Emva phayaa ngo-1887, ingcali yefiziksi yaseSkotlani uWilliam Thomson yacebisa imodeli yakhe yejiyometri yesakhiwo se-ether, ekucingelwa ukuba sisixhobo esijikeleza yonke indawo, ukungcangcazela okuzibonakalisa kuthi njengamaza ombane, kuquka nokukhanya. Nangona ukungaphumeleli ngokupheleleyo kwe-ether theory, imodeli yejometri yaqhubeka ikhona, kwaye kwi-1993, uDenis Ware noRobert Phelan bacebise imodeli engaphezulu yesakhiwo esikwazi ukuzalisa indawo kangangoko kunokwenzeka. Ukususela ngoko, le modeli inomdla kakhulu kwiimathematika okanye amagcisa, kodwa uphando olutshanje luye lwabonisa ukuba lunokwenza isiseko sobuchwepheshe bexesha elizayo obusebenzisa ukukhanya endaweni yombane. Yintoni i-Ware-Phelan igwebu, yintoni eyenza ingaqhelekanga, kwaye ingasetyenziselwa njani ukubamba ukukhanya? Siza kufumana iimpendulo kule mibuzo neminye kwingxelo yeqela lophando. Hamba.
Isiseko sophando
Ngokwenyani ikhulu leminyaka eyadlulayo kuluntu lwenzululwazi kwakukho ithiyori enomdla kakhulu malunga nomcimbi othile wayo yonke into ejikelezileyo. Le thiyori ijolise ekuchazeni ubunjani bamaza ombane. Kwakukholelwa ukuba i-ether ijikeleze yonke into kwaye ingumthombo wala maza. Izinto ezifunyaniswe yinzululwazi ezalandela ingcamango ye-ether zayitshabalalisa ngokupheleleyo.
UWilliam Thomson
Noko ke, ngowe-1887, xa ingcamango ye<em>ether yayizele ukomelela nokuthandwa, izazinzulu ezininzi zavakalisa iimbono zazo ngokuphathelele indlela kanye kanye i<em>ether enokuzalisa ngayo yonke indawo. UWilliam Thomson, nokwabizwa ngokuba nguLord Kelvin, wayenjalo. Wayekhangela isakhiwo esasiza kugcwalisa ngokupheleleyo indawo ukuze kungabikho iindawo ezingenanto. Olu phendlo kamva lwabizwa ngokuba yingxaki kaKelvin.
Umzekelo wamandulo: khawucinge ngebhokisi equlathe iinkonkxa zecola. Phakathi kwabo, ngenxa yobume be-cylindrical, i-voids ivela, i.e. indawo engasetyenziswanga.
UThomson, ngaphezu kokukholelwa ukuba uMhlaba wawungekho ngaphezu kwe-40 yezigidi zeminyaka ubudala, ucebise isakhiwo esitsha sejometri, esaphuculwa nguDenis Ware noRobert Phelan, ngenxa yoko kwathiwa igama labo.
Ulwakhiwo lweWare-Phelan lusekwe kwinqatha lobusi elizalisa indawo ngepolyhedra edibeneyo, engashiyi ndawo ingenanto. Ikhekheba lobusi, esidla ngokucinga ngalo njengehexagons enkosi kwinqatha lobusi, liza ngokweemilo ezininzi ezahlukeneyo. Kukho cubic, octahedral, tetrahedral, rhombic dodecahedral, njl.
Ubume beWare-Phelan
Into engaqhelekanga malunga nama-honeycombs e-Ware-Phelan kukuba aqukethe iimilo zejometri ezahlukeneyo kunye nezinto. Embindini wayo, igwebu elifanelekileyo lamaqamu alinganayo.
Isinyanya sobugwebu ngulo wacetywa nguLord Kelvin, ebesele eqhelene nathi. Noko ke, inguqulelo yakhe yayiquka iikyubhiki zobusi ezimfutshane. Isakhiwo se-Kelvin yayiyi-honeycomb ye-convex ye-honeycomb eyenziwe yi-octahedron ene-truncated, eyi-polyhedron enobuso obune, egcwalisa indawo (i-tetradecahedron), enobuso obu-6 kunye nobuso obu-8 be-hex.
