Kalelo mu 1887, katswiri wa sayansi ya zakuthambo wa ku Scotland, William Thomson, anapereka chitsanzo chake cha mmene kamangidwe ka etha, kamene kanali kofala kwambiri, ndipo kugwedezeka kwake kumaonekera kwa ife monga mafunde a electromagnetic, kuphatikizapo kuwala. Ngakhale kulephera kwathunthu kwa chiphunzitso cha ether, chitsanzo cha geometric chinapitirizabe kukhalapo, ndipo mu 1993, Denis Ware ndi Robert Phelan adalongosola chitsanzo chapamwamba kwambiri cha dongosolo lokhoza kudzaza malo momwe angathere. Kuyambira nthawi imeneyo, chitsanzochi chakhala chosangalatsa kwambiri kwa akatswiri a masamu kapena ojambula, koma kafukufuku waposachedwapa wasonyeza kuti akhoza kupanga maziko a matekinoloje amtsogolo omwe amagwiritsa ntchito kuwala m'malo mwa magetsi. Kodi thovu la Ware-Phelan ndi chiyani, chomwe chimapangitsa kuti likhale lachilendo, ndipo lingagwiritsidwe ntchito bwanji kuyatsa? Tipeza mayankho ku mafunso awa ndi ena mu lipoti la gulu lofufuza. Pitani.
Maziko ofufuza
Kwenikweni zaka zana zapitazo mu gulu la asayansi panali chiphunzitso chochititsa chidwi kwambiri pa nkhani inayake ya chirichonse chozungulira. Mfundo imeneyi inali yofuna kufotokoza mmene mafunde a electromagnetic amayendera. Ankakhulupirira kuti ether imazungulira chirichonse ndipo ndiye gwero la mafundewa. Zimene asayansi atulukira zomwe zinatsatira chiphunzitso cha ether zinaziwonongeratu.
William Thomson
Komabe, mu 1887, pamene chiphunzitso cha ether chinali chodzala ndi mphamvu ndi kutchuka, asayansi ambiri anafotokoza maganizo awo ponena za mmene ether ingadzazire mlengalenga. William Thomson, yemwe amadziwikanso kuti Lord Kelvin, anachita chimodzimodzi. Anali kufunafuna kamangidwe kamene kangadzaze bwinobwino malowo kuti pasakhale malo opanda kanthu. Kufufuza kumeneku kunadzatchedwa kuti vuto la Kelvin.
Chitsanzo chakale: lingalirani bokosi lomwe lili ndi zitini za kola. Pakati pawo, chifukwa cha mawonekedwe a cylindrical, voids amawuka, i.e. malo osagwiritsidwa ntchito.
Thomson, kuwonjezera pa kukhulupirira kuti Dziko Lapansi silinapitirire zaka 40 miliyoni, adakonza dongosolo latsopano la geometric, lomwe linasinthidwa ndi Denis Ware ndi Robert Phelan, chifukwa cha dzina lawo.
Mapangidwe a Ware-Phelan amachokera ku zisa zomwe zimadzaza danga ndi polyhedra yosagwirizana, osasiya malo opanda kanthu. Chisa cha uchi, chomwe nthawi zambiri timachiwona ngati ma hexagon chifukwa cha zisa, chimakhala ndi mawonekedwe osiyanasiyana. Pali cubic, octahedral, tetrahedral, rhombic dodecahedral, etc.
Ware-Phelan kapangidwe
Chinthu chachilendo pa zisa za uchi wa Ware-Phelan ndikuti zimakhala ndi mawonekedwe osiyanasiyana a geometric ndi zinthu. Pakatikati pake, ndi thovu labwino la thovu lofanana.
Kholo la thovu ili linali loperekedwa ndi Lord Kelvin, yemwe timawadziwa kale. Komabe, Baibulo lake linali la zisa zofupikitsidwa za uchi za kiyubiki. Maonekedwe a Kelvin anali zisa za uchi za yunifolomu yopangidwa ndi octahedron yofupikitsidwa, yomwe ndi polyhedron yokhala ndi nkhope zinayi, yodzaza malo (tetradecahedron), yokhala ndi nkhope 6 masikweya ndi nkhope 8 za hex.
