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1、COL11(6),060501(2013)CHINESEOPTICSLETTERSJune10,2013SimplifiedmodeanalysisofguidedmoderesonancegratingswithasymmetriccoatingsJunWu(Çd),ChangheZhou(±~à)*,HongchaoCao(ùù),AnduoHu(S),WentingSun(©x),andWeiJia(_)LaboratoryofInformationOpticsandOpto-electronicTechnology,ShanghaiInstituteofOpticsa
2、ndFineMechanics,ChineseAcademyofSciences,Shanghai201800,China∗Correspondingauthor:chazhou@mail.shcnc.ac.cnReceivedJanuary21,2013;acceptedFebruary27,2013;postedonlineApril29,2013Asimplifiedmodalmethodtoexplaintheresonancephenomenoninguidedmoderesonance(GMR)grat-ingswithasymmetriccoatingsispre
3、sented.Theresonanceobservedisduetotheinteractionoftwopropagationmodesinsidethegrating.Thereflectivityspectraandelectricfielddistributionscalculatedfromthesimplifiedmodalmethodarecomparedusingrigorouscoupled-waveanalysis(RCWA).Thein-fluencesofhigh-orderevanescentmodesontheresonancepeakareanalyze
4、d.AmatrixFabry-Perot(FP)resonanceconditionisdevelopedtoevaluatetheresonancewavelength.AnexplanationfortheresonancephenomenonobservedbasedontheFPresonancephaseconditionisalsoproposedanddemonstrated.ThesimplifiedmethodprovidesclearphysicalinsightsintoGMRgratingsthatareusefulfortheanalysisofava
5、rietyofotherresonancegratings.OCIScodes:050.0050,050.1950,260.5740.doi:10.3788/COL201311.060501.Themodalmethod,firstproposedbyBottenetal.of-usingasimplephaseselectionrule[10].Whilethemeth-fersasimpleandphysicalunderstandingofthediffrac-odsproposedinRefs.[7,8]mainlyapplytoHCGswithtionprocessth
6、attakesplaceinsidegratings[1].However,symmetriccoatings,theyareessentiallyvariationsofthewhilethismethodhaslongbeenproposed,itisnotwidelysimplifiedmodalmethod.used.In2005,TishchenkorestudiedthemodalmethodThemodalmethodproposedinRefs.[7–10]isappliedindeeplamellargratingsandproposedinteresting
7、con-toHCGswithsymmetriccoatings(alsoknownasfree-cepts,suchasimpedancematchingandasimplifiedstandinggratings)andhasbeensuccessfullyemployedmodalmethod[2].Clausnitzeretal.formallyproposedainvertical-cavitysurface-emittinglasersandhollow-coresimplifiedmodalme
