Investigation of Chromatic Dispersion and Pulse Broadening Factor of Two New Multi-clad Optical Fibers

Transcription

1 6 CSNS tertiol ourl of Coputer Siee Network Seurity VOL.6 No.8 August 6 vestigtio of Chroti ispersio Pulse Broeig Ftor of Two New Multi-l Optil Fibers Ali Rosti Mortez Svi Oskouei Photois Norystls Reserh Lb. (PNRL Fulty of Eletril Coputer Egieerig iversity of Tbriz Tbriz 66 r Tel/Fx: Sury this pper two ew iterestig ulti-l optil fibers re itroue their properties fro y spets re ivestigte opre together. For the propose optil fibers two i hrteristis suh s ispersio pulse broeig re lulte eostrte. Sesitivity of the propose fibers to optil geoetril preters re lulte isusse. e show tht itroue type- optil fiber is so sesitive to optil geoetril preters th type-. So type- is better th type- fro otrol of the hrteristi of the fiber poit of view is esy for tuig. Also i sll wvelegths ets of optil geoetril preters o ispersio pulse broeig is osierble th lrge wvelegths. Our siultios show tht i type- zeroispersio wvelegth oves to lrge wvelegths. ey wors Multi-l optil Fibers ispersio Pulse Broeig. troutio Reetly high-spee brob optil ouitio is bsi e i iustry. Highspee t ouitio is oe of serious request for rel tie proessig. Optil fiber bse ouitio is oe of best ltertives for these purposes. Optil fiber bse high-spee ouitios ee low ispersio s well s ispersio slope lrge bwith supporte by optil physil eiu. Nowys pplitios suh s tie ivisio ultiplexig (OTM ese wvelegth ivisio ultiplexig (M re usul tsks i iustry. Thus with osierig these pplitios proviig lrge bwith highspee ouitio possibility usig optil fibers is highly iterestig. For ouitio usig sigle wvelegth ispersio shifte fibers is eough. But for pplitios suh s M sie there re y wvelegths s rriers this etho t provie high-spee possibility. these pplitios physil eius ielly shoul be provie flt iiu uifor ispersio s well s ispersio slope. Also with evelopig flt ispersio hrteristi olier ets suh s Four ve Mixig (FM beuse of phse isthig oes't liit the bwith of the fiber the uber of hels i M pplitios. For this purpose there re soe publishe ppers tht isusse ew fiber strutures to obti these properties. As first iterestig work we poit out to pper presete by R.. Vrshey et l []. this pper optil flt fiber ws presete to iiize ispersio ispersio slope. this esig ore rius etive re rrier wvelegth re μ6.μ.μ respetively whih re use orig to their lultio ispersio urtio withi 6 ispersio slope t. μ re.7. ps / k..ps / k. respetively. The presete pper itroues 8 bwith tht is sll for toy M pplitios. Also the reporte ispersio is eough high for high-spee t trsissio. Filly the presete work ilues oly C L bs for t trsissio. A seo work reporte by X. Ti et l [] tht isuss bout iresig of the etive re for R R triplel fibers. This pper reporte. ps / k. for ispersio withi 6 wvelegth urtio. Also for this esig ispersio slope reporte bout.6 ps / k. withi 6 wvelegth urtio. The propose esig hs sll bwith for M pplitios lso high ispersio i this urtio. The lulte ispersio slope i this pper is ot so sll for high-spee t trsissio. There re other ppers presete to iiize ispersio shift to requeste vlues [-6]. these works ispersio lultio iiiztio shiftig were isusse. The obtie results o't stisftory. Also i [ 7] there re very iterestig ethos presete for ispersio opestio geet. For this purpose i this pper two ew fiber strutures re osiere ivestigte fro ispersio pulse broeig ftor poit of views. For this purpose fiels istributio isie the propose fibers bse o the Mxwell's equtios re lulte. The usig boury oitios guie oes wve vetors re obtie. sig wveguie teril ispersio reltios the propose strutures re evlute siulte results re presete i results setio. Also for pulse

