Department of Electrical and Computer Systems Engineering

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1 Department of Electrical an Computer Systems Engineering Technical Report MECSE-7- Design of ispersion flattene an compensating fibers for ispersion-manage optical communication systems L.N. inh, K-Y Chin an D. Sharma

2 > JLT-xxxxx- MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma Design of ispersion flattene an compensating fibers for ispersion-manage optical communications systems L. N. inh, Member IEEE, K-Y Chin an D. Sharma Abstract Single moe optical fibers having minimum non-zero ispersion over the spectral winows of an 55 nm region are essential for the multi-channel operation of ense wavelength multiplexe systems an minimizing the nonlinear four wave mixing effects This paper emonstrates that nonzero ispersion flattening of the ispersion factor extens over a wavelength range of more than 5 nm is achievable. We present the esign of the ispersion flattening of the non-zero ispersion fiber (NZ-DF with minimum of ispersion factor, as well as ispersion compensating fiber (DCF that allows complete ispersion compensation over entire S- to L-bans of the thir communications winow.the overall ispersionlength (DL prouct of a fiber span can be tailore to be close to zero. Hence the esigne composite fiber length of a kappa value of with a DL prouct of zero for the span length of Kms of the fiber is emonstrate. The effects of the geometrical an inex istribution parameters of the triple-cla profile to sensitivity of the total ispersion factor of the DFF an DCF are analyze. We also outline esign guielines for ientifying the critical parameters an steps for tailoring the fiber ispersion property. Key wors: optical fibers; optical fiber ispersion; wavelength ivision multiplexe optical fiber systems, Gb/s transmission systems. INTRODUCTION Single moe optical fiber with minimum ispersion at the two optical winows in the nm an 55 nm wavelength are expecte to be critically important for ultra-long high-spee an ultra-high capacity optical communication systems an networks in the near future global internetworking. In particular for optical communications transmission system that employs wavelength multiplexing optical carriers. The Manuscript receive November 8,. The authors are with Department of Electrical an Computer Systems Engineering, Monash University, Victoria 68, Australia ( le.nguyen.binh@eng.monash.eu.au. THE CONTENT OF THIS REPORT IS THE SUJECT OF A TECHNICAL PAPER SUMITTED TO THE IEEE JOURNAL OF LIGHTWAVES TECHNOLOGY eman to expan the transmission capacity requires investigation of wavelength ivision multiplexe telecommunications an the pulse broaening effects of optical fibers over the optical spectrum. The availability of single moe optical fibers with a minimum an flattene characteristics in ispersion an insensitive to micro-bening loss an other aitional losses will enhance the system engineering of these fibers. In aition the commercial availability of Er:ope fiber amplifiers have allowe system esigners to investigate the use of near-zero ispersion optical fibers to exten the repeaterless istance. Optical amplifiers using Pr:ope glass for the nm has also been evelope an woul be potentially use for optical fiber systems an networks. Furthermore New types of optical amplifiers, incluing both lumpe an istribute types, such as Raman, EDFAs an hybri EDFA plus Raman offer very ultra-wie ban DWDM optical communications. It is therefore expecte that optical channels over the entire spectrum between these wavelength winows woul be use []. Ultra-high spee an ultra-wie banwith optical systems are require for maximizing the capacity of the optical transmission meium. It is thus esire to esign an evelop optical fibers that woul have minimum non-zero an flattene ispersion over this ultra-broa spectral range. Furthermore practical emonstrations of optical soliton fiber systems [] have attracte interests to esign of optical fibers which exhibit appropriate ispersion property to esign ispersion-allocate [] or ispersion-manage [] optical fiber systems. The optical soliton transmission systems require accurate preiction of the ispersion factor of fibers in each section of transmission istance. Avance esign of single moe fibers have been reviewe in numerous papers. Recently we have introuce key strategies for the esign of optical fibers with moifie ispersion characteristics [5]. This paper presents a new algorithm for fining in the sale point of the waveguie epenent parameter that plays a maor role in the waveguie ispersion factor for simplifying further the esign of the ispersion profile of single moe fibers to ensure minimum ispersion. In this paper we present the following aspects of ispersion flattening in a non-uniform core optical fiber as follows. In the next section the backgroun for moeling of ispersion

