zahiri shekaru ɗari da suka gabata a cikin al'ummar kimiyya akwai ka'ida mai ban sha'awa game da wani lamari na duk abin da ke kewaye. Wannan ka'idar an yi niyya ne don bayyana yanayin igiyoyin lantarki. An yi imani da cewa ether yana kewaye da komai kuma shine tushen waɗannan raƙuman ruwa. Binciken kimiyya wanda ya bi ka'idar ether ya lalata shi gaba daya.
William Thomson
Duk da haka, a cikin 1887, lokacin da ka'idar ether ta cika da ƙarfi da shahara, yawancin masana kimiyya sun bayyana ra'ayoyinsu game da yadda ainihin ether zai iya cika dukkan sararin samaniya. William Thomson, wanda kuma aka fi sani da Lord Kelvin, bai togiya ba. Ya kasance yana neman tsarin da zai cika sararin samaniya yadda ya kamata don kada a sami wuraren da ba kowa. Daga baya aka kira wannan binciken matsalar Kelvin.
Misali na farko: yi tunanin akwatin da ke dauke da gwangwani na cola. Tsakanin su, saboda siffar cylindrical, voids suna tasowa, watau. sarari mara amfani.
Thomson, baya ga imani cewa duniya ba ta wuce shekaru miliyan 40 ba, ya gabatar da wani sabon tsari na geometric, wanda Denis Ware da Robert Phelan suka inganta, sakamakon haka aka sanya musu suna.
Tsarin Ware-Phelan ya dogara ne akan saƙar zuma wanda ke cika sararin samaniya tare da polyhedra da ke rarrabuwar kawuna, ba tare da komai ba. Kambun zuma, wanda yawanci muna tunaninsa a matsayin hexagons godiya ga saƙar zuma, a zahiri yana zuwa da siffofi daban-daban. Akwai cubic, octahedral, tetrahedral, rhombic dodecahedral, da dai sauransu.
Tsarin Ware-Phelan
Abun da ba a sani ba game da saƙar zuma na Ware-Phelan shine cewa sun ƙunshi siffofi da abubuwa daban-daban na geometric. A ainihinsa, kumfa ce mai kyau na kumfa masu girman daidai.
Kakan wannan kumfa shine wanda Ubangiji Kelvin ya gabatar, wanda ya riga ya saba da mu. Duk da haka, sigarsa ta ƙunshi gajerun saƙar zuma masu siffar sukari. Tsarin Kelvin wani nau'in zumar zuma ne mai dunƙulewa da aka kafa ta wani tsattsauran octahedron, wanda ke da fuska huɗu, polyhedron mai cika sararin samaniya (tetradecahedron), mai fuskoki 6 murabba'i da fuskoki 8 hex.
An dauki wannan zaɓi don haɓaka sararin samaniya don kusan shekaru ɗari, har sai Ware da Phelan sun buɗe tsarin su a cikin 1993.
Pentagondodecahedron da decahedron
Babban bambanci tsakanin saƙar zuma na Ware-Phelan da wanda ya gabace shi shine amfani da nau'ikan nau'ikan abubuwa guda biyu, waɗanda, duk da haka, suna da girma iri ɗaya: pentagondodecahedron (dodecahedron tare da alamar tetrahedral) da XNUMXhedron mai jujjuyawa.
A cikin aikin da muke la'akari a yau, masana kimiyya daga Jami'ar Princeton sun yanke shawarar yin amfani da kumfa na Ware-Phelan a cikin hotuna. Da farko, ya wajaba a gano ko irin waɗannan kumfa suna da giɓi na bandeji na photonic (PBGs), waɗanda ke toshe yaduwar haske a duk kwatance kuma ga duk polarizations akan nau'ikan mitoci masu yawa.
A cikin binciken su, masana kimiyya sun nuna cewa hanyar sadarwa ta photonic ta 16,9D dangane da kumfa Ware-Phelan yana kaiwa ga PBG mai mahimmanci (XNUMX%) tare da babban digiri na isotropy*, wanda shine muhimmin dukiya don da'irori na photonic.
Isotropy* - makamantansu na zahiri a duk kwatance.
Kelvin kumfa da C15 kumfa kuma sun yi kyau a cikin sharuddan PBG, amma sun kasance ƙasa da tsarin Ware-Phelan a wannan batun.
