Polarized modes Dispersion in Anisotropic Optical Fiber Communication lines

Transcription

1 Polarized mode Diperion in Anioropic Opical Fiber Communicaion line MOHAMMED YOUSEF AL-GAWAGZEH MOHAMMED RASOUL AL-HADIDI RAMI AL-RZOOQ Deparmen Of Compuer Engineering Faculy of Engineering, AL-Balqa Applied Univeriy, AL-Sal JORDAN Abrac:- Equaion are derived for calculaion of he propagaion conan and of he diperion of he fundamenal mode in anioropic waveguide.thi work how how o obain approximae analyic expreion which can be ued o calculae wih ufficien accuracy for pracical applicaion he waveguide and polarizaion diperion of he dominan orhogonally polarized mode in anioropic opical fiber waveguide and diribuion of elecric and magneic field of hee mode are obained in a ranvere cro ecion of he waveguide. I i hown ha he anioropy of a dielecric in he ranvere cro ecion and he ellipical of he hape of hi cro ecion aler he waveguide diperion of mode in uch waveguide compared wih an ioropic waveguide. In he cae of waveguide which conerve he ae of polarizaion of he ranmied ignal he change in he waveguide diperion due o he ranvere anioropy of he refracive index are coniderably greaer han he change due o he ellipical of he hape of he ranvere cro ecion of he waveguide. In a waveguide wih a ranvere anioropy of he refracive index he maximum waveguide diperion of wo muually orhogonal mode occur a differen frequencie. Key-Word: - Dipeion, Anioropy, ioropic dielecric, polarizaion, Tranvere cro ecion, Perurbaion. 1 Inroducion Fiber opic ranmiion and communicaion are echnologie ha are conanly growing and becoming more modernized and increaingly being ued in he modern day indurie.however, diperion i one of he properie of opical fiber ha caue aenuaion or a marked decreae in ranmied power. Diperion occur when he ligh raveling down a fiber opic cable become longer in wavelengh and evenually diipae.the broadening of ligh pule, called diperion i a criical facor limiing he qualiy of ignal ranmiion over opical link. Diperion i a conequence of he phyical properie of he ranmiion medium. for example he ingle mode fober, ued in high-peed opical nework are ubjeced o chromaic diperion ha caue pule broadening depending on wavelengh, and o polarizaion mode diperion ha caue pule broadening depending on polarizaion. Exceive preading will caue bi o overflow heir inended ime lo and overlap adjacen bi and hen he receiver may hen have difficully dicerning and properly inerpreing adjacen bi, increaing he bi error rae(ber) [1]. The polarizaion-mode diperion in opical fiber ha araced coniderable aenion over he pa few year. Differen echnique for polarized mode diperion (PMD) meauremen and characerizaion have been repored in many reference. Two main facor conribue o PMD in circular fiber: he deformaion of he circular Geomery of he fiber and he inernal ree which lead o re anioropy, boh of which could happen during manufacuring. Oher facor ha could conribue o PMD in fiber are bend, wi, and cabling proce. A circular fiber wih mall core ellipical deformaion caue a difference beween he group velociie in he wo orhogonal ISSN: Iue 1, Volume 8, January 009

2 polarizaion of he fundamenal mode.thi difference conribue o he overall diperion and he effec i referred o a polarizaion-mode diperion. The magniude of PMD in fiber depend on hi difference in propagaion conan. In ordinary ep-index ingle-mode fiber, PMD vanihe ouide he ingle-mode wavelengh region. To improve fiber performance in long-haul high bi rae yem, a zero PMD mu be wihin he ingle-mode wavelengh region. Anioropic waveguide are propoed for he ue in long-range communicaion opical communicaion yem and for inegraed opical device where conervaion of a given ae of polarizaion of he ranmied radiaion i an eenial requiremen. Calculaion