3 > JLT-xxxxx- flattene triple-cla fiber an an overview of the group velocity ispersion is also given with the view to focus to the evelopment of the new algorithm for tailoring the ispersion characteristics of the triple-cla inex profile fibers. Section then gives the esign guielines for esign of non-uniform core inex profile to achieve significantly large waveguie ispersion to equalize that of the material ispersion. In particular the operating regions of the waveguie parameters are specifie to obtain such equalization. Simulate results an iscussions will be given in Sections with a summary of the finings is given in Section 5. n ( with the first erivative given by ( n (5 DESIGN PARAMETERS AND EQUATIONS A. The Group Velocity Dispersion (GVD the secon erivative is given by The total ispersion factor, D in the unit of ps/(km-nm of a single optical fiber is given by: 5 ( n (6 DM DW c D β π ( where the parameter β is well known as the GVD parameter; D M an D W are the material an waveguie ispersion factors respectively. Although these factors are well known we believe that a brief summary of the meaning of these factors is essential to present our new algorithm for esigning the tripe cla optical fibers with ispersion flattene characteristics. an thir erivative given by ( n (7 In case that the higher orer ispersion is necessary the thir orer effect of the propagation parameter along the z-irection shoul be taken into account as ω β ω β β ( The material ispersion in an optical fiber is ue to the refractive inex of silica, the material use for fiber fabrication, changes with the optical frequency. The refractive inex n( is approximate by the well known Sellmeier equation: The material ispersion factor, D M is then given by: n M ( ( n c D M (8 where is the resonance wavelength an is the oscillator strength. Here n stans for n or n epening on whether the ispersive properties of the core or claing are consiere. These constants have been tabulate for several kins of fibers in Table. The first three Sellmeier terms, i.e., a, are use. where c is the velocity of light in vacuum. In the spectral range of.5 µm-.66 µm, it can also accurately approximate to the first orer by an empirical relation [6] given by: ZD M D (9 The first, secon an thir erivatives of the Sellmeier s equation can be easily obtaine using symbolic calculation software packages, e.g. Mathematica. The erivatives of the refractive inex as a function of wavelength can then be use to efine the parametersβ, β an the material ispersion factor, D M as: where ZD is the zero material ispersion wavelength. For instance, ZD.76 µm is only for pure silica. ZD can vary in the range µm for optical fibers whose core an claing are ope to vary the refractive inex. The effect of waveguie ispersion D W on pulse spreaing can be approximate in assuming that the refractive inex of the MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma

4 > JLT-xxxxx- MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma material is inepenent of the wavelength. The contribution of D W to the total ispersion parameter D, given by ( epens on the V parameter of the fiber an is given by [6] : n n ( Vb DW V c V ( where V is the normalize frequency an b is the normalize propagation constant which is efine accoring to ifferent regions across the core an claing layers. The normalize waveguie ispersion parameter V (Vb/V epens strongly on V an plays a central role in the pulse spreaing in single moe step-inex fibers. For ope silica fibers, the attenuation minima are in the nm an 55 nm wavelength winows. Segmente-layerinex fibers (e.g. ispersion-flattene fibers are use for high capacity an long istance optical transmission links because of its low total ispersion in that range. It is apparent that ispersion flattening in the wavelength region of the interest can be achieve only if a layer with a lower refractive inex than that of the uniform claing is introuce close to the core ( i.e. epresse claing [5]. n n...( / V ( V (π / a / V b( v n n n 5.98((π / a ( / V ((π / a ( / V n ( / n n a where n a n b n ( i ( i /( ( i ( A /( ( ( c (.5 ( ( E GH ( ( ( D /(8.5 ( E ( F / E in which the coefficients A-H are given by ( D b( i with (i E b( i F ( b( i ( G ( b( i ( 5 D ps / nm km or alternatively as [6, 5] ( H ( b( i ( ( ( πc β A b( i 5 πc β ( b( i ( n n b( v C b( b( i (. The Dispersion Slope The ispersion slope is efine as S S where β an πc ( ( b( v δ n ( ( n n b( v β ( b( v π c n n b( v ( b ( v 6... with... n b( v b( v b( v n n b v π.99 a.996 n (.8 ( V ( V bv.99 (π / a ((.996 / V (... n n (π / a... C. Triple-Cla Profile In this section the relationship between the fiber geometrical structure, the inex profile, its total ispersion, the funamental moe spot size are examine. The sensitivity of the total ispersion of fibers ue to changes in the structural parameters (a, a a, n, n, n, n, n are shown in Figure. Ten ifferent fiber material types are use as core materials an/or claing.the maximum ispersion not higher than ps/(nm.km is set as an example in this work, over the wavelength range of to 58nm an even longer. These materials an their Sellmeir s coefficients are tabulate in Table. They are coe Types - numerically or alphabetically A to H. The waveguie ispersion plays an important role in 'shaping' the total ispersion curve. As there are three layers of claing (Figure, it is expecte to obtain three waveguie ispersion factors for the three claing regions, namely D W, D W an D W. Hence, the effects of each structural parameter are examine to satisfy specific ispersion characteristics. Eq.( clearly shows that the waveguie ispersion epens on the waveguie ispersion parameter, V (Vb/V.

