- Email: [email protected]
Low-insertion loss Raman fiber modulator
15 July 2001
Optics Communications 194 (2001) 303±308
www.elsevier.com/locate/optcom
Low-insertion loss Raman ®ber modulator I. Torres-Gomez, A.N. Starodumov *, V.N. Filippov, Yu.O. Barmenkov, A. Martõnez-Rios Centro de Investigaciones en Optica, Lomadel Bosque 115, Col. Lomas del Bosque, Apdo. Postal 1-948, C.P. 37150 Le on, Gto., Mexico Received 12 January 2001; received in revised form 23 April 2001; accepted 23 April 2001
Abstract Characteristics of the Raman-eect based modulator for high power Yb-doped ®ber lasers have been analyzed by numerical simulation. Insertion loss, backre¯ection, and contrast ratio are considered as functions of the laser power and Ge concentration in ®ber. The optimum GeO2 doping has been shown to improve the eciency of the modulator at powers of 5±20 W, providing the insertion loss to be less than 1 dB at 20 W. At higher powers, pure silica ®bers become competitive, providing insertion loss of 0.6 dB at laser powers of 80 W. Ó 2001 Published by Elsevier Science B.V. PACS: 42.81.Dp Keywords: Fiber optic stimulated Raman scattering; Insertion loss; Modulator; Fiber laser
High power ®ber lasers have been a subject of considerable interest for applications in telecommunications, materials processing, and medicine [1±4]. Compact diraction-limited sources with output powers ranging from 1 to 150 W have appeared to be an alternative to single-mode crystalline lasers [5]. Numerous applications in printing and material processing require a pulsed operation of highpower ®ber lasers. However, it is quite dicult to provide for ecient modulation and simultaneously to prevent optical damage in bulk modulators for optical powers beyond 20 W. Integrated electrooptical and electroabsorption modulators
* Corresponding author. Tel.: +52-47-17-58-23; fax: +52-4717-50-00. E-mail address: [email protected] (A.N. Starodumov).
have a low threshold for optical damage and cannot be applied in powerful ®ber lasers. An interesting solution using a ``master±oscillator ampli®er'' scheme has been proposed by IREPolus Group [6]. In this method, a low power modulated signal accompanied by an auxiliary signal at other wavelength is ampli®ed in a two (or three)-stage modulator. The auxiliary signal with complementary modulation must experience the same ampli®cation to balance the gain. Polarizationinsensitive isolators between ampli®ers add to the cost of the system and may limit the transmitted power. Recently, an all-®ber nonlinear modulator, based on transferring an amplitude modulation from a low-power signal at the Stokes frequency onto a high power beam through stimulated Raman scattering (SRS), has been proposed [7] and demonstrated [8]. High resistance to optical
0030-4018/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII: S 0 0 3 0 - 4 0 1 8 ( 0 1 ) 0 1 2 6 6 - 4
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I. Torres-Gomez et al. / Optics Communications 194 (2001) 303±308
damage, the lack of back re¯ection and quite simple optical scheme make this modulator very attractive for application in high power ®ber lasers. The characteristics of this modulator depend on input power, the ®ber composition, and the coupling and transmission loss. With an increase of germanium concentration the eciency of SRS increases because of, ®rst, an enhancement in the Raman gain; second, a reduction in the mode ®eld diameter (keeping the ®ber single-mode), which increases the power density in the core. The latter leads to an increase of the coupling loss when a laser output ®ber is spliced with the modulator's ®ber. The competition between the Raman gain and losses results in a complex dependence of the modulator's characteristics on the ®ber composition. In this work we have analyzed the transmission, coupling and total insertion loss, back re¯ections, and modulation depth of the nonlinear optical modulator as functions of the laser power and of the GeO2 concentration in a ®ber. The optimum GeO2 doping and the amplitude of the Stokes signal have been shown to improve the eciency of the modulator, providing insertion loss of 0.6±1 dB. The basic idea of the modulator is to use an all®ber element for transferring an amplitude modulation from a low-power signal at the Stokes wavelength (kS 1117 nm) onto a high power beam at kP 1060 nm through stimulated Raman scattering. Fig. 1 shows schematically the Raman eect-based modulator. A cladding-pumped single-mode Yb-doped ®ber laser (CPFL) is considered as an optical source with output powers of 5±100 W. The CPFL terminates with a singleclad ®ber (usually, Flexcore ®ber 1060). The modu-
