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Abstract
We perform a systematic spectroscopic study in channel waveguides of potassium gadolinium lutetium double tungstate doped with different Er3+ concentrations. Transition cross sections of ground-state absorption (GSA) and excited-state absorption (ESA), as well as stimulated emission (SE) at the pump wavelength around 980 nm are determined. ESA is directly measured by the pump-probe technique. Evaluation of GSA and ESA spectra indicates that ESA may be diminished by an appropriate choice of pump wavelength near 980 nm. Besides, GSA and SE at the signal wavelength around 1.5 µm are measured and the wavelength-dependent gain cross section as a function of excitation density is determined. Non-exponential luminescence decay curves from the 4I13/2 and 4I11/2 levels are analyzed and the probabilities of the energy-transfer-upconversion (ETU) processes (4I13/2, 4I13/2) → (4I15/2, 4I9/2) and (4I11/2, 4I11/2) → (4I15/2, 4F7/2) are quantified. Despite the large interionic distance between neighboring rare-earth sites in potassium double tungstates, the probability of ETU is comparatively large because of the large cross sections of the involved transitions. A rate-equation analysis of the influence of ETU and ESA on gain at ∼1.5 µm is performed, revealing that ETU from the 4I13/2 amplifier level strongly limits the gain when the doping concentration increases above ∼6at.%. The calculated maximum achievable internal net gain per unit length amounts to ∼15 dB/cm for an optimized Er3+ concentration of ∼4 × 1020 cm−3 and a launched pump power of 300 mW at a pump wavelength of 984.5 nm, in reasonable agreement with recent experimental results.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The rare-earth-doped potassium double tungstates KY(WO4)2, KGd(WO4)2, and KLu(WO4)2 are widely investigated laser materials, see [1] and references therein. The thermomechanical [2] and spectroscopic properties [3] of these materials are superior to those found in many glass and crystalline hosts, mainly due to their strong anisotropy and high refractive index [3,4]. Channel waveguides in these materials have shown excellent performance in optical amplification [5] and lasing [6,7]. For Er3+-activated waveguide amplifiers and lasers operating in the telecom C-band at wavelengths near 1.5 µm [8], see Fig. 1, usually low Er3+ concentrations of ∼1-2 × 1020 cm−3 are chosen, because energy-transfer upconversion (ETU) between neighboring active ions depopulates the upper level of the amplifier transition and imposes a maximum attainable gain value on each host material [10–15]. Nevertheless, with a long spiral waveguide an internal net gain of 20 dB was demonstrated [16]. Incorporation of Er3+ in potassium double tungstates is possible up to the stoichiometric compound KEr(WO4)2, resulting in an Er3+ concentration of 6.3 × 1021 cm−3 [17]. The large inter-ionic distance between neighboring rare-earth sites [18,19] in potassium double tungstates reduces the probability of ETU and potentially allows for higher doping levels [20].
Fig. 1. Simplified energy-level diagram of Er3+ displaying the most relevant transitions for amplification around 1530 nm: the GSA transitions 4I15/2 → 4I13/2 around 1480 nm and 4I15/2 → 4I11/2 around 980 nm, the ESA transition 4I11/2 → 4F7/2 around 980 nm, the ground-state luminescence (LUM) transitions, as well as stimulated-emission (SE) transitions 4I13/2 → 4I15/2 and 4I11/2 → 4I15/2 around 1530 nm and 980 nm, respectively, non-radiative multiphonon decay (NR), and the ETU process ETU1 (4I13/2, 4I13/2) → (4I15/2, 4I9/2). τi are the measured and estimated (*) [3,9] luminescence lifetimes. In high-phonon oxide materials, leading to multiphonon quenching of luminescence lifetimes, other processes usually have a smaller influence: the ETU process ETU2 (4I11/2, 4I11/2) → (4I15/2, 4F7/2) and the cross-relaxation process CR (2H11/2/4S3/2, 4I15/2) → (4I9/2, 4I13/2).