5 Refractive Inex > JLT-xxxxx- MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma Normalise Relative Inex type A ( ( C ( D ( E (5 F (6 G (7 H (8 I (9 J Doping Conc.: Si : % % % 96.9% % 9.% % 9.% % pure % 86.5% % 9.9% % 86.7% % 99% % 5.% Table : Sellmeier's coefficients for silica base material an oping concentration for the esign. n n n n D D n n a a a Raius (b D S S Normalise Raius (b Figure Refractive inex profile of a triple-cla fiber inicating: (a the unnormalize inex profile, an (b the normalize profile n D Numerous attempts to approximate this equation to represent this curve. Thus, the moeling of this curve is to be etermine prior to esigning the fiber. D. Profile Construction The refractive inex profile of the triple-cla step-inex fiber is shown schematically in Figure (a. Figure (b shows the unnormalize profile an Figure (c shows the normalize profile where ai - the i th outer raius, ni - the refractive inex of the i-th layer an n - the refractive inex of the uniform claing. The refractive inex of the i-th layer relative to that of the uniform claing is thus given by [9,]: i n i n n The normalize outer raius is efine as S i a a i The normalize relative inex of the i-th layer is efine as D i i ( ( ( with S an D. It is convenient to express the egrees of freeom in terms of the structural parameters a, S, S, n, D, D an n. A uniform claing of pure silica (Fiber Type A is chosen for analysis in this paper an the Sellmeier expansion is use to calculate the refractive inex an its erivatives with wavelength. Ten ifferent material types (type A to type J of the silica base an ifferent oping concentration of opants as tabulate in Table are also use in the analysis as the core materials of the single-moe triple-cla optical fibers in orer tailoring the total ispersion factor meeting the requirement of maximum total ispersion not larger than a certain limit of ispersion. In this paper we set this limit to ps/(nm.km in the operating wavelength range of nm to 58 nm. This limit can be varie if esire. However in orer to place minimum ifficulty for manufacturing the fiber the limit of ps/(nm.km is sufficient for large banwith-length prouct. A simulation program using MATLA for triple-cla ispersion-flattene single moe fibers is evelope in which ten ifferent material types (type A to type J of single-moe triple-cla optical fibers are use in the esign to meet specifie ceiling of maximum total ispersion in the operating wavelength range of nm to 58 nm. The V-epenent parameter representing the waveguie ispersion parameters D W can be etermine as there is no exact expression to represent the curve. Seven fiber parameters namely core raius (a, first claing raius (a, secon claing raius (a, core inex (n, first claing inex (n, secon claing inex (n an outer claing inex (n that constitute seven egrees of freeom in esigning these fibers.

6 > JLT-xxxxx- 5 MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma The effects of these parameters on total ispersion are stuie an analyze. Furthermore the effects of oping concentration on total ispersion are briefly iscusse. E. Waveguie Guiing Parameters of TheTriple-Cla Profile Fiber The transverse propagation constants of the guie optical fiels u/a an v/a in the core an claing (evanescent fiel regions respectively are given for the core an the fist an secon claing layers (with subscripts, an respectively of the triple-cla inex profile fibers as u a k n β (a u a k n β (b u a k n β (c v a k n β (5a v a β k n (5b v a β k n (5c where β, β an β are the propagation constants in the z- irection of the guie waves in the core an first an secon claing layers of the triple-cla fiber which are given by β k ( b ( n n n β k ( b ( n n n (7b β k ( b ( n n n (7c Thus, the normalize frequencies for all layers can be expresse as efine as V a k n n V ak n n V a k n n Veff ka n ( n n ( n n ( n n r a ln V eff ( The spot size is chosen so that there is a non-zero minimum ispersion can be obtaine an satisfies the requirement for maximum effective area so as to maximize the nonlinear threshol power.. Furthermore with the Gaussian approximation the transverse intensity I(r of the funamental moe is given by: I ( r exp r r ( The waveguie ispersion factors for triple-cla are the extension of equation (an are given by: D W D W D W n n c n n c V V n n V c ( V V b ( V b V ( V V b (a (b (c where the normalize waveguie ispersion factor is V (Vb/V efine with appropriate parameters V for ifferent claing layers. For triple-cla fiber we have the following three normalize waveguie ispersion parameters K K V v v (a (6a V ( V b u K ( K ( v u K (8a (8b (8c ( The spot size r can be foun both analytically an [6, 7]: empirically as where V K V ( V b u ( ( K K v u K K K K V V v v (b V ( V b u ( ( K K v u K K K K V V v v (c with ESSELK (v K ESSELK (v (5a ESSELK (v K ESSELK(v (5b ESSELK (v K ESSELK(v (5c ESSELK i are the i-th orer moifie essel functions. Finally, it is straightforwar to fin the total ispersion of a triple-cla optical fiber that is given by:

7 > JLT-xxxxx- 6 MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma DTOT DM DW DW DW F. Dispersion compensation (6 The esign of fibre esign for Gb/s for the C, L an S ban is the focus of this paper. This section is ivie into two main parts. The first part eals with the esign of DFF for C-an an L- ans. The concept of a DFF has been investigate in the late 97 s for single channel transmission in orer to ensure that the transmission is loss limite rather than ispersion limite an many publishe works can be referre to Refs [5-]. In Ref.[6] a thorough investigation has been carrie out for the oubly cla DFF with in-epth calculations on cut-off properties an inex profile influences. Practical results in this paper were being compare in this works. In [7] mathematical equation like essel functions etc are use for estimating V( (V/V. The iea of DCF ha also been investigate since the early seventies an then extensively accelerate after the avent of optical amplifiers in the 99 s as the transmission system coul no longer be loss limite but ispersion limite.. In [8] extensive mathematical concepts of DCF were presente. Though the Refractive Inex Profile (RIP is not an ieal stepinex type,. The esign principles for DCF have been well escribe. In [9] the concept of figure of merit is use. This figure of merit is efine as the ratio of the fiber ispersion factor to attenuation an Ref[8] investigates how ispersion, loss an effective area of the DCF interplay to etermine the performance of a ispersion-manage optical transmission system. In [], the concept of figure of merit is further stuie. In [] an optimal esign for DCF an its fabrication are given. This paper eals with a grae inex profile rather than a step-inex one. The Dispersion Slope Compensation Ratio (DSCR is uemploye which is simply the ratio of ispersion slope of DCF to the Dispersion factor of the DCF ivie by ratio of the ispersion slope of the DFF to the Dispersion of DFF as DSCR S DCF /D DCF. D DFF / S DFF (7 This concept is use in [6] an a term Kappa is coine instea for DSCR. Currently many manufacturers specify this value of Kappa for their DCF moules. All the above references use triple cla optical fiber for the esign of both DFF an DCF. APPROXIMATION OF WAVEGUIDE DISPERSION PARAMETER CURVES The three V (Vb/V curves expressing (a - c are the exact solutions for the secon-half of the complete curve shown in Figure. However, to the best of our knowlege neither simple approximation nor exact representation of V (Vb/V curve are available in any publishe works. Most publishe works [9, ] an the algorithm evelope in Ref. [] are far too complicate to analyze an for clarity, particularly at the esign inception stage. Therefore, we evelop, in this section, a simple algorithm to preict the behavior of V (Vb/V curve in the following steps. V (Vb/V First-half of V (Vb/V curve Equation.68,.69 or.7 Secon-half of V (Vb/V curve Figure V (Vb/V complete curve, otte line is obtaine from (a, (b an (c. STEP The exact V (Vb/V curves evelope in (a-(c are use for the secon-half (after the maximum peak of the curves. The peaks of the respective curves can be accurately etermine. y inspecting a number of family V (Vb/V curves reporte in [] an [5] are plotte as shown in Figure, an it is surprising that we can preict the peaks by crossing the curves by a cubic equation given by a simple equation, V (Vb/V Equation.75 D D D Curve V V Curve ( Vb Curve V Figure V (Vb/V family curves V (8 Thus, the intercepting point, point D(Dx,Dy (Figure is the corresponing peak of one of the curves. A correction factor can be use to moify (7 if require, mainly the constant of the cubic equation. Higher orer polynomial is foun to be unnecessary in this case. V

8 > JLT-xxxxx- 7 MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma V (Vb/V D(Dx,Dy not to scale graient at point D x Dx Cx V L L Figure The variation of the waveguie parameter V (Vb/V as a function of the V-parameter. The behavior of the right half of the curve is estimate with a number of preicte points. STEP From Figure an referring to point D(Dx,Dy, we coul fin the graient at that point an hence the point Cx shown in the same figure by using (7 : STEP Cx Dx V V V Dy ( Vb at( Dx, Dy (9 Having foun point C(Cx, we coul preict point (x, i.e. the cutoff point for V (Vb/V curve by using (8. STEP x Dx ( Cx Dx (9 Now consiering the curve from point to point D, we have to introuce aitional points in orer to obtain the esire shape. Likewise, a few points are selecte to represent the curve in the right-half of the V (Vb/V curve. All together, we have selecte ten points to represent the V (Vb/V curve. Having obtaine the significant points, our next task is to interpolate all the points to form a smooth curve. Spline interpolation metho has been aopte for this purpose. STEP 5 As we are using the V (Vb/V curve to fin the waveguie ispersions efine in (a -(c the curves as shown in Figure 5 can be represente by a general mathematical expression as a function of wavelength. Thus, a polynomial of 9-th orer given by (9 has been chosen for this purpose. For single-moe, the normalize frequency is given by, V i ci. 5 ( where ci is the cutoff wavelength of i-th claing region. Figure 5 The optical waveguie parameter curves for optical fibers with three claing types. Hence, the 9-th orer of V (Vb/V polynomial can be approximate by, ( Vb V V.5 c.5 c.5 c.5 c P P P P... P9 ( or V V ( Vb 9 P m m m.5c ( where P,P,P,...,P 9 are the polynomial constants which have been obtaine by using the polyfit function in MATLA []. The esign presente above involves seven egrees of freeom. y analyzing the effect of each parameter we woul be able to preict the changes of the ispersion factor an ientify the main factors that woul play a maor role in the tailoring of this factor. Ten ifferent types of materials as liste in Table have been use in the core/claing regions to esign ispersion flattene fibers in orer to meet the requirement which shoul not be zero but have some finite ispersion so that the four mixing effects o not occur between aacent wavelength channels. Material types A,, C, D, E, F, G, I an J can be use as either core or claing materials of optical fibers that woul satisfy the ispersion-flattening limit requirement. Material type H has the total ispersion of about 9 ps/(nm-km in the range -58 nm. Analyzing all the total ispersion curves leas to a conclusion that the fiber with material type J gives the best performance in ispersion flattening as a total ispersion less than ps/(nm-km from 8 nm to 6 nm can be achieve. There is a maximum of three zero ispersion points. The first an secon zero ispersion points are approximately locate in the two fiber winows ( nm an 55 nm. It is well known that from the silica loss any wavelength above 7 nm woul cause severe attenuation loss in transmission. On average, the thir zero-ispersion point is above 7 nm. Thus, we are not intereste in it or unless we coul esign it as such that this point lies within the fiber winows. 9