lator includes a wavelength-division multiplexer (WDM1) made of the same type of the ®ber as that of the ®ber laser output. Thus, we suppose the splicing loss between two ®bers to be negligible (0.05 dB). The WDM1 combines the low-power modulated Stokes signal and the high-power pump. The insertion loss of the WDM1 is estimated to be 0.2 dB as for standard WDMs. The second WDM separates the ampli®ed Stokes signal and modulated pump. A directly modulated laser diode operating at the Stokes wavelength is the most appropriate source of the Stokes signal. As an alternative, the Raman ®ber laser or Yb-doped ®ber laser at wavelength kS 1117 nm with output powers in the range 50±500 mW can be used. The performance of the modulator is determined by three parameters: the lack of back re¯ection, the insertion loss, and the modulation depth. The ®rst condition is practically satis®ed if an all-®ber modulator is used. In this case, the loss due to back re¯ection depends on the refractive index dierence between the cores of the modulator's ®ber (nm ) and WDM's ®ber (nWDM ). The back re¯ection loss is given by [9] " # 2 2 nWDM nm LF 10 log 1 4nWDM1 nm and is estimated to be less than 10 3 dB for the refractive index dierence of 0.02. The Rayleigh and Brillouin scattering may also contribute to the back re¯ection. Stimulated Brillouin scattering (SBS) is practically negligible at ®ber length intensity products less than 5 1011 W/cm and laser bandwidths of 0.3±1 nm, corresponding to the high-power (<100 W) double-clad lasers.
Fig. 1. Raman eect-based modulator.
I. Torres-Gomez et al. / Optics Communications 194 (2001) 303±308
We have estimated the contribution of Rayleigh scattering into back re¯ections using a k 4 dependence on wavelength and experimentally measured value [10] of the Rayleigh scattering coecient R. For 100 W of the pump power and 10-m length ®ber the back re¯ected power was calculated to be 2.7 mW that is 2:7 10 5 of the pump power at R 27 10 8 m 1 . The back re¯ected light is slightly ampli®ed due to SBS. Nevertheless, such a low level of the re¯ected light does not aect the operation of the pump laser. However, the back re¯ected light at the Stokes wavelength may aect the operation of the Stokes laser, because the output power of the Stokes laser and intrinsic noise are much less than those of the pump laser. Thus, a polarization-insensitive isolator should be placed between the laser at the Stokes frequency and WDM1. The insertion loss of the modulator depends on splicing and ®ber (transmission) losses, and losses introduced by WDM. The splicing loss for singlemode ®bers with Gaussian mode pro®les is calculated as 2 LS dB 20 log 4
3 Wm WM
2
WM Wm
5
2
where WWDM and Wm are the mode-®eld radii of the multiplexor's and modulator's ®bers, respectively. In its turn, the mode-®eld diameter depends on wavelength, the core diameter and the ®ber composition. We consider the core diameter as a function of the germanium concentration ®xing a normalized frequency parameter V. It should be noted that the NA of the modulator's ®ber can be made to match that of the laser output ®ber irrespective of the germanium concentration. In this case, the splicing loss can be ignored. As a result, doping with germanium with only contribute to the transmission loss. The transmission loss in the ®ber of the modulator depends on a laser output power. With an increase of the optical power the length of the effective Raman interaction becomes shorter, reducing the length of the modulator. The length of the modulator was determined as that length where 99% of the pump power is transferred to the
305
Stokes wave. A pump power transfer to the ampli®ed spontaneous Raman scattering in the absence of the modulated signal, and ampli®cation of the residual injected Stokes signal between two Stokes pulses, may also contribute to the transmission loss. To optimize the parameters of the modulator we have developed a model taking into account the above discussed eects. The Raman gain process is described by a system of coupled equations dIP z dz