of he parameer of mode in uch waveguide are uually carried ou by approximae mehod baed on perurbaion heory; he underlying aumpion in hee mehod i ha he mode field in anioropic waveguide differ lile from he field in an ioropic waveguide. Approximae mehod make i poible o calculae, wih a preciion ufficien for pracical purpoe, he characeriic of mode in dielecric waveguide wih a relaively weak hape or permiiviy anioropy. However, hee mehod are unuiable for deerminaion of he characeriic of mode and field in waveguide wih an arbirary anioropy []. Anioropic opical fiber waveguide capable of conerving he polarizaion of he ranmied ignal are currenly he ubjec of inenive inveigaion. Thi propery i very imporan for variou fiberopic device and for long diance opical communicaion yem [3, 15,17,18]. Anioropic waveguide are underood o be hoe wih a deparure of he ranvere cro ecion from he circular ymmery (which i known a he hape anioropy) and wih an anioropy of he permiiviy (refracive index) induced by mechanical ree. In pracice, he parameer of anioropic waveguide can be calculaed convenienly by approximae mehod which are ufficienly accurae for he purpoe [-4]. One of hee mehod, which belong o he cla of perurbaion heory echnique, i he mehod of hif formula []. Thi mehod wa decribed in [5-8] o calculae he propagaion conan and criical wavelengh of all he mode in anioropic dielecric waveguide. We hall ue hi mehod o calculae he diperion of mode in uch waveguide. Chromaic diperion i an imporan characeriic of a medium and can ignificanly degrade he inegriy of wave packe. In pracice, chromaic diperion i no uniformly diribued and ofen exhibi random variaion in pace and ime. On he oher hand, wave propagaion hrough he medium i much faer han emporal variaion of he chromaic diperion.herefore; hee random variaion can be reaed a muliplicaive noie ha doe no change in ime. he overall chromaic diperion in an opical fiber come from wo oure.the fir ource i he medium ielf. The econd ource i he pecific geomery of he waveguide profile. Maerial diperion in he opical fiber i a relaively able parameer uniformly diribued along he fiber. However waveguide diperion i no nearly a able. Exiing echnology doe no ye provide accurae conrol of he waveguide geomery of modern fiber where dependence of diperion on wavelengh i complex. A a reul, he magniude of random variaion of fiber chromaic diperion are ypically he ame a, or in ome cae even greaer han, ha of he mean diperion [4].The chromaic diperion i he mo imporan facor ha deermine he widh of a pa band of ingle-mode waveguide. I can be eparaed ino he maerial diperion and he waveguide (mode) diperion [9]. Procedure According o general waveguide heory, guided mode, and alo radiaion mode, in a circularly ymmeric waveguide can be labeled according o heir azimuhally or angular ymmery order. We have aken advanage of hi fac o olve he differen angular order, v, eparaely. In pracical erm, he ue of roaional ymmery reduce he original D problem (field depending on he wo ranvere coordinae) ino a ID one (field depending on he radial coordinae only). Thi provide no only a higher accuracy for a given number of auxiliary mode, bu alo he differen band rucure for every angular order. Figure 1 how he wo differen band-gap rucure and he modal diperion curve for he guided mode in fiber for v = 1 and v = 0,, including in he laer cae he pecrum of TE mode and omiing TM mode a hey are very imilar. guided mode appear in he forbidden band gap a heir correponding angular order v. In paricular, he ingle guided mode hown in he upper forbidden band for v = 1 i he fundamenal mode of he fiber, which, due o he roaional ymmery of he index profile, correpond o a polarizaion double HE11, a denoed in andard waveguide heory. No oher higher-order mode of any angular ecor appear in ISSN: Iue 1, Volume 8, January 009

