An Er:Yb co-doped P2O5-La2O5 based glass has been synthesized and used for producing 1.6 cm-long active optical waveguides using a low repetition (1 kHz) rate Ti:Al2O3 fs-laser amplifier. Before processing, the laser energy deposition profile for an elliptically shaped beam was simulated, and the best processing conditions for optimizing the focal volume shape, minimizing non-linear propagation effects, were determined. Under these conditions, a multi-scan writing approach was used to maximize the refractive index change induced and to minimize the transmission losses. After processing, the optical powers propagating inside the waveguide (pump absorption, co- and counter-propagating ASE, low signal gain, …) were measured for uni- and bi-directional pumping schemes, and the measurements were simulated and fitted using an ad hoc developed model to describe the behavior of laser written waveguides. The measurements provide internal gain figures comparable to the best ones reported in phosphate glasses for low repetition rate writing even with larger insertion losses. The simulations provide access to key parameters of the waveguide characteristics (coupling losses and propagation losses, Yb3+ ⇔ Er3+ energy transfer rates, Er3+ upconversion coefficient), which have been used to model the expected performance of these structures in terms of length and doping level. A moderate increase of the Er3+ and Yb3+ doping level would potentially lead to net gain values up to 9.4 dB for a waveguide length of 25 mm.
©2011 Optical Society of America
Femtosecond laser writing of waveguides is a technique based on the refractive index modification induced inside a transparent material when a femtosecond pulsed-laser is tightly focused underneath its surface. A certain amount of laser energy is deposited in the focal volume and its nearby region through multi-photon and avalanche ionization, eventually leading to an increase of the local refractive index of the material. A waveguide can be then written by translating the sample along a given scanning direction, i.e., perpendicularly to the irradiation beam axis. Since femtosecond waveguide writing in a silicate glass was first reported by Davis et. al. , several passive (directional couplers , 2D and 3D splitters , etc.) and active devices (waveguide amplifiers and lasers ) have been demonstrated in a variety of transparent materials processed either in the low (LRR) or in the high repetition (HRR) rate regimes. In the LRR, the time separation between pulses is long enough so that the material temperature can recover its initial value before the arrival of the next irradiation pulse, while in HRR the laser pulses are temporally close so as to induce cumulative thermal effects .
Active devices oriented towards the third window of optical communications (C-band) are of particular interest. They typically make use of rare earth (RE) Erbium ions to amplify the signal, and most of the times also of Ytterbium as pump acceptor. The goodness of such devices is determined on the one hand by the spectroscopic properties of the ions embedded in the glass matrix (such as the mean decay lifetime of the levels involved and the non radiative energy transfer rates) and, on the other hand, by the passive characteristics of the written waveguide (such as the total insertion losses (IL), propagation losses (PL) and coupling losses (CL)). When considering their performance and optimization, it must be though considered that ultrafast laser written waveguides show several distinct features which make necessary the use of specific modeling/characterization techniques .
In this work we have prepared an Er:Yb co-doped lanthanum phosphate glass and used it for producing active optical waveguides using a low repetition (1 kHz) rate Ti:Al2O3 fs-laser amplifier. Our aim is to show that a rigorous modeling of the performance of the produced waveguides enables a reliable predictive optimization of the waveguide and material parameters, leading to strongly improved results. The manuscript is structured as follows: Section 2 is devoted to the experimental details, including the glass fabrication, waveguide writing procedure, and its passive and active characterization. In Section 3.A, the numerical model is used to fit to the experimental data. The best-fit parameters thus obtained are then used in section 3.A and the following sections (3.B and 3.C) to predict the behavior of waveguides with different operational (i.e. single or bi-directional pumping), processing (i.e. length) or material parameters (i.e. RE doping levels).
2. Experimental Details
2.A Preparation of the Glass, and Structural / Optical Characterization
The host material for the laser written waveguides is an Er:Yb co-doped lanthanum phosphate glass produced by melting and annealing procedure at the LPG facilities. We chose a P2O5-La2O3-Al2O3 based composition with large phosphate content given the excellent properties of RE-doped phosphate glasses as host laser media , related to the large RE solubility in the phosphate matrix, and their broad absorption/emission bands and long fluorescence lifetimes. Pure P2O5 has a low melting point and high thermal expansion coefficient. The incorporation of La2O3 and Al2O3 results in glasses with far superior mechanical properties, higher glass transition temperature (Tg) and smaller expansion coefficient [8,9] that can be doped with very large amounts of RE ions, i.e. Er or Yb, for fiber amplifiers/lasers [10,11].