xS gR fPS IP zIS z hmS Dm xP
aP IP z 3a
dIS z gR fSP IP zIS z hmS Dm dz
aS IS z
3b
where subscripts P and S relate to the pump and Stokes waves, I z is the intensity corresponding to the total power divided by the mode eective area, fPS;SP are the coecients corresponding to the overlapping integrals of the pump and Stokes modes, gR k is the Raman gain coecient, Dm is the bandwidth of the Raman gain. Terms g IP (hmS Dm) describe spontaneous Raman scattering into one axial mode. The exact system of equations taking into account the spectral and temperature characteristics of spontaneous Raman scattering has been derived in Ref. [10] for broadband (100 nm) Raman ampli®ers. In our model, the pump and Stokes signal are supposed to be much narrower (with bandwidth of a few nanometers). Therefore, we presented terms with spontaneous Raman scattering in simpli®ed form. The pump light is supposed to be depolarized. The properties of Raman scattering in ®bers have been studied since the ®rst demonstration of SRS in optical ®bers [11]. Short response time ( 6 100 fs) and gain properties make SRS an attractive mechanism for light ampli®cation, nonlinear optical switching, and signal processing [10±14]. Davey et al. [15], have shown that ®bers doped with GeO2 exhibit larger Raman gain, which depends on germanium concentration as gR k
9:4 10 k
14
1 0:08D
4
306
I. Torres-Gomez et al. / Optics Communications 194 (2001) 303±308
where D is the germanium concentration (in mol.%) in a ®ber core. As well as the Raman gain, the ®ber loss increases with germanium doping. Assuming Rayleigh scattering as a major contributor to the ®ber loss with the wavelength dependence of k 4 and using experimental data [16], one can calculate the loss coecient at an arbitrary wavelength. Using the set of Eqs. (2) and (3) we have calculated coupling, transmission, and insertion losses as functions of the germanium concentration and of the optical power. Fig. 2 shows an increase of the coupling loss with germanium concentration when splicing the Flexcore ®ber with the modulator's ®ber. Curve A corresponds to the losses calculated with Eq. (2), while curve B corresponds to splicing losses obtained experimentally with the tapering technique. On the left side of Fig. 2 we drive the transmission loss at laser powers of 5 W (squares), 20 W (rombs), and 80 W (triangles) versus GeO2 concentration. As is seen from Fig. 2, the transmission loss at low powers (<10 W) strongly decreases by adding germanium in the core. At moderate powers the variations of the transmission loss are less becoming negligible at powers beyond 80 W. The level of the transmission loss strongly depends on the Stokes signal/pump power ratio. At a low level of the injected Stokes signal, the growth
of the ampli®ed spontaneous noise may result in additional depletion of the pump wave. This eect becomes signi®cant when the Stokes signal/pump power ratio is less than (or about) 10 3 . With an increase of the injected Stokes signal, the modulator length becomes shorter, lowering the ampli®ed spontaneous noise (less than 1% of the pump power). Thus, the pump depletion due to ampli®ed spontaneous Raman scattering is the major contributor to the transmission loss at the Stokes/ pump ratio 6 10 3 , while at ratios larger than 5 10 3 this contribution becomes less than 0.5 dB at powers higher than 20 W. Fig. 3 shows the transmission loss as a function of the Stokes/pump ratio for dierent pump powers in the ®ber with 4 mol.% of GeO2 . Fig. 4(a) and (b) shows the insertion loss as a function of the germanium concentration (the loss of 0.2 dB introduced by WDM1 are also considered). In Fig. 4(a) the coupling loss is calculated taking into account curve A, while in Fig. 4(b) we used the experimental data for the coupling loss corresponding to the curve B in Fig. 2. As is seen, there are optimum concentrations of germanium at powers <20 W, which provide a minimum of the insertion loss. For powers beyond 20±30 W, a silica ®ber has the lowest insertion loss. Taking
Fig. 2. Coupling and transmission loss.
