Maximum Transmission Through Slits in Adjacent Parallel Conducting Plates

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1 Mimum Trnmiion Through Slit in djcent rllel Conducting lte Jong-Ig Lee wn-yong Jung 2 Young-Soon Lee 3 nd Young-Ki Cho 2 Deprtment of Electronic Eng Dongeo Univ Bun Kore E-mil : leeji@dongeockr 2 School of Electricl Eng nd Computer Science Kungpook Ntionl Univ Degu 72-7 Kore E-mil : kcho@eeknuckr 3 School of Electronic Eng Kumoh Ntionl Intitute of Technolog Gumi Geongbuk 73-7 Kore E-mil : lee@kumohckr btrct In thi tud the problem of electromgnetic coling through lit in two conducting prllel-plte i tudied for the ce tht the tructure i illuminted b TE (to the lit i polrized plne wve with min interet on the undertnding bout mimum trnmiion mechnim It i oberved tht the mimum of the normlized trnmitted power with repect to the incident power denit become / wvelength irrepective of the lit width nd the incident ngle of the TE wve when the ditnce between the litted conducting prllel-plte i much mller thn the wvelength For the ce tht the lit i fed b prllel-plte wveguide (W the trnmitted power beond the litperforted conducting plte i mimized for the ce tht the cvit formed between the edge of the lit i reonted In ddition the equivlent conductnce of the coling lit for the ce of mimum trnmiion i cloe to tht for the nrrow lit /2 INTORDUCTION The problem of electromgnetic coling between two hlf-pce region through perture in litted prllel conducting creen h been conidered b Levitn [] In the tud [] where the tructure h been treted minl implified Ner-field Scnning Microcope (NSM it h been oberved tht the trnmitted power through the lit become mimized when the trnvere hift between the lit pproche multiple of hlf wvelength In thi tud the problem of electromgnetic coling through lit in two conducting prllel-plte which eprte two hlf pce i tudied for the ce tht the tructure i ecited b TE (to the lit i polrized plne wve with min interet on the mimum trnmiion mechnim (ee Fig [] It i oberved tht the trnmitted power beond the lit-perforted conducting plte i mimized when the lterl diplcement(hift between the lit become pproimtel multiple of the hlf wvelength found in [] For the ce tht the ditnce between the litted conducting plte i much mller thn the wvelength the mimum of the normlized trnmitted power with repect to the incident power denit mount to / wvelength independent of the incident ngle of the TE wve nd the lit width Some dicuion re given to eplin thi intereting phenomenon from the viewpoint of cvit reonnce nd to connect it with the mimum trnmiion through nrrow lit in thick conducting creen [2] which re thought to be in working principle identicl with ech other In ddition for the ce tht the lit i ecited b the TEM mode wve in prllel-plte wveguide (W (ee Fig 2 inted of the TE polrized plne wve in Fig l it i oberved tht the power coled(trnmitted to the hlf pce region i mimized when the cvit reontor formed between the edge of the coling lit in the prllel conducting plne i reonted 2 TEORY Fig how cro-ectionl view of pir of litted conducting prllel-plte ( z nd z d which eprte two hlf pce region nd 3 In Fig ( i the width of lit S ( S d i ditnce between the plte nd L i the ditnce in the lterl ( direction between the edge of two lit The tructure i invrint to the -i nd ecited b

