Optimization of silica fiber Raman amplifier using the ... - CiteSeerX

1 July 2000

Optics Communications 181 Ž2000. 145–151 www.elsevier.comrlocateroptcom

Optimization of silica fiber Raman amplifier using the Raman frequency modeling for an arbitrary GeO 2 concentration in the core Hong-Seok Seo, K. Oh ) Department of Information and Communications, Kwangju Institute of Science and Technology, 1 Oryong-dong Puk-ku, Kwangju, 500-712, South Korea Received 23 February 2000; received in revised form 28 April 2000; accepted 28 April 2000

Abstract Spectral characteristics of Raman gain were theoretically investigated for step index silica optical fibers with various GeO 2 concentrations. The evolution of stimulated Raman scattering cross sections for the 1st and the 2nd Stokes shifts along fiber lengths were rigorously analyzed using the Raman frequency modeling, for the first time. By the energy transfer from the 1st to the 2nd Stokes shift, saturation in the Raman gain was observed and the onset of the energy transfer was theoretically predicted. Optimal fiber lengths for Raman amplifiers where the 1st Stokes power reaches the maximum were calculated for arbitrary GeO 2 concentration and pumping power. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Optical fiber; Raman amplifier; 2nd Stokes; Optimum Raman medium length; Optimum germanium concentration

1. Introduction As the wavelength division multiplexing ŽWDM. technique is being established as a standard for optical communication systems, silica fiber Raman amplifiers have been intensively studied for their flexible control of bandwidth and spectral position of optical gain as an alternative to rare earth doped fiber amplifiers. Especially, recent development of high power semiconductor lasers has stimulated research on high power fiber lasers that can be used as

) Corresponding author. Tel.: q82-62-970-2213; fax: q82-62970-2204; e-mail: [email protected]

a compact pump light source for Raman amplifiers. With these high power pump sources, advantages of Raman amplifier such as high gain over ; 30 dB and large bandwidth over ; 100 nm w1x, regained attention in both 1.3 and 1.5 mm communication windows. Raman gain efficiency, however, is limited by its inherent nonlinear nature to about 1.21 = 10y1 1 cmrW much lower than those in erbium doped fiber amplifiers. To obtain a signal gain over 30 dB, Raman amplifiers require a high pumping power over a few watts and a long fiber length of a few kms. GeO 2 doped silica fibers have showed most desirable potential to improve the gain characteristics of Raman amplifiers being intensively studied for practical applications. In these fibers, Raman gain

0030-4018r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 0 0 . 0 0 7 2 9 - X

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H.-S. Seo, K. Oh r Optics Communications 181 (2000) 145–151

coefficients are known to be proportional to concentration of GeO 2 in the core. Increase of doping concentration of germanium, however, induces the optical loss due to Rayleigh scattering. Therefore, optimization of germanium concentration is necessary to obtain both high Raman gain and low loss at the same time. In order to optimize the gain and alleviate high pump power requirements, various experimental and theoretical attempts in material and waveguide structure have been reported. Dianov et al. first reported reduction of pump power requirement to 300 mW for the gain of 30 dB at the 1st Stokes shift in a germanosilicate fiber w2x. Recently Dianov et al. w3x further developed a Raman fiber with a lower loss and a higher GeO 2 concentration to improve the threshold in pump power as well as the small signal gain. In theoretical studies, Davey et al. w4x calculated the small signal gain variation as a function of GeO 2 concentration using an analytic gain formula. His analysis, however, was limited only to the 1st Stokes shift neglecting the energy transfer to the 2nd Stokes shift. Kao and Wu w5x calculated the cross talk among WDM channels and signal to noise ratio in Raman medium with assumption that Raman gain spectrum is Lorentzian. They, however, also ignored the 2nd Stokes, which affects small signal gain of the 1st Stokes. Liu and Garmire w6x calculated the stimulated Raman Stokes spectrum in fused silica core fiber but the effects of GeO 2 on the Raman gain and Rayleigh scattering loss were not treated. Thus far the evolution of the 1st and the 2nd Stokes shifts in germanosilicate fiber Raman amplifiers has not been rigorously analyzed in the spectral domain including the effects of GeO 2 both on the gain and Rayleigh scattering loss. In our studies we incorporated, for the first time to the best knowledge of authors, both the energy transfer to the 2nd Stokes and the GeO 2 related Rayleigh scattering loss terms w7x in the analysis of gain characteristics of germanosilicate fibers using a numerical Raman frequency modeling w6x. The optimum length where the Raman small signal gain at the 1st Stokes shift reaches its maximum was calculated as a function of pump power for a given GeO 2 concentration. We, furthermore, obtained the optimum GeO 2 concentration for Raman amplifiers considering the 2nd Stokes and optical loss terms.

