- Email: [email protected]
Er-codoped integrated waveguides
Optical Materials 33 (2010) 231–235
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Optical Materials journal homepage: www.elsevier.com/locate/optmat
Study of an optimised bidirectional pump scheme for fs-laser written Yb/Er-codoped integrated waveguides J.A. Vallés a,⇑, M.Á. Rebolledo a, V. Berdejo a, A. Ferrer b, A. Ruiz de la Cruz b, J. Solís b a b
Departamento de Física Aplicada – I3A, Facultad de Ciencias, Universidad de Zaragoza, C/Pedro Cerbuna 12, 50009 Zaragoza, Spain Laser Processing Group, Instituto de Óptica-CSIC, Serrano 121, 28006 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 27 May 2010 Received in revised form 28 August 2010 Accepted 1 October 2010 Available online 29 October 2010 Keywords: Yb3+/Er3+ doped glasses fs-Laser written waveguides Waveguide amplifiers Waveguide lasers
a b s t r a c t The influence of the working conditions on the performance of bidirectionally pumped fs-laser written Yb/Er-codoped waveguide active devices is numerically analysed. The large variations in the optimal length of the waveguide, the gain dependence on the pump wavelengths and the more efficient pumpto-signal power conversion that can be obtained by asymmetric pump configurations for largesignal-regime waveguide amplifiers or waveguide lasers confirm the need of accurate modelling to achieve optimised designs for these devices. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The development of femtosecond laser waveguide writing has enabled the production guiding structures with novel characteristics, like 3D configurations, which are impossible to achieve with standard fabrication methods. This technique is based on the structural modifications caused by non-linear absorption in a transparent material when an infrared fs-laser beam is focused underneath its surface [1]. If upon laser exposure the material undergoes a positive refractive index change in the focal volume region, a waveguide can be readily written by translating the sample in a direction perpendicular to the incident beam axis. The production of active devices is straightforward if the material is doped with luminescent ions. Amongst these devices, integrated waveguide amplifiers and lasers stand out because of their strong potential in applications demanding compact, stable and energy efficient devices [2]. Due to their spectroscopic characteristics, erbium and ytterbium are among the most suitable dopants for the production of active devices. In what regards the host materials, phosphate glasses have attracted special interest because of their capability to incorporate large rare-earth doping levels that the short length of integrated devices imposes [3]. The desirable optimisation of the performance of active fs-written integrated devices requires not only the improvement of fabrication procedures (i.e. the use of an appropriate repetition rate for ⇑ Corresponding author. Tel.: +34 976 762444; fax: +34 976 761233. E-mail address: [email protected] (J.A. Vallés). 0925-3467/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2010.10.001
a given material or structure [4], the use of beam shaping techniques [5] or the control of aberration effects [6]) but also an important effort with regards to both characterization and modelling. On the one hand, the characterization of fs-laser written optical waveguides involves additional difficulties (they are not transversally accessible and depending on the processing conditions transmission loss which may not be describable by Rayleigh scattering model [7]) that have required the development of specific techniques [8]. On the other, once the material/waveguide characteristic parameters are determined, the influence of the working conditions on the performance of the active device (laser or amplifier) has to be analysed: pump scheme (uni- or bi-directional pump configuration), pump wavelength(s), pump power imbalance, signal power level, laser wavelength, laser ring transmission coefficient, etc. Similarly, an optimal waveguide length for each configuration has to be evaluated. In this paper we study the influence of the working conditions on the performance of bidirectionally pumped waveguide active devices in order to achieve optimised designs for amplifiers and lasers starting from the characteristic parameters of the material and the laser written waveguides. In order to improve the performance of the Yb/Er-codoped fs-laser written waveguide active devices in most experimental setups a dual-pumping configuration is usually preferred [9,10]. Using this pump scheme a higher pump level is globally achieved for the waveguide, whereas the depopulation of Er3+-ion first excited energy level due to the cooperative upconversion is attenuated. Nevertheless, to our knowledge no detailed analysis of the optimum configurations has ever been reported.