The glass was ad hoc prepared from a mixture of Al(PO3)3, H3PO4, La2O3, with small amounts of SiO2, K2CO3 and CeO2, as well as Er2O3 and Yb2O3. The reagents were mixed and melted at 1400 °C for one hour in a Pt crucible. The melt was then poured in a preheated brass mould and cooled down to room temperature. The produced glass piece was then milled, melted and poured again two more times in order to obtain a transparent and homogenous glass, which was annealed for 15 minutes at a temperature close to Tg (≈600°C) and further cooled at 3 °C/min down to room temperature to eliminate any residual stress. The sample with approximate dimensions of 1.0 x 0.4 x 1.6 cm3 was finally grinded and polished to optical quality. The density of the glass sample was determined by the Archimedes method to be 3.013 g/cm3.
The highly hygroscopic nature of the phosphorous containing reagents, along with the vaporization of P2O5 that occurs during the melting process, lead to a final glass composition different than the one corresponding to the initial reagents proportion. For such a reason, the final molar composition of the glass had to be determined by PIXE (Particle Induced X-Ray Emission) measurements: 7Al2O3-70P2O5-12La2O3 plus certain minority amounts of SiO2, K2O and CeO2. The final doping concentrations were measured to be 1.8 and 3.2 wt. % of Er2O3 and Yb2O3 respectively. In order to improve the quantification of these doping components, protons of 5.5 MeV energy and a LEGe X-ray detector were used. With this set-up the K emission lines of La, Ce, Er and Yb were excited, detected and used for quantification. Lower energy elements (Al, P, Si and K) were also detected simultaneously using a Mylar funny filter of 1mm with a hole of 1mm of diameter. An electron gun was used to avoid bremsstrahlung radiation due to the isolation character of the samples.
The refractive index (n) of the glass was determined by spectroscopic ellipsometry measurements, yielding n(800 nm) = 1.556. The spectral absorption of the glass, α(λ) (Fig. 1 ), was obtained from spectral transmittance measurements performed with a spectrophotometer, and shows the characteristic Yb3+ and Er3+ absorption bands around 980 and 1530 nm respectively. The spectra shown in Fig. 1 have been corrected to consider the Fresnel losses and show thus a baseline close to zero. The lifetime of the Er3+-ion first excited energy level, 4I13/2, was measured by photoluminescence measurements and set to be of 6.32 ms.
2.B Waveguide Writing Procedure
The waveguide writing setup is based on a commercial femtosecond laser amplifier operating at 800 nm, delivering 120 fs pulses at a repetition rate of 1 kHz (LRR) and maximum pulse energy of 1 mJ. The writing beam is shaped with a 450 μm width slit in order to produce a quasi-elliptical beam, and thus a disk-like shaped focal volume . The polarization of the beam was modified with a quarter wave plate from linear to circular, in order to reduce the propagation losses of the final structure , as well as to reduce the non linear refractive index experienced by the writing beam as explained in references [14,15]. Additionally, to further reduce the nonlinear propagation during the writing process, the pulse duration was stretched to 450 fs by detuning the optimal grating-mirror distance of the compressor stage of the fs laser amplifier. Under such conditions, the beam was attenuated down to 0.75 μJ/pulse and focused 100 μm below the surface of the sample with an aspherical lens (numerical aperture, NA = 0.4). The sample was then translated at a constant velocity of 20 μm/s along an axis perpendicular to the beam and parallel to the slit’s long axis. Since a single scan exposure does not generate a refractive index contrast high enough for supporting a guided mode, the 1.6 cm-long structure so-generated was re-scanned 80 times over exactly the same region in order to improve the refractive index contrast and reduce the propagation losses as shown in . The cross section of the final waveguide presents a nearly circular shape with an approximate diameter of 10.5 µm, as measured with an optical microscope.
2.C Characterization of the Waveguide
2.C.1 Passive Characterization
Near field images of the propagated modes at 1550 nm and 980 nm in the written waveguide are shown in Figs. 2a and 2b respectively. The images have been obtained with a 50X near infrared microscope objective corrected for chromatic aberration. Both images were taken in the same spatial conditions, in such a way that they correspond exactly to the same spatial region of the output face of the waveguide. From the overlap integral of both modes, a power transfer factor K = 0.7285 as defined in reference , has been obtained. From the intensity profiles over the maximum intensity pixels, an estimation of the mode field diameters has been done, leading to values of 7.3 µm and 5.1 µm (at full width half maximum) for the 1550 nm and 980 nm guided modes, respectively.