3 hi band for he elecion of he geomeric parameer fixed in Fig.. The ranvere ineniy diribuion for any of he wo polarizaion of he fundamenal mode, HE11, and he fir inraband guided mode, TE 01, in Fig. are viualized in Fig. (a) and (b), repecively, for λ = 0. 8μm. Fig. 1. Band-gap rucure and modal diperion relaion curve for wo angular ecor: (a) V = 1 (HE mode), and (b) V = 0 (only TE mode). In boh cae, Λ = 1.190μm and a = 0.48μm. dimenionle coordinae: x / Λ. Fig.. Tranvere ineniy diribuion for: (a) he fundamenal guided mode HE 11 in Fig. 1, and (b) he fir inraband guided mode TE 01 in Fig. 1. In boh cae, λ = 0. 8μm. We have exenively udied he diperion properie of differen high-index-core Braggfiber deign We expec o ailor he chromaic diperion of uch fiber by manipulaing he geomery of he mulilayered cladding. The oal diperion, D, can be given, a a fir approximaion, in erm of he maerial diperion, D m, and he geomeric waveguide diperion, D g, uing he approximae expreion (D= D m + D g ). The maerial diperion i an inpu of he problem. The geomeric diperion of he fiber i given in erm of he geomeric modal effecive refracive index, n g, a D g (A) = - (A/c)d n/da. and, hen, aring from he approximae value for Λ and a, we can fine une hee parameer o obain he expeced diperion behaviour. Uing hi procedure, we have udied he diperion properie of differen fiber deign in wo differen wavelengh window, he fir one locaed around 0.8 μ m and he econd one in he viciniy of he opical communicaion window (around 1.55 μ m ),we would like o emphaize ha all reul refer o he fundamenal mode of a ingle-mode rucure in he upper forbidden band ha correpond o a polarizaion double HE 11. I hould be reed a well ha he high accuracy required o calculae D i fully provided by our modal mehod. In Fig. 3 we preen ome example of poiive, nearly-zero, and negaive flaened diperion deign a 0.8 μ m All of hem how a zero hird-ordered diperion poin. Noe ha he geomeric parameer of he blue curve in Fig. 3 ju correpond o ha of he plo in Fig. 1 and. I i prey clear he unabiliy of he rucure, even in he region well below he criical ilica zero-diperion wavelengh (1.3 μ m ). I i pecially remarkable he poibiliy of obaining a flaened poiive diperion profile cenered around 0.8 μ m (red curve) ha can faciliae he abilizaion of ulrahor olion pule generaed a hi wavelengh by a more effecive uppreion of higher-order diperion erm. Fig. 3. Poiive ( Λ = μ m and a = 0.66 μ m ), nearly-zero ( Λ = μ m and a = 0.48 μ m ), and negaive ( Λ = 1.10 μ m and a = 0.3 μ m ) flaened diperion curve near 0.8 μ m. ISSN: Iue 1, Volume 8, January 009

4 λ ( μm) Fig. 4. Poiive ( Λ = μ m and a = μ m, nearly-zero ( Λ = 4.10 μ m and a = μ m ), and negaive ( Λ = μ m and a = 0.08 μ m ) ulraflaened diperion curve near 1.55 μ m. High-index-core fiber can alo be deigned o achieve ulra flaened diperion behaviour around 1.55 μ m Figure 4 how he curve for he diperion coefficien D correponding o hree differen Bragg configuraion. Noe ha hi ulra flaened behaviour i preerved in a large wavelengh window ha exend over everal hundred of nanomere and, unlike flaened diperion, permi o obain a poin wih zero fourh-order diperion. The unabiliy of he rucure i alo clearly demonraed by he fac ha hee deign own poiive, negaive, and zero D. If we go one ep furher, we can alo recognize divere inermediae iuaion in which D ha a low value and a he ame ime he four-ordered diperion coefficien i null a 1.55 μ m. Some oluion for uch a challenging ak are ploed in Fig. 5. In paricular, we would like o poin ou ha he examinaion of he blue curve in Fig. 6 reveal a fiber deign wih an ulra flaened diperion regime and a low diperion value around 1.55 μ m preening a poin of zero hird- and fourh-ordered