An gudanar da irin wannan binciken a baya, amma sun mayar da hankali kan busassun kumfa mai nau'i biyu. Daga nan an gano cewa busassun busassun kumfa mai nau'i biyu na nuna PBG kawai don jujjuyawar wutar lantarki. Matsalar ita ce akwai polarizations guda biyu a cikin kumfa na XNUMXD.
Duk da yuwuwar matsalolin, 30D kumfa za a iya la'akari da wani abu mai ban sha'awa a fagen photonics, a cewar masu binciken. Akwai dalili akan haka: Dokokin Filato sun tabbatar da cewa gefuna sun zama na musamman na tetrahedral. Kuma wannan babban ƙari ne don cibiyoyin sadarwar photonic. Misali mai ban mamaki na wannan shine lu'u-lu'u tare da PBG na XNUMX%.
Kumfa yana da kayan tetrahedral na daidaitawar lu'u-lu'u na lu'u-lu'u, amma ya bambanta da cewa yana da gefuna masu lankwasa da ɗan gajeren tsayin da ba daidai ba. Ya rage kawai don gano yadda kuma har zuwa menene irin waɗannan bambance-bambancen ke shafar kaddarorin photonic.
Idan haƙarƙari na busassun kumfa na 17D ya yi kauri, yana yiwuwa a ƙirƙiri hanyoyin sadarwa na photonic (hotunan da ke ƙasa) waɗanda ke nuna PBGs masu faɗi na photonic har zuwa XNUMX%, kwatankwacin ko sama da waɗanda na yau da kullun na lu'ulu'u na photonic masu haɗa kansu.
Hoto #1: Hanyoyin sadarwar kumfa na Photonic da aka samu ta hanyar kauri gefuna na tsarin Ware-Phelan (hagu), tsarin Kelvin (tsakiya) da C15 kumfa (dama).
Don aiwatar da irin wannan samfurin a aikace, busassun busassun dole ne a fara yin crystallized sa'an nan kuma an rufe shi da kayan aikin dielectric. A zahiri, PBG na kumfa zai kasance ƙasa da na crystal crystal, amma wannan rashin amfani za a iya shawo kan da dama abũbuwan amfãni. Na farko, haɗin kai na kumfa na iya ba da damar samar da samfurori da sauri. Na biyu, photonic foam heterostructures, bisa binciken da ya gabata, na iya samun aikace-aikace da yawa.
Sakamakon bincike
Da farko, ya zama dole don nazarin busassun kumfa, wanda aka bayyana a matsayin ƙananan ƙananan yanki na yanki na interfacial tessellation* dangane da ƙayyadaddun ƙayyadaddun ƙira, ta yadda jigota ta ƙarshe ta bi dokokin Filato.
Tsayawa* - raba jirgin zuwa sassan sassan da ke rufe dukkan jirgin gaba daya ba tare da barin gibi ba.
Don gina kumfa na Ware-Phelan, Kelvin, da C15, masana kimiyya sun fara da ma'auni na Voronoi tesllations don lu'ulu'u na BCC, A15, ko C15, bi da bi.
zane na Voronoi
An zaɓi sigogi ta yadda duk sel masu rabuwa suna da girma iri ɗaya.
An yi nazarin hanyoyin sadarwar da aka kafa daga gefuna masu lanƙwasa na kumfa da kuma daga madaidaiciyar tessellation gefuna na magabata. Don kimanta topology na kowane nau'in kumfa, lissafin zobe*.
Kididdigar zobe (ƙididdigar zobe)*Binciken halayen topological kayan cibiyar sadarwa (ruwa, crystalline ko tsarin amorphous) galibi yana dogara ne akan ka'idar jadawali ta amfani da nodes don atom da shaidu don haɗin gwiwar interatomic. Rashin ko wanzuwar haɗin kai tsakanin nodes biyu an ƙaddara ta hanyar nazarin ayyukan cikakken radial rarraba tsarin. A cikin kayan cibiyar sadarwa, jerin nodes da hanyoyin haɗin gwiwa da aka haɗa a jere ba tare da zoba ana kiran hanya. Bayan wannan ma'anar, zobe hanya ce kawai rufaffiyar. Idan ka bincika takamaiman kumburin cibiyar sadarwa a hankali, za ka ga cewa wannan kumburin na iya shiga cikin zobba da yawa. Kowane ɗayan waɗannan zoben yana da girman nasa girma kuma ana iya rarraba shi bisa alakar da ke tsakanin nodes da hanyoyin haɗin da suka haɗa shi.