2 CSNS tertiol ourl of Coputer Siee Network Seurity VOL.6 No.8 August 6 6 broeig siilr tretet is oe. Our results show the pbility of itroue type- fiber for tuig of zero-ispersio wvelegth uifority of ispersio. Thus the propose is pble for lrge rge of tuig. Orgiztio of the pper is s follows. Mthetil oelig for ispersio lysis pulse broeig is presete i setio. setio siultio results isussio re illustrte. Filly the pper es with olusio.. Mthetil Moelig this setio the followig speil fiber strutures (Fig. for ispersio urve ivestigtio re osiere. The refrtive iex istributio futio is efie s follows. ( r r r b = b r r r here r is the rius positio of optil fiber. - - Fig. The iex of refrtio profiles of two fibers with efie preters - b - ( For these strutures the etive iex of refrtio is give by = β / k where β is the propgtio wve vetor of guie oes k is the wve uber i vuu. Bse o the etive refrtive iex the propose strutures (- - be ivie to three regios of opertio respetively whih is efie s follows. : ( : : : : : ( Now orig to the Mxwell's equtios the followig tble shows fiel istributio for these strutures (type- type- respetively. Also for these strutures the followig orlize frequeies iex of refrtios re use. -: β V = k k B = (- -: β V = k k B =. (-b Now boury oitios (eletri geti fiels otiuities i b be pplie to the presete fiel istributios i Tble- below eterits ( re obtie. Fiig zeros of the etioe bove eterits will itroue guiig wve vetors t y give wvelegths. Plese refer to the ppeix. these tbles trsversl wve vetors re give s follows. = k β = β k = k β k = β = k β = β k b = β k = β k. P P = = = Q Q P = = L L ( Bse o obtie guie wve vetors bsi reltios for wveguie teril ispersios the followig reltio gives totl ispersio for the itroue sigle oe ulti-l optil fibers. λ ( VB N Δ ( VB = [ + Δ ] V λ V λ V ( where N = λ is the group iex of the λ outer lig lyer. Also the Selleier forul be use for lultio of teril ispersio (. For pulse broeig ftor the λ λ followig reltio is use.

3 6 CSNS tertiol ourl of Coputer Siee Network Seurity VOL.6 No.8 August 6 σ Cβ ( λ Z β ( λ Z = [( + + σ t t i i ( β( λ Z + ( + C ] t i where σ C t i λ Z β β re pulse broeig σ ftor hirp preter iitil full with t hlf xiu of iput pulse wvelegth iste seo erivtive of the guie wve vetor thir erivtive of the guie wve vetor respetively. For iorportig the optil geoetril preters i siultio esy olusios we efie the followig preters i siultio setio the ets of these preters re ivestigte. -: Optil Preters: R = R = R = Δ = ( Geoetril Preters: b P = Q = L = -: Optil Preters: R = R = R = Δ = ( Geoetril Preters: b P = Q = L =. Siultio Results isussio this setio siulte results re presete isusse. First we osier ispersio behvior of the propose two strutures. These siultios hve bee oe orig to = μ Q =. P =. 7 L =.6 R =. R =. 6 R = 7 geoetril optil preters. Eh preter is vrie oe t tie to ivestigte the et of this preter o ispersio urve broeig ftor t.μ fter k trsissio. ispersio of the propose strutures versus ore rius is illustrte i Fig.. As it is see for these three ore rius i type- the ispersio try to be uifor for =.7μ zero-ispersio wvelegth is shifte to higher wvelegths with irese of ore rius. So these strutures be optiize to obti optiu flt sooth ispersio hrteristi. Also wvelegth urtio of tuig for type- is wie opre type-. The et of Δ o ispersio hrteristi i the fibers is illustrte i Fig.. Zero-ispersio wvelegth is irese with irese of Δ. Also tuig rge for type- is wie opre type-. ispersio ispersio x wvelegth(u Fig. ispersio Vs. velegth for troue x - -=u -=.u -=.u Typr-=u -elt=. -elt=. -elt=. -elt= wvelegth(u Fig. ispersio Vs. velegth for troue Effet of L o ispersio urve lso is illustrte i Fig.. Effet of P Q o ispersio urves re illustrte i Figs. ( 6. rese of P use irese i zero-ispersio wvelegth. But irese of Q erese the zero-ispersio wvelegth. ispersio x L=.6 -L=.7 -L=.6 -L= wvelegth(u Fig. ispersio Vs. velegth for troue