2. Analysis In order to calculate the amplified gain and optimum length of Raman medium for various Germanium concentrations at a given pump power, Raman frequency modeling initially developed by Liu et al. w6x was used. The governing equations are given as below; d I0 dz d Ii dz

n

s ya 0 I0 y I0

ks1

g ji

Ý C j Ij g

js0

dz

n

Ý

C i Ii

jm ksiq1

Ý js0

g i k Ik

ksiq1

ny1

s ya n In q In

Ž 1.

0m

n

Ý g ji Ij y Ii Ý js0

iy1

g0 k

ks1

iy1

s ya i Ii q Ii

q d In

n

Ý g 0 k Ik y Ý C 0 I 0 g

gik

Ž 2.

gi m

ny1

g jn I j q

g jn

Ý C j Ij g

js0

g ji s Ž 1.2 = 10y11rl j . s Ž x GeO 2 ,Õi .

Ž 3.

jm

n2

2

n2 q D n2

Ž 4. Ci s p Ž n12 y n 22 . Ž 1.5 = 10y2 7 cm3 . rl4i

Ž 5.

where intensity I represents the instantaneous intensity at a distance z, measured in a moving coordinate system which travels at the group velocity of the propagating optical pulse. Parameters with the subscript ‘0’ correspond to variables at the pump frequency. The subscript ‘n’ means the final frequency shift fixed at 1000 cmy1 in this paper. Through the analysis, we have assumed the pump and signal wavelengths are 1.24 mm and 1.31 mm, respectively. Ii is the intensity at the frequency n i . a i is the fiber loss coefficient which is related germanium concentration. g ji is the Raman gain at the frequency n i caused by the pump at the frequency n j w4x. g jirg jm represents the normalized line shape of the Raman gain curve defined in Eq. Ž4. and Ref. w4x. g jm is the maximum value of Raman gain, g ji . Ci is the spontaneous Raman scattering term represented in Eq. Ž5. and Ref. w6x. n1 and n 2 are the refractive index of core and cladding, respectively. D n is defined as Ž n1 y n 2 .rn 2 , and s is Raman cross section area as a function of the GeO 2 concentration and the frequency, n i w4x. Terms in right-hand side of Eq. Ž1.


Fig. 1. Illustration of frequency interval and notations w6x. n i Stokes signal obtains gain from n j , j- i and gives its energy to n k , k ) i. The frequency interval, D n is 6.66 cmy1 and nn 1000 cmy1 in this simulation.

correspond to the Rayleigh scattering loss, the energy conversion into k th Stokes shift, and losses induced by the spontaneous Raman scattering at the pump frequency, respectively. Terms in right-hand side of Eq. Ž2. are the Rayleigh scattering loss, the Raman gain from jth Stokes shift, the energy transfer into k th Stokes, losses induced by the spontaneous Raman scattering from jth Stokes, and losses induced by the spontaneous Raman scattering at the frequency component, n i . Fig. 1 explains frequency intervals and notations of Eqs. Ž1. – Ž3.. In a Raman medium the signal at n i obtains a gain from low frequency signals at n j , j - i, and gives its energy to higher frequencies n k , k ) i. In this simulation, we divided the frequency range of total 1000 cmy1 into 150 frequency slots and each slot had a uniform 6.66 cmy1 frequency interval. Each slot corresponds to about 1 nm spacing for the pump at 1.24 mm used in a 1.31 mm amplifier. This Raman frequency model is valid for calculation of Raman Stokes spectrum in

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a nonlinear regime, where only the stimulated Raman scattering is dominant nonlinear effect. Table 1 shows the range of pump power and Raman medium length where the above assumption holds for various index differences. If the initial pulse width is greater than 100 ps, as in 10 Gbps data rate, the group velocity dispersion effect is negligible since the Raman medium length is shorter than the dispersion length L D , defined as T02rb 2 , where T0 is initial pulse width and b 2 is group velocity dispersion w10x. In the same manner, the self phase modulation ŽSPM. effect can be also ignored if the Raman medium length is shorter than the nonlinear length, Lnl , which will be explained in Section 3. In order to calculate the gain spectrum in terms of Raman medium length, pumping power, and GeO 2 concentration, the governing Eqs. Ž1. – Ž3. were solved by using 4th order Runge–Kutta method. For numerical stability, the mesh size of the fiber length, D z was chosen as 50 cm, and total Raman medium length for the analysis was about 100 km. Power is calculated from intensity times effective core area. The effective core area, A, is defined as below w8,9x; p As

Ž W12 q W22 .