Hanyar farko don ayyana zobe ita ce ta Shirley W. King. Don nazarin haɗin SiO2 mai gilashi, ta bayyana zobe a matsayin hanya mafi guntu tsakanin maƙwabta biyu mafi kusa na kumburin da aka ba.
A cikin yanayin binciken da aka yi la'akari, an yi lissafin adadin mafi ƙarancin zobe a kowane gefe a cikin tantanin halitta naúrar.
Ɗayan tantanin halitta a cikin ƙirar Kelvin yana da murabba'i 2 da hexagons 4 a kowace vertex, amma TCP (tetrahedralally kusa-cushe) kumfa yana da fuska pentagonal da hexagonal kawai (matsakaicin: 5.2 da 0.78 a cikin kumfa Ware-Phelan; 5.3 da 0.71 a cikin kumfa C15). Voronoi tessellations A15 da C15 sune tsarin TCP tare da mafi girma da ƙarami adadin gefuna (f) ta 1 cell. Don haka, tsarin Ware-Phelan yana da mafi girman adadin fuskoki (f = 13 + 1/2), kuma C15 shine mafi ƙarancin adadin fuskoki (f = 13 + 1/3).
Bayan kammala shirye-shiryensu na ka'idar, masanan sun fara yin ƙirar hanyar sadarwa ta photonic bisa busassun haƙarƙarin kumfa, watau. kumfa-photon cibiyar sadarwa. An gano cewa a ƙimar PBG na 20% aikin tsarin yana haɓaka, amma a 15% kumfa Ware-Phelan ya zama mara ƙarfi. Don haka, masana kimiyya ba su yi la'akari da kumfa mai ruwa ba, inda iyakokin Plateau ke da sassan giciye. Maimakon haka, an mayar da hankali kan busassun kumfa, inda masana kimiyya za su iya ƙara kaurin haƙarƙari a hankali.
Bugu da kari, kowane gefe shi ne matsakaicin axis na spherocylinder (capsule), inda radius shine ma'aunin kunnawa.
Masu binciken sun tunatar da mu cewa irin waɗannan hanyoyin sadarwa na kumfa ba su da kumfa a zahiri, amma saboda sauƙi a cikin rahoton nasu za a kira su "kumfa" ko "cibiyar kumfa."
A lokacin simintin, an yi la'akari da siga ɛ (Dielectric bambanci) - rabo daga dielectric akai-akai na kayan da high da ƙananan rufi dabi'u. Ana ɗaukar bambancin dielectric tsakanin 13 da 1, wanda aka saba amfani da shi a cikin wallafe-wallafen a matsayin ma'auni lokacin kwatanta aikin zane-zane na kayan hoto daban-daban.
Ga kowane cibiyar sadarwa, radius na gefuna (spherocylinders) an inganta shi don matsakaicin rabo na ratar band da tsakiyarsa: ∆ω/ωm, ku ∆ω shine fadin mitar band, kuma ωm - mita a cikin yankin.
Hoto #2: Tsarin zonal na Photonic na Ware-Phelan kumfa (ja), kumfa Kelvin (blue), da C15 kumfa (kore).
Bayan haka, an auna girman PBG kuma an gano su: 7.7% don kumfa Kelvin, 13.0% don kumfa C15 da 16.9% don kumfa Ware-Phelan. Rage girman yanki yana ƙara girman PBG da 0.7%, 0.3 ko 1.3%.
Kamar yadda ya fito fili daga bincike, hanyoyin sadarwa na TCP suna da girman PBG da yawa fiye da hanyoyin sadarwar Kelvin. Daga cikin hanyoyin sadarwa na TCP guda biyu, kumfa Ware-Phelan yana da girman bandgap mafi girma, wanda ke yiwuwa saboda ƙaramin canji a tsayin hanyar haɗin gwiwa. Masana kimiyya sun yi imanin cewa bambance-bambance a cikin tsayin haɗin gwiwa na iya zama babban dalilin da ya sa a cikin tsarin su, watau. a cikin kumfa Ware-Phelan, PBG bai kai na lu'u-lu'u (31.6%) ko a cikin tsarin Laves (28.3%) ba.
Wani muhimmin al'amari mai mahimmanci a cikin photonics shine isotropy na PBG, wanda ke ba da damar ƙirƙirar jagororin raƙuman ruwa na siffar sabani. Photonic quasicrystals, kazalika da amorphous photonic cibiyoyin sadarwa, sun fi isotropic fiye da na gargajiya photonic lu'ulu'u.