Olu khetho lokwandisa ukuzaliswa kwendawo lwaluthathwa njengento efanelekileyo malunga nekhulu leminyaka, de i-Ware nePhelan bavula isakhiwo sabo kwi-1993.
iPentagondodekahedron kunye nedekahedron
Umahluko omkhulu phakathi kwe-honeycomb ye-Ware-Phelan kunye ne-predecessor yayo kukusetyenziswa kweentlobo ezimbini zezinto ezidibeneyo, nangona kunjalo, ezinomthamo ofanayo: i-pentagondodecahedron (i-dodecahedron ene-tetrahedral symmetry) kunye ne-14hedron ene-symmetry ejikelezayo.
Kumsebenzi esiwuqwalaselayo namhlanje, izazinzulu ezivela kwiYunivesithi yasePrinceton zagqiba ekubeni zisebenzise i-Ware-Phelan foam kwi-photonics. Okokuqala, kwakuyimfuneko ukufumanisa ukuba amagwebu anjalo anezikhewu ze-photonic band (PBGs), ezithintela ukusasazwa kokukhanya kuzo zonke iinkalo kunye nazo zonke iipolarizations kuluhlu olubanzi lweefrikhwensi.
Kuphononongo lwabo, izazinzulu zibonise ukuba inethiwekhi ye-photonic ye-16,9D esekwe kwi-Ware-Phelan foam ikhokelela kwi-PBG ebalulekileyo (XNUMX%) enezinga eliphezulu isotropy*, eyipropati ebalulekileyo kwiisekethe ze-photonic.
I-Isotropy* - iipropati ezifanayo kuwo onke amacala.
I-Kelvin foam kunye ne-C15 foam nayo yasebenza kakuhle ngokwemiqathango ye-PBG, kodwa yayingaphantsi kwesakhiwo se-Ware-Phelan kulo mba.
Izifundo ezifanayo ziye zaqhutywa ngaphambili, kodwa zigxile kwi-foam eyomileyo enamacala amabini. Kwaye kwafunyaniswa ukuba i-amorphous eyomileyo ye-amorphous foam ibonisa i-PBG kuphela kwi-polarization yombane enqamlezileyo. Ingxaki kukuba kukho iipolarizations ezimbini kwi-3D foam.
Ngaphandle kobunzima obunokwenzeka, i-foam ye-30D inokuthathwa njengento ethembisayo kwintsimi yeefotoni, ngokutsho kwabaphandi. Kukho isizathu soku: Imithetho ye-Plateau iqinisekisa ukuba imiphetho yenze iingqimba ze-tetrahedral kuphela. Kwaye oku kukudibanisa okukhulu kwiinethiwekhi zefotonic. Umzekelo obalaseleyo wale diamond enePBG ye-XNUMX%.
I-foam inepropathi ye-tetrahedral ye-diamond lettice coordinates, kodwa iyahluka ngokuba ine-canges egobileyo kunye nobude bebhondi obungalinganiyo kancinane. Kuhlala kuphela ukufumanisa ukuba njani kwaye kangakanani umahluko onjalo uchaphazela iipropathi zefotonic.
Ukuba iimbambo ze-17D i-foam eyomileyo zenziwe zityebile, kunokwenzeka ukwenza uthungelwano lwefotonic (imifanekiso engezantsi) ebonisa i-PBG ye-photonic echazweyo ukuya kwi-XNUMX%, xa ithelekiswa okanye iphakamileyo kunemizekelo eqhelekileyo yeekristale zefotoni ezidibeneyo.
Umfanekiso #1: Uthungelwano lweFotoni lwefoam olufunyenwe ngokujiya imiphetho yesakhiwo seWare-Phelan (ngasekhohlo), isakhiwo seKelvin (embindini) kunye neC15 foam (ekunene).
Ukuphumeza imodeli enjalo ekusebenzeni, i-foam eyomileyo kufuneka iqale i-crystallized kwaye ifakwe nge-dielectric material. Ngokwemvelo, i-PBG ye-foam iya kuba ngaphantsi kwe-crystal ye-photonic, kodwa oku kungalunganga kunokoyiswa ngenani leenzuzo. Okokuqala, ukulungelelaniswa kwe-foam kunokuvumela ukuveliswa ngokukhawuleza kweesampuli ezinkulu. Okwesibini, i-photonic foam heterostructures, esekelwe kuphando lwangaphambili, ingaba noluhlu olubanzi lwezicelo.