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2. The characteristic parameters of the Yb3+/Er3+ system We have used the model for an Yb/Er-codoped phosphate glass waveguide amplifier pumped in the 980 nm band described in detail in Ref. [11], using the available parameters of a commercial phosphate glass (QX (Kigre Inc.) doped with 4% wt. of Yb2O3 and 2% wt. of Er2O3) where several research groups have reported results on the production of waveguides by fs laser writing. The decay rates, absorption and emission cross sections and energy transfer rate constants that are required as input in the calculations are all based on measurements on Yb3+/Er3+-codoped phosphate glass. The fluorescence lifetime of the Yb3+ ion first excited energy level (2F5/2) is assumed to be 1.1 ms [13] and that of the Er3+-ion first excited energy level (4I13/2) is 7.9 ms, according to the material supplier. Finally, the predominantly non-radiative decay rate from Er3+-ion level 4I11/2 is 3.6 105 s1 [12]. For the energy-transfer mechanisms coefficients we assume average values in Yb3+/Er3+-codoped phosphate glass: the homogeneous upconversion coefficient is C = 1 1024 m3/s [13] and the Yb3+ Er3+ energy transfer coefficient is 1 1022 m3/s [14]. Both absorption and emission cross section distributions for the 1535-nm band were taken from Ref. [11]. In order to determine the Yb3+ ion absorption cross sections for the 980 nm band (2F7/2 2F5/2 transition) we have measured the absorption spectrum of a sample of the above indicated commercial glass, as shown in Fig. 1. The absorption peak was observed at 975.5 nm with a FWHM of 7.5 nm. We have subtracted from the absorption spectrum the smaller Er3+ ion contribution calculated using the absorption cross section distribution reported by Hwang et al. [15]. To calculate the emission cross sections we use Mc Cumber theory [16], which was demonstrated to be applicable to rare earth ions and to provide accurate enough cross section values [17]. The ratios between emission and absorption cross sections for 980-nm pump wavelength for the Yb3+ and Er3+ ions are assumed to be 1.3 [15] and 0.78 [18], respectively. The calculated absorption and emission cross sections for both ions for the more usual pump laser wavelengths (976 nm and 980 nm) are summarized in Table 1. Whereas the values of Er3+ ion absorption cross section are very similar for both pump wavelengths, that of Yb3+ ion absorption cross section at 976 nm is 2.5 times larger than that at 980 nm. In the light of this ratio, pumping near the peak wavelength will be more suitable for short-length materials with high dopant concentrations, whereas longer active materials with lower concentration are more effectively pumped at a detuned wavelength from the absorption peak.
Fig. 1. Absorption spectrum of an Yb/Er-codoped QX glass made by Kigre, Inc. in the 980-nm band (2F7/2 ) 2F5/2 transition).
Table 1 Absorption and emission cross sections for the Yb3+ and Er3+ ions and for the more usual pump laser wavelengths (976 nm and 980 nm). kp (nm) 976 976 980 980
Ion 3+
Yb Er3+ Yb3+ Er3+
Absorption (m2) 25
10.9 10 1.5 1025 4.3 1025 1.6 1025
Emission (m2) 11.6 1025 0.96 1025 5.6 1025 1.2 1025
3. Results 3.1. Waveguide amplifier In Fig. 2, the simulated amplifier set up is shown. We assume a bidirectional pump scheme using two pump laser diodes incoupled at each waveguide end. Two WDMs allow the incoupling of the pump and the signal powers and the outcoupling of the amplified signal and the co- and counterpropagating amplified spontaneous emission (ASE±). For the calculation of the propagation of the optical powers (pump, signal and ASE±) along the fs-written active waveguide as a function of its characteristic parameters, we have used the model and the numerical procedure thoroughly described in Ref. [11]. 3.1.1. Experimental/numerical check The applicability of the model and the numerical procedure to fs-laser written waveguides has been checked against the gain measurements by Osellame et al. [19] on a 22-mm long waveguide written in a commercial phosphate glass (QX, Kigre Inc.) doped with 4% wt. of Yb2O3 and 2% wt. of Er2O3. After the passive characterization of the waveguide they reported an excellent mode matching with standard telecom fibres and calculated a 0.1 dB/facet coupling loss and a 0.4 dB/cm propagation loss. In Fig. 3 we have plotted (a) the measured small signal internal gain as a function of wavelength (Fig. 10 in Ref. [19]) with a total power level of 490 mW in a bipropagating pumping scheme and (b) our numerical results. If we take into account that the measurement in Fig. 3a was reported to have an accuracy of 0.5 dB, the good agreement between experimental/numerical internal gain spectra verifies the reliability of both our model and the characteristic parameters. 3.1.2. Small signal gain and pump wavelength dependence In Fig. 4, we plot the dependence of the small signal gain on the waveguide length for a symmetrical bidirectional pump configuration (same input pump powers at both waveguide ends), using two 976 nm pump laser diodes. As in the rest of the following calculations on the amplifier performance the signal wavelength is 1534 nm, the mode intensity profile is that of a standard telecom fibre for this wavelength (see Fig. 7 in Ref. [19]) and the insertion losses (coupling losses + propagation losses) are those reported
Fig. 2. Scheme of the bidirectionally pumped Yb/Er-codoped phosphate waveguide amplifier.