Fig. 3. Transmission loss versus Stokes/pump power ratio.
I. Torres-Gomez et al. / Optics Communications 194 (2001) 303±308
307
the insertion loss at powers <20 W. At the power of 80 W, the insertion loss varies from 0.2 to 0.1 dB with the germanium concentration in the range of 0±18 mol.%. Concerning the modulation depth, this parameter depends on the initial modulation depth of the Stokes signal. Ampli®ed spontaneous Raman scattering in the absence of the modulated signal, and ampli®cation of the residual Stokes signal, may aect the modulation depth. The high contrast of 35±40 dB of the injected Stokes signal and the Stokes signal/pump power ratio of 10 2 ±5 10 3 provide a modulation depth better than 20 dB. In conclusion, we have demonstrated that an optimum GeO2 doping improves the eciency of the Raman-based modulator at powers of 5±30 W, providing the total insertion loss of 0.9±1.5 dB at the Stokes/pump power ratio is more than 5 10 3 . At higher powers, pure silica ®bers become competitive, providing insertion loss of 0.6 dB at laser powers of 80 W. Using the NA matched ®bers permits to get the insertion loss less than 0.5 dB. The total back re¯ections due to Rayleigh backscattering, Brillouin scattering and re¯ection from the splice between the two ®bers have been calculated to be less than 10 4 at pump powers <100 W.
Acknowledgements This work was supported by CONACyT grant no. 32195E.
Fig. 4. Insertion loss at dierent optical powers. Coupling loss corresponds: (a) to the curve A in Fig. 2; (b) to the curve B.
into account the losses introduced by WDM2 we calculated the total insertion loss to vary from 1.5 dB at 5 W to 0.6 dB to 80 W of the laser power. In the case of ®bers with matched numerical apertures, the insertion loss depends on the transmission loss only and decreases with germanium concentration according to the curves in Fig. 2. For such ®bers, germanium doping strongly decreases
References [1] H. Po, E. Snitzer, L. Tumminelli, F. Hakimi, M.N. Chu, T. Haw, Double clad high brightness Nd laser pumped by GaAl As phased array, Post-deadline paper PD07, Optical Fiber Communication Conference, Houston, TX, 1989. [2] J.D. Minelly, W.L. Barnes, R.I. Laming, P.R. Morkel, J.E. Townsend, S.G. Grubb, D.N. Payne, Diode-array pumping of Er3 =Yb3 co-doped ®ber lasers and ampli®ers, IEEE Photon. Technol. Lett. 5 (1993) 301±303. [3] S.D. Jackson, T.A. King, High power diode-claddingpump Tm doped silica ®ber laser, Opt. Lett. 23 (1998) 1462±1464.
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[4] V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P.S. Yeh, E. Zucker, 110 W ®bre laser, Electron. Lett. 35 (1999) 1158±1160. [5] V.P. Gapontsev, High power ®ber lasers, X Conference on Laser Optics, St. Petersburg, 2000, ThPl-5, p. 31. [6] V. Fomin, Pulsed ®ber lasers for marking and printing applications, X Conference on Laser Optics, St. Petersburg, 2000, ThSW1-12, p. 36. [7] A.N. Staroumov, L.A. Zenteno, N. Arzate, P. Gavrilovic, Nonlinear-optical modulator for high-power ®ber lasers, Opt. Lett. 22 (1997) 286±288. [8] I. Torres, A.N. Starodumov, Yu.O. Barmenkov, L.A. Zenteno, P. Gavrilovic, Raman eect based modulator for high power ®ber lasers, Appl. Phys. Lett. 72 (4) (1998) 401± 403. [9] F.C. Allard, Fiber Optics Handbook For Engineers and Scientists, McGraw-Hill, New York, 1989, pp. 3.13±3.14. [10] H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, E. Rabarijaona, Pump interactions in a 100 nm bandwidth Raman ampli®er, IEEE Photon. Technol. Lett. 11 (1999) 530±532.