9 > JLT-xxxxx- 8 MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma G. Effect of Core an Claing Raius on the Total Dispersion Figures 6, 7, 8 an 9 show various curves of core/claing raius against total ispersion. We observe the following effects of each core/claing raius on the ispersion characteristics: (i As the core raius, a, is increase the total ispersion curve is shifte upwars at the same time the secon zero ispersion point is shifte to the higher wavelength. Meanwhile, the first zero ispersion point remains unchange an the thir zero ispersion point graually shifte to the lower wavelength. y simulating an analyzing the behavior of the ispersion curves, we obtain the maximum sensitivity of changes in a to total ispersion in the fiber winows region is about ps/(nm-km-mm. (ii As the first claing raius, a, is reuce the total ispersion curve is shifte upwars. The maximum sensitivity of changes in a to total ispersion in the fiber winows region of 6.68 ps/(nm-km-mm is obtaine. (iii As the secon claing raius is reuce, a, the total ispersion curve is shifte upwars, but the first zero ispersion point are shifte to the lower wavelength, a maximum sensitivity of changes in a to total ispersion in the fiber winows region of.99 ps/(nm-km-mm is obtaine. Figure 7 Spectral istribution of the total ispersion factor with the core raius of the triple cla optical fiber as a parameter Figure 8 Spectral istribution of the total ispersion factor with the first claing raius of the triple cla optical fiber as a parameter. Figure 6 Material, waveguie an total ispersion of 'type A' as the core material of a triple cla profile as a parameter. Figure 9 Spectral istribution of the total ispersion factor with the secon cla raius of the triple cla optical fiber as a parameter

10 > JLT-xxxxx- 9 MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma. n to total ispersion in the fiber winows region is 59, ps/(nm-km per unit refractive inex. (iii As the secon claing refractive inex, n, is ecrease the total ispersion curve is shifte upwars but the first zero ispersion point is shifte to the lower wavelength. Meanwhile, the secon zero ispersion point almost remains unchange. Further simulation results that the maximum sensitivity of changes in n to total ispersion in the fiber winows region is 6666 ps/(nm-km per unit refractive inex. Figure The Spectral istribution of the total ispersion factor of triple-cla fibers with the core refractive inex of the triple cla optical fiber as a parameter. From the above results, we can conclue that the change in core raius, a is very sensitive to the total ispersion factor with a sensitivity of unit ispersion per unit µm as compare to that of the outer raius of the secon layer a. Thus, the selection of a is very critical to achieve a specifie ispersion factor for the triple-cla fiber, an hence the manufacturing tolerance or the eformation of the fiber core raius uring installation. Extreme care shoul be carrie out especially the bening curvature an pressure applie uring installation. The sensitivity of each core raius is compare with respect to that of the secon claing layer as shown in Table. Thus the manufacturing tolerance of the fiber core raius must be controlle accurately as compare to those of the claing layers. Figure Dispersion factor versus wavelength with the first claing refractive inex of triple cla profile as a parameter. a A a Normalise Sensitivity Table Normalise sensitivity comparison of core, first an secon claing raius H. Effect of Refractive Inices of the claing layers on Total Dispersion Referring to Figures,, an, various curves of core / claing refractive inices versus the fibre total ispersion are plotte. These curves show the following effects: (i As the core refractive inex, n, is reuce, the total ispersion curve is shifte upwars. Several curves are obtaine an the maximum sensitivity of changes in n to total ispersion in the fiber winows region is 5, ps/(nmkm per unit relative refractive inex is observe.. (ii When the first claing refractive inex, n, is increase the total ispersion curve is shifte upwars an the first zero ispersion wavelength is move towars higher wavelength region. We have obtain the maximum sensitivity of changes in Figure Spectral istribution of the total ispersion factor with the secon claing refractive inex of the triple cla profile as a parameter