2 TE (to the lit i ie E polrized plne which i incident on the lit S with n incident ngle The - component incident plne wve cn be given b i ep( jk ( where k k (in ˆ co zˆ ˆ z zˆ k n k rn k 2 / nd i the free pce wvelength The equivlence principle i emploed to divide the originl problem into three equivlent itution where the equivlent mgnetic current heet [ E ˆ ( E ˆ ( over the lit S ] nd M [ E ˆ ( M E ˆ ( over the lit S ] on both ide of the horted lit S nd S repectivel [] lit S : width lit S : width L where the ubcript denote the -component nd the region while the ercript repreent the ource of the field The continuit of tngentil field cro the lit S nd S led to the coled integrl eqution for the mgnetic current ditribution which re equl to the tngentil electric field ditribution E nd E over the lit B emploing the pule (piecewie contnt bi function nd the point mtching method the eqution re olved numericll b the method of moment From the knowledge of the electric ditribution E nd E one cn compute ll the quntitie of interet uch the coled power through S the guided power nd long the guiding tructure (formed in the region 2 between the conducting prllel-plte t z nd z d nd the coled power through S into the region 3 Similrl for the ce tht the tructure i ecited b the TEM wve in W hown in Fig 2 the problem cn be olved following the me procedure in the bove ce of TE polrized plne wve incidence in Fig TM(E = wve region ( r z region 2 ( r2 region 3 r3 litted conducting plne z= z=d Fig Slitted conducting prllel-plte illuminted b TE( E polrized plne wve B epreing the field in the ech region in term of the c field due to the incident TE wve ( nd the mgnetic current heet M nd M over the lit S nd S one find tht the -component mgnetic field in ech region cn be epreed c M (2 M M (3 M 3 3 (4 TEM wve lit S h i r : width region prllel-plte wveguide ( r litted conducting plne lit S : width z region 2 ( r2 L region 3 r3 z= z=d Fig 2 Slitted conducting prllel-plte ecited b the TEM wve in W imple equivlent circuit repreenttion for the TEM wve in the W i hown in Fig 3 in which the normlized 2 Interntionl Smpoium on ntenn nd ropgtion IS 26

3 equivlent dmittnce of the lit S cn be obtined from the voltge reflection coefficient [3] Y / Y g jb ( /( (5 v v with Y /( h nd v / r Y =/h Y S (=G S +jb S tht nd /2 /2 D( d In Fig 4 ll the quntitie re nerl independent of the incident ngle Mot of the coled power through the lit S become trnmitted power into the region 3 ie Between the guided TEM mode power ( nd long the region 2 the coled power beond the wide lit S i ver mll nd negligible [4] z=(lit ( S (=g S +jb S z=(lit (b Normlized power D(/D m Fig 3 Simple equivlent circuit repreenttion for the TEM wve in the W in Fig 2 ( unnormlized (b normlized 3 RESULTS ND DISCUSSIONS In the prior work [] in which the propoed coling problem w tudied minl from the viewpoint of Nerfield Scnning Microcope (NSM it h been oberved tht the pek of the trnmitted power into the region 3 re occurred when the lterl diplcement(hift L between the lit S nd S pproche multiple of the hlf wvelength of the TEM mode wve guidble long the direction in the region 2 In ddition it h been hown tht the pek vlue of trongl depend on the ditnce d between the litted conducting plte owever in the tud [] it eem to hve pid little ttention on the mimum of the pek vlue nd the dependenc of the trnmitted power on the incident ngle Fig 4 how the normlized power ( incident ngle [degree] Fig 4 Normlized power wrt the incident power denit Ce of 2 d r r2 r3 nd L 4944 in Fig ence the wide trnvere lit in W with mll guide height cn be pproimtel regrded n open end hown in Fig 5 which behve like lightl lo mgnetic wll [4] nd the equivlent lit dmittnce Y ( G jb h mll rdition conductnce G ( /2 which i much mller thn the uceptnce B ie G B to the incident power denit 2 ( /2 of the TM wve nd normlized ngulr power denit D( / D of the trnmitted wve into the region 3 For reference note m Fig 5 Rdition problem from n open lit fed b W with mll guide height nd it reciprocl (coling problem through open lit illuminted b plne wve Interntionl Smpoium on ntenn nd ropgtion IS 26 3

