The Parameters affecting on Raman Gain and Bandwidth for

IJCSI International Journal of Computer Science Issues, Vol. 9, Issue 5, No 3, September 2012 ISSN (Online): 1694-0814 www.IJCSI.org

225

The Parameters affecting on Raman Gain and Bandwidth for Distributed Multi-Raman Amplifier 1

Fathy M. Mustafa1, Ashraf A. Khalaf2 and F. A. El-Geldawy3 Electronics and Communications Engineering Department, Bani-suef University, Egypt 2

Electronics and Communications Engineering Department, Mina University, Egypt

3

Electronics and Communications Engineering Department, Mina University, Egypt

Abstract Due to the benefits of Raman amplifier for Long-Haul UW-WDM Optical Communications Systems, we interest in this paper to investigate the parameters affecting on Raman gain and bandwidth, and also we are analyzed four and eight Raman pumping of special pump power and pumping wavelengths to show the effect of this parameters on gain and bandwidth. The model equations are numerically handled and processed via specially cast software (Matlab). The gain is computed over the spectral optical wavelengths (1.45µm ≤ λ signal ≤ 1.65µm). Keywords: Raman amplifier, Distributed multi-pumping

Raman amplifier (DMRA), Raman gain, pumping power and wavelength, ultra wide-wavelength division multiplexing (UWWDM).

1. Introduction There are mainly three reasons for the interest in Raman amplifier. First its capability to provide distributed amplification second is the possibility to provide gain at any wavelength by selecting appropriate pump wavelengths, and the third is the fact that the amplification bandwidth may be broadened simply by adding more pump wavelengths. An important feature of the Raman amplification process is that amplification is achievable at any wavelength by choosing the pump wavelength in accordance with the signal wavelength [1]. The term distributed amplification refers to the method of cancellation of the intrinsic fiber loss. the loss in distributed amplifiers is counterbalanced at every point along the transmission fiber in an ideal distributed amplifier [1]. In the late eighties, Raman amplification was perceived as the way to overcome attenuation in optical fibers and research on long haul transmission was carried out demonstrating transmission over several thousand kilometers using distributed Raman amplification. However, with the development and

commercialization of erbium-doped fiber amplifiers through the early nineties, work on distributed Raman amplifiers was abandoned because of its poor pump power efficiency when compared to erbium-doped fiber amplifiers (EDFAs). In the mid-nineties, highpower pump lasers became available and in the years following, several system experiments demonstrated the benefits of distributed Raman amplification including repeater-less undersea experiments, high-capacity terrestrial as well as submarine systems transmission experiments, shorter span single-channel systems including 320 Gbit/s pseudo linear transmissions, and in soliton systems [1]. distributed Raman amplifiers improved noise performance because of amplification at any wavelength controlled simply by selecting the appropriate pump wavelength, extended bandwidth achieved by using multiple pumps when compared to amplification using EDFAs, and finally control of the spectral shape of the gain and the noise figure, which may be adjusted by combining and controlling the wavelength and power among multiple pumps [1]. The use of distributed Raman amplification has already been demonstrated in ultra-high-capacity optical communication systems as the enabling method to transmit 40Gbit/s per channel in a wavelength-division-multiplexed transmission system [1]. Ultra long-haul (ULH) and ultrahigh-capacity (UHC) dense wavelength-division-multiplexed (DWDM) optical communication systems have recently attracted considerable attention due to their potential to greatly reduce bit-transport costs while addressing the ever-increasing demand for voice and data traffic. A flexible all-Raman pumping scheme, including forward-and backward-pumping of the fiber span and backward pumping of the dispersion compensation modules (DCMs), can be used as a common platform

Copyright (c) 2012 International Journal of Computer Science Issues. All Rights Reserved.