diperion a hi wavelengh imulaneouly. Thi i a facinaing reul. However, one ha o ake ino accoun ha in our approach ligh i guided in ilica, no in air, and conequenly, in principle, i uffer from reidual aborpion lo and nonlinear effec a four-wave mixing. The performance of our opical propoal finally depend on he paricular applicaion[16]. Fig.5. Diperion (olid curve) and relaive diperion lope (broken curve), defined a RDS = (dd/da)/d, correponding o hree differen elecion of he rucural parameer o achieve zero four-ordered diperion a 1.55 μ m : red curve ( Λ = μ m and a = μ m, blue curve ( Λ = μm and a = μ m, and green curve ( Λ =4.465 μ m and a = μ m. Anioropic waveguide are propoed for he ue in long-range communicaion opical communicaion yem and for inegraed opical device where conervaion of a given ae of polarizaion of he ranmied radiaion i an eenial requiremen. Calculaion of he parameer of mode in uch waveguide are uually carried ou by approximae mehod baed on perurbaion heory. The underlying aumpion in hee mehod i ha he mode field in anioropic waveguide differ lile from he field in an ioropic waveguide. Approximae mehod make i poible o calculae, wih a preciion ufficien for pracical purpoe, he characeriic of mode in dielecric waveguide wih a relaively weak hape or permiiviy anioropy. However, hee mehod are unuiable for deerminaion of he characeriic of mode and field in waveguide wih an arbirary anioropy. A relaively imple bu quie effecive mehod for calculaion of he parameer of mode (propagaion conan, criical frequencie, ec.) in complex dielecric waveguide i he mehod of hif formula. we will ue hi mehod o calculae he parameer of guided wave in anioropic dielecric waveguide and o deermine he diribuion of he field of uch wave. We hall conider he waveguide diperion aociaed wih he guiding properie of ISSN: Iue 1, Volume 8, January 009

5 waveguide. Wave-guide diperion, anoher ype, i very imilar o maerial diperion in ha hey boh caue ignal of differen wavelengh and frequencie o eparae from he ligh pule. however, wave-guide diperion depend on he hape,deign,and chemical compoiion of he fiber core. Only 80% of he power from a ligh ource i confined o he core in a andard ingle-mode fiber, while he oher 0% acually propagae hrough he inner layer of he cladding. Thi 0% ravel a a faer velociy becaue he refracive index of he cladding i lower han ha of he core.conequenly,ignal of differing frequencie and wavelengh are dipered and he pule become indiinguihable. An increae in he waveguide diperion in an opical fiber can be ued in order o counerbalance maerial diperion [].The parameer of mode in anioropic dielecric waveguide can be deermined by he a mehod of hif formula which i ued o find he normalized field frequency k ( a ) = ω / c where ω i he angular frequency, C i he velociy of ligh in free pace, and he aring poin in he calculaion i he ranvere wave number a for he field of a guided mode ouide he waveguide, which i he ame for wave in he inveigaed waveguide and in a comparion or reference waveguide ( a = a). Here and laer he quaniie idenified by a ilde refer o an inveigaed anioropic dielecric waveguide, wherea hoe wihou a ilde repreen a comparion waveguide[3].the waveguide diperion of any mode in a dielecric waveguide i defined a he produce he propagaion conan of hi mode and i frequency. The propagaion conan of a mode in an anioropic waveguide obained by he mehod of hif formula can be wrien a follow[,7,8]: h = h + Δh + Δh + Δh, (1) l where h and h are he propagaion conan of a mode in he inveigaed anioropic waveguide and of he correponding mode in a circular ioropic comparion waveguide; Δh,and Δh l, are he correcion decribing he influence of he ranvere and longiudinal (axial) anioropie of he refracive index, repecively; Δh i he influence