4 CSNS tertiol ourl of Coputer Siee Network Seurity VOL.6 No.8 August 6 6 ispersio x P=.7 -P=. -P=.7 -P= velegth(u Fig. ispersio Vs. velegth ispersio x R=. -R=.7 -R=. -R= wvelegth(u ispersio x Q=. -Q=. -Q=. -Q= wvelegth(u ispersio x Fig. 8 ispersio Vs. velegth -R=6 -R=9 -R=6 -R=9 ispersio x Fig. 6 ispersio Vs. velegth -R=. -R=. -R=. -R= wvelegth(u Fig. 7 ispersio Vs. velegth wvelegth(u Fig. 9ispersio Vs. velegth Pulse broeig for these fibers ( C = t i = ps is osiere with hge of syste preters. Clerly type- hs sll broeig ftor but it is sesitive to ore rius opre type- tht illustrte i Fig.. Effet of Δ o pulse broeig for two fibers is ivestigte illustrte i Fig.. this figure lso siilr to the previous figure the situtio for type- is better th type- but type- is sesitive Effets of R R R o ispersio urve re illustrte i the followig. Fro these preters R hs strog et o zero-ispersio shift i type- optil fiber. Also R hs't y osierble et o type-. Pulse Broeig Ftor -=u type-=.u -=.u -=u.. iste. x Fig. Pulse Broeig Ftor Vs. iste

5 6 CSNS tertiol ourl of Coputer Siee Network Seurity VOL.6 No.8 August 6 Pulse Broeig Ftor elt=. elt=. Pulse Broeig Ftor -Q=. -Q=. -Q=. -Q=... iste. x Fig. Pulse Broeig Ftor Vs. iste Effet of L o pulse broeig is illustrte i Fig.. this se lso the situtio for type- is better th type-. Pulse broeig is erese with irese of L. Effets of P Q o pulse broeig ftor re illustrte i Figs. (. These preters hve't osierble ets o pulse broeig. Aywy the situtio for type- is better th type-. Pulse Broeig Ftor -L=. -L=.7 -L=. -L=.7.. iste. x Fig. Pulse Broeig Ftor Vs. iste Pulse Broeig Ftor.. iste. x Fig. Pulse Broeig Ftor Vs. iste -R=. -R=. -R=. -R=... iste. x Fig. Pulse Broeig Ftor Vs. iste Effets of R R R o pulse broeig re illustrte i Figs. ( 6 7. Sll R big R re better fro pulse broeig poit of view. Also situtio for type- is better opre type-. Pulse Broeig Ftor -P=. -P=.7 -P=.7 -P=. Pulse Broeig Ftor -R=.7 -R=. -R=. -R=.7.. iste. x Fig. Pulse Broeig Ftor Vs. iste.. iste. x Fig. 6 Pulse Broeig Ftor Vs. iste