[11] R.H. Stolen, E.P. Ippen, Raman gain in optical waveguides, Appl. Phys. Lett. 22 (6) (1973) 276±278. [12] D.I. Chang, S.V. Chernikov, M.J. Guy, J.R. Taylor, H.J. Kong, Opt. Commun. 142 (1997) 289±293. [13] E.A. Kuzin, G. Beltran-Perez, M.A. Basurto-Pensado, R. Rojas-Laguna, J.A. Andrade-Lucio, M. Torres-Cisneros, E. Alvarado-Mendez, Opt. Commun. 169 (1999) 87±91. [14] A.N. Starodumov, Yu.O. Barmenkov, A. Martõnez, I. Torres, L.A. Zenteno, Experimental demonstration of Raman eect-based optical transistor, Opt. Lett. 23 (6) (1998) 352±354. [15] S.T. Davey, D.L. Williams, B.J. Ainslie, W.J.M. Rothwell, B. Wake®eld, Optical gain spectrum of GeO2 ±SiO2 Raman ®bre ampli®ers, IEEE Proc. Part J 136 (6) (1989) 301± 306. [16] E.M. Dianov, V.M. Mashinsky, V.B. Neustruev, O.D. Sazhin, A.N. Guryanov, V.F. Khopin, N.N. Vechkanov, Origin of excess loss in single-mode optical ®bers with high GeO2 -doped silica core, Opt. Fiber Technol. 3 (1997) 77± 86.
Optics Communications 194 (2001) 303±308
www.elsevier.com/locate/optcom
Low-insertion loss Raman ®ber modulator I. Torres-Gomez, A.N. Starodumov *, V.N. Filippov, Yu.O. Barmenkov, A. Martõnez-Rios Centro de Investigaciones en Optica, Lomadel Bosque 115, Col. Lomas del Bosque, Apdo. Postal 1-948, C.P. 37150 Le on, Gto., Mexico Received 12 January 2001; received in revised form 23 April 2001; accepted 23 April 2001
Abstract Characteristics of the Raman-eect based modulator for high power Yb-doped ®ber lasers have been analyzed by numerical simulation. Insertion loss, backre¯ection, and contrast ratio are considered as functions of the laser power and Ge concentration in ®ber. The optimum GeO2 doping has been shown to improve the eciency of the modulator at powers of 5±20 W, providing the insertion loss to be less than 1 dB at 20 W. At higher powers, pure silica ®bers become competitive, providing insertion loss of 0.6 dB at laser powers of 80 W. Ó 2001 Published by Elsevier Science B.V. PACS: 42.81.Dp Keywords: Fiber optic stimulated Raman scattering; Insertion loss; Modulator; Fiber laser
High power ®ber lasers have been a subject of considerable interest for applications in telecommunications, materials processing, and medicine [1±4]. Compact diraction-limited sources with output powers ranging from 1 to 150 W have appeared to be an alternative to single-mode crystalline lasers [5]. Numerous applications in printing and material processing require a pulsed operation of highpower ®ber lasers. However, it is quite dicult to provide for ecient modulation and simultaneously to prevent optical damage in bulk modulators for optical powers beyond 20 W. Integrated electrooptical and electroabsorption modulators
* Corresponding author. Tel.: +52-47-17-58-23; fax: +52-4717-50-00. E-mail address: [email protected] (A.N. Starodumov).