of he hape anioropy on he propagaion conan of mode in a dielecric waveguide. Anioropic waveguide are ued mainly in he ingle-mode regime. We hall herefore conider only he dominan mode in uch waveguide. Bearing in mind ha he difference beween he refracive indice of he core and cladding in fiber waveguide i mall, we can decribe a follow he correcion o he propagaion conan of he dominan HE 11, mode in a fiber waveguide, due o he influence of he ranvere and longiudinal anioropie of he refracive index and due o he ellipiciy of he hape of he ranvere cro ecion: Δh x = 0 () Δh y / h = δ B[1 + J 0 ( u) / J1 ( u)] (3) u Δhl / h = δlδ ( 1 ) + J 0 ( u B ) B [1 J0 ( u )/ uj1 ( )/ J 1 ( u )] (4) o, e ( ) ( u )/ J ( ) /uj 3 1 u 3 Δ h / h =± δδ (1 B) B[1 + 1 υ / u J0 +υ J0 ( u ) 1 ( u )] (5) where Δ = ( n1 n ) / n ; δ = (n y n x ) / n δ l = ( nz nx )n ; δ = (a b ) /( a + b) ; n x, n y and nz are he componen of he refracive index enor of he core of he inveigaed anioropic fiber waveguide; n 1 = n x i he refracive index of he core of he comparion waveguide; n i he refracive index of he cladding which i he ame for boh waveguide; a and b are he major and minor emi axe of he ellipe repreening he ranvere cro ecion of he core of he inveigaed waveguide; B = υ / V ;V = u + υ ;u and υ are he inernal and exernal normalized ranvere wave number of he mode. Equaion () decribe he dominan mode in a waveguide wih a ranvere anioropy of he dielecric in which he elecric field vecor i polarized along he X axi, wherea Eq. (3) applie o a mode polarized along he Y axi. In Eq. (5) he upper ign applie o he odd (o) and he lower ign o he even (e) dominan mode in an ellipic fiber waveguide. In dielecric waveguide he longiudinal (axial) anioropy creaed in he proce of heir drawing from a blank i fairly weak: δ 10 5 l [10]. Moreover, he longiudinal componen of he mode field in fiber waveguide i very mall compared wih he ranvere componen. Therefore, he influence of he longiudinal anioropy of he refracive index on he propagaion conan of mode i le han he influence of he ranvere anioropy of he refracive index or of he hape anioropy, o ha we hall ignore he effec of he longiudinal anioropy. Thi alo follow from a ISSN: Iue 1, Volume 8, January 009

6 comparion of Eq. ()- (5) bearing in mind ha we 3 ypically have Δ 10. By definiion he waveguide diperion in anioropic fiber waveguide, ubjec o Eq. (1), can be wrien in he form: dh Δh dh d Δh = (1 + ) + h ( ), (6) dk h dk dk h where Δh = Δh + Δh applie o an ellipic waveguide wih a ranvere anioropy of he dielecric; in paricular, we have Δh = Δh for a circular waveguide wih a ranvere anioropy of he dielecric and Δh = Δh for an ellipic waveguide wih an ioropic dielecric. The propagaion conan of he dominan mode in a circular ioropic comparion waveguide can be repreened by: 1/ h = k[ n + ( n1 n ) B] or, wihin erm of he order of Δ, by h = kn [1 + ΔB + Δ B(1 ) / ] (7) B Then, he waveguide diperion of hi waveguide can be wrien a follow: dh = n [ 1 + ΔB + Δx 0 (1 B) + dk 5 Δ (1 B ) B + x0 x0 B x0 B ] (8) where x 0 = [ K 0 ( υ) / K1( υ)] Subiuing in Eq. (6) he expreion (), (3), and (5) we obain a formula for he calculaion of he waveguide diperion of an anioropic fiber waveguide: dh dh = + D + D (9) dk dk where dh /dk i defined by Eq. (8), wherea x = 0 (10) D and y u 1/ u u u D = n δ B{ 1 x0 + 5 x 0 ( 1) x υ υ υ υ 4 u u u 5 / + ( 1) x 0 + x 3 0 υ υ υ 3/ 0 4 V u u 1/ 3/ + Δ( 1 B)[1 x0 + 3x0 + υ(1 3 ) x 4 0 υ υ υ 4 u u u u 5 / ( ) x (1 + ) x 3 0 υ υ υ υ 4 u u 3 u 7 / + (1 + ) x0 x0 ]} (11) 3 υ υ υ decribe he influence of he ranvere anioropy of he dielecric on he mode diperion of he dominan mode polarized along he X and Y axe, repecively, and o, e u 1/ D = ± nδ Δ B( 1 B)[1 ( υ) x0 υ 4 u u u 3 / + ( 5 5 3u ) x 0 + (9 υ ) x 3 0 υ υ υ 4 4 u u