11 > JLT-xxxxx- MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma DESIGN ALGORITHM FOR DFF: Step : Initially the material ispersion is calculate base on the materials table in Table. Figure shows typical curve for material ispersion against wavelength: Figure The spectral istribution of the total ispersion factor varies with the outer claing refractive inex of the triple cla profile as a parameter (iv As the outer claing refractive inex, n, is ecrease the total ispersion curve is shifte upwars but the first an secon zero ispersion points are shifte to longer spectral region. We obtain a maximum sensitivity of changes in n to total ispersion in the fiber winows region is,85 ps/(nm-km per unit refractive inex change -. We thus conclue that changes in outer refractive inex, n is sensitive to the total ispersion (i.e.,85 unit ispersion per unit refractive inex compare to the n. Thus, selecting n is very critical to the triple-cla step-inex optical fiber. The normalize sensitivity of the refractive inices of the core an the claing layers with respect to the refractive inex of the thir claing layer n is shown in Table. This layer is chosen for normalization ue to its closeness to the claing outer most claing layer. It shows clearly that the outer most claing layer is the most sensitive as inicate an the egree of sensitivity so that esigner can have a clear choice of the geometrical parameters of the fiber. Normalize Sensitivity n n N N Table Normalize sensitivity comparison of core, first, secon an outer refractive inex I. Effect of Doping Concentration on the Total Dispersion Figure inicates that increasing oping concentration woul shift the total ispersion curve own slightly. The change is quite small an an estimate change of.5 unit ispersion per unit concentration. Thus the oping concentration in the core region oes not play a maor role in the flattening of the total ispersion curve. The oping concentration woul thus be the last factor to consier in the esign of the triple-cla step-inex fibers. This factor shoul be consiere for its contribution to the attenuation of optical signals. Figure : Spectral variations of the material ispersion (green, waveguie ispersion (blue an total ispersion (re. The fibre profile is: Core Type Material (, Core Raius.865µm, Inex ifference.98%. Step : The criteria for the esign of ispersion - free fibers is to compensate for this material ispersion by the waveguie ispersion or effectively the group elays of the re shift an blue shifts are in opposite irections. Thus the waveguie ispersion is calculate for various claing layers, which can balance the material ispersion for the range of. to.7 µm. To calculate waveguie ispersion the parameter V ( ( Vb V is estimate so that the chirp of the blueshift woul be in the opposite irection of that exerts on the re shift chirping effect ue to the material refractive inex over the ultra-wie spectral range. This is illustrate in Figure. Step : The waveguie ispersion is ae to the material ispersion an thus the total ispersion for the range of. to.7 µm. It is observe that very low non- zero value obtaine to avoi the four wave mixing effects. The total ispersion curve can be shown in Figure 5. DESIGN PROCEDURES FOR DISPERSION COMPENSATING FIER: Similarly to the esign of DFF, the algorithm use in esigning DCF is performe except there is only a ifference in that DCF is a section of fibre eploye in the link that shoul compensate the GVD of various components in the fibre. The group velocities of say a RED SHIFT part of the signal are in opposite with those of LUE SHIFT section. When the signal travels through long stretch of Dispersion Flattene fibre then these signals lag in istance ue to various velocity of propagation. The DCF compensates this anomaly. The basic equation require is D ff Lff Dcf Lcf, i.e. the ispersion allowance is maintaine over several spans of the link.

12 > JLT-xxxxx- MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma J. Design Steps: Step : Select the material type for the DCF. Then change the raius of the fibre core to aroun µm an check the ispersion curve. Step : Change the inex slier so that the Dispersion of the fibre becomes very negative. Check the winow such that D ff Lff Dcf Lcf as shown in Figure 5 an Figure 7. Figure 7 Various combinations of raius, type of material, RI profile an length of the fibre euce in the esign that satisfies the ispersion flattening. Corresponing ispersion factors an slopes are shown in Figures 8 an Figure 5 The ispersion-length prouct over ultra-wie spectral range CASE STUDIES The spectral ispersion characteristics of the esigne fibers can be matche with any specific ispersion characteristics for both the DFF an DCF. This section presents two case stuies of typical esigns of the ispersion flattene an compensate fibers. It is imperative to ustify the results with the values obtaine for all the parameters use such as the number of guie moes, the core an claing layer raii, relative inex ifference, spot size etc. The selection of the parameters can be inserte in winows provie in Figure 7. This allows fine austment of the parameters. The results are presente in Figures an with winows numbere from left to right an top to bottom for the esign cases presente in the next sections. K. Design case : In this case the Core material is of Type an results are obtaine for the DFF an DCF as shown in Figure 8 for transmission of at least Gb/s over several hunre kms. Figure 6: Dispersion factor of the DCF with a profile of: Core Type Material G (7, Raius.5998µm Relative inex ifference.57 % an DCF length.9 Km. DFF (TYPE Core (DCF Type 7 Core Figure 8 Dispersion manage optical fibre span The following results are obtaine an illustrate with the winows numbere from left to right an top to bottom in Figure 9 as follows: Winow : This is the most important winow of the plot as it inicates the ispersion of the optical fibre use for communications systems. We esign a ispersion-flattene fibre for a range from S ban to L bans an hence it is important to notice the changes in this winow so that the requirements are met. This winow can be calle as the GUIDING WINDOW for our esign. The Dispersion Flattene Fibre (DFF characteristics are satisfie with a low ispersion range of ps/nm-km to ps/nm-km in the range. nm to.6 nm. Winow : The ispersion of the ispersion compensate fibre is esigne such that the Kappa Value approaches unity.