2

Ž 6.

W s a Ž 0.65 q 1.619Vy1 .5 q 2.879Vy6 . Vs

2p

l

(Ž n y n .

a

2 1

2 2

Ž 7. Ž 8.

where W1 , W2 are mode field radii at the pump, 1.24 mm and the signal, 1.31 mm, respectively, a, n1 , n 2 are core radius, core and cladding refractive index, respectively, and V is fixed as 2.0 by decreasing core radius for core index increased by germanium.

Table 1 Group velocity dispersion, b 2 , optimum length, Lopt , dispersion length, L D , and nonlinear length, Lnl , in terms of index difference and pump power w10,11x. Each pump power is a threshold value, where Lopt does not exceed Lnl for the given index difference. Initial pulse width is assumed by 100 ps to calculate L D . Each parameter is defined and explained in text. Dn

Pump power

Gain ŽdB.

b 2 Žps 2rkm.

Lopt Žkm.

L D Žkm.

Lnl Žkm.

0.01 0.015 0.02 0.025 0.03 0.035 0.04

0.195 0.195 0.195 0.2 0.24 0.28 0.32

27.77 31.70 31.41 30.16 32.15 32.88 32.86

9.82 15.53 22.33 31.02 40.70 46.88 31.98

21.15 12.61 8.52 5.94 3.81 2.59 1.84

1018.01 643.91 447.82 322.37 245.70 213.31 312.39

35.967 18.3 14.38 7.65 3.93 2.738 2.29

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Fig. 2. Normalized Raman gain distribution in pure silica core w6x. Two peaks is shown at 440 cmy1 and 485 cmy1 . The maximum peak value is 1.21=10y1 1 r l pump cmrW in a shifted frequency, 440 cmy1 , where l pump is the wavelength of pumping source.

Fig. 2 shows the normalized Raman gain spectrum in pure silica core w6x. The peak of Raman gain has 1.21 = 10y1 1rl pump cmrW at a shifted frequency, 440 cmy1 , where l pump is the wavelength of pump. The Raman gain bandwidth is about 8 THz Ž64 nm. in FWHM. When GeO 2 is doped in the silica core, the Raman gain peak shifts to a shorter wavelength, 420 cmy1 , with an increased peak gain value and a narrowed bandwidth. Fig. 3 shows the Raman gain spectra for various core to cladding index difference, Dn, due to GeO 2 in the core when pumped at 1.24 mm w4x. As GeO 2 is doped in the silica core, Rayleigh scattering coefficient increases

Fig. 3. Raman gain distribution of germanium doped fiber pumped by 1.24 mm pumping source. D n is defined by n1 y n 2 where n1 and n 2 are core and cladding refractive index, respectively. The peak of Raman gain value is located at 1.31 mm w4x.

Fig. 4. Loss distribution in terms of index difference between core and cladding at 1.31 mm w7x.

and Fig. 4 shows the attenuation of optical fiber at 1.31 mm manufactured by modified chemical vapor deposition ŽMCVD. technique as a function of germanium concentrations w7x. Based on these previously reported data on the Raman gain and optical loss, we solved the governing equations numerically expanding the frequency range to include the 2nd Stokes shift effects in order to estimate the signal gain, the optimum fiber length, and the optimum GeO 2 concentration. 3. Results and discussion When a Raman medium is pumped, optical signals initially experience amplification at the frequency range of the 1st Stokes shift by the stimulated Raman scattering process. If these signals at the 1st Stokes shift are further more amplified to exceed a threshold power level, part of the energy is transferred into the 2nd and higher order Stokes shifts. In most of Raman amplifiers, gain is obtained in the frequency range of the 1st Stokes shift. In amplifier design, thus, it is critical to understand how the energy is transferred from the 1st to the 2nd Stokes shift for various parameters such as GeO 2 concentration, fiber length, and pump power. In Figs. 5 and 6, the evolution of the 1st and the 2nd Stokes power is shown for germanosilicate fiber that has a index difference, D n, of 0.01 pumped by 2 W at 1.24 mm. The fiber loss was set at 0.627 dBrkm for 1.24 mm. When the fiber is pumped and