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Fig. 5. Small signal gain vs. waveguide length for a 200 + 200 mW bidirectional pump configuration for different combinations of pump wavelengths.
pump wavelength combinations (Fig. 5), it is clear that the one with two 976 nm pump laser diodes offers the higher optimal gain (gain value for optimal waveguide length. Nevertheless, if the waveguide length longer than the optimal, the use of one or two 980 nm pump laser diodes may be a suitable option since the amplified signal is comparatively reabsorbed at a lower rate. The results for the 980 nm/976 nm combination which are not plotted in Fig. 5, in practice, coincide with those of the 976 nm/980 nm combination.
Fig. 3. Internal gain as a function of wavelength of a 22-mm long waveguide written in a commercial phosphate glass (QX, Kigre Inc.) doped with 4% wt. of Yb2O3 and 2% wt. of Er2O3 (a) measured (Fig. 10 in Ref. [19]) and (b) numerical.
3.1.3. Saturating signal So far we have considered only small signal gain regime. In Fig. 6 we compare the gain dependence on the waveguide length for 30 dBm, 0 dBm and 10 dBm signal powers. As it could be expected, since the Er3+-ion first excited level is strongly depopulated for large signals, the optimal waveguide length for large signal gets shorter when compared to the small signal regime and the corresponding optimal gain value gets lower. Additional effects can be observed if an imbalanced pump scheme is allowed. For rare-earth doped fibre amplifiers it has been observed that symmetrical bidirectional pump configuration is not always the optimum one and the suitable pump imbalance may depend on the fibre parameters and the amplifier working conditions [20]. In Fig. 7 gain is plotted vs. relative backward pump power (RBPP) for 30 dBm and
Fig. 4. Small signal gain vs. waveguide length for a symmetrical bidirectional pump configuration (same input pump powers at both waveguide ends), using two 976 nm pump laser diodes for 4 input pump powers.
by Osellame [19], that is, the coupling losses are 0.1 dB/facet and the propagation losses are 0.4 dB/cm The optimal length of the waveguide (length corresponding to the maximum gain) increases with the input pump power (Fig.4). When compared with other
Fig. 6. Gain vs. waveguide length for a 200 + 200 mW bidirectional pump configuration using two 976 nm pump laser diodes for 30 dBm, 0 dBm and 10 dBm signal powers.
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Fig. 7. Signal gain dependence on relative backward pump power (RBPP) for a bidirectional pump configuration using two 976 nm pump laser diodes with total pump power of 400 mW for 30 dBm and 10 dBm signal powers. The waveguide length for each signal power is the optimum one for a symmetric pump configuration (see Fig. 6).
Fig. 9. Laser power at the output of the waveguide as a function of the waveguide length for 4 values of the ring transmission coefficient. The input pump power is 200 mW at each waveguide end and the laser wavelength is 1534 nm.
10 dBm signal powers. As the total power is constant the gain maximum will show the pump power ratio that offers higher pump-tosignal power conversion efficiency. As it was reported in Ref. [20], whereas for 30 dBm the curve is totally symmetrical and 50/50 seems to be the best choice for the forward/backward pump power ratio, for 10 dBm instead the gain maximum is slightly shifted towards a relatively larger backward pump power ratio, 40/60.
3.2. Waveguide laser The simulated waveguide ring laser set up is shown in Fig. 8. Two 976-nm pump lasers are used and two 980/1550 WDM allow the incoupling of the pump. The ring configuration consists of the active medium, the Yb/Er-codoped phosphate glass waveguide, a tunable band pass filter that allows the selection of the laser wavelength, an optical isolator that causes that the only allowed laser emission will be copropagating referred to the propagation of the power emitted by pump laser diode 1 and finally to close the ring configuration a coupler to extract the laser output power. We will analyse the laser performance as a function of the ring transmission coefficient, T, which determines the amount of laser power propagating inside the waveguide. In Fig. 9 the laser power at the output of the waveguide (ASE+) as a function of the waveguide length is shown for 4 values of T.
Fig. 8. Scheme of the bidirectionally pumped Yb/Er-codoped phosphate waveguide laser.