Iziphumo zophando
Okokuqala, kwakuyimfuneko ukuba kufundwe i-foam eyomileyo, echazwa njenge-minima yendawo yommandla we-interfacial itessellation* ngokuxhomekeke kwimithintelo yevolumu, ukuze ijometri yokugqibela ithobele imithetho yePlateau.
Tessellation* - ukwahlula inqwelomoya ibe ngamacandelo aquka ngokupheleleyo inqwelomoya ngaphandle kokushiya izithuba.
Ukwakha i-Ware-Phelan, i-Kelvin, kunye ne-C15 foams, izazinzulu zaqala ngee-tessellations ze-Voronoi ezinobunzima be-BCC, i-A15, okanye i-C15 crystals, ngokulandelanayo.
Umzobo weVoronoi
Iiparamitha zikhethwe ngendlela yokuba zonke iiseli zokwahlula zibe nomthamo ofanayo.
Uthungelwano olwenziwe ukusuka kwincam egobileyo yamagwebu kwaye ukusuka kwincam ye-tessellation ethe tye yezandulela zazo zaphononongwa. Ukuvavanya i-topology yazo zonke iintlobo zogwebu, izibalo zeringi*.
Iinkcukacha-manani zeringi (izibalo zeringi)*Uhlalutyo lweempawu ze-topological zezixhobo zenethiwekhi (i-liquids, i-crystalline okanye i-amorphous systems) ihlala isekelwe kwi-theory yegrafu isebenzisa ii-nodes ze-athomu kunye neebhondi zokudibanisa i-interatomic. Ukungabikho okanye ubukho bonxibelelwano phakathi kweenodi ezimbini kumiselwa ngokuhlalutya imisebenzi yokusasazwa kweradial epheleleyo kunye nenxalenye yenkqubo. Kwimathiriyeli yenethiwekhi, ukulandelelana kweenodi kunye neekhonkco eziqhagamshelwe kuthotho ngaphandle kokudibana kubizwa ngokuba ngumendo. Ukulandela le ngcaciso, iringi yindlela nje evaliweyo. Ukuba uphonononga ngononophelo i-node ethile yenethiwekhi, unokubona ukuba le node inokuthatha inxaxheba kumakhonkco amaninzi. Nganye kula makhonkco ibonakaliswe ngemilinganiselo yayo kwaye inokuhlelwa ngokusekelwe kubudlelwane phakathi kweenodi kunye neekhonkco ezizenzayo.
Indlela yokuqala yokuchaza umsesane yanikwa nguShirley W. King. Ukufunda uqhakamshelwano lweglasi ye-SiO2, uchaza umsesane njengeyona ndlela imfutshane phakathi kwabamelwane ababini abakufutshane benodi enikiweyo.
Kwimeko yophononongo oluqwalaselwayo, izibalo zenziwe ngenani lezangqa ezimfutshane kwi-vertex kwiyunithi yeseli.
Iseli enye kwimodeli ye-Kelvin inezikwere ezi-2 kunye ne-4 i-hexagons kwi-vertex, kodwa i-TCP (i-tetrahedral i-close-packed) i-foam inobuso be-pentagonal kunye ne-hexagonal kuphela (i-avareji: 5.2 kunye ne-0.78 kwi-Ware-Phelan foam; 5.3 kunye ne-0.71 kwi-C15 foam). I-Voronoi tessellations i-A15 kunye ne-C15 zizakhiwo ze-TCP ezinenani elikhulu nelincinci leedges (f) ngeseli enye. Ngoko ke, ulwakhiwo lweWare-Phelan lunelona nani likhulu lobuso (f = 13 + 1/2), kwaye i-C15 lelona nani lincinci lobuso (f = 13 + 1/3).