Tsarin kumfa-photonic da ke ƙarƙashin binciken kuma yana da babban matakin isotropy. Da ke ƙasa akwai dabara don ƙayyade ƙididdigar anisotropy (watau matakin bambanci a cikin kaddarorin wani yanayi) PBG (А):
A: = (√Var[ωHDB]+Var[ωLAB]) / ωm
An gano kumfa C15 yana da mafi ƙarancin anisotropy (1.0%), sannan kumfa Weir-Phelan (1.2%) ya biyo baya. Saboda haka, waɗannan sifofi suna da isotropic sosai.
Amma tsarin Kelvin yana nuna ƙimar anisotropy na 3.5%, wanda ke kusa da na tsarin Laves (3.4%) da lu'u-lu'u (4.2%). Duk da haka, ko da waɗannan alamun ba su kasance mafi muni ba, saboda akwai kuma tsarin tsarin cubic mai sauƙi tare da anisotropy coefficient na 8.8% da hexagonal lu'u-lu'u cibiyoyin sadarwa tare da 9.7%.
A aikace, lokacin da ya zama dole don cimma matsakaicin ƙimar PBG, wani lokaci ya zama dole don canza wasu sigogi na jiki na tsarin. A wannan yanayin, wannan siga shine radius na spherocylinders. Masanan sun gudanar da lissafin lissafi inda suka tantance alakar da ke tsakanin gap din band din photonic da fadinsa a matsayin aiki. ɛ. Ga kowane ƙimar da aka samu, an inganta radiyon don haɓaka ∆ω/ ωm.
Hoton No. 3: kwatanta ∆ω / ωm na cibiyoyin sadarwar kumfa da aka yi nazari (C15, Kelvin, Weir-Phelan) da sauran tsarin (lu'u-lu'u, lu'u-lu'u hexagonal, Laves, SC - cubic na yau da kullum).
Kumfa Weir-Phelan yana kula da girman PBG masu karɓa na 8% har zuwa bambancin dielectric ɛ≈9, kuma an ƙara radius don cimma matsakaicin ƙimar PBG na 15%. PBGs suna ɓacewa lokacin ɛ <6.5. Kamar yadda aka zata, tsarin lu'u-lu'u yana da PBG mafi girma a cikin duk tsarin da aka yi nazari.
Don ƙarin cikakken sani tare da nuances na binciken, Ina ba da shawarar dubawa и masa.
Epilogue
Babban dalili don gudanar da wannan binciken shine sha'awar amsa tambayar ko cibiyoyin sadarwar kumfa na iya nuna cikakken PBG. Mayar da gefuna na busassun tsarin kumfa zuwa hanyoyin sadarwa na photonic ya nuna cewa za su iya.
A halin yanzu, kumfa ba tsari ne na musamman da aka yi nazari ba. Tabbas, akwai karatun da ke ba da sakamako mai kyau dangane da hanyoyin sadarwar amorphous, amma an gudanar da su akan ƙananan abubuwa. Yadda tsarin zai kasance yayin da girmansa ya karu har yanzu ba a sani ba.
A cewar marubutan binciken, aikinsu ya buɗe dama da dama don ƙirƙira a gaba. Kumfa yana da yawa a cikin yanayi kuma yana da sauƙin ƙirƙira, yana sa wannan tsarin ya zama mai ban sha'awa don aikace-aikace masu amfani.
Masana kimiyya suna kiran Intanet ɗaya daga cikin mafi girman aikace-aikacen binciken su. Kamar yadda masu binciken da kansu suka ce, isar da bayanai a kan fiber na gani ba sabon abu ba ne, amma har yanzu haske yana canza zuwa wutar lantarki a inda yake. Kayan bandgap na Photonic na iya ba da haske sosai daidai fiye da igiyoyin fiber na gani na al'ada kuma suna iya aiki azaman transistor na gani waɗanda ke yin lissafin ta amfani da haske.
Duk yadda tsare-tsaren suka yi girma, akwai sauran aiki da yawa a gabansu. Duk da haka, ba saɓanin gudanar da bincike ko sarƙaƙƙiyar aiwatar da gwaje-gwajen ba za su iya shawo kan sha'awar masana kimiyya da sha'awarsu ta inganta duniyar fasaha ba.
Godiya da kallon, tsaya sha'awar kuma sami kyakkyawan karshen mako kowa! 🙂
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