Fig. 10. Laser power at the output of the waveguide as a function of the RBPP for a bidirectional pump configuration using two 976 nm pump laser diodes with total pump power of 400 mW for 4 values of the ring transmission coefficient. The laser wavelength is 1534 nm and the waveguide length is the optimal one for each value of T.
The input pump power is 200 mW at both waveguide ends and the laser wavelength is 1534 nm. Each ring transmission coefficient value limits a waveguide length range where gain inside the waveguide for a single trip is high enough to overcome ring losses and allow laser action. For instance, for T = 0.2, the waveguide length range where gain is higher than 6.99 dB (=10 log 0.2) spans approximately from 3 to 6 cm. In Fig. 9 it can be clearly noticed how, as the laser power inside the waveguide increases (increasing T values), the optimal length value decreases as it happened for the waveguide amplifier in large signal regime. In Fig. 10, we have plotted the laser power at the output of the waveguide as a function of the RBPP for a bidirectional pump configuration using two 976 nm pump laser diodes with total pump power of 400 mW for 4 values of the ring transmission coefficient. The laser wavelength is 1534 nm and the waveguide length is the optimal one for each value of T, according to the results shown in Fig. 9. The asymmetric behaviour as a function of the RBPP is more noticeable for the laser configuration than for the amplifier in large signal regime. This is due to the fact that a larger amount of laser power (compared to that of saturating signal) propagates inside the waveguide. Finally, to know the best performance in terms of
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the forward/backward pump ratio may increase pump-to-signal power conversion efficiency. Acknowledgements This work was partially supported by the University of Zaragoza under Project 223/88 and by the Spanish Ministry of Science and Innovation under TEC2008-01183 Project. A. Ruiz de la Cruz acknowledges his I3P-CSIC postdoctoral contract (co-funded by the European Social Fund) and A. Ferrer acknowledges his grant under Project TEC 2006-04538. References
Fig. 11. Relative outcoupled laser power and laser emitted power as a function of the ring transmission coefficient. The input pump power is 200 mW at each waveguide end, the laser wavelength is 1534 nm and the waveguide length is the optimal one for each value of T.
laser emitted power the ratio of laser power outcoupled of the ring can be related to T by assuming realistic values for the losses introduced by the other ring components: 1 dB for each WDM and 0.6 dB for the optical isolator and the tunable filter. In Fig. 11 this relation is plotted together with the laser emitted power vs. ring transmission coefficient. The optimum configuration is found for T = 0.3, in which 23% of the laser power inside the ring is outcoupled. 4. Conclusions Modelling is essential in order to achieve optimised designs for active devices based on fs-laser written waveguides. In particular, the optimal length of the device strongly depends not only on the material and waveguide characteristic parameters but also on the amplifier or laser working conditions. A symmetric pump configuration usually offers a good performance for waveguide active devices in small signal regime. However, for large-signal-regime waveguide amplifiers or for waveguide lasers a suitable choice of
[1] K.M. Davis, K. Miura, N. Sugimoto, K. Hirao, Opt. Lett. 21 (1996) 1729–1731. [2] S. Taccheo, G. della Valle, R. Osellame, G. Cerullo, N. Chiodo, P. Laporta, O. Svelto, A. Killi, U. Morgner, M. Lederer, D. Kopf, Opt. Lett. 29 (2004) 2626–2628. [3] D.L. Veasey, D.S. Funk, Ph.M. Peters, N.A. Sanford, G.E. Obarski, N. Fontaine, M. Young, A.P. Peskin, W.-C. Liu, S.N. Houde-Walter, J.S. Hayden, J. Non-Cryst. Solids 263–264 (2000) 369–381. [4] C.B. Schaffer, J.F. García, E. Mazur, Appl. Phys. A 76 (2003) 351–354. [5] M. Ams, G.D. Marshall, D.J. Spence, M.J. Withford, Opt. Express 13 (2005) 5676–5681. [6] C. Mauclair, G. Cheng, N. Huot, E. Audouard, A. Rosenfeld, I.V. Hertel, R. Stoian, Opt. Express 17 (2009) 3531–3542. [7] L. Tong, R.R. Gattass, I. Maxwell, J.B. Ashcom, E. Mazur, Opt. Commun. 259 (2006) 626–639. [8] J.A. Vallés, A. Ferrer, J.A. Sanchez-Martín, A. Ruiz de la Cruz, M.A. Rebolledo, J. Soils, IEEE J. Quantum Electron. 46 (2010) 996–1002. [9] G. Della Valle, R. Osellame, P. Laporta, J. Opt. A: Pure Appl. Opt. 11 (2009) 013001. [10] G.D. Marshall, P. Dekker, M. Ams, J.A. Piper, M.J. Withford, Opt. Lett. 33 (2008) 956–958. [11] J.A. Vallés, M.A. Rebolledo, J. Cortés, IEEE J. Quantum Electron. 42 (2006) 152– 159. [12] S. Honkanen, T. Ohtsuki, Sh. Jiang, S. Iraj Najafi, N. Peyghambarian, Proc. SPIE 2996 (1997) 32–40. [13] S. Taccheo, P. Laporta, S. Longhi, C. Svelto, Opt. Lett. 20 (1995) 889–891. [14] V.P. Gapontsev, S.M. Matitsin, A.A. Isineev, V.B. Kravchenko, Opt. Laser Technol. 14 (1982) 189–196. [15] B.-C. Hwang, S. Jiang, T. Luo, J. Watson, G. Sorbello, N. Peyghambarian, J. Opt. Soc. Am. B 17 (2000) 833–839. [16] D.E. McCumber, Phys. Rev. 134 (1964) A299–A306. [17] R.M. Martin, R.S. Quimby, J. Opt. Soc. Am. B 23 (2006) 1770–1775. [18] J.A. Lázaro, J.A. Vallés, M.A. Rebolledo, Pure App. Opt. 7 (1998) 1363–1371. [19] R. Osellame, N. Chiodo, G. della Valle, G. Cerullo, R. Ramponi, P. Laporta, A. Killi, U. Morgner, O. Svelto, IEEE J. Sel. Top. Quantum Electron. 12 (2006) 277–285. [20] J.A. Vallés, J.A. Lázaro, M. Hotoleanu, M. Karasek, E. Voiculescu, J. Mod. Opt. 45 (1998) 2551–2560.
Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Study of an optimised bidirectional pump scheme for fs-laser written Yb/Er-codoped integrated waveguides J.A. Vallés a,⇑, M.Á. Rebolledo a, V. Berdejo a, A. Ferrer b, A. Ruiz de la Cruz b, J. Solís b a b
Departamento de Física Aplicada – I3A, Facultad de Ciencias, Universidad de Zaragoza, C/Pedro Cerbuna 12, 50009 Zaragoza, Spain Laser Processing Group, Instituto de Óptica-CSIC, Serrano 121, 28006 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 27 May 2010 Received in revised form 28 August 2010 Accepted 1 October 2010 Available online 29 October 2010 Keywords: Yb3+/Er3+ doped glasses fs-Laser written waveguides Waveguide amplifiers Waveguide lasers
a b s t r a c t The influence of the working conditions on the performance of bidirectionally pumped fs-laser written Yb/Er-codoped waveguide active devices is numerically analysed. The large variations in the optimal length of the waveguide, the gain dependence on the pump wavelengths and the more efficient pumpto-signal power conversion that can be obtained by asymmetric pump configurations for largesignal-regime waveguide amplifiers or waveguide lasers confirm the need of accurate modelling to achieve optimised designs for these devices. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The development of femtosecond laser waveguide writing has enabled the production guiding structures with novel characteristics, like 3D configurations, which are impossible to achieve with standard fabrication methods. This technique is based on the structural modifications caused by non-linear absorption in a transparent material when an infrared fs-laser beam is focused underneath its surface [1]. If upon laser exposure the material undergoes a positive refractive index change in the focal volume region, a waveguide can be readily written by translating the sample in a direction perpendicular to the incident beam axis. The production of active devices is straightforward if the material is doped with luminescent ions. Amongst these devices, integrated waveguide amplifiers and lasers stand out because of their strong potential in applications demanding compact, stable and energy efficient devices [2]. Due to their spectroscopic characteristics, erbium and ytterbium are among the most suitable dopants for the production of active devices. In what regards the host materials, phosphate glasses have attracted special interest because of their capability to incorporate large rare-earth doping levels that the short length of integrated devices imposes [3]. The desirable optimisation of the performance of active fs-written integrated devices requires not only the improvement of fabrication procedures (i.e. the use of an appropriate repetition rate for ⇑ Corresponding author. Tel.: +34 976 762444; fax: +34 976 761233. E-mail address: [email protected] (J.A. Vallés). 0925-3467/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2010.10.001
a given material or structure [4], the use of beam shaping techniques [5] or the control of aberration effects [6]) but also an important effort with regards to both characterization and modelling. On the one hand, the characterization of fs-laser written optical waveguides involves additional difficulties (they are not transversally accessible and depending on the processing conditions transmission loss which may not be describable by Rayleigh scattering model [7]) that have required the development of specific techniques [8]. On the other, once the material/waveguide characteristic parameters are determined, the influence of the working conditions on the performance of the active device (laser or amplifier) has to be analysed: pump scheme (uni- or bi-directional pump configuration), pump wavelength(s), pump power imbalance, signal power level, laser wavelength, laser ring transmission coefficient, etc. Similarly, an optimal waveguide length for each configuration has to be evaluated. In this paper we study the influence of the working conditions on the performance of bidirectionally pumped waveguide active devices in order to achieve optimised designs for amplifiers and lasers starting from the characteristic parameters of the material and the laser written waveguides. In order to improve the performance of the Yb/Er-codoped fs-laser written waveguide active devices in most experimental setups a dual-pumping configuration is usually preferred [9,10]. Using this pump scheme a higher pump level is globally achieved for the waveguide, whereas the depopulation of Er3+-ion first excited energy level due to the cooperative upconversion is attenuated. Nevertheless, to our knowledge no detailed analysis of the optimum configurations has ever been reported.