13 > JLT-xxxxx- MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma Winow : The ispersion slope of both the DFF an DCF are plotte where the blue line inicates the slope of DFF an green line inicates the slope of DCF. Winow : This winow shows the plot of V ( (V/V versus normalize frequency. The blue line inicates the characteristics of V( (Vb/V versus V while the green line inicates the characteristics of V( (Vb/V versus V Winow 5: The refractive inex of the fibre is shown in this winow. The blue line shows the RIP of Core which varies µm µm. The RI of first claing is the green line which varies µm Finally the re line inicates the RI of outer claing which varies µm µm. Winow 6: shows the spot-size of the DFF as a function of the operating wavelength. Reasonable spot size is obtaine as compare with the stanar single moe fibre G.65 or G.655. Winow : shows the plot of V( (Vb/V versus normalize frequency. The blue line inicates the characteristics of V( (Vb/V versus V while the green for V( (Vb/V versus V Winow 5: The refractive inices profiles (RIP of the fibre are shown. The blue line shows the RIP of Core which varies µm µm. The RIP of first claing is the green line which varies µm Finally the re line inicates the RI of outer claing which varies µm µm. Winow 6: shows the spot-size of the DFF. This varies with the wavelength an similar with case stuy for its effective area. Winow 7: shows the rise time buget of the fibre. The green line is the theoretical value, which is taken as.5/ ns. The reason being that we are taking NRZ format, which is taken theoretically as.75/ ns. ut taking practical consierations the value is ecrease to.5/ ns. Winow 7 shows the rise time buget of the fibre. The green line is the theoretical value, which is taken as.5/ ns. The reason being that we are taking NRZ format, which is taken theoretically as.75/ ns. ut taking practical consierations the value is ecrease to.5/ ns. Winow 8: gives the KAPPA value which meets the criteria Kappa value reaches unity. Winow 9: gives the DL prouct of the link, which is very close to Zero hence efficient transmission for ultra-long reach is expecte. L. Design case : In this case the Core is mae of Type E material for the DFF an DCF as shown in Figure 9. DFF (TYPE 5 Core (DCF Type 7 Core Figure 9 Dispersion-manage fibre span with ifferent core materials Figures illustrates the simulate an esigne results as follows: Winow : The DFF characteristics are met properly with a non-zero an low ispersion range lower than few ps/nm-km over the spectral range nm to 6 nm. Winow : The total ispersion factor of the DCF is esigne such that the Kappa Value can reach unity. Winow : The ispersion slopes of both the DFF an DCF are plotte where the blue line inicates the slope of DFF an green line for DCF. Winow 8: gives the KAPPA value which satisfies the criteria for a Kappa value approaching unity. Winow 9: gives the DL prouct of the ispersionmanage link, which is very close to Null, hence error-free transmission is expecte. M. Design Summary From the esign case stuies illustrate above it can be conclue that the fiber types J, an E satisfy the specification of ispersion having less than ps/(nm-km in a wier spectral range (i.e. 8 nm to 6 nm an the total ispersion in this region is almost uniform with very low ispersion ripple ( ±. ps/(nm-km. Waveguie ispersion parameter V (Vb/V curve can be moele to obtain the total waveguie ispersion in triple-cla step-inex optical fiber. The extreme sensitivity (88.88 unit ispersion per unit µm of the fiber total ispersion to variation in core raius (a is a unique property of all ispersion - flattene fibers an ispersion-compensate fibers. The changes in outer claing refractive inex are critical (i.e.,85 unit ispersion per unit refractive inex. Doping concentration has a little effect on the total ispersion (i.e..5 unit ispersion per unit concentration. The changes in core raius, a an outer claing, n, are very sensitive to the total ispersion. Thus the contributions of these two parameters shoul be consiere before varying other five parameters. y analyzing the effects of each of the seven geometrical an inex profile parameters an the contribution of material ispersion ue to ifferent types of a set of materials as core or claing to the waveguie ispersion factor, one coul esign the triple-cla profile to satisfy any ispersion flattening an compensating factors over an ultra-wie spectral range as illustrate in the two esign cases.