have a low threshold for optical damage and cannot be applied in powerful ®ber lasers. An interesting solution using a ``master±oscillator ampli®er'' scheme has been proposed by IREPolus Group [6]. In this method, a low power modulated signal accompanied by an auxiliary signal at other wavelength is ampli®ed in a two (or three)-stage modulator. The auxiliary signal with complementary modulation must experience the same ampli®cation to balance the gain. Polarizationinsensitive isolators between ampli®ers add to the cost of the system and may limit the transmitted power. Recently, an all-®ber nonlinear modulator, based on transferring an amplitude modulation from a low-power signal at the Stokes frequency onto a high power beam through stimulated Raman scattering (SRS), has been proposed [7] and demonstrated [8]. High resistance to optical
0030-4018/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII: S 0 0 3 0 - 4 0 1 8 ( 0 1 ) 0 1 2 6 6 - 4
304
I. Torres-Gomez et al. / Optics Communications 194 (2001) 303±308
damage, the lack of back re¯ection and quite simple optical scheme make this modulator very attractive for application in high power ®ber lasers. The characteristics of this modulator depend on input power, the ®ber composition, and the coupling and transmission loss. With an increase of germanium concentration the eciency of SRS increases because of, ®rst, an enhancement in the Raman gain; second, a reduction in the mode ®eld diameter (keeping the ®ber single-mode), which increases the power density in the core. The latter leads to an increase of the coupling loss when a laser output ®ber is spliced with the modulator's ®ber. The competition between the Raman gain and losses results in a complex dependence of the modulator's characteristics on the ®ber composition. In this work we have analyzed the transmission, coupling and total insertion loss, back re¯ections, and modulation depth of the nonlinear optical modulator as functions of the laser power and of the GeO2 concentration in a ®ber. The optimum GeO2 doping and the amplitude of the Stokes signal have been shown to improve the eciency of the modulator, providing insertion loss of 0.6±1 dB. The basic idea of the modulator is to use an all®ber element for transferring an amplitude modulation from a low-power signal at the Stokes wavelength (kS 1117 nm) onto a high power beam at kP 1060 nm through stimulated Raman scattering. Fig. 1 shows schematically the Raman eect-based modulator. A cladding-pumped single-mode Yb-doped ®ber laser (CPFL) is considered as an optical source with output powers of 5±100 W. The CPFL terminates with a singleclad ®ber (usually, Flexcore ®ber 1060). The modu-
lator includes a wavelength-division multiplexer (WDM1) made of the same type of the ®ber as that of the ®ber laser output. Thus, we suppose the splicing loss between two ®bers to be negligible (0.05 dB). The WDM1 combines the low-power modulated Stokes signal and the high-power pump. The insertion loss of the WDM1 is estimated to be 0.2 dB as for standard WDMs. The second WDM separates the ampli®ed Stokes signal and modulated pump. A directly modulated laser diode operating at the Stokes wavelength is the most appropriate source of the Stokes signal. As an alternative, the Raman ®ber laser or Yb-doped ®ber laser at wavelength kS 1117 nm with output powers in the range 50±500 mW can be used. The performance of the modulator is determined by three parameters: the lack of back re¯ection, the insertion loss, and the modulation depth. The ®rst condition is practically satis®ed if an all-®ber modulator is used. In this case, the loss due to back re¯ection depends on the refractive index dierence between the cores of the modulator's ®ber (nm ) and WDM's ®ber (nWDM ). The back re¯ection loss is given by [9] " # 2 2 nWDM nm LF 10 log 1 4nWDM1 nm and is estimated to be less than 10 3 dB for the refractive index dierence of 0.02. The Rayleigh and Brillouin scattering may also contribute to the back re¯ection. Stimulated Brillouin scattering (SBS) is practically negligible at ®ber length intensity products less than 5 1011 W/cm and laser bandwidths of 0.3±1 nm, corresponding to the high-power (<100 W) double-clad lasers.
Fig. 1. Raman eect-based modulator.