u + ( 3u ) x 4 0 υ υ υ 4 u u 5 / u ( 1) x0 + 3 x0 ] (1) υ υ υ decribe he influence of he hape anioropy of he ranvere cro ecion on he waveguide diperion of he dominan odd (upper ign) and even (lower ign) mode. Thee expreion can alo be ued o calculae he polarizaion diperion in an anioropic fiber waveguide: dβ dh dh x y y = = D (13) dk dk dk in he cae of waveguide wih a ranvere anioropy of he dielecric, e o dβ dh dh = = D (14) dk dk dk In he cae of waveguide wih an ellipic ranvere cro ecion, and dβ y = D + D (15) dk In he cae of ellipic waveguide wih a ranvere anioropy of he dielecric. Here, e o β = β + β, β = h x h y, β = h h ; e o and h y, h and h are he propagaion conan of, repecively, he dominan mode polarized along he X and Y axe, and of he even and odd dominan mode in an ellipic waveguide. The expreion for he polarizaion diperion in an ioropic waveguide wih an ellipic ranvere h x ISSN: Iue 1, Volume 8, January 009

7 cro ecion, imilar o Eq. (14), had been obained earlier by oher auhor (ee, for example, Ref. 11). Moreover, experimenal value of he polarizaion diperion in an opical waveguide wih a ranvere anioropy of he refracive index and an ellipic waveguide were obained in Ref. 1. Therefore, i i poible o compare he value of he polarizaion diperion calculaed uing Eq. (13)-(15) wih hee experimenal value. The anioropy of he refracive index in he ranvere cro ecion of a waveguideδ, can be calculaed fromeq. (7) of Ref. 1 if we know he exernal preure p on he waveguide core. The coninuou line in Fig. 6 repreen he polarizaion diperion dβ / dλ for a circular anioropic fiber 3 waveguide wih Δ =.10 calculaed from (13). For variou value of λ ( λ i he wavelengh). The dahed line are drawn hrough he experimenal poin aken from Ref. 1. The experimenal value hemelve are repreened by circle in Fig. 6. I i hu clear ha he expreion derived above are ufficienly accurae for pracical calculaion of he waveguide and polarizaion diperion of he dominan orhogonally polarized mode in an anioropic fiber waveguide. A waveguide can conerve ably a given polarizaion ae of he ranmied ignal if a ranvere anioropy of he permiiviy and δ 10 4 i eablihed in he waveguide[13]. Figure 7 how he value of he waveguide diperion for anioropic fiber waveguide wih 3 Δ = Curve -5 denoe he waveguide diperion of mode polarized along he Y axi raveling in waveguide wih anioropy δ of 5.10, 10,10, and Curve 1 repreen. 3 Reul and Dicuion The waveguide diperion of mode polarized along he X axi in he ame waveguide. Moreover, hi curve repreen alo he waveguide diperion of he dominan mode in an ioropic waveguide. The abcia in Fig. 7 give he value of he normalized frequencyv = π Rn Δ / λ, where R i he waveguide radiu. I i clear from Fig. 7 ha he anioropy of he dielecric increae rongly (or reduce, depending on he ign ofδ ) he waveguide diperion of opical fiber waveguide. The maximum waveguide diperion for waveguide wih differen value of he ranvere anioropy of he inulaorδ, i aained a differen frequencie. Fig.6: calculaed and experimenal value. We can ee from Fig. 6 ha he difference beween he calculaed and experimenal value of he polarizaion diperion doe no exceed 7% of waveguide parameer indicaed in Fig. 6. In an inveigaion [1] of an ellipic waveguide 3 wih δ =0.1 and Δ =.9.10 a λ = 1.1 μ i wa found ha dβ 6 dβ 6 = wherea = i he dk dk value obained from Eq. (14) for a waveguide wih he ame parameer. I herefore follow ha ifδ 0. 1, hen calculaion baed on Eq. (14) are ubjec o an error no exceeding 9.4%. Fig.7:Value of normalized frequencie. ISSN: Iue 1, Volume 8, January 009