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2. The characteristic parameters of the Yb3+/Er3+ system We have used the model for an Yb/Er-codoped phosphate glass waveguide amplifier pumped in the 980 nm band described in detail in Ref. [11], using the available parameters of a commercial phosphate glass (QX (Kigre Inc.) doped with 4% wt. of Yb2O3 and 2% wt. of Er2O3) where several research groups have reported results on the production of waveguides by fs laser writing. The decay rates, absorption and emission cross sections and energy transfer rate constants that are required as input in the calculations are all based on measurements on Yb3+/Er3+-codoped phosphate glass. The fluorescence lifetime of the Yb3+ ion first excited energy level (2F5/2) is assumed to be 1.1 ms [13] and that of the Er3+-ion first excited energy level (4I13/2) is 7.9 ms, according to the material supplier. Finally, the predominantly non-radiative decay rate from Er3+-ion level 4I11/2 is 3.6 105 s1 [12]. For the energy-transfer mechanisms coefficients we assume average values in Yb3+/Er3+-codoped phosphate glass: the homogeneous upconversion coefficient is C = 1 1024 m3/s [13] and the Yb3+ Er3+ energy transfer coefficient is 1 1022 m3/s [14]. Both absorption and emission cross section distributions for the 1535-nm band were taken from Ref. [11]. In order to determine the Yb3+ ion absorption cross sections for the 980 nm band (2F7/2 2F5/2 transition) we have measured the absorption spectrum of a sample of the above indicated commercial glass, as shown in Fig. 1. The absorption peak was observed at 975.5 nm with a FWHM of 7.5 nm. We have subtracted from the absorption spectrum the smaller Er3+ ion contribution calculated using the absorption cross section distribution reported by Hwang et al. [15]. To calculate the emission cross sections we use Mc Cumber theory [16], which was demonstrated to be applicable to rare earth ions and to provide accurate enough cross section values [17]. The ratios between emission and absorption cross sections for 980-nm pump wavelength for the Yb3+ and Er3+ ions are assumed to be 1.3 [15] and 0.78 [18], respectively. The calculated absorption and emission cross sections for both ions for the more usual pump laser wavelengths (976 nm and 980 nm) are summarized in Table 1. Whereas the values of Er3+ ion absorption cross section are very similar for both pump wavelengths, that of Yb3+ ion absorption cross section at 976 nm is 2.5 times larger than that at 980 nm. In the light of this ratio, pumping near the peak wavelength will be more suitable for short-length materials with high dopant concentrations, whereas longer active materials with lower concentration are more effectively pumped at a detuned wavelength from the absorption peak.
Fig. 1. Absorption spectrum of an Yb/Er-codoped QX glass made by Kigre, Inc. in the 980-nm band (2F7/2 ) 2F5/2 transition).