Njira iyi yowonjezeretsa kudzaza malo idawonedwa ngati yabwino kwa zaka pafupifupi zana, mpaka Ware ndi Phelan adatsegula dongosolo lawo mu 1993.
Pentagondodecahedron ndi decahedron
Kusiyanitsa kwakukulu pakati pa uchi wa Ware-Phelan ndi wotsogolera wake ndi kugwiritsa ntchito mitundu iwiri ya zinthu zomwe zimapangidwira, zomwe, komabe, zimakhala ndi voliyumu yofanana: pentagondodecahedron (dodecahedron yokhala ndi tetrahedral symmetry) ndi XNUMXhedron yokhala ndi mawonekedwe ozungulira.
Mu ntchito yomwe tikukambirana lero, asayansi ochokera ku yunivesite ya Princeton adaganiza zogwiritsa ntchito thovu la Ware-Phelan muzithunzithunzi. Choyamba, kunali koyenera kudziwa ngati thovu zotere zili ndi mipata ya gulu la photonic (PBGs), zomwe zimalepheretsa kufalikira kwa kuwala kumbali zonse ndi polarizations pamitundu yosiyanasiyana.
Mu kafukufuku wawo, asayansi adawonetsa kuti 16,9D photonic network yochokera ku thovu la Ware-Phelan imatsogolera ku PBG yofunikira (XNUMX%) yokhala ndi digiri yayikulu ya isotropy*, yomwe ndi katundu wofunikira kwa maulendo a photonic.
Isotropy* - zofanana zakuthupi mbali zonse.
Kelvin thovu ndi C15 thovu anachitanso bwino ponena za PBG, koma iwo anali otsika kwa dongosolo Ware-Phelan pankhaniyi.
Maphunziro ofananirako adachitika kale, koma adayang'ana pa thovu louma la mbali ziwiri. Kenako anapeza kuti awiri azithunzithunzi amorphous youma thovu amasonyeza PBG kokha yopingasa magetsi polarization. Vuto ndiloti pali polarizations ziwiri mu XNUMXD thovu.
Ngakhale pali zovuta zomwe zingakhalepo, thovu la 30D limatha kuonedwa ngati chinthu chodalirika pazithunzi zazithunzi, malinga ndi ofufuza. Pali chifukwa chake: Malamulo a Plateau amaonetsetsa kuti m'mphepete mwake mumakhala ma vertices a tetrahedral okha. Ndipo ichi ndi chowonjezera chachikulu cha ma photonic network. Chitsanzo chochititsa chidwi cha izi ndi diamondi yokhala ndi PBG ya XNUMX%.
Chithovucho chili ndi katundu wa tetrahedral wa ma coordinates a diamondi, koma amasiyana chifukwa ali ndi m'mphepete mwake komanso kutalika kwake kosagwirizana pang'ono. Zimangotsala kuti mudziwe momwe komanso momwe kusiyana kumeneku kumakhudzira mawonekedwe a photonic.
Ngati nthiti za thovu louma la 17D zakhala zokulirapo, ndizotheka kupanga makanema ojambulidwa (zithunzi pansipa) zomwe zikuwonetsa ma PBG odziwika mpaka XNUMX%, ofananira kapena apamwamba kuposa zitsanzo zamagalasi odzipangira okha.
Chithunzi #1: Mawonekedwe a thovu a Photonic omwe amapezedwa pokulitsa m'mphepete mwa kapangidwe ka Ware-Phelan (kumanzere), kapangidwe ka Kelvin (pakati) ndi thovu la C15 (kumanja).