The insertion losses were determined at 1620 nm in order to avoid absorption from the Erbium ions. The estimation was performed by measuring the output power of the waveguide when coupled to a Corning® HI 1060 fiber and comparing the obtained value with the output power of the fiber itself. The CL were estimated from the overlap integrals of the guided modes of both the waveguide and the fiber, according to reference . The PL were estimated by subtracting the CL from the IL, once computed the Fresnel losses at both facets. By assuming a λ−4 Rayleigh scattering law, the PL value obtained at 1620 nm can be extrapolated to 1535 nm, which is the wavelength of the Erbium ions peak emission (see Fig. 1). According to these measurements, the waveguide presents IL≈2.8 dB, with PL≈0.5 dB/cm and CL≈0.8 dB/facet, plus 0.2 dB/facet of Fresnel losses. In these estimations, due to the use of fiber and sample position stages lying in the horizontal plane (ϕ = 0°) with azimuth control (variable θ), we have neglected any possible losses caused by angular mismatch between the waveguides and the fiber. Even if present, angular mismatch losses should show a smooth cos(θ) dependence, which would make them nearly undistinguishable from true mode mismatch losses (θ = 0). Similarly, as an initial step of the measurements, the signal output was optimized as a function of the distance between the fibers and the waveguide in an iterative procedure. Therefore possible losses associated to fiber-waveguide distance mismatch are considered as negligible.
2.C.2 Active Characterization
For the active characterization experiments, an optical amplifier was built using the fs-laser written waveguide as the active medium. In Fig. 3 the amplifier setup is shown.
The bidirectional pump scheme allows the use of two 976-nm pump laser diodes (PL1 and PL2) incoupled at each waveguide end, providing 374.5 mW and 355.2 mW respectively. Two wavelength-division multiplexers (WDMs) allow the in-coupling of the pump and the signal powers, as well as the outcoupling of the amplified signal and the co- and counterpropagating amplified spontaneous emission (ASE ± ). The input and output single mode fibers (SMFs, Corning® HI 1060) were butt coupled to the waveguide using an index-matching fluid. Although a lower gain performance is obtained, unidirectional pump measurements were also carried out, since for unidirectional pump measurements, PL2 can be replaced by a power meter, enabling the simultaneous registration of both, the pump and signal powers outcoupled of the waveguide.
Unidirectional pump measurements. We first measured the output pump power and co- and counter propagating (ASE ± ) spectra as a function of the input pump power from PL1. Then, signal power from a tunable laser was coupled into the waveguide at the ASE ± peak wavelength, 1535 nm, and the output signal power was measured also as a function of the input pump power. The input signal power was kept constant at −35 dBm approximately to ensure a small signal regime. We also measured the signal attenuation (−11.7 dB, for zero pump power) in order to determine relative gain for unidirectional pumping as shown in Fig. 4a . From the phosphate glass absorption spectrum, the total intrinsic absorption at the signal wavelength is calculated to be −7.4 dB and, therefore, the value for insertion losses can be estimated as 4.3 dB, which is consistent with the one obtained from the passive measurements (Section 2.C.1)
Bidirectional pump measurements. Using the bidirectional pump scheme in Fig. 3, we kept the maximum available input pump power from PL1, 374.5 mW, and measured the small signal gain as a function of the input pump power from PL2.
Figure 4(a) shows the measured relative gain (also known as signal enhancement) at the peak of the ASE+ spectrum (1535 nm) as a function of the input power from PL1. The measured intrinsic absorption at this wavelength is also represented. For input pump powers over 230 mW approximately, the relative gain compensates the 7.4 dB absorption resulting in a positive internal gain. In Fig. 4(b) the measured relative gain is plotted as a function of the input pump power from PL2 when PL1 is kept at its maximum output power. Note that the last point of 4(a) is the same as the first one in 4(b). The maximum relative gain is 10.9 dB (internal gain is 3.5 dB) for total input pump power 374 mW + 355 mW. The insertion losses, 4.3 dB, prevent from achieving net gain and global amplification.