226

yielding excellent system performance for 10 Gb/s ULH and 40Gb/s signals and ULH transmission over 2500 km in a hybrid configuration [2]. It was shown how that amplification scheme provides enough gain to handle discrete losses from optical add/drop multiplexers (OADMs) inserted along the transmission. A comprehensive experimental investigation of an all-Raman ultra wide signal-band transmission system for both 10 and 40 Gb/s line rates was done [2]. The most important feature of Raman-gain spectrum is that the peak-gain wavelength only depends on the pump wavelength. The peak-gain wavelength for each pump still exists although the total gain spectrum of a multi-pumped fiber Raman amplifier (FRA) is the comprehensive result of all pumps [3].

bandwidth are processed through a numerical solution of the mathematical model. 2. Mathematical Model In the present section, we cast the basic model and the governing equation to process N-Raman amplifiers in a cascaded form of special pumping powers Pr1, Pr2, Pr3, Pr4, ……., PrN and corresponding pumping wavelengths λr1, λr2, λr3, λr4, ……., λrN. The map of δ-g is as shown in Fig. 1, where δ is the Raman shift and g is the Raman differential gain coefficient; both were cast based on [7-11] as: 1

10 ,

Two critical merits of distributed Raman amplifier (DRA) are the low noise and the arbitrary gain band. Experiments show that 2.5 Gb/s system could be up graded to 10Gb/s by only adding a Raman amplifier [4]. Raman amplifiers pumped at multiple wavelengths draw significant attention in high-speed long-haul WDM transmission, for example, because of their wideband flat-gain profile (100nm with 12 channelWDM pumping) and superior signal-to-noise ratio (SNR) performance. However, they require numbers of high power pump lasers to achieve high-gain and high bandwidth which makes it very expensive at the initial deployment stage where the WDM bandwidth is not in full use. While modular band-by-band and high upgrade like EDFA-based WDM systems reduces system introduction cost very much, in which either C or L-band EDFAs can be added later when a new bandwidth becomes needed. However, such modular addition of amplifiers is not possible for a DRA in which a transmission fiber is shared as common-gain medium. Neglecting nonlinear pump interaction or saturation WDM-pumped Raman amplifier gain can be approximated as the linear superposition of Raman gains induced by each pump laser [5]. Currently, RFAs are the only silica-fiber based technology that can extend the amplification bandwidth to the S band while providing performance and reliability comparable with those of EDFAs. However, the noise figure remains high compared to that of the C and L bands [6]. In this paper, the parameters affecting on Raman gain coefficient and Raman differential gain and

Figure 1 Gain, g, of multi-pump Raman amplifier.

The map of δ–g shown in Fig. 1 describes the basic model. This section depends on the position of the gain of each amplifier with wavelength, where the gain of each amplifier consists of three parts (three equations). A special software program is used to indicate the position of δo,i or λo,i and studying the total gain of the amplifiers. In this case, the basic model depends on using more than one amplifier which is put in a cascaded form to increase the bandwidth of the amplifier to multiplexing more signals in the transmission system. The overall amplifier bandwidth increases and the gain flatness improved depend on the position of each amplifier corresponding to other amplifiers. This is achieved by more trials of changing of δo,i or λ o,i for each amplifier. The general equations representing the Raman gain in the three regions are respectively [11]. ,

440

,

0

440

2

Where 10 ,


3


227

,

,

,

7.4

Where ,

.

,

,

.

10

. ,

. ,

4

,

,

/

and

10 ,

5

10 ,

6

.

е

,

7

440

∆λ = λ2 – λ1 = 15 nm = (fixed value) 1

8

10 ,

0.044 ,

,

.

,

,

,

15

∆λ = λ2 – λ1 = 16 nm = (fixed value)

And ,

е

,

9

440

1

10 ,

0.044

16

Where, λr is Raman pump wavelength and λo ≥ 1.35um. The shift δo,i is the Raman shift that indicates the position of each amplifier. By changing this position, the total bandwidth and the flatness of the amplifier are changed. We are interested in obtaining a large bandwidth with flatness by more trials of changing δo.i or λo,i. In this case, one uses δ > δr or λ > λr and δo ≥ δr or λo ≥ λr, where λr is Raman pump wavelength. Raman differential gain constant, g, and the effective core area, A, are defined as [8]: 1.34

1

10

80

17

Where ,

,

.

0

,

440

10

,

.

. ,

10 ,

,

11

With 1 cm-1 = 30 GHz [12], where λo,i indicates the offset wavelength and λr,i indicates the pumping wavelength of each amplifier. These wavelengths are then used to indicate δo,i for each amplifier. ,

,

,

,

,

. ,

,

, ,

√∆

0.3

,

19

Where, λr is the pump wavelength, Ws and Wr are the mode field radii of two light waves coupled with each other with W=Ws at λ= λs and W=Wr at λ= λr and ∆ is the relative refractive index difference, n1 is refractive index of the core and NA is the numerical aperture. Neglecting the cross coupling among the signal channels, one has the differential equation governing the signal propagation for N-channels Raman pumping [9]:

13 ,

. ,

10 ,

0.21

12

Where, 7.4 10 / is the differential Raman gain constant (of pure SiO2 at λ = 1.34 µm), and

.