Kuti mugwiritse ntchito chitsanzo choterocho, chithovu chowuma chiyenera kutsukidwa poyamba ndikuchikutidwa ndi dielectric material. Mwachibadwa, PBG ya thovu idzakhala yotsika kuposa ya photonic crystal, koma kuipa kumeneku kungagonjetsedwe ndi ubwino wambiri. Choyamba, kudzipanga nokha kwa thovu kumatha kuloleza kupanga mwachangu zitsanzo zazikulu. Kachiwiri, ma heterostructures a thovu a photonic, kutengera kafukufuku wam'mbuyomu, amatha kukhala ndi ntchito zambiri.
Zotsatira za kafukufuku
Choyamba, kunali koyenera kuphunzira thovu louma, lomwe limatanthauzidwa ngati minima yapafupi ya dera lapakati tessellation* kutengera zovuta za voliyumu, kotero kuti geometry yomaliza imvera malamulo a Plateau.
Tessellation* - kugawa ndege kukhala zigawo zomwe zimaphimba ndege yonse popanda kusiya mipata.
Kuti apange thovu la Ware-Phelan, Kelvin, ndi C15, asayansi adayamba ndi ma tessellations olemera a Voronoi a BCC, A15, kapena C15 makhiristo, motsatana.
Chithunzi cha Voronoi
Magawo adasankhidwa mwanjira yakuti maselo onse olekanitsa anali ndi voliyumu yofanana.
Maukonde opangidwa kuchokera m'mbali zokhotakhota za thovu komanso kuchokera m'mbali zowongoka za ma tessellation omwe adawatsogolera adawerengedwa. Kuwunika topology yamitundu yonse ya thovu, ziwerengero za mphete*.
Ziwerengero za mphete (ziwerengero za mphete)*Kuwunika kwa mawonekedwe a topological of network materials (zamadzimadzi, crystalline kapena amorphous systems) nthawi zambiri zimatengera chiphunzitso cha ma graph pogwiritsa ntchito mfundo za ma atomu ndi ma bond polumikizana ndi interatomic. Kusakhalapo kapena kukhalapo kwa kulumikizana pakati pa mfundo ziwiri kumatsimikiziridwa posanthula ntchito za kugawa kwathunthu ndi pang'ono kwa dongosolo. Muzinthu zapaintaneti, mndandanda wa mfundo ndi maulalo olumikizidwa mosadukizana amatchedwa njira. Kutsatira tanthauzo ili, mphete ndi njira yotsekedwa. Ngati muyang'ana mosamala maukonde enaake, mutha kuwona kuti mfundoyi imatha kutenga nawo mbali mu mphete zambiri. Chilichonse mwa mphetezi chimadziwika ndi miyeso yake ndipo chikhoza kugawidwa potengera maubwenzi pakati pa mfundo ndi maulalo omwe amapanga.
Njira yoyamba yofotokozera mphete inaperekedwa ndi Shirley W. King. Kuti aphunzire kulumikizana kwa magalasi a SiO2, amatanthauzira mphete ngati njira yayifupi kwambiri pakati pa oyandikana nawo awiri apafupi a node yopatsidwa.
Pankhani ya phunziro lomwe likuganiziridwa, kuwerengera kunapangidwa ndi chiwerengero cha mphete zazifupi kwambiri pa vertex mu selo imodzi.
Selo imodzi mu chitsanzo cha Kelvin ili ndi mabwalo a 2 ndi ma hexagoni 4 pa vertex, koma TCP (tetrahedral close-packed) thovu ili ndi nkhope za pentagonal ndi hexagonal (pafupifupi: 5.2 ndi 0.78 mu thovu la Ware-Phelan; 5.3 ndi 0.71 mu thovu la C15). Voronoi tessellations A15 ndi C15 ndi nyumba za TCP zomwe zili ndi chiwerengero chachikulu komanso chaching'ono kwambiri cha m'mphepete (f) pa selo 1. Chifukwa chake, mawonekedwe a Ware-Phelan ali ndi nkhope zazikulu kwambiri (f = 13 + 1/2), ndipo C15 ndiye chiwerengero chochepa kwambiri cha nkhope (f = 13 + 1/3).