14 > JLT-xxxxx- MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma CONCLUSIONS The emans of optical fibres having non-zero flattene an corresponing compensating ispersion factors over the ultrawie spectral ban of nm to 55 nm (an even wier, this paper has escribes in etails the strategy an esign proceures for tailoring the ispersion properties of optical fibers having triple-cla inex profiles. The esign has been limite by several stringent conitions of the seven geometrical an inex profile parameters. We have presente a number of efficient esign algorithms base on the approximation an fitting the sale points of the waveguie ispersion curves. Surprisingly these points follow a simple cubic function. A very accurate preiction of the waveguie ispersion is escribe allowing esigning a best-fit curve to tailor the total ispersion factor over a ultra-wie spectrum. This has been emonstrate in the two case stuies using ifferent core materials. Varying the seven egrees of freeom base on the geometrical an inex parameters the effects of core an claing raii, refractive inices an oping concentrations on the total ispersion are analyze an the esign sensitivities are rawn. Our esign algorithms ensure a systematic sequence to satisfy stringent esign specifications with ease. The evelope metho presente in this paper is vali an applicable to other geometrical an inex profiles. The sensitivity of these ispersion flattening an compensating fibers to the polarization ispersion is of much interest an will be reporte in the near future. The esign guielines presente herewith woul be applicable to the esign an manufacturing of broaban ispersion flattene an ispersion compensation fibers for ultra-long reach an ultra-wieban DWDM optical fiber communications transmission systems. REFERENCES: [] L.N. inh. an H.C. Chong, Dense wavelength ivision multiplexing packet switching networks, J. Elect. Electron. Eng. (Aust, pp , Sept an references therein. [] see for example: M. Nakazawa et al., Fiel emonstration of soliton transmission at Gbits/sec. over,5 Km an Gb/sec. over, km in the Tokyo metropolitan optical network, Proc. th Int. Conf. Integrate Optics an Optical Com., Post Dealine paper PD -, vol., Hong Kong, June 995; A. Weing, New metho for optical transmission beyon ispersion limit, Elect. Lett., vol. 8, pp. -, 99. [] N. Nakazawa, an H. Kubota, Optical soliton communication in a positively ispersion-allocate optical fiber transmission line, Elect. Lett., vol., pp. 6-7, 995. [] R. Ohhira, A. Hasegawa an Y. Koama., Methos of constructing a long haul soliton transmission system with fibers having a istribution in ispersion, Opt. Lett., vol., pp. 7-7, 995. [5] See for examples an references therein: L.N. inh an S.V. Chung, A generalize approach to single-moe ispersion-moifie optical fiber esign, Opt. Eng., 996. [6] G.P. Agrawal, Fiber-optic communications systems, Wiley, 99. [7] A.W. Snyer, "Unerstaning Mono-moe Optical Fibers", Proc. IEEE, vol. 69, No., Jan 98, pp 6-. [8] D. Marcuse, "Loss-Analysis of Single-Moe Fiber Splices", ell Syst. Tech. J., vol. 56, No. 5, 977, pp [9] Y. Li, C.D.Hussey, an T.A. irks, Triple-cla singlemoe fibers for ispersion shifting, IEEE J. Lightwave Tech., LT-, pp. 8-89, 99. [] Y. Li an Hussey C. D., Triple-cla single-moe fibers for ispersion flattening, Opt. Eng., vol., pp , 99. [] Liu, Y., V.L. Da Silva., A. A. J. hagavatula, D.Q. Chowhury, an M.A. Newhouse., Single-moe ispersion shifte fibers with large effective area for amplifie systems, IOOC 95 Postealine paper PD--9, pp. 7-8, Hong Kong, June 995. [] The MathWorks Inc., MATLA high performance numeric computation, Aug. 98. [] S.V Chung., Simplifie analysis an esign of single moe optical fibers, Ph. D. issertation, Monash University, Australia, 987. [] See for example an references therein C.D. Poole, J.M. Wiesenfel, D.J. DiGiovanni an A.M. Vengsarkar, Optical fiber-base ispersion compensation using higher orer moes near cut-off, IEEE J. Lightw. Tech., vol., Oct. 99, pp [5] L..Jeunhomme, Single Moe Fibre Optics, Principles an Applications, DekkerPub 98.

15 > JLT-xxxxx- MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma [6] M. Monroe, Propagation in Doubly Cla Single Moe Optical Fibres, IEEE Journal of Quantum Electronics, vol QE-8, No, pp 55-5, April 99. [7] L.N. inh Design guielines for ultra-broaban ispersion flatten optical fibres with segmente core inex profile, Department of Electrical an Computer Systems Eng, Monash university, Technical report No. MECS.. eports/postinex.html [8] K. Thyagraan, R.K.Varshney, P.Palai, A. K. Ghatak, an I.C. Goyal, Novel esign of a ispersion compensating fibre, IEEE Photonics Tech Lett, Vol 8, No, pp 5-5, Nov-996. [9] F. Forghieri, R. W.Tkach, A.R. Chraplyvy, A.M Vengsarkar, AT&T ell Laboratories, Dispersion Compensating Fibre: is there a figure of merit, OFC 96 Technical Digest, pp [] G.E. erkey, M.R. Sozanki, Negative Slope Dispersion Compensating Fibres, Science an Technology Division, Corning, WM--WM-. [] M. Hirano, A. Taa, T. Kato, M. Onishi, Y. Makio, M. Nishimura, Dispersion Compensating Fibre over nm-anwith, Proc. 7 th ECOC. Th.M.., 9-95.

16 MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma > JLT-xxxxx- 5 FIGURE 9

17 MECSE-7-: "Design of ispersion flattene an compensating...", L.N. inh, K-Y Chin an D. Sharma > JLT-xxxxx- 6 Figure FIGURE