Emva kokugqiba ukulungiswa kwethiyori, izazinzulu zaqala ukwenza imodeli yenethiwekhi ye-photonic esekelwe kwiimbambo ze-foam ezomileyo, i.e. inethiwekhi ye-foam-photon. Kwafunyaniswa ukuba kwixabiso le-PBG le-20% yokusebenza kwenkqubo yandiswa, kodwa kwi-15% i-foam ye-Ware-Phelan iba yinto engazinzanga. Ngesi sizathu, izazinzulu azikhange ziqwalasele igwebu elimanzi, apho imida yePlateau inamacandelwana e-tricuspid. Endaweni yoko, kugxininiswa kwizakhiwo ezinogwebu ezomileyo, apho izazinzulu zinokunyusa ngokuthe ngcembe ubukhulu beembambo.
Ukongezelela, i-edge nganye yi-axis medial ye-spherocylinder (i-capsule), apho i-radius iparameter yokulungisa.
Abaphandi bayasikhumbuza ukuba uthungelwano lwe-foam alukho ugwebu ngendlela yokoqobo, kodwa ngenxa yokulula kwingxelo yabo baya kubizwa ngokuba "yi-foam" okanye "inethiwekhi ye-foam."
Ngexesha lokulinganisa, iparameter ithathelwe ingqalelo ɛ (ukungafani kwe-dielectric) - umlinganiselo we-dielectric constants of materials kunye namaxabiso aphezulu kunye ne-insulation aphantsi. Umahluko we-dielectric uthathwa ukuba uphakathi kwe-13 kunye ne-1, esetyenziswa ngokuqhelekileyo kuncwadi njengomgangatho xa kuthelekiswa nokusebenza kwezinto ezahlukeneyo zoyilo lwe-photonic.
Kuthungelwano ngalunye, iradiyasi yemiphetho (i-spherocylinders) ilungiselelwe umlinganiselo ophezulu wesithuba sebhendi kunye nombindi wayo: ∆ω/ωm, apho ∆ω bububanzi band frequency, kwaye ωm - ukuphindaphinda ngaphakathi kwendawo.
Umfanekiso #2: Isakhiwo sezonal ye-Photonic ye-Ware-Phelan foam (obomvu), i-Kelvin foam (eluhlaza okwesibhakabhaka), kunye ne-C15 foam (eluhlaza).
Okulandelayo, ubukhulu bePBG bulinganiswe kwaye bufunyenwe: 7.7% ye-Kelvin foam, i-13.0% ye-C15 foam kunye ne-16.9% ye-Ware-Phelan foam. Ukunciphisa indawo kwandisa ubukhulu bePBG nge-0.7%, 0.3 okanye 1.3%.
Njengoko kwacaca kuhlalutyo, iinethiwekhi ze-TCP zineesayizi ezinkulu ze-PBG kunenethiwekhi ze-Kelvin. Kwiinethiwekhi ezimbini ze-TCP, i-Ware-Phelan i-foam inobukhulu obukhulu be-bandgap, ekucingelwa ukuba ibangelwa utshintsho oluncinci kubude bekhonkco. Iingcali zenzululwazi zikholelwa ukuba ukungafani kobude bobhondi kusenokuba sesona sizathu siphambili sokuba kutheni kwinkqubo yabo, oko kukuthi. kwi-Ware-Phelan foam, i-PBG ingaphantsi kwe-diamond (31.6%) okanye kwi-Laves system (28.3%).
Umba obaluleke ngokulinganayo kwifotonics yi-isotropy ye-PBG, evumela ukudalwa kwamaza e-waveguides e-arbitral shape. I-Photonic quasicrystals, kunye ne-amorphous photonic networks, i-isotropic ngakumbi kune-classical photonic crystals.
Ulwakhiwo lwe-foam-photonic phantsi kophononongo lukwanalo nenqanaba eliphezulu le-isotropy. Ngezantsi ifomyula yokumisela i-anisotropy coefficient (oko kukuthi, iqondo lomahluko kwiipropati zendawo ethile) PBG (А):
A: = (√Var[ωHDB]+Var[ωLAB]) / ωm
I-foam ye-C15 ifunyenwe ine-anisotropy ephantsi kakhulu (1.0%), ilandelwa yi-Weir-Phelan foam (1.2%). Ngenxa yoko, ezi zakhiwo ziphezulu isotropic.