18

Where

With

.

,

2

10 ,

14

And


20


228

Where, i = 1,2,3,…… …..N, M is thhe number off pumps, Si is signal s powerr and PRj iss the pump power. Assume the R.H.S off equation (20) equals gti , as: ,

21

The total gain coefficcient in m¯¹ which w represents the th total gain coefficientt of the i signal s due too the Npumpingg. It is clear that t gti is a function f of thhe set of variabless {signal waavelength, fiiber radius, Raman wavelenggth, relativee refractivee index diffference, Raman power}. p This term can be written in thee form: ,

respectivelyy, where the sum of pumpping power iss one watt. The thhree gain cooefficients gdid , gci, and gti are displayed foor each case. 3.1 Effect of o Relative Refractive Index I Difference on Raman Gain Figure 2, exxplains the rrelation betw ween Raman gain and relativee refractive index differencce, and this figure f is plotted foor special pum mping wavelengths. It's found f that Ramann gain increasses with the relative refraactive index differeence.

22

Define gci , the total gain g coefficieent per watt, as a ,

23

Then, thee total differeential gain, gdid , is: ,

24

The threee gain coeffficients gdi, gci and gti are a also functionss of the propaagation distaance. 3. Simullation Results and Discu ussions The gainn and bandw width for disstributed muulti-pump Raman amplifier (DMRA) is optimized. Optimal results show s that thhe parameteers effecting on the Raman gain and baandwidth, whhere the gainn of the amplifierr change according to the pumping p wavelenggths and rellative refracttive index difference and also the banddwidth, ∆λr, can be evidently e broadeneed by meanns of increasing the number of pumps and a accordingg to the posittion of each amplifier a and the gain is increeases with increase the relative refractivee index differrence. In this paaper, we disccuss two diffeerent modelss namely four andd eight Ramaan pumping optical waveelengths and pum mping power are shown in the table I and II

Figure 2 Ramaan gain versus reelative refractive index difference..

Then for Raman ampliffier to get amplifier with high gain must be b design orr used fiber with high rellative refractive inndex differennce and alsso used pum mping source suitable wavelength's whhere if pum mping wavelength increased w we get lossess is increasess and this not requuired in desiggn. So, the relative refracctive index difference d off the materials must m be takeen in accouunt in design for optical amplifiers.

3.2 Effect of Pumpingg Waveleng gth on Ram man Gain If pumpingg wavelengths increasees, Raman gain decreases. Figure 3, eexplains the relation betw ween Raman gainns, g m/w, and pumpingg wavelengtth, λr, µm. This figgure is plottedd at different values of relative refractive index diffference, where w pum mping wavelengthss for optical signals is in a range from m 1.4 to 1.55 µm. This range iss suitable forr Raman ampplifier to avoid noise and lossees.



229

we get if rellative refractiive index diffference increeases the mode field radii ddecreases buut the numeerical aperture inncreases annd we neeed the two are increases inn design, too avoid lossees in transm mitted signal whenn you are cooupling betw ween the diffferent fibers this achieved bby using soources with high pumping waavelength's.

3.4 Relation betweeen Mode Field F Radii and Pumping Wavelength W h

Figure 3, Variation of Ram man gain, g, with pumping wavele ength, λr,

um

Where iff pumping waavelength abbove 1.55 µm m we get losses and noise is laarge and thiss not requiredd for the signal trransmitted (this ( is disaadvantages) but we need am mplifier withh high gain, so to avvoid this problem must be inncrease relattive refractivve index differencce to get balaance betweeen gain and pumping p wavelenggth. Then, anny source haaving a pumpping wavelenngth and pumpingg power muust be suitaable for thee choice design too obtain suitaable gain andd bandwidth.

The mode field f radii aree proportionaal to the pum mping wavelengthss. Figure 55, explains this relatioon at special values of the relative refractive index i difference in i the waveelength rangee 1.4 – 1.5 µm. Then, one can c get the R Raman gain which w dependds on pumping wavelengths w and mode filed radii which w depend on the t relative reefractive indeex differencee.