Structuring channel waveguides into layers provides a laterally confined propagation of signal and pump light with excellent mode overlap and high intensities within the active region [21], thereby enabling the utilization of higher doping concentrations to achieve higher gain per unit length. In this work we present a systematic study of the most relevant spectroscopic processes in Er3+-doped potassium double tungstate waveguides. Ground-state-absorption (GSA) and stimulated-emission cross sections of the 4I15/2 ↔ 4I13/2 and 4I15/2 ↔ 4I11/2 transitions are determined. Due to the rather high phonon energies of ∼904–935 cm−1 present in potassium double tungstates [22,23], leading to fast multiphonon relaxation and accordingly short lifetime [24] of the 4I11/2 level (τ2 ≈ 135 µs) and, particularly, the 4I9/2 level (τ3 ≈ 1 µs) [3], their excitation rapidly decays to the 4I13/2 level. Decay curves and lifetimes of luminescence from the 4I13/2 and 4I11/2 levels are presented, from which microscopic parameters of migration and ETU from the 4I13/2 level are determined and the macroscopic ETU parameter is obtained. The macroscopic parameter of ETU from the 4I11/2 level is estimated. Pump excited-state absorption (ESA) on the 4I11/2 → 4F7/2 transition around 980 nm is measured. The influence of ETU and pump ESA on optical gain at ∼1.5 µm is analyzed by use of a rate-equation model.
2. Transition cross sections
Crystalline layers of KGdxLuyEr1-x-y(WO4)2 (abbreviated hereafter as KGLW:Er3+) with five different Er3+ concentrations, lattice matched by appropriate Gd3+ and Lu3+ concentrations (see Table 1), were grown by liquid-phase epitaxy (LPE) onto undoped KY(WO4)2 substrates [25,26]. Rib channel waveguides were microstructured by Ar+ etching [21] parallel to the Ng axis in the Nm−Ng plane of the crystalline layer, hence the optical modes propagate with a polarization of either E||Nm or E||Np. Composition and channel thickness (t), width (w), rib height (d), and length (ℓ) of each investigated sample are shown in Table 1.
Table 1. Optimized compositions of layers with different Er3+ concentrations, and waveguide dimensions.
2.1 Ground-state-absorption and -emission cross sections
Luminescence spectra, with the luminescence polarized parallel to the three principal optical axes, E||Np, E||Nm, and E||Ng, on the transitions 4I13/2 → 4I15/2 near 1.5 µm and 4I11/2 → 4I15/2 near 1 µm were recorded during pump excitation by a continuous-wave (CW) Ti:sapphire laser operating at the wavelength of 984.5 nm or 800 nm, respectively. The sample with the lowest doping concentration (sample I) was chosen to minimize re-absorption effects. The polarized luminescence intensity Iq(λ) was collected from the plane perpendicular to the excitation incidence and the spectra were dispersed by a spectrometer (Horiba-Yvon iHR550) with a resolution of 0.4 nm and detected by a cooled InAs detector. Emission cross sections were calculated from the Füchtbauer-Ladenburg equation for monoclinic biaxial crystals [27,28],
Fig. 2. (a) Emission and (b) absorption cross sections of the 4I13/2 ↔ 4I15/2 transition. (c) Emission and (d) absorption cross sections of the 4I11/2 ↔ 4I15/2 transition.
Using the reciprocity theorem [30], the related absorption cross sections on the transitions 4I15/2 → 4I13/2, see Fig. 2(b), and 4I15/2 → 4I11/2, see Fig. 2(d), were calculated from
2.2 Pump excited-state-absorption cross sections
The Er3+ ion is known for its large number of ESA transitions from the 4I13/2, 4I11/2, and 4S3/2 levels [36]. Excitation spectra of short-wavelength luminescence obtained by GSA and ESA of a single pump source [9] provide an indication of the presence of ESA but do not deliver the actual ESA spectra, because the wavelength dependence of GSA modifies the excitation density and the ESA rate. Pump-probe ESA measurements in an Er3+-doped KY(WO4)2 bulk crystal parallel to the three crystallographic axes, E||a, E||b, and E||c, were presented in [3], but due to the usually low excitation density in bulk materials ESA transitions were observed only from the 4I13/2 level. With the tight mode confinement in our channel waveguides, a significantly higher excitation density is achieved in the 4I11/2 level and ESA from this level can be detected as well.
ESA in the wavelength range 950−1030 nm was measured in a pump-probe setup [37,38], in which the signal and the pump are counter-propagating through the sample. A channel waveguide (sample II) with a length of ℓ = 8.6 mm and an Er3+ concentration of 0.95 × 1020cm−3 was chosen. Approximately 500 mW of pump power at λP = 800 nm (E||Nm) from a CW Ti:Sapphire laser modulated at ∼11 Hz by a chopper were incident on the sample, exciting the Er3+ ions from the ground state to the 4I9/2 level, from which fast multiphonon relaxation populated the 4I11/2 level. A super-continuum white-light source (Fianium) modulated at ∼1 kHz by a second chopper was used as the signal. The transmitted signal intensity Ip(λ) or Iu(λ) under pumped or unpumped conditions, respectively, was dispersed by a spectrometer with a resolution of 0.3 nm and detected by a silicon detector. The difference signal ΔI(λ) = Ip(λ) − Iu(λ) was amplified by a double lock-in technique. The difference signal accounts for GSA (4I15/2 → 4I11/2), ESA (4I11/2 → 4F7/2), and SE (4I11/2 → 4I15/2) present in the wavelength range 950−1030 nm. Following the analysis in [37], we obtain the spectra defined by
Fig. 3. Experimental pump-probe spectra combining the contributions from ESA, GSA, and SE parallel to the (a) Nm and (b) Np axis. Comparison of GSA and ESA cross sections for (c) E||Nm and (d) E||Np.