This maximum relative gain value in Fig. 4(b) (~7 dB/cm) compares well with the largest previously reported ones in the literature for low repetition rate fs-laser waveguide writing in Yb/Er-codoped phosphate glass. In Ref. 17, Ams et al. reported a peak relative gain per unit length of 7.3 dB/cm for 710 mW total pump power, what gives a relative gain of 10.95 dB for a 1.5 cm long waveguide written in a custom Er/Yb-codoped phosphate glass from Kigre Inc. (QX 2% wt Er, 4% wt Yb). Although the relative gain values nearly coincide, the relative gain value in Ref. 17 benefited from the low IL~1.4 dB (CL are 0.4 dB/facet  and PL lower than 0.4 dB/cm) which favors a higher pump-to-signal conversion efficiency. This fact evidences the good performance of our phosphate glass even more considering that our doping levels are smaller (1.8 wt. % Er2O3, 3.2 wt.% Yb2O3). Even lower IL (CL are 0.1 dB/facet and PL lower than 0.4 dB/cm) have been obtained by using high repetition rate fs-laser waveguide writing systems . With these IL figures, waveguides written in a commercial glass (QX, Kigre Inc.) doped with 2% wt of Er2O3 and 4% of Yb2O3 providing net gain (peak value of 6 dB) and laser action in the whole telecommunications C-band have been demonstrated.
Considering these performance figures, in order to increase the internal gain of our waveguides and to achieve net gain a twofold improvement can be devised. On the one hand, the active performance can be improved by finding optimal rare earth ion doping concentrations and waveguide lengths. On the other, a reduction of IL by optimizing the writing process to obtain more uniform waveguides and better mode profiles would render additional benefits. In order to evaluate the potential improvement associated to these strategies, we numerically fitted the experimental results above shown and then simulated the expected waveguide amplifier performance with modified material/waveguide parameters using the best-fit parameters thus obtained.
3. Numerical Fit and Simulation
For the calculation of the propagation of the optical powers (pump, signal and ASE ± ) in 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. 19. They have already been successfully tested on fs-laser written waveguides in Yb/Er-codoped phosphate glass in Ref. 20.
3.A Fitting Method and Best-fit Parameters
As above indicated, a unidirectional pump scheme allows the simultaneous measurement of signal and pump outcoupled powers. In order to use the fitting procedure described in Ref. 19, we used the measurements of the net gain and the pump power attenuation as a function of the input pump power from PL1. The procedure is based on the fact that some of the parameters to be determined have a higher influence on pump power attenuation and some others on the net gain. This allows an iterative fitting procedure to be performed until the desired global convergence is reached.
The measured rare earth ion doping concentrations, some waveguide’s modes parameters (mode profiles both for pump and signal wavelengths, and the mismatch between their mode centers), as well as Er3+ spectroscopic parameters (lifetime of the Er3+-ion first excited energy level, 4I13/2) are kept fixed during the fitting process. Similarly, some values taken from the literature for other spectroscopic parameters are assumed as constants. In particular, the fluorescence lifetime of the Yb3+ ion first excited energy level (2F5/2) is taken to be 1 ms , and the predominantly non-radiative decay rate from Er3+-ion level 4I11/2 is set to 3.6 x 105 s−1 . Finally, initial values for the Er3+ ion absorption cross section distribution for the 1535-nm band and for the Yb3+ ion absorption cross section for 976 nm (2F7/2 ⇒ 2F5/2 transition) were calculated from the measured absorption spectrum and dopant concentrations. Moreover, the emission cross section distribution for the 1535-nm band was calculated from the absorption distribution using Mc Cumber theory , which was demonstrated to be applicable to rare earth ions and to provide accurate enough cross section values . Therefore, the parameters whose values are determined during the fitting process are the coupling and propagation losses and the coefficients of the non-radiative energy-transfer mechanisms.
In Figs. 5(a) and 5(b) the experimental values of pump power attenuation and net gain are plotted as a function of the input pump power from PL1, together with the numerical fits for these dependences. Except for net gain values in the low pump power regime a good agreement is achieved for both dependences. In Fig. 5(b) two distinct pump regimes can be appreciated (below and above approximately 150 mW). At low pump the Er3+ ion population is not inverted and most of the signal is absorbed whereas at high pump powers gain saturation is caused by both Er3+-ion upconversion and the limited efficiency of the energy transfer mechanism from Yb3+ to Er3+.