3.3 Relaation betw ween Mode Field Rad dii and

Relativee Refractivee Index Diffference

The modde field radii are inversely proportionaal to the relative refractive r index differencee. Figure 4, explains thee variation off the mode fiield radii with relaative refractive Index difference at special pumpingg wavelengths.

Figure 5, 5 Variation of m mode field radii versus v pumpingg waavelengths.

If pumping wavelength increase thee mode field radii increase soo, in design we must takke in accounnt the pumping wavelength w and also relative index i difference where, w if relative index difference incrrease the mode fieeld radii decrreases.

3.5 Relation betweeen Mode Field F Radii and C Area Effective Core

Figure 4, 4 Variation of mode m field radii with relative reefractive indeex difference , ∆% ∆

Figure 6, explains e the relation betw ween mode field radii of pum mping signal, wr, and effecctive core areea, A, where the mode m field raddii increases with the effeective core area. This curve is plotted at special valuues of mode field radii of the signal, ws. TThis result is useful wheree; the effective coore area affeects in Ramaan gain and must be taking into account.



230

Since Ramaan gain is prooportional to relative refraactive index differrence and eeffective coree area, thenn this result is very v useful to indicate the parameters affecting in Raman gain to obtain a maximum m annd flat gain.

Figure 6, 6 Variation of mode m field radii of pumping siggnal, wr, with effecctive core area, A, µm2.

Figure 7, 7 displays the relation between moode field radii of signal, s ws, annd effective core c area, A, A where, the mode field radii increases wiith the effecttive core area expponentially acccording to above a equation. This curve is plotted for sppecial value of mode fieldd radii of pumpingg signal, wr .

Figure 8, Variation of efffective core area, A, um2 versuus relative inddex difference, ∆.

In design too avoid this disadvantagge must be used source withh high pum mping waveelength in range r (1.45µm ≤ λ signal ≤ 1.55µm) becausee of it is impoortant for used fibeer with effecttive core areaa is large to avoid a the losses in signals w which occurs when couupling between diffferent fibers..

Figure 7, Variation of mode field radii of signal, ws, versus v effective core area, A, A µm2

Then froom figures 6 and 7, we get for increease the area of the t fiber (diam meter of the core of the fiber) f we get moode field radii r increasse and this also advantagges for coupling signalss between different fibers to get high effiiciency to traansmitted thee signals between different joinnts and differrent fibers.

3.6 Relaation betweeen Effectivve Core Areea and Relativee Refractivee Index Diffference Figure 8, 8 shows thee relation beetween the effective e core areea and the reelative indexx difference, ∆. This curve is plotted at sppecial pumpinng wavelenggths. It is clear thhat the efffective coree area deecreases (exponenntially) with ∆. ∆

3.7 Effect of Number of pumping (numbeer of plifier) on thhe Gain and d the Flatnesss of optical amp the Gain In this casee we discusss two differennt models naamely four and eigght Raman pumping opttical wavelenngths and pumpinng powers inn this case we w get the gaain of the amplifieers increasedd and the flatness of the gain is improved with increassing the numbber of pumping. ber of opticaal amplifier = 4 3.7.1 Numb Taable I Number of ampliffiers = 4 10 0 , 1 0.0 044 λ1 – λo = fixed f (0.0962294798) and λ2 – λ1 = 16 nm λr 1.4 1.42 1.467 1.5

λo 1.4332 1.4552 1.4999 1.552

λ1 1.5282994799 1.5482994799 1.5952994799 1.6162994799


λ2 1.544294799 1.564294799 1.611294799 1.632294799

Pp(W) 0.2 0 0.25 0 0.25 0.3


231

Differen ntial gain Figure 9, displays thee differential Raman gainn, g, with wavelenggth, λ, at different d values of the relative refractivee index differrence. If relaative index difference increasees, Raman gaains increasees.