8 Fig.8:- maximum value of diperion. Moreover, he maximum waveguide diperion of orhogonally polarized mode raveling in anioropic fiber waveguide alo occur a differen frequencie. Coninuou curve in Fig. 8 are he normalized frequencie V a which he waveguide diperion ha i maximum value, ploed for waveguide wih δ 0 (curve 1) and δ 0 (curve ). The deviaion from he circular ranvere cro ecion of a waveguide (hape anioropy) alo aler he waveguide diperion. In hi cae he waveguide diperion of even orhogonally polarized mode of ellipic waveguide wih differen degree of ellipiciy δ ha i maximum value a he ame frequencyv = π R n Δ / λ where R = ( a + b) / i he radiu of a comparion waveguide (dahed line in Fig.8). A hi frequency he waveguide diperion of he dominan mode of he circular comparion waveguide alo ha i maximum value. The waveguide diperion of an ellipic waveguide agree, wih he accuracy of he caer in he graph, wih he value of he waveguide diperion for a circular waveguide (curve 1 in Fig. 7). Figure 9 make i poible o deermine he order of he waveguide diperion of an ellipic waveguide. The coninuou and dahed curve in Fig. 9(a) repreen he value of he waveguide diperion for even and odd mode of an 3 ellipic waveguide wih Δ = 3.10 and wih differen value of he raio of he minor and major emi axe of he ranvere-cro ecion ellipe b /a calculaed for V=.010, wherea he correponding curve in Fig. 9(b) give he reul of calculaion for V= In hi paper we have dicued he diperion properie of fiber. We have numerically demonraed he abiliy of hee rucure o how, for ome pecific deign, a flaened diperion behavior (one poin of zero hird-order diperion) around 0.8 μ m and even an ulraflaened behavior (one poin of zero fourhorder diperion) around 1.55 μ m Moreover, we have recognized ome configuraion exhibiing poiive, negaive, or nearly-zero conan diperion in boh wavelengh window. Finally, a noeworhy fiber deign ha combine low and nearly-conan chromaic diperion abou 1.55 μm wih zero hird- and fourh-order diperion a 1.55 μm ha been idenified. Alo he ingle-mode fiber provide a oluion o he problem of polarizaion and diperion. we hu derived expreion for he calculaion of he waveguide and polarizaion diperion of dominan orhogonally polarized mode in anioropic fiber waveguide. The anioropy of he dielecric in he ranvere cro ecion a well a he hape anioropy aler he waveguide diperion of hee mode compared wih ha in an ioropic waveguide. In he cae of waveguide capable of conerving he Polarizaion of he ranmied ignal ( δ 10 4 ).alo in hi work, he polarizaion and polarizaion-mode diperion in fiber have been dicued. Analyi of opical fiber ha mainain polarizaion over long lengh, provide zero polarizaion-mode diperion. he zero polarizaionmode diperion ingle-mode deign i a diperionhifed fiber ha provide large effecive area and hence reduce ignal diorion due o nonlineariy in fiber.a comprehenive analyi of polarizaionmode diperion in muliple-clad fiber due o ellipiciy of fiber cro-ecion wa carried ou uing a perurbaion echnique. The deign of large effecive area ingle-mode diperion-hifed fiber ha provide zero polarizaion-mode diperion a he wavelengh 1.55 μm wa accomplihed uing he analyi developed. ISSN: Iue 1, Volume 8, January 009

9 The influence of change in he anioropy on he waveguide diperion of he fundamenal mode in an anioropic dielecric-waveguide i differen from he effec of he permiiviy anioropy. The propoed mehod can be ued o calculae he main parameer of guided wave in anioropic (in a wide ene) dielecric waveguide which can conerve a given ae of polarizaion of he ranmied ignal. Thi mehod ha been ued o calculae he propagaion conan and he waveguide diperion of he fundamenal mode in an anioropic dielecric waveguide and he diribuion of he field of hee mode. The reul how ha under he influence of he anioropy of he dielecric an energy po decribing he diribuion of he field of he fundamenal mode in dielecric waveguide loe i circular ymmery and become an ellipe elongaed along he coordinae