Atamaliza kukonzekera kwawo kwamalingaliro, asayansi adayamba kutsanzira ma network a photonic pogwiritsa ntchito nthiti zowuma zowuma, i.e. foam-photon network. Zinapezeka kuti pa mtengo wa PBG wa 20% ntchito ya machitidwe imakwezedwa, koma pa 15% thovu la Ware-Phelan limakhala losakhazikika. Pachifukwa ichi, asayansi sanaganizirepo chithovu chonyowa, pomwe malire a Plateau ali ndi magawo a tricuspid. M'malo mwake, cholinga chake chinali pazipangidwe za thovu zouma, zomwe asayansi amatha kuwonjezera kukula kwa nthiti pang'onopang'ono.
Kuphatikiza apo, m'mphepete uliwonse ndi gawo lapakati la spherocylinder (kapisozi), pomwe radius ndi gawo lokonzekera.
Ofufuzawo akutikumbutsa kuti maukonde a thovu ngati amenewa sakhala thovu kwenikweni, koma pofuna kuphweka mu lipoti lawo adzatchedwa "foam network" kapena "foam network."
Pakuyerekeza, parameter idaganiziridwa Ι (kusiyana kwa dielectric) - gawo la zinthu zosinthika za dielectric zomwe zili ndi zida zapamwamba komanso zotsika. Kusiyanitsa kwa dielectric kumaganiziridwa kuti kuli pakati pa 13 ndi 1, yomwe imagwiritsidwa ntchito kwambiri m'mabuku ngati muyezo poyerekezera magwiridwe antchito amitundu yosiyanasiyana yazithunzi.
Pa netiweki iliyonse, ma radius a m'mphepete (spherocylinders) amakongoletsedwa ndi chiΕ΅erengero chachikulu cha kusiyana kwa gulu ndi pakati: βΟ/Οm, ku βΟ ndi frequency band wide, ndi Οm - pafupipafupi mkati mwa zone.
Chithunzi #2: Zithunzi zamtundu wa Ware-Phelan thovu (wofiira), thovu la Kelvin (buluu), ndi thovu la C15 (lobiriwira).
Kenaka, kukula kwa PBG kunayesedwa ndipo kunapezeka kuti: 7.7% ya thovu la Kelvin, 13.0% ya thovu la C15 ndi 16.9% ya thovu la Ware-Phelan. Kuchepetsa kwa dera kumawonjezera kukula kwa PBG ndi 0.7%, 0.3 kapena 1.3%.
Monga zidawonekera pakuwunika, maukonde a TCP ali ndi kukula kwakukulu kwa PBG kuposa maukonde a Kelvin. Pa maukonde awiri a TCP, thovu la Ware-Phelan lili ndi kukula kwakukulu kwa bandgap, komwe mwina kuli chifukwa chakusintha kwakung'ono kwautali wa ulalo. Asayansi amakhulupirira kuti kusiyana kwa kutalika kwa mgwirizano kungakhale chifukwa chachikulu chomwe mu dongosolo lawo, i.e. mu thovu la Ware-Phelan, PBG ndi yocheperako kuposa diamondi (31.6%) kapena mu Laves system (28.3%).
Mbali yofunika kwambiri mu photonics ndi isotropy ya PBG, yomwe imalola kupanga ma waveguides a mawonekedwe osagwirizana. Photonic quasicrystals, komanso ma amorphous photonic network, ndi isotropic kuposa classical photonic crystals.
Mapangidwe a thovu-photonic omwe akuphunziridwa alinso ndi digiri yapamwamba ya isotropy. Pansipa pali chilinganizo chodziwira kuchuluka kwa anisotropy (ie, kuchuluka kwa kusiyana kwazinthu zamalo ena) PBG (Π):
A: = (βVar[ΟHDB]+Var[ΟLAB]) / Οm
Foam ya C15 inapezeka kuti ili ndi anisotropy yotsika kwambiri (1.0%), yotsatiridwa ndi thovu la Weir-Phelan (1.2%). Chifukwa chake, mapangidwe awa ndi isotropic kwambiri.