Figgure 9, Variationn of differential Raman gain with w wavelength.

to peak vallue at 1.54 µm, then thee gain is staart to decrease exxponentially ttended to zero at 1.65 µm m. In this case c more tthan one paarameter can be control in gain g coefficient per unit watt such that effective core c area, relative refractive index i difference, pumping wavelengthss and pum mping powers. So these param meters take inn account for any design. Whhere each parameter can effecteed in design. In this casee we obtaineed, total banndwidth =1000nm, where λ1t = 1.49 µm (for all amplifiers) and λ2t = 1.59 a µm (for all amplifiers). In this caase we obtained, total baandwidth =110nm, where λ1t = 1.51 µm (for all amplifiers) and λ2t = 1.62 µm (for all amplifiers). a Total gain coefficient c Figure 11, displays thee variation of o the total gain coefficient with w wavelength. In this case, c a bandw width of 100 nm iss obtained.

We notee that Ramann gain is staarts to increaase from the first pumping waavelength to reach to peaak value at 1.54 µm, then the gain iss start to decrease d exponenntially tendedd to zero at 1.65 1 µm. Beccause of optical amplifiers a andd optical signals are opeerated in range 1.445 µm to 1.665 µm. In this case c we obtained, total bandwidth =100nm, = where λ1t1 = 1.49 µm (for all ampllifiers) and λ2t2 = 1.59 µm (for all a amplifiers)). Gain coeefficient perr unit watt The gain coefficientt/unit watt, ∑ gi / Ai, m¯¹ W¯¹ against wavelength w is shown in Fig. 10, at different values of relative refrractive index difference.

Figure 11, Variation of totaal gain coefficientt with wavelengthh.

By similar we w note the ttotal gain coeefficient is staart to increase froom the first ppumping wavvelength to reach r to peak vaalue at 1.544 µm, the gain is staart to decrease exponentially e tended to zero at 1.665µm. Gain in thiss case is aaffected by pumping p pow wers, effective core area and rrelative indexx difference. mping powerrs increase the total gaain is Where pum increase so Raman ampplifiers is useed to sourcess with high pumpinng powers.

Figure 10, Gain coefficientts per unit watt aggainst wavelengtth.

We notee that gain coefficient/unit watt is starts s to increasee from the firrst pumping wavelength w t reach to



232

3.7.2 Nu umber of opttical amplifieer = 8 Table II Number N of am mplifiers = 8 λ1 – λo = fixed (0.0993262399) and λ2 – λ1 = 16 nm λr 1.41 1.44 1.45 1.46 1.47 1.48 1.49 1.5

λo 1.41 1 1.444 1 1.455 1 1.466 1 1.478 1 1.489 1 1.501 1 1.512

λ1 1.5033262399 1.5377262399 1.5488262399 1.5599262399 1.5711262399 1.5822262399 1.5944262399 1.6055262399

λ2 1.519262399 1.553262399 1.564262399 1.575262399 1.587262399 1.598262399 1.610262399 1.621262399

Pp(W) 0.14 0.12 0.14 0.10 0.14 0.12 0.11 0.13

man gain andd the gain cooefficient The diffeerential Ram per unit watt are dissplayed, resppectively, in Figs. 12 and 13, while the total gain is dissplayed in Figg. 14. In this casee, a 110 nm m bandwidthh is obtained. Peak value in this case at 1.55 1 µm for the t different gain. g

Figure 14, 1 Variation of tootal gain coefficieent with wavelenggth.

4. Conclusion The bandw width and the gain of multi-distribbuted Raman amplifier (MDRA A) is effecteed by the set s of variables {λλs, λr, ∆, thee locations of the maximum constant gaain interval, number of optical ampplifier, pumping poower and efffective core area}. We have obtained baandwidth and gain at different value off ∆ % for use 4 annd 8 optical R Raman amplifiers. A summary of the obtained results, in two cases, is found inn the following coomparison tabble. Table of maaximum gain and bandwiddth for two caases. No of opticaal amplifiers 4

Figure 12, Variation of diffeerential Raman gain g with wavelenngth.