I. Torres-Gomez et al. / Optics Communications 194 (2001) 303±308
We have estimated the contribution of Rayleigh scattering into back re¯ections using a k 4 dependence on wavelength and experimentally measured value [10] of the Rayleigh scattering coecient R. For 100 W of the pump power and 10-m length ®ber the back re¯ected power was calculated to be 2.7 mW that is 2:7 10 5 of the pump power at R 27 10 8 m 1 . The back re¯ected light is slightly ampli®ed due to SBS. Nevertheless, such a low level of the re¯ected light does not aect the operation of the pump laser. However, the back re¯ected light at the Stokes wavelength may aect the operation of the Stokes laser, because the output power of the Stokes laser and intrinsic noise are much less than those of the pump laser. Thus, a polarization-insensitive isolator should be placed between the laser at the Stokes frequency and WDM1. The insertion loss of the modulator depends on splicing and ®ber (transmission) losses, and losses introduced by WDM. The splicing loss for singlemode ®bers with Gaussian mode pro®les is calculated as 2 LS dB 20 log 4
3 Wm WM
2
WM Wm
5
2
where WWDM and Wm are the mode-®eld radii of the multiplexor's and modulator's ®bers, respectively. In its turn, the mode-®eld diameter depends on wavelength, the core diameter and the ®ber composition. We consider the core diameter as a function of the germanium concentration ®xing a normalized frequency parameter V. It should be noted that the NA of the modulator's ®ber can be made to match that of the laser output ®ber irrespective of the germanium concentration. In this case, the splicing loss can be ignored. As a result, doping with germanium with only contribute to the transmission loss. The transmission loss in the ®ber of the modulator depends on a laser output power. With an increase of the optical power the length of the effective Raman interaction becomes shorter, reducing the length of the modulator. The length of the modulator was determined as that length where 99% of the pump power is transferred to the
305
Stokes wave. A pump power transfer to the ampli®ed spontaneous Raman scattering in the absence of the modulated signal, and ampli®cation of the residual injected Stokes signal between two Stokes pulses, may also contribute to the transmission loss. To optimize the parameters of the modulator we have developed a model taking into account the above discussed eects. The Raman gain process is described by a system of coupled equations dIP z dz
xS gR fPS IP zIS z hmS Dm xP
aP IP z 3a
dIS z gR fSP IP zIS z hmS Dm dz
aS IS z
3b
where subscripts P and S relate to the pump and Stokes waves, I z is the intensity corresponding to the total power divided by the mode eective area, fPS;SP are the coecients corresponding to the overlapping integrals of the pump and Stokes modes, gR k is the Raman gain coecient, Dm is the bandwidth of the Raman gain. Terms g IP (hmS Dm) describe spontaneous Raman scattering into one axial mode. The exact system of equations taking into account the spectral and temperature characteristics of spontaneous Raman scattering has been derived in Ref. [10] for broadband (100 nm) Raman ampli®ers. In our model, the pump and Stokes signal are supposed to be much narrower (with bandwidth of a few nanometers). Therefore, we presented terms with spontaneous Raman scattering in simpli®ed form. The pump light is supposed to be depolarized. The properties of Raman scattering in ®bers have been studied since the ®rst demonstration of SRS in optical ®bers [11]. Short response time ( 6 100 fs) and gain properties make SRS an attractive mechanism for light ampli®cation, nonlinear optical switching, and signal processing [10±14]. Davey et al. [15], have shown that ®bers doped with GeO2 exhibit larger Raman gain, which depends on germanium concentration as gR k
9:4 10 k
14
1 0:08D
4
306
I. Torres-Gomez et al. / Optics Communications 194 (2001) 303±308