Table 2. Parameters used in the determination of ESA cross sections
The ESA spectra are blue-shifted with respect to the GSA spectra, see the comparison in Fig. 3(c) and 3(d), thus a longer pump wavelength will evoke less ESA. On the other hand, the GSA cross sections at the long-wavelength side of the spectra are lower, thereby leading to lower pump absorption. Pumping at 984.5 nm instead of the GSA peak for E||Nm at 979 nm is promising, because the decrease in GSA is insignificant, whereas the ESA is substantially lower, see Fig. 3(c). Although a longer pump wavelength within the same multiplet-to-multiplet transition generally leads to larger stimulated emission on the pump wavelength, hence lower inversion and lower gain, this effect amounts to a difference of only a few percent between 979 nm and 984.5 nm, whereas the improvement due to diminished ESA is significantly larger.
3. Luminescence decay and energy-transfer processes
With a setup similar to the one presented in [10], luminescence decay on the transitions 4I13/2 → 4I15/2 at 1535 nm, 4I11/2 → 4I15/2 at 1010 nm, and 4S3/2 → 4I15/2 at 545 nm was measured. A fiber-coupled laser diode with λp = 1480 nm or 976 nm directly excited the 4I13/2 or 4I11/2 level, respectively. The luminescence decay at 545 nm was detected after 976 nm excitation. The diode power was square-wave modulated by a function generator at a frequency of 20 Hz and a duty cycle of 50%, which allowed the Er3+ population densities to reach equilibrium before the pump was switched off. A glass light guide with a diameter of 0.6 mm was placed perpendicularly close to the in-coupling end of the waveguide, thereby collecting the luminescence from the region of maximum excitation density and minimizing re-absorption effects. The collected light was dispersed in a monochromator (H25 Yvon-Jobin) and detected by an InGaAs detector (ETX100 T) or a silicon detector (PIN-3CD). The current was amplified (FEMTO dhpca-100) and recorded by an oscilloscope (HP Infinium 54845A) which was triggered by the same function generator modulating the pump diode. 4096 samples were averaged by the oscilloscope.
3.1 Luminescence decay and energy-transfer upconversion from 4I13/2
Normalized luminescence-decay curves at 1535 nm for the five different Er3+ concentrations (see Table 1) were recorded for four different pump powers, see Fig. 4(a)−4(d). The spectroscopic processes affecting luminescence decay on the 4I13/2 → 4I15/2 transition are depicted in Fig. 1. After pump excitation into the 4I13/2 level, this level is depleted via ETU1 (4I13/2, 4I13/2) → (4I15/2, 4I9/2), thereby populating the 4I9/2 level, followed by a fast non-radiative multi-phonon relaxation to 4I11/2. In the luminescence-decay curves of Fig. 4(a)−4(d), a fast non-exponential decay is observed during the first ∼1.5 ms due to migration-accelerated ETU1, which is accentuated for higher Er3+ concentrations and higher pump powers. The decay slows down and after 8 ms an exponential decay is observed. The intrinsic luminescence lifetime of the 4I13/2 level was extracted from this exponential decay at delay times > 8 ms for all luminescence-decay curves, and an average of τ1 = 3.05 ms was obtained, see Fig. 4(e). Unlike in other materials [10,39,40], the exponential tail does not exhibit a concentration-dependent quenching for the concentration range studied. This finding could be a consequence of the high-purity raw materials and the high crystallinity of the LPE layers, as well as the large distance between neighboring rare-earth sites. Also in similar LPE-grown lattice-matched KGdxLuyYzYb1-x-y-z(WO4)2 layers, for which concentration quenching of the Yb3+ lifetime is usually expected in other host materials already for ∼10at.% of Yb3+, only a rather weak quenching was observed up to 57at.% [26].
