VNU JOURNAL O F S C IE N C E , Mathematics - Physics, T.XXI, N02, 2006 C R O SS T A L K E F F E C T IN THE CASE O F TH R EE MONOMODE PLAN WAVE GUIDES D inh V an H oang, Mai H ong H anh College o f sciences V ietnam N ational U niversity A b stra c t In th is paper, we exam ined the crosstalk effect in the case of th re e monomode pro p ag atin g wave in th ree plan wave guides On th e basis of solving p ro pagatin g wave equations, we have received the influence of s tru c tu re p a m e te r as the refractive index difference, the lengths of p ro p a g a tin g waves, th e d iam eter of wave guides, th e sep arated distance betw een two adjacen t wave guides etc on the crosstalk effect Key words: wave guides optics, optical communication L I n tr o d u c tio n Since th e n in e tie s of la s t cen tu ry , m ankind h as gone into th e period of infob rea k out By th e tech n iq u e WDM, one can obtain a larg e gigabit a t far in te rv a l of optical tra n s m iss io n line H ow ever, one of th e defects in th is m u ltican al com m unication is th e exhib itio n of c ro sstalk effect - th e power exchange betw een th e two w aves p ro p a g a tin g in two ad jacen t canals T his phenom enon re s u lts in the noise of in fo rm a tio n which needed exclude T he c ro ssta lk effect h a s been studied in the case of two ad jacen t can a ls th a t m ay be co nsidered as two p la n wave guides [1-4] In th is p a p er, we h ave e n la rg ed th e resea rch to th e case th re e ad ja ce n t plan w ave guides On th e b a sis of resolving th e p ro p ag atin g wave equations p re se n te d in section , we h av e m ade a stu d y of th e influence of s tru c tu re p a m e te rs of wave guides as th e d iffe re n t of refractiv e index, th e len g th of p ropagating wave, the d iam ete r of w ave guide e tc on th e c ro sstalk in te rv al - a ch arac teristic q u a n tity of c ro sstalk effect T hese re s e a rc h ’s re s u lts have been in d icated in section A t last, discussion a n d conclusions h ave given in section B a sic e q u a tio n s We supposed th e re a re th re e p lan wave guides in which the p lan w aves p ro p ag ate follow ing th e Oz directio n as seen in fig T hese wa-ve guides h av e th e w idths of lị, l2ĩ / 3, th e refractive index n u n 2i n an d s e p a tin g d ista n c e s of d u d T he p ro p a g a tin g w aves h ave forms: E i (y,z) = a iul(y)e~jp'* (1 ) E 2(y,z) = a2u2(y)e~J^ (2) 34 C ro s sta lk Effect in th e C ase o f Three M on om ode P la n W ave G u id e s E 3{y,z) = azu A y ) e ilhz 35 (3) H ere a u a 2, a - c o n stan ts, /?!, jS2, /?3 - p ro p ag atio n c o n sta n ts, u x(y)f u 2(y), ỉ/3(y) - am p litu d e functions of waves W hen th e pow er exchange betw een th e wave guides a p p eared , c o n sta n ts a x become functions slowly changed by z The H elm holtz e q u atio n for each wave, in th is case, h a s th e follow ing form: V2i£ +k?Eị = - S m (i,m = 1,2,3) (4) H ere th e source Sm d e m o n stra te s th e field of one wave suffered th e influence of th e a n o th e r wave Follow ing [ ] we can give s m = K - n 2) K K = K - k 2) K (5) 27Ĩ W ith k0 = — - wave num ber, A - velocity of lig h t in vacuum A From (4), (5), we have the system of equations for three plan wave guides, as follows v 2£ , + k fE l = - ( k ị - k 2)E (6 ) V 2E + % E = -[(* 32 - k 2)E3 + (kỉ - k 2)Ex] (7) V % +k%E3 = - ( k l - k 2)E (8) d2a Solving th is system of eq u atio n s a fte r th e a p p ro x im atio n of neg lectin g — dzÔCL■ before — - , we received a new system of equations: dz Dinh Van Hoangy Mai Hong H an h 36 (9) ^ = - j C 2la2(z)eJ dz ( 10) dz % = - j C l2aẠ z)e-j^ - jC 32a3(z)e-J^ ( 11) w ith &p\ —P\ $2 >^03 ~ Pz 02 C 32 = k ĩ —ị? \ 0/? I u3(y)u2(y)dy p2 Ả c 23 = o n í í u3(y)u2(y)dy 2/*3 T his system is solved n u m erically for d ifferen t cases, depending on th e diverse form s of function Ui(y) T he in flu e n c e o f str u c tu r e p a m eter o f w ave g u id e s on th e c r o ssta lk in terv a l 3.1 D e fin itio n : C ro ssta lk in te rv a l L is th e in te rv al d eterm in ed since the tran sm issio n of lig h t in one w ave guide begins u n til th e power exchange a p p ears 3.2 E xpression o f fu n c tio n Uị(y) a n d va lu es o f p a r a m e te r We ta k e for function Ui(y) th e follow ing expressions ( 12 ) Uj(y) = Ae s'y-,u2(y) = Be Sỉy;u3(y) = Ce s*y w here A = c =1, B =1,