axe which coincide wih he principal axe of he permiiviy enor. he influence of change in he anioropy on he waveguide diperion of he fundamenal mode in an anioropic dielecric-waveguide i differen from he effec of he permiiviy anioropy. Fig.9 :-( a) value of he waveguide diperion for even and odd mode. (b) Reul of calculaion for V= Concluion The change due o he anioropy of he dielecric are much greaer han he change in he waveguide diperion due o he hape anioropy. The ranvere anioropy of he refracive index i he reaon why he waveguide diperion of he mode polarized along muually perpendicular direcion have maxima a differen frequencie. The propoed mehod can be ued o calculae he main parameer of guided wave in anioropic (in a wide ene) dielecric waveguide which can conerve a given ae of polarizaion of he ranmied ignal. Thi mehod ha been ued o calculae he propagaion conan and he waveguide diperion of he fundamenal mode in an anioropic dielecric waveguide and he diribuion of he field of hee mode.. The reul how ha under he influence of he anioropy of he dielecric an energy po decribing he diribuion of he field of he fundamenal mode in dielecric waveguide loe i circular ymmery and become an ellipe elongaed along he coordinae axe which coincide wih he principal axe of he permiiviy enor. 5 Suggeion For Furher Inveigaion The analyi of polarizaion-mode diperion preened here accoun for fiber cro-ecion ellipical deformaion. However, in addiion o core ellipiciy, random reidual re alo conribue o polarizaion-mode diperion. Thu, he analyi of polarizaion-mode diperion hould be exended o random anioropy in he fiber. Reference: [1] C. Gilda,Diperion in Opical fiber,anriu corporaion,draf TIA FOTP-14-A (004). [] V. V. Shevchenko, Mode Polarizaion ranformaion in opical waveguide, Radioelekron.Vol 6, No. 5, 00,p [3] M.Y. AL-Gawagzeh, The effec of anioropy implemenaion on componen of opical ranmiion line, Inernaional Conference on Informaion and Communicaion Technologie: From Theory o Applicaion, 004, p [4] F. Ruhl and A. W. Snyder, Single-mode, ingle-polarizaion fiber made of birefringen maerial, J Op. Soc. Am,Vol.73,No.9,1983,p ISSN: Iue 1, Volume 8, January 009

10 [5] S. C. Rahleigh, Polarizaion characeriic of anioropic ingle-mode fiber waveguide J. Lighwave Technol. Vol.1, No.3, 1983, p [6] W. Snyder and W. R. Young, Mode of opical wavequide,j. Op. Soc. Am.,Vol 68,No.3,1978,p [7] A.B. Androilk,G.V Faeeva, Radiaion caering in ingle-layer opical fiber,springerlink,vol34,no.6,1991,p [8] A V Belov e al, Maerial diperion in quarz gla fiber waveguide, Sov. J. Quanum Elecron,Vol. 8, 1978, p [9] G.Cancellieri,P.Fanini, and U. Peciarelli,Effec of join on ingle-mode ingle-polarizaion opical fiber link, Appl. Op. Vol.4, 1985, p [10] J.M Arnold, Anioropic Effec in non-linear opicalwavequide, wavemoion, Vol.34, No.3, 001, p [11] D. I. Mirovikil, I. F. Budagyan, and V. F. Dubrovin, Microwave Opicand Holography [in Ruian], Nauka, Mocow (1983), p. 99. [1] M. J. Adam, An Inroducion o Opical Waveguide, Wiley, New York(1981). [13] N. Imoo, N. Yohizawa, J.-I. Sakai, and H. Tuchiya, IEEE J. Quanum Elecron. QE-16, 167 (1980). [14] R. H. Solen, V. Ramawamy, P. Kaier, and W. Pleibel, Sov. J. Quanum Elecron, April [15] C. Vlcek, Sudy of Exernal Effec on he Polarizaion Properie of Seleced Fiber Segmen.WSEAS Tranacion on Communicaio, Iue 4, Volume 5, April 006. [16] J. A.Monoriu & oher, High-index-core bragg fiber:diperion properie,opical Sociey of America,vol.11,No.1,june 003. [17] P.Kryzof, Idenificaion of Polarizaion Configuraion baed on Torion and Curvaure Calculaion, WSEAS Tranacion on Communicaio, Iue 4, Volume 5, April 006. [18] G. S. Kliro, J. Konaninidi, C. Thrakia, WSEAS Tranacion on Communicaio, Iue 8, Volume 5, Augu, 006. ISSN: Iue 1, Volume 8, January 009