Koma mawonekedwe a Kelvin akuwonetsa coefficient ya anisotropy ya 3.5%, yomwe ili pafupi kwambiri ndi ya Laves system (3.4%) ndi diamondi (4.2%). Komabe, ngakhale zizindikirozi si zoipa kwambiri, chifukwa palinso yosavuta kiyubiki kachitidwe ndi anisotropy coefficient 8.8% ndi hexagonal diamondi maukonde ndi 9.7%.
M'zochita, pamene kuli kofunikira kukwaniritsa phindu lalikulu la PBG, nthawi zina ndikofunikira kusintha magawo ena a thupi. Pankhaniyi, chizindikiro ichi ndi utali wozungulira wa spherocylinders. Asayansiwo adawerengera masamu momwe adatsimikiza ubale pakati pa kusiyana kwa gulu la photonic ndi m'lifupi mwake ngati ntchito. Ι. Pa mtengo uliwonse womwe umapezeka, utali wozungulirawo udakonzedwa kuti ukule βΟ/Οm.
Chithunzi Nambala 3: kuyerekezera βΟ / Οm ya ma network a thovu omwe amaphunzira (C15, Kelvin, Weir-Phelan) ndi zina (diamondi, diamondi ya hexagonal, Laves, SC - cubic wokhazikika).
Foam ya Weir-Phelan imakhala ndi kukula kovomerezeka kwa PBG kwa 8% mpaka kusiyanitsa kwa dielectric Ιβ9, ndipo radius idawonjezedwa kuti ikwaniritse phindu lalikulu la PBG la 15%. PBGs kutha pamene Ι <6.5. Monga zikuyembekezeredwa, mawonekedwe a diamondi ali ndi PBG yayikulu kwambiri pakati pazinthu zonse zomwe zaphunziridwa.
Kuti mudziwe zambiri za ma nuances a phunziroli, ndikupangira kuyang'ana ΠΈ kwa iye.
Epilogue
Cholinga chachikulu chochitira phunziroli ndi kufuna kuyankha funso ngati maukonde a thovu amatha kuwonetsa PBG yonse. Kutembenuza m'mphepete mwa zinthu zowuma za thovu kukhala ma photonic network kwawonetsa kuti angathe.
Pakali pano, thovu si dongosolo makamaka kuphunzira. Zachidziwikire, pali maphunziro omwe amapereka zotsatira zabwino pamaneti amorphous, koma adachitidwa pazinthu zazing'ono kwambiri. Momwe dongosololi lidzakhalira pamene miyeso yake ikuwonjezeka sizikudziwika.
Malinga ndi olemba a phunziroli, ntchito yawo imatsegula mwayi wambiri wopanga mtsogolo. Chithovu ndi chofala kwambiri m'chilengedwe komanso chosavuta kupanga, zomwe zimapangitsa kuti kamangidwe kake kakhale kokongola kwambiri pakugwiritsa ntchito.
Asayansi amatcha intaneti imodzi mwazofunikira kwambiri pakufufuza kwawo. Monga momwe ofufuzawo amanenera, kutumiza deta pa fiber optical sikwatsopano, koma kuwala kumasinthidwabe kukhala magetsi kumalo ake. Zida za Photonic bandgap zimatha kuwunikira bwino kwambiri kuposa zingwe wamba za fiber optic ndipo zimatha kukhala ngati ma transistors omwe amawerengera pogwiritsa ntchito kuwala.
Ngakhale kuti mapulaniwo ali aakulu bwanji, pali ntchito yambiri yoti ichitike. Komabe, ngakhale zovuta zopangira kafukufuku kapena zovuta zoyeserera zomwe zingagonjetse chidwi cha asayansi ndi chikhumbo chawo chofuna kupititsa patsogolo luso laukadaulo.
Zikomo powerenga, khalani ndi chidwi komanso khalani ndi sabata yabwino anyamata! π
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