149

Fig. 5. Spontaneous Raman scattering signals amplified by pumping power was plotted in terms of wavelength and medium length. The pumping power is 2.0 W, optical loss is 0.64 dBrkm at 1.24 mm, and D n is 0.01. When the Raman medium length is 4.5 km, Stokes signals reach maximum.

the probe signal is absent, incoherent optical signals are generated by spontaneous Raman scattering at the 1st Stokes band. As these signals propagate along the fiber, they experience the gain, whose spectrum is shown in Fig. 3. The 1st Stokes peak power

reaches the maximum 125 mW for the fiber length of 4.5 km. As the gain medium length is further increased to 9.5 km, the 1st Stokes power serves as a pump for the 2nd Stokes and the energy starts to be converted into the 2nd Stokes. Thus, for given opti-

Fig. 6. 2nd Stokes signals amplified from energy of 1st Stokes power was plotted in terms of wavelength and medium length. The pumping power is 2.0 W, optical loss is 0.64 dBrkm at 1.24 mm, and D n is 0.01. As the medium length is increased, 2nd Stokes signals is growing.

150


cal fiber parameters and pump power, there exists an optimal fiber length that will maximize the 1st Stokes power before the onset of conversion to the 2nd Stokes. Fig. 7 shows the small signal Raman gain as a function of pump power for the optimal fiber length where the 1st Stokes power reaches the maximum. The signal at 1.31 mm was assumed to have the power of y20 dBm. The optical loss at the signal wavelength, 1.31 mm was assumed to vary in the range of 0.36 dBrkm and 3.91 dBrkm for fibers of Dn in the range of, from 0.01 to 0.04, following a similar functional behavior as shown in Fig. 4. The small signal gain linearly increases and then saturates as the pump power increases. The gain saturation is attributed to the energy transfer from the 1st to the 2nd Stokes band. Nonlinear spectral broadening by SPM can be induced when the signal power is greater than 10 dBm Ž30 dB gain.. The dotted line represents the threshold where the optimum Raman medium length, L opt , exceeds the nonlinear length, L nl , defined as L optrH0L op tg Psig Ž L.d L, where g is given as a function of GeO 2 concentration in Refs. w10,11x. The range where SPM effects could not be ignored is shown in Fig. 7. In Fig. 8, the small signal gain at 1.31 mm was plotted as a function of the index difference, D n, of the fiber for the optimal fiber length. Here we assumed that the index difference is due to GeO 2 doping. The Raman small signal gain was found to reach its maximum when the index difference is near 0.015 for all of pump powers in the range of 0.05 to

Fig. 7. Small signal Raman gain characteristics in terms of pump power.

Fig. 8. Small signal Raman gain characteristics in terms of germanium concentration. The optimum germanium concentration is D ns 0.015 irrespective of pumping power.

0.2 W. As the index difference further increases to 0.04, the highest value achievable by present fabrication techniques, the gain decreases rapidly due to Rayleigh scattering loss as shown in Fig. 4. Therefore it is found that the GeO 2 concentration also has an optimal value corresponding to the index difference of 0.015 due to the trade off between Raman gain and Rayleigh scattering loss. In Fig. 9, the optimal fiber length was plotted as a function of pump power for various index differences. Similar to Fig. 8, the optimal fiber length reaches maximum and then decrease as the pump power increases. As long as the pump energy is transferred only to the 1st

Fig. 9. Optimum Raman medium length in terms of pumping power. The optimum Raman medium length is decreasing as index difference is increasing.


Stokes band, the optimal length increases proportional to the pump power. When pump power reaches over a certain value, the 1st Stokes power is transferred to the 2nd Stokes wave and the optimal length abruptly decreases to result in signal gain saturation. The dotted line is the threshold of nonlinear length, Lnl , causing nonlinear spectral broadening induced by SPM, which is dominant when pump power is over 0.2 W and optimum Raman medium length exceeds the nonlinear length. 4. Conclusion Including the effects of GeO 2 both on optical loss and Raman gain, a rigorous numerical analysis on the evolution of optical power from the 1st Stokes to the 2nd Stokes in the fiber was performed. We have numerically found that the energy transfer from the 1st to the 2nd Stokes band defined the optimal fiber length and subsequently resulted in gain saturation for Raman amplifiers at 1.3 mm with the pump wavelength at 1.24 mm. The GeO 2 concentration was found to have an optimal value corresponding to the index difference of 0.015 to compensate Rayleigh scattering loss. Acknowledgements This work was partly supported by UFON, an ERC program sponsored by KOSEF, and BK21 program, supported by MOE in Korea.

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