8

Figuree 13, Gain coefficcients per unit waatt against waveleength.

g max

∆%

2.43226 × 10-13 1.82445 × 10-13 1.21663 × 10-13 5.05777 × 10-13 3.79333 × 10-13 2.52889 × 10-13

0.8 0.6 0.4 0.8 0.6 0.4

BW(nnm) 100 110

From table we w concludee that: 1- If numbber of optical amplifiers inncreases, Raaman gains inncrease. 2- If relativve index diffeerence increaase then we gets Raman gain is increease. 3- Also, for f each ccase only if relative index i difference increasess, Raman gaiin is increasee. 4- Bandwidth, flatnesss of the gain and maximum value of o the gain depends onn the positioon of amplifieers correspoonding to each other's and numberr of amplifierrs where, in case1 bandw width is equal to 100 nm despite the number n of opptical amplifieer is four, butt case 2 banddwidth is equual to 110 nm m for numberr of optical amplifiers a is eight and gaains in casee 2 is maximum and more



233

flatness than in case 1, because of number of optical amplifiers is large. 5. References [1] C. Headley, G. P. Agrawal "Raman Amplification in Fiber Optical Communication Systems", Elsevier Inc. 2005. [2] D. F. Grosz, A. Agarawal, S. Banerje, D. N. Maywar, and A. P. Kung, "All-Raman Ultra LongHaul Signal-Wideband DWDM Transmission Systems with OADM Capability", J. Lightwave Technol., Vol. 22, No. 2, pp. 423-432, 2004. [3] P. Xiao. O. Zeng, J. Huang, and J. Liu, "A New Optimal Algorithm for Multi-Pumping Sources of Distributed Fiber Raman Amplifier," IEEE Photonics Technol. Lett., Vol. 15, No.2, pp. 206208, 2003. [4] X. Liu and B. Lee, "A Fast Stable Method for Raman Amplifier Propagation Equation," Optics Express, Vol. 11, No. 18, pp. 2163-2176, 2003. [5] N. Kikuchi, "Novel In-Service Wavelength-Based Upgrade Scheme for Fiber Raman Amplifier, "IEEE Photonics Technol. Lett., Vol. 15, No. 1, pp. 27-29, 2003.

Communication Systems," Bulletin of Faculty of Electronic Engineering, Menouf, 32951, Egypt, 2004. [12] A. Yariv, Optical Electronics in Modern Communications, 5th ed., Oxford Univ. Press, 1997. Fathy M. Mustafa received the B.Sc. degree in Electronics and communications department with honors from the Faculty of Engineering, Fayoum University, Fayoum, Egypt, in 2003. He is currently working a research assistant in Electronics and communications department at Bani-suef University. He is earned the M.Sc degree in Electronics and communication engineering in 2007 from Arab Academy for Science and Technology & Maritime Transport College of Engineering and Technology, Alexandria, Egypt. He is joined the PhD program in Mina university in 2011. Her areas of interest include optical communications, optical amplifiers. Ashraf A. Khalaf: received his B.Sc. and M.Sc. degrees in electrical engineering from Minia university, Egypt, in 1989 and 1994 respectively. He received his Ph.D in electrical engineering from Graduate School of Natural Science and Technology, Kanazawa university, Japan in 2000. He works at electronics and communications engineering Department, Minia University. He is a member of IEEE since 12 years. F. A. El-Geldawy: in He is a professor Electric Engineering Dept.,faculty of engineering, Minia, Egypt.

[6] Y. Cao and M. Raja, "Gain-Flattened UltraWideband Fiber Amplifiers," Opt. Eng., Vol. 42, No. 12, pp. 4447-4451, 2003. [7] M. S. Kao and J. Wu, "Signal Light Amplification by Stimulated Raman Scattering in an N-Channel WDM Optical Communication System", J. Lightwave Technol., Vol.7, No. 9, pp. 1290-1299, 1989. [8] T. Nakashima, S. Seikai, N. Nakazawa, and Y. Negishi, "Theoretical Limit of Repeater Spacing in Optical Transmission Line Utilizing Raman Amplification," J. Lightwave Technol., Vol. LT-4, No. 8, pp. 1267-1272, 1986. [9] Y. Aoki, "Properties of Fiber Raman Amplifiers and Their Applicability to Digital Optical Communication Systems," J. Lightwave Technol., Vol. 6 No. 7, pp. 1227-1239, 1988. [10] W. Jiang and P. Ye., "Crosstalk in Raman Amplification for WDM Systems," J. Lightwave Technol., Vol. 7, No. 9, pp. 1407-1411, 1989. [11] A. A. Mohammed, "All Broadband Raman Amplifiers for Long-Haul UW-WDM Optical


The Parameters affecting on Raman Gain and Bandwidth for

The Parameters affecting on Raman Gain and Bandwidth for

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