In Table 1 the best-fit parameters obtained are summarized. The values for the Yb3+ ⇒ Er3+ energy-transfer (CET = 1.2 x 10−23 m3/s) and back transfer coefficients (CBT = 1.0 x 10−22), are in good agreement with other values of energy-transfer coefficients reported in Yb3+/Er3+-codoped phosphate glasses [19,25]. The Er3+-ion upconversion coefficient, CUP = 4.8 x 10−24 m3/s, is similar to the values reported in Ref. 26. Both values for CL, 1.8 dB/facet at 976 nm and 0.9 dB/facet at 1535 nm, agree well with the ones that can be calculated from the overlapping integral of the waveguide and coupling fiber mode profiles if the excitation fiber is assumed to be aligned with the signal mode center, 1.4 dB/facet and 0.8 dB/facet, respectively. The value of PL at 976 nm is given by Rayleigh scattering λ−4 law which is assumed for these losses. If the best-fit values for CL and PL are considered, the best-fit value for IL at 1535 nm is 3.4 dB, which differs 0.6 dB from the IL experimental value in section 2.C.1 and only 0.3 dB from the IL experimental value from signal attenuation measurements in section 2.C.2. Finally, in order to achieve the fits shown in Figs. 5(a) and (b), the initial value for the Yb3+ ion absorption cross section at 976 nm was increased up to 16.8 x 10−25 m2 (23%), a value similar to that reported for QX glass by Kigre Inc . whereas the Er3+ ion absorption cross section distribution for the 1535-nm band was scaled by a factor 1.17. The difference in the absorption cross section values from those obtained from bulk material absorption measurements to those obtained from fits of the active waveguide performance can be attributed to the effective character of the last ones due to the approximations that the propagation of the optical powers along the waveguide involves
To verify the reliability of the results derived from the fitting process to predict the amplifier performance, we have used the best-fit parameters (summarized in Table 1) to calculate the net gain in a dual-pump scheme as a function of the input pump power from PL2 (keeping PL1 at its maximum available power: 374.5 mW). This dependence is plotted in Fig. 6 together with the experimental results. A quite good agreement between measured and calculated results can be appreciated.
3.B Optimal Length
By using the above determined parameters, it is now possible to simulate the performance of the amplifier and to evaluate its potential improvement in terms of the waveguide (length, IL) or material (doping level) parameters. In order to estimate the relative influence of coupling and propagation losses, we separately analyze the effect on the amplifier gain of realistic reductions in the CL or the PL. The values (CL 0 = 0.1 dB/facet, PL 0 = 0.4 dB/cm) reported in Ref. 4 are taken as a reference. It must be noted that in our waveguide, as it was commented already in section 3.A, the spatial mismatch between signal and pump guided modes can be understood as an indirect source of losses. Therefore, in order to effectively reduce the CL to the reference value in our simulation, the relative shift between pump and signal waveguide modes is cancelled. In Fig. 7 , the net gain of a bidirectionally pumped amplifier (374.5 mW + 355.2 mW) is plotted against waveguide length for 4 different simulated waveguides: BF (Best-fit) - using the best-fit parameters obtained in Section 3.A; RCL (Reduced coupling losses) - same parameters as in BF, but CL are reduced to CL 0; RPL (Reduced propagation losses) – same parameters as in BF, but PL are reduced to PL 0; RCL & RPL (Reduced coupling & propagation losses) – same parameters as in BF, but both CL and PL are reduced to CL 0 and PL 0 respectively.
The optimal length for BF is 1.37 cm and the maximum net gain is only 0.03 dB higher than for L = 1.6 cm. Therefore, in practice, no significant gain increase has to be expected by just changing the length of the waveguide. When the dependences of RCL and RPL are compared it can be noticed how for RCL a higher net gain peak is reached (2.70 dB vs. 2.02 dB) for a shorter optimal length (2.35 cm vs. 3.25 cm). Finally, a large net gain (8.05 dB for a 4.85 cm waveguide length) could be obtained if the losses were reduced to CL 0 and PL 0.