6 CSNS tertiol ourl of Coputer Siee Network Seurity VOL.6 No.8 August 6 6 Pulse Broeig Ftor R=6 R=9.. iste. x Fig. 7 Pulse Broeig Ftor Vs. iste Aorig to the siulte results the followig olusios be obtie. - Zero-ispersio wvelegth is shifte to higher wvelegths with erese of R i both type of fibers the et i low sll wvelegths is stroger. Also with irese of R the slope of ispersio is erese. Filly et of R o type- is serious th o type-. - Zero-ispersio wvelegth is shifte to higher wvelegths with erese of R i both type of fibers the et o type- is serious. - Chge of R hve t osierble et o zero-ispersio wvelegth i both fibers. - rese of Δ P L hve osierble et o type- fiber irese the zeroispersio wvelegth to higher wvelegths.. Alysis Siultio of ispersio legth Higher-orer ispersio legth Nolier-et legth Aorig to Eqs. (-8 the etive-re A ispersio legth L the higher orer ispersio legth L olier et legth L Nl s futio of wvelegth λ re showe respetively i figs. (--(- for - - optil fibers. ti L = (7 β L NL = (8 Pγ k here γ = P re olier ouplig A oiiet iput pulse power olier refrtive iex oiiet. our siultio P = w =.e ( / V. These siultios hve bee oe orig to = μ Q =. P =. 7 L =.6 R =. R =. 6 R = 7 geoetril optil troue preters. - Fig.. 8 shows tht the etive re of - is lrger th etive re of -. t is useful to iti tht the higher etive re the loger olier et legth. t is obvious i Fig (-. ith osierig of Figs. (8- it be see tht L L L L. NL Cosequetly the i liittio ftor i log hul ouitio systes is ispersio vlue for oo trsissio legths higher orer ispersio olier et o the pulse broeig be igore with efie preters i this pper. etive re(u wvelegth(u Fig 8 Effetive re Vs. wvelegth A = π Ψ Ψ ( r ( r rr rr ( L = i t β (6

7 66 CSNS tertiol ourl of Coputer Siee Network Seurity VOL.6 No.8 August 6 higher-orer ispersio legth(k 8 6 olier-et legth(k 8 6 ispersio legth(k 6 x wvelegth(u Fig 9 ispersio legth Vs. wvelegth wvelegth(u Fig higher- orer ispersio legth Vs. wvelegth wvelegth(u Colusio this pper two ew ulti-l optil fibers hve bee osiere their ispersio pulse broeig were stuie. Our siulte results hve show tht itroue type- optil fiber hs high sesitivity to optil geoetril preters. Also i wie rge it hrteristis be tue. This is iterestig poit for tuig purpose. Also the other fiber hs sll sesitivity to those preters. Fro tolere of preters poit of view this fiber is stble. Also i sll wvelegths the ets of optil geoetril preters re strog opre to higher wvelegths tht re sturtio i ispersio behvior for both strutures. Filly type- hs sll ispersio slope opre to type- lrge zero-ispersio wvelegth. Referees [] R.. Vrshey A.. Ghtk. C. Goyl S. Atoy C esig of Flt Fiel Fiber with very sll ispersio Slope Optil Fiber Tehology 9 ( pp [] X. Ti X. Zhg ispersio-flttee esigs of the Lrge etive-re Sigle-oe Fibers with Rig ex Profiles Optis Couitios ( -. [] X. Zhg X. Ti Alysis of veguie ispersio Chrteristis of - -type triple-l Sigle-oe Fibers Optis & Lser Tehology ( 7-. [] T. to M. Hiro A. T. Foku T. Fujii T. Ooishi. okoy M. oshi M. Oishi ispersio flttee trsissio lie osistig of wieb o-zero ispersio shifte fiber ispersio opestig fiber oule Optil Fiber Tehology 8 ( -9. [] Govi P. Agrwl Fiber-Opti Couitio Systes oh wiley & Sos Thir Eitio. [6] X. Zhg X. g The Stuy of Chroti ispersio Chroti ispersio Slope of - -type triple-l Sigle-oe Fibers Optis & Lser Tehology 7 ( [7] A. Ghtk. Thygrj troutio to Fiber Optis Cbrige iversity Press. Fig olier- et legth Vs. wvelegth

8 CSNS tertiol ourl of Coputer Siee Network Seurity VOL.6 No.8 August 6 67 : ( = (6 : ( = (7 = : ( (8 = : ( (9

9 68 CSNS tertiol ourl of Coputer Siee Network Seurity VOL.6 No.8 August 6 Tble-- Trsversl Fiel istributio for ifferet regios etive-refrtive iex rges Regio (- (- (- r r r A A A r r r r r r B + C B + C B + C( r r + E( r r r r + E( + E( V r r r r r r F + G F + G F + G V r r H H r H Tble--b Trsversl Fiel istributio for ifferet regios etive-refrtive iex rges Regio (- (- (- r r r A A A r r r r r r B + C B + C B + C r r r r r r + E( + E( + E( V r r r r r r F + G F + G F + G V r H r r H H