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1、J.Phys.:Condens.Matter8(1996)1085–1108.PrintedintheUKREVIEWARTICLECalculatingphotonicbandstructureJBPendryTheBlackettLaboratory,ImperialCollege,LondonSW72BZ,UKReceived20November1995Abstract.Photonicmaterialsstructuredonthescaleofthewavelengthoflighthavebe
2、comethesubjectofanactivefieldofresearchfedbythehopeofcreatingnovelproperties.Theoryplaysacentralrolereinforcedbythedifficultyofmanufacturingphotonicmaterials:unusuallywearebetterabletodesignaphotonicmaterialthantobuildit.Inthisreviewweexploretheapplicationo
3、fscatteringtheorytoMaxwell'sequationsthathasenabledtheorytomakesuchacentralcontribution:implementationofMaxwell'sequationsonadiscretemesh,developmentoftheelectromagnetictransfermatrix,order-Nmethods,andadaptivemeshes.Atthesametimewepresentapplicationstoaf
4、ewkeyproblemsbywayofillustration,anddiscussthespecialcircumstancesofmetallicphotonicstructuresandtheiruniqueproperties.1.IntroductionAsopticsmergeswithelectronicstofuelarevolutionincomputingandcommunication,itisnaturaltocompareandcontrastelectronsandphoto
5、ns.Theformerareforthemomentthemoreactivemembersofthepartnership,butforfutureprogresswelookincreasinglytophotons.Electronshaveenjoyedtheadvantageinthiscontestbecauseoftheeasewithwhichtheycanbecontrolled:pipeddownwires,storedinmemories,orswitchedfromonechan
6、neltoanother.Semiconductorsarethemediuminwhichtheyoperate,andsemiconductorsenjoytheircontrolofelectronicpropertiesbecauseofdiffractioneffectsintheatomiclattice.Structureandfunctionoperateharmoniouslytogetherinthesematerialstodeliverthepropertiesweneed.Pho
7、tonsalsohaveawave-likenaturebutontoolargeascaletobediffractedbyatomiclattices.Thereforetoalargeextenttheyhaveescapeddetailedengineeringoftheirproperties.However,thereisnoreasonthatweshouldnotartificiallystructurematerialsonthescaleofthewavelengthoflighttop
8、roducebandgaps,defectstates,delaylinesandothernovelpropertiesbyanalogywiththeelectroncase.Thisagendaofreworkingsemiconductorphysicsforthephotonhasbeenseizedupon,largelybycondensed-mattertheoristswellversedintheintri