3.C Rare-earth Doping Dependence
We have also analyzed how the substrate rare-earth doping level influences the amplifier net gain. For simplicity, we do not study any Yb3+/Er3+ concentrations combination and reduce our analysis to waveguides in which the Yb2O3 concentration in the glass composition doubles that of the Er2O3, as it is the case in most of the reported efficient devices based on fs-laser written Yb/Er-codoped waveguides. For the glass density indicated in Section 2.A, a 1% wt. of Er2O3 corresponds to an Er3+ ion density of 9.5 x 1025 m−3. In Fig. 8 the net gain of a bidirectionally pumped amplifier (374.5 mW + 355.2 mW) is plotted against the erbium concentration for a 25 mm long waveguide for the same 4 simulated waveguides as in Fig. 7. It can be seen that the BF waveguide is close also to the optimum Er3+ ion concentration, but as the net gain values increase (due to the losses reduction), the optimum Er3+ ion concentration shifts towards higher values: 2.7% wt for the RPL waveguide, 3.0% wt for the RCL one and 3.9% wt for the RPL & RPC waveguide. For the RPL & RPC waveguide a 9.4 dB maximum net gain is obtained. This remarkable figure indicates that the Yb3+/Er3+-codoped P2O5-La2O5 based glass is potentially an excellent host for integrated waveguide active devices.
An Er:Yb codoped P2O5-La2O5 based glass has been synthesized and used for producing 1.6 cm-long active optical waveguides using a low repetition (1 kHz) rate Ti:Al2O3 fs-laser amplifier. After processing, the performance parameters of the produced active waveguides and the measurements simulated using a model ad hoc developed for the describing the behavior of laser written waveguides. The simulations provide access to key parameters of the waveguide performance that have been used to model the expected performance of structures optimized in terms of length, doping level and losses. A moderate increase of the Er, Yb doping level would potentially lead to net gain values up 9.4 dB for a waveguide length of 25 mm.
This work was partially supported by the Spanish Ministry of Science and Innovation under TEC2008-01183, MAT2009-14282-C02-01 and FIS2010-20821 projects, and by the Diputación General de Aragón. A. Ruiz de la Cruz acknowledges an I3P-CSIC postdoctoral contract (co-funded by the European Social Fund). A. Ferrer acknowledges a grant under Project TEC 2006-04538.
References and links
2. K. Minoshima, A. M. Kowalevicz, I. Hartl, E. P. Ippen, and J. G. Fujimoto, “Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator,” Opt. Lett. 26(19), 1516–1518 (2001). [CrossRef] [PubMed]
4. R. Osellame, N. Chiodo, G. Della Valle, G. Cerullo, R. Ramponi, P. Laporta, A. Killi, U. Morgner, and O. Svelto, “Waveguide lasers in the C-band fabricated by laser inscription with a compact femtosecond oscillator,” IEEE J. Sel. Top. Quantum Electron. 12(2), 277–285 (2006). [CrossRef]
5. S. M. Eaton, H. Zhang, M. L. Ng, J. Li, W. J. Chen, S. Ho, and P. R. Herman, “Transition from thermal diffusion to heat accumulation in high repetition rate femtosecond laser writing of buried optical waveguides,” Opt. Express 16(13), 9443–9458 (2008). [CrossRef] [PubMed]
6. J. A. Vallés, A. Ferrer, J. A. Sánchez-Martin, A. R. de la Cruz, M. A. Rebolledo, and J. Solis, “New Characterization Technique for Femtosecond Laser Written Waveguides in Yb/Er-Codoped Glass,” IEEE J. Quantum Electron. 46(6), 996–1002 (2010). [CrossRef]
7. J. H. Campbell and T. I. Suratwala, “Nd-doped phosphate glasses for high-energy/high-peak-power lasers,” J. Non-Cryst. Solids 263–264(1-2), 318–341 (2000). [CrossRef]
8. R. K. Brow, E. Metwalli, and D. L. Sidebottom, “Properties and Structure of Lanthanum Phosphate Glasses,” Proc. SPIE 4102, 88–94 (2000). [CrossRef]