Table 1 Absorption and emission cross sections for the Yb3+ and Er3+ ions and for the more usual pump laser wavelengths (976 nm and 980 nm). kp (nm) 976 976 980 980
Ion 3+
Yb Er3+ Yb3+ Er3+
Absorption (m2) 25
10.9 10 1.5 1025 4.3 1025 1.6 1025
Emission (m2) 11.6 1025 0.96 1025 5.6 1025 1.2 1025
3. Results 3.1. Waveguide amplifier In Fig. 2, the simulated amplifier set up is shown. We assume a bidirectional pump scheme using two pump laser diodes incoupled at each waveguide end. Two WDMs allow the incoupling of the pump and the signal powers and the outcoupling of the amplified signal and the co- and counterpropagating amplified spontaneous emission (ASE±). For the calculation of the propagation of the optical powers (pump, signal and ASE±) along the fs-written active waveguide as a function of its characteristic parameters, we have used the model and the numerical procedure thoroughly described in Ref. [11]. 3.1.1. Experimental/numerical check The applicability of the model and the numerical procedure to fs-laser written waveguides has been checked against the gain measurements by Osellame et al. [19] on a 22-mm long waveguide written in a commercial phosphate glass (QX, Kigre Inc.) doped with 4% wt. of Yb2O3 and 2% wt. of Er2O3. After the passive characterization of the waveguide they reported an excellent mode matching with standard telecom fibres and calculated a 0.1 dB/facet coupling loss and a 0.4 dB/cm propagation loss. In Fig. 3 we have plotted (a) the measured small signal internal gain as a function of wavelength (Fig. 10 in Ref. [19]) with a total power level of 490 mW in a bipropagating pumping scheme and (b) our numerical results. If we take into account that the measurement in Fig. 3a was reported to have an accuracy of 0.5 dB, the good agreement between experimental/numerical internal gain spectra verifies the reliability of both our model and the characteristic parameters. 3.1.2. Small signal gain and pump wavelength dependence In Fig. 4, we plot the dependence of the small signal gain on the waveguide length for a symmetrical bidirectional pump configuration (same input pump powers at both waveguide ends), using two 976 nm pump laser diodes. As in the rest of the following calculations on the amplifier performance the signal wavelength is 1534 nm, the mode intensity profile is that of a standard telecom fibre for this wavelength (see Fig. 7 in Ref. [19]) and the insertion losses (coupling losses + propagation losses) are those reported
Fig. 2. Scheme of the bidirectionally pumped Yb/Er-codoped phosphate waveguide amplifier.
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233
Fig. 5. Small signal gain vs. waveguide length for a 200 + 200 mW bidirectional pump configuration for different combinations of pump wavelengths.
pump wavelength combinations (Fig. 5), it is clear that the one with two 976 nm pump laser diodes offers the higher optimal gain (gain value for optimal waveguide length. Nevertheless, if the waveguide length longer than the optimal, the use of one or two 980 nm pump laser diodes may be a suitable option since the amplified signal is comparatively reabsorbed at a lower rate. The results for the 980 nm/976 nm combination which are not plotted in Fig. 5, in practice, coincide with those of the 976 nm/980 nm combination.
Fig. 3. Internal gain as a function of wavelength of a 22-mm long waveguide written in a commercial phosphate glass (QX, Kigre Inc.) doped with 4% wt. of Yb2O3 and 2% wt. of Er2O3 (a) measured (Fig. 10 in Ref. [19]) and (b) numerical.
3.1.3. Saturating signal So far we have considered only small signal gain regime. In Fig. 6 we compare the gain dependence on the waveguide length for 30 dBm, 0 dBm and 10 dBm signal powers. As it could be expected, since the Er3+-ion first excited level is strongly depopulated for large signals, the optimal waveguide length for large signal gets shorter when compared to the small signal regime and the corresponding optimal gain value gets lower. Additional effects can be observed if an imbalanced pump scheme is allowed. For rare-earth doped fibre amplifiers it has been observed that symmetrical bidirectional pump configuration is not always the optimum one and the suitable pump imbalance may depend on the fibre parameters and the amplifier working conditions [20]. In Fig. 7 gain is plotted vs. relative backward pump power (RBPP) for 30 dBm and
Fig. 4. Small signal gain vs. waveguide length for a symmetrical bidirectional pump configuration (same input pump powers at both waveguide ends), using two 976 nm pump laser diodes for 4 input pump powers.
by Osellame [19], that is, the coupling losses are 0.1 dB/facet and the propagation losses are 0.4 dB/cm The optimal length of the waveguide (length corresponding to the maximum gain) increases with the input pump power (Fig.4). When compared with other
Fig. 6. Gain vs. waveguide length for a 200 + 200 mW bidirectional pump configuration using two 976 nm pump laser diodes for 30 dBm, 0 dBm and 10 dBm signal powers.
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Fig. 7. Signal gain dependence on relative backward pump power (RBPP) for a bidirectional pump configuration using two 976 nm pump laser diodes with total pump power of 400 mW for 30 dBm and 10 dBm signal powers. The waveguide length for each signal power is the optimum one for a symmetric pump configuration (see Fig. 6).