where D is the germanium concentration (in mol.%) in a ®ber core. As well as the Raman gain, the ®ber loss increases with germanium doping. Assuming Rayleigh scattering as a major contributor to the ®ber loss with the wavelength dependence of k 4 and using experimental data [16], one can calculate the loss coecient at an arbitrary wavelength. Using the set of Eqs. (2) and (3) we have calculated coupling, transmission, and insertion losses as functions of the germanium concentration and of the optical power. Fig. 2 shows an increase of the coupling loss with germanium concentration when splicing the Flexcore ®ber with the modulator's ®ber. Curve A corresponds to the losses calculated with Eq. (2), while curve B corresponds to splicing losses obtained experimentally with the tapering technique. On the left side of Fig. 2 we drive the transmission loss at laser powers of 5 W (squares), 20 W (rombs), and 80 W (triangles) versus GeO2 concentration. As is seen from Fig. 2, the transmission loss at low powers (<10 W) strongly decreases by adding germanium in the core. At moderate powers the variations of the transmission loss are less becoming negligible at powers beyond 80 W. The level of the transmission loss strongly depends on the Stokes signal/pump power ratio. At a low level of the injected Stokes signal, the growth
of the ampli®ed spontaneous noise may result in additional depletion of the pump wave. This eect becomes signi®cant when the Stokes signal/pump power ratio is less than (or about) 10 3 . With an increase of the injected Stokes signal, the modulator length becomes shorter, lowering the ampli®ed spontaneous noise (less than 1% of the pump power). Thus, the pump depletion due to ampli®ed spontaneous Raman scattering is the major contributor to the transmission loss at the Stokes/ pump ratio 6 10 3 , while at ratios larger than 5 10 3 this contribution becomes less than 0.5 dB at powers higher than 20 W. Fig. 3 shows the transmission loss as a function of the Stokes/pump ratio for dierent pump powers in the ®ber with 4 mol.% of GeO2 . Fig. 4(a) and (b) shows the insertion loss as a function of the germanium concentration (the loss of 0.2 dB introduced by WDM1 are also considered). In Fig. 4(a) the coupling loss is calculated taking into account curve A, while in Fig. 4(b) we used the experimental data for the coupling loss corresponding to the curve B in Fig. 2. As is seen, there are optimum concentrations of germanium at powers <20 W, which provide a minimum of the insertion loss. For powers beyond 20±30 W, a silica ®ber has the lowest insertion loss. Taking
Fig. 2. Coupling and transmission loss.
Fig. 3. Transmission loss versus Stokes/pump power ratio.
I. Torres-Gomez et al. / Optics Communications 194 (2001) 303±308
307
the insertion loss at powers <20 W. At the power of 80 W, the insertion loss varies from 0.2 to 0.1 dB with the germanium concentration in the range of 0±18 mol.%. Concerning the modulation depth, this parameter depends on the initial modulation depth of the Stokes signal. Ampli®ed spontaneous Raman scattering in the absence of the modulated signal, and ampli®cation of the residual Stokes signal, may aect the modulation depth. The high contrast of 35±40 dB of the injected Stokes signal and the Stokes signal/pump power ratio of 10 2 ±5 10 3 provide a modulation depth better than 20 dB. In conclusion, we have demonstrated that an optimum GeO2 doping improves the eciency of the Raman-based modulator at powers of 5±30 W, providing the total insertion loss of 0.9±1.5 dB at the Stokes/pump power ratio is more than 5 10 3 . At higher powers, pure silica ®bers become competitive, providing insertion loss of 0.6 dB at laser powers of 80 W. Using the NA matched ®bers permits to get the insertion loss less than 0.5 dB. The total back re¯ections due to Rayleigh backscattering, Brillouin scattering and re¯ection from the splice between the two ®bers have been calculated to be less than 10 4 at pump powers <100 W.
Acknowledgements This work was supported by CONACyT grant no. 32195E.
Fig. 4. Insertion loss at dierent optical powers. Coupling loss corresponds: (a) to the curve A in Fig. 2; (b) to the curve B.
into account the losses introduced by WDM2 we calculated the total insertion loss to vary from 1.5 dB at 5 W to 0.6 dB to 80 W of the laser power. In the case of ®bers with matched numerical apertures, the insertion loss depends on the transmission loss only and decreases with germanium concentration according to the curves in Fig. 2. For such ®bers, germanium doping strongly decreases
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