Kodwa i-Kelvin structure ibonisa i-anisotropy coefficient ye-3.5%, esondele kakhulu kwi-Laves system (3.4%) kunye nedayimane (4.2%). Nangona kunjalo, nalezi zikhombisi azikho zimbi kakhulu, kuba kukho neenkqubo ezilula ze-cubic ezine-coefficient ye-anisotropy ye-8.8% kunye ne-diamond networks ene-hexagonal ene-9.7%.
Ngokwenza, xa kuyimfuneko ukufezekisa ixabiso eliphezulu le-PBG, ngamanye amaxesha kuyimfuneko ukutshintsha iiparitha ezithile zomzimba zesakhiwo. Kule meko, le parameter yiradius ye-spherocylinders. Izazinzulu zenze izibalo zemathematika apho zagqiba khona ubudlelwane phakathi kwe-gap ye-photonic band kunye nobubanzi bayo njengomsebenzi. ɛ. Ngexabiso ngalinye elifunyenweyo, iradiyasi yalungiswa ukuze yandiswe ∆ω/ωm.
Umfanekiso we-3: ukuthelekiswa kwe-∆ω / ωm yothungelwano lwe-foam olufundiweyo (i-C15, i-Kelvin, i-Weir-Phelan) kunye nezinye izakhiwo (i-diamond, i-diamond ene-hexagonal, i-Laves, i-SC - i-cubic eqhelekileyo).
I-Weir-Phelan i-foam igcina ubungakanani bePBG obamkelekileyo be-8% ukuya kuthi ga kwi-dielectric umahluko ɛ≈9, kwaye i-radius yandisiwe ukufezekisa ixabiso eliphezulu le-PBG ye-15%. PBGs shwaka xa ɛ < 6.5. Njengoko kulindelekile, isakhiwo sedayimani sine-PBG inkulu phakathi kwazo zonke izakhiwo ezifundiweyo.
Ukuze ufumane ulwazi oluthe kratya malunga nee-nuances zophononongo, ndincoma ukujonga и kuye.
Ipilo
Eyona njongo iphambili yokuqhuba olu phononongo ngumnqweno wokuphendula umbuzo wokuba uthungelwano lwe-foam lungabonisa i-PBG epheleleyo. Ukuguqula imida yezakhiwo ze-foam ezomileyo kwiinethiwekhi ze-photonic zibonise ukuba ziyakwazi.
Okwangoku, i-foam ayikho isakhiwo esifundwe ngokukodwa. Ewe kunjalo, kukho izifundo ezinika iziphumo ezilungileyo ngokwendlela yothungelwano lwe-amorphous, kodwa zenziwa kwizinto ezincinci kakhulu. Indlela eya kuziphatha ngayo le nkqubo njengoko imilinganiselo yayo isanda ayikacaci.
Ngokutsho kwababhali bophononongo, umsebenzi wabo uvula amathuba amaninzi okwenziwa kwezinto ezizayo. I-Foam ixhaphake kakhulu kwindalo kwaye kulula ukuyivelisa, okwenza esi sakhiwo sibe nomtsalane kakhulu kwizicelo ezisebenzayo.
Izazinzulu zibiza i-Intanethi njengenye yezona zinto zinqwenelekayo kuphando lwabo. Njengoko abaphandi ngokwabo bathi, ukuhambisa idatha kwi-fiber optical akuyona into entsha, kodwa ukukhanya kusaguqulwa kube ngumbane kwindawo eya kuyo. Izixhobo ze-Photonic bandgap zinokukhokelela ukukhanya ngokuchanekileyo ngakumbi kuneentambo eziqhelekileyo zefiber optic kwaye zinokusebenza njengee-transistors ezibonakalayo ezenza izibalo zisebenzisa ukukhanya.
Enoba zinkulu kangakanani na izicwangciso, usemninzi umsebenzi omele wenziwe. Nangona kunjalo, akukho kuntsonkotha kokwenza uphando okanye ukuntsonkotha kokuphumeza imifuniselo akunakuloyisa ulangazelelo lwezazinzulu kunye nomnqweno wazo wokuphucula ihlabathi letekhnoloji.
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