Fig. 9. Laser power at the output of the waveguide as a function of the waveguide length for 4 values of the ring transmission coefficient. The input pump power is 200 mW at each waveguide end and the laser wavelength is 1534 nm.
10 dBm signal powers. As the total power is constant the gain maximum will show the pump power ratio that offers higher pump-tosignal power conversion efficiency. As it was reported in Ref. [20], whereas for 30 dBm the curve is totally symmetrical and 50/50 seems to be the best choice for the forward/backward pump power ratio, for 10 dBm instead the gain maximum is slightly shifted towards a relatively larger backward pump power ratio, 40/60.
3.2. Waveguide laser The simulated waveguide ring laser set up is shown in Fig. 8. Two 976-nm pump lasers are used and two 980/1550 WDM allow the incoupling of the pump. The ring configuration consists of the active medium, the Yb/Er-codoped phosphate glass waveguide, a tunable band pass filter that allows the selection of the laser wavelength, an optical isolator that causes that the only allowed laser emission will be copropagating referred to the propagation of the power emitted by pump laser diode 1 and finally to close the ring configuration a coupler to extract the laser output power. We will analyse the laser performance as a function of the ring transmission coefficient, T, which determines the amount of laser power propagating inside the waveguide. In Fig. 9 the laser power at the output of the waveguide (ASE+) as a function of the waveguide length is shown for 4 values of T.
Fig. 8. Scheme of the bidirectionally pumped Yb/Er-codoped phosphate waveguide laser.
Fig. 10. Laser power at the output of the waveguide as a function of the RBPP for a bidirectional pump configuration using two 976 nm pump laser diodes with total pump power of 400 mW for 4 values of the ring transmission coefficient. The laser wavelength is 1534 nm and the waveguide length is the optimal one for each value of T.
The input pump power is 200 mW at both waveguide ends and the laser wavelength is 1534 nm. Each ring transmission coefficient value limits a waveguide length range where gain inside the waveguide for a single trip is high enough to overcome ring losses and allow laser action. For instance, for T = 0.2, the waveguide length range where gain is higher than 6.99 dB (=10 log 0.2) spans approximately from 3 to 6 cm. In Fig. 9 it can be clearly noticed how, as the laser power inside the waveguide increases (increasing T values), the optimal length value decreases as it happened for the waveguide amplifier in large signal regime. In Fig. 10, we have plotted the laser power at the output of the waveguide as a function of the RBPP for a bidirectional pump configuration using two 976 nm pump laser diodes with total pump power of 400 mW for 4 values of the ring transmission coefficient. The laser wavelength is 1534 nm and the waveguide length is the optimal one for each value of T, according to the results shown in Fig. 9. The asymmetric behaviour as a function of the RBPP is more noticeable for the laser configuration than for the amplifier in large signal regime. This is due to the fact that a larger amount of laser power (compared to that of saturating signal) propagates inside the waveguide. Finally, to know the best performance in terms of
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the forward/backward pump ratio may increase pump-to-signal power conversion efficiency. Acknowledgements This work was partially supported by the University of Zaragoza under Project 223/88 and by the Spanish Ministry of Science and Innovation under TEC2008-01183 Project. A. Ruiz de la Cruz acknowledges his I3P-CSIC postdoctoral contract (co-funded by the European Social Fund) and A. Ferrer acknowledges his grant under Project TEC 2006-04538. References
Fig. 11. Relative outcoupled laser power and laser emitted power as a function of the ring transmission coefficient. The input pump power is 200 mW at each waveguide end, the laser wavelength is 1534 nm and the waveguide length is the optimal one for each value of T.
laser emitted power the ratio of laser power outcoupled of the ring can be related to T by assuming realistic values for the losses introduced by the other ring components: 1 dB for each WDM and 0.6 dB for the optical isolator and the tunable filter. In Fig. 11 this relation is plotted together with the laser emitted power vs. ring transmission coefficient. The optimum configuration is found for T = 0.3, in which 23% of the laser power inside the ring is outcoupled. 4. Conclusions Modelling is essential in order to achieve optimised designs for active devices based on fs-laser written waveguides. In particular, the optimal length of the device strongly depends not only on the material and waveguide characteristic parameters but also on the amplifier or laser working conditions. A symmetric pump configuration usually offers a good performance for waveguide active devices in small signal regime. However, for large-signal-regime waveguide amplifiers or for waveguide lasers a suitable choice of
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