9. M. Karabulut, E. Metwalli, and R. K. Brow, “Structure and properties of lanthanum-aluminum-phosphate glasses,” J. Non-Cryst. Solids 283(1-3), 211–219 (2001). [CrossRef]
10. Y.-W. Lee, M. J. F. Digonnet, S. Sinha, K. E. Urbanek, R. L. Byer, and S. Jiang, “High-Power Yb3+-Doped Phosphate Fiber Amplifier,” IEEE J. Sel. Top. Quantum Electron. 15(1), 93–102 (2009). [CrossRef]
11. R. A. Martin and J. C. Knight, “Silica-Clad Neodymium-Doped Lanthanum Phosphate Fibers and Fiber Lasers,” IEEE Photon. Technol. Lett. 18(4), 574–576 (2006). [CrossRef]
12. Y. Cheng, K. Sugioka, K. Midorikawa, M. Masuda, K. Toyoda, M. Kawachi, and K. Shihoyama, “Control of the cross-sectional shape of a hollow microchannel embedded in photostructurable glass by use of a femtosecond laser,” Opt. Lett. 28(1), 55–57 (2003). [CrossRef] [PubMed]
13. M. Ams, G. D. Marshall, and M. J. Withford, “Study of the influence of femtosecond laser polarisation on direct writing of waveguides,” Opt. Express 14(26), 13158–13163 (2006). [CrossRef] [PubMed]
14. W. Gawelda, D. Puerto, J. Siegel, A. Ferrer, A. Ruiz de la Cruz, H. Fernández, and J. Solis, “Ultrafast imaging of transient electronic plasmas produced in conditions of femtosecond waveguide writing in dielectrics,” Appl. Phys. Lett. 93(12), 121109-1–121109-3 (2008). [CrossRef]
15. A. Ferrer, A. Ruiz de la Cruz, D. Puerto, W. Gawelda, J. A. Vallés, M. A. Rebolledo, V. Berdejo, J. Siegel, and J. Solis, “In situ assessment and minimization of nonlinear propagation effects for femtosecond-laser waveguide writing in dielectrics,” J. Opt. Soc. Am. B 27(8), 1688–1692 (2010). [CrossRef]
16. A. K. Mairaj, H. N. Ping Hua, Rutt, and D. W. Hewak, “Fabrication and characterization of continuous wave direct UV (λ=244 nm) written channel waveguides in chalcogenide (Ga:La:S) glass,” J. Lightwave Technol. 20(8), 1578–1584 (2002). [CrossRef]
17. M. Ams, G. D. Marshall, P. Dekker, M. Dubov, V. K. Mezentsev, I. Bennion, and M. J. Withford, “Investigation of ultrafast laser-photonic material interactions: challenges for directly written glass photonics,” IEEE J. Sel. Top. Quantum Electron. 14(5), 1370–1381 (2008). [CrossRef]
18. M. Ams, G. D. Marshall, D. J. Spence, and M. J. Withford, “Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses,” Opt. Express 13(15), 5676–5681 (2005). [CrossRef] [PubMed]
19. J. A. Vallés, M. A. Rebolledo, and J. Cortes, “Full characterization of Er/Yb-codoped phosphate glass waveguides,” IEEE J. Quantum Electron. 42(2), 152–159 (2006). [CrossRef]
20. J. A. Vallés, M. A. Rebolledo, V. Berdejo, A. Ferrer, A. Ruiz de la Cruz, and J. Solis, “Study of an optimised bidirectional pump scheme for fs-laser written Yb/Er-codoped integrated waveguides,” Opt. Mater. 33(2), 231–235 (2010). [CrossRef]
21. E. Tanguy, C. Larat, and J. P. Pocholle, “Modelling of the erbium-ytterbium laser,” Opt. Commun. 153(1-3), 172–183 (1998). [CrossRef]
22. S. Honkanen, T. Ohtsuki, Sh. Jiang, S. I. Najafi, and N. Peyghambarian, “High Er concentration phosphate glasses for planar waveguide amplifiers,” Proc. SPIE 2996, 32–40 (1997). [CrossRef]
23. D. E. McCumber, “Theory of phonon-terminated optical masers,” Phys. Rev. 134(2A), A299–A306 (1964). [CrossRef]
24. R. M. Martin and R. S. Quimby, “Experimental evidence of the validity of the McCumber theory relating emission and absorption for rare-earth glasses,” J. Opt. Soc. Am. B 23(9), 1770–1775 (2006). [CrossRef]
25. B. Majaron, M. Čopič, M. Lukač, and M. Marinček, “Influence of hole burning on laser pumping dynamics and efficiency in Yb:Er phosphate glasses,” Proc. SPIE 2138, 183–190 (1994). [CrossRef]
26. J. A. Vallés, J. Solis, J. A. Sánchez-Martín, A. Ruiz de la Cruz, M. A. Rebolledo, and A. Ferrer, “Assesment of Rayleigh and non-Rayleigh contributions to the transmission losses in fs-laser written Er/Yb-codoped phosphate glass waveguides,” J. Laser Micro/Nanoeng. 5, 39–42 (2010).