4 Since mot of the field re confined in the vicinit of the lit the rdition pttern D( from the lit S into the region 3 how nerl omni-directionl chrcteritic From thi one cn epect tht the coled power into the W region would be nerl contnt irrepective of the incident ngle of the plne wve when the lit i illuminted b plne wve reciprocl problem hown in Fig 5 Though the lit S ( i mll compred to the wvelength it hould be regrded wide lit becue the W formed between two conducting plte ( z nd z d h much mller guide height d thn the lit width ie d ence the wide lit S cn be regrded two open end S nd S hown in Fig 6 Now one cn notice tht there re three nrrow lit S S nd S of open end tpe hown in Fig 6 in which two lit S nd S which re illuminted b the plne wve re coling edge while S become rditing edge lit uch the independence of ll the power quntitie on the incident ngle in Fig 4 cn be undertood nd S which behve like the lo mgnetic wll mentioned bove Note tht thi reonnce phenomenon i the me the trnmiion reonnce in the coling problem through nrrow lit in thick conducting creen [2] which require the me condition from the viewpoint of the equivlent circuit repreenttion the mimum rdition condition (reonnce of n input dmittnce in the trnmiion line model [5] of the rectngulr microtrip ptch ntenn Normlized dmittnce (=g +jb g b h/ = =2 d= L=4944 r = r2 = r3 = Coled power Fig 7 Coled power h/ nd equivlent lit dmittnce g jb Fig 6 Enlrged view of the region ner the coling lit to illutrte cvit formed between the lit It i worth while to note tht the coled power mount to 383 / irrepective of the lit width Net we re to emine the trnmiion chrcteritic of the litted conducting plte for the ce tht the lit S i ecited b the TEM wve of W hown in Fig 2 In order to invetigte the tructure the normlized equivlent dmittnce of the lit S i computed in ddition to which men the effective lit width of the lit S eff of the coled power ( nd The plot for width (ctull lit S of with d cn be increed to it mimum vlue /( co m when the cvit eff (of length L formed between the nrrow open lit S the normlized equivlent dmittnce nd the trnmitted power re hown in Fig 7 in which mot of the coled power re trnmitted into the region 3 ie while the guided wve power nd re 4 Interntionl Smpoium on ntenn nd ropgtion IS 26

5 negligible hown in Fig 7 the conductnce g G / Y linerl incree long with the guide height h nd it i ver cloe to the dhed line h / which correpond to the conductnce G /2 of nrrow lit [4] In order to chieve impece mtching ( j for obtining mimum coling through S there might be lot of poible combintion of the geometricl prmeter which would be different from thoe for the mimiztion of 4 CONCLUSION The problem of electromgnetic coling through djcent litted conducting prllel plte re invetigted for the ce tht TM polrized plne wve i incident on the lit From ome reult it i oberved tht the mimum trnmitted power normlized to the incident power denit i / wvelength independent of the ctul lit width nd the incident ngle of the plne wve The mechnim of the mimum coling in the propoed geometr i found to be the me tht through nrrow lit in thick conducting creen REFERENCES [] Y Levitn Electromgnetic coling between two hlfpce region eprted b two lot-perforted prllel conducting creen IEEE Trn Microwve Theor Tech vol 36 no pp Jn 988 [2] RF rrington nd DT ucklnd Electromgnetic trnmiion through nrrow lot in thick conducting creen IEEE Trn ntenn ropgt vol 28 no 5 pp Sept 98 [3] JI Lee J Ko nd YK Cho Coling through lit in flnged prllel-plte wveguide with conducting trip in roc IS 4 vol pp ugut 24 [4] JI Lee J Ko nd YK Cho note on diffrction nd equivlent dmittnce propertie of trnvere lit in prllel-plte wveguide IEICE Trn Com vol E86-B no 2 pp Dec 23 [5] G Dernerd Linerl polrized microtrip ntenn IEEE Trn ntenn ropgt vol 22 no 6 pp Nov 976 Interntionl Smpoium on ntenn nd ropgtion IS 26 5

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