Fig. 4. Experimental luminescence-decay curves (continuous lines) at 1535 nm and theoretical decay curves (dashed lines) simultaneously fitted for all decay curves. The incident pump power at λp = 1480 nm was (a) 25 mW, (b) 45 mW, (c) 108 mW, and (d) 148 mW. (e) Exponential intrinsic lifetime of the 4I13/2 level versus Er3+ concentration. (f) Macroscopic ETU parameter WETU,1 for different doping concentrations. Data points represent the coefficients for the doping concentrations of the studied samples. The dotted line is calculated from Eq. (5).
The luminescence-decay curves of Fig. 4(a)−4(d) were investigated using the analysis by Agazzi et al. [10]. The modified Zubenko equation [10,41]
In Al2O3:Er3+, the concentration-independent micro-parameter of the ETU1 process has a value of CETU,1 = 2.5 × 10−39 cm6/s [10], which is less than half the value we find in KGLW:Er3+. This result demonstrates that the large transition cross sections in KGLW:Er3+ over-compensate the large distance between neighboring rare-earth ions. Using the overlap integral of the Förster-Dexter theory [43] for energy migration and ETU,
3.2 Luminescence decay and energy-transfer upconversion from 4I11/2
Luminescence decay on the 4I11/2 → 4I15/2 transition was measured at 1010 nm after direct excitation into the 4I11/2 level at 976 nm. Luminescence decay on the 4S3/2 → 4I15/2 transition was measured at 545 nm after GSA (4I15/2 → 4I11/2) and subsequent upconversion by ESA (4I11/2 → 4F7/2) and ETU2 (4I11/2, 4I11/2) → (4I15/2, 4F7/2), from where non-radiative multiphonon relaxation populates the thermally coupled 2H11/2 and 4S3/2 levels, see Fig. 1. Decay curves measured in the lowest-doped sample (sample I) are presented in Fig. 5(a) and 5(b). An exponential decay is observed in both cases. The exponential fits suggest 4I11/2 and 4S3/2 intrinsic lifetimes of τ2 = 135 ± 8 µs and τ5 = 25 ± 2 µs, respectively.
Fig. 5. Luminescence decay curves recorded at (a) 1010 nm on the transition 4I11/2 → 4I15/2 and (b) 550 nm on the transition 4S3/2 → 4I15/2 after excitation of sample I with a laser diode operating at 976 nm. Experimental values (data points) and exponential least-squares fit (red line).
The luminescence decay curves from the 4I11/2 level in the higher-doped samples exhibits a more complex temporal dynamics. Figure 6 displays the curves for the highest doped sample (sample V) for different pump powers. For low pump power, the first temporal component exhibits a decay time close to the intrinsic lifetime τ2 of the emitting level, whereas the second component arises, because the ETU1 process re-populates the 4I11/2 level (Fig. 1), and has a decay time similar to half the decay time of the 4I13/2 level in which the ETU process originates [37,44]. The first component of the 4I11/2 decay becomes faster with increasing pump power because of the ETU process ETU2 (4I11/2, 4I11/2) → (4I15/2, 4F7/2). Assuming that after short-pulse excitation ions upconverted from 4I13/2 by the process ETU1 to 4I9/2 relax to 4I11/2 via multiphonon relaxation, and ions upconverted from 4I11/2 by the process ETU2 return to 4I11/2 via multiphonon relaxation, in a simplified way the population densities N2(t) and N1(t) can be approximated by the rate equations [37]
Fig. 6. Luminescence decay curves recorded at 1010 nm on the transition 4I11/2 → 4I15/2 after excitation of sample V with a laser diode operating at 976 nm for five different incident pump powers. Experimental values (data points) and exponential least-squares fit (red line).
Investigations in amorphous Al2O3:Er3+ [37] have shown that the microscopic parameters of migration within the 4I11/2 level determined from the spectral-overlap integral of the resonant transitions (4I11/2 → 4I15/2, 4I15/2 → 4I11/2) and of ETU determined from the spectral-overlap integral of the resonant transitions (4I11/2 → 4I15/2, 4I11/2 → 4F7/2) provide similar results for the concentration-independent macroscopic ETU parameter CETU,2 as the evaluation from luminescence-decay curves from the 4I11/2 level. Thanks to the measured ESA cross sections of Fig. 3(c) and 3(d), it is possible to calculate the strength of the resonant ETU2 process using the ESA, GSA, and emission cross sections from Figs. 3(c) and 3(d), 2(c), and 2(d), respectively. With Eq. (6), the microscopic parameters of migration and ETU are determined as CDD,2 = 2.98 × 10−39 cm6/s and CDA,2 = 2.98 × 10−39 cm6/s, respectively, which coincidentally are the same until the third digit. With these CDD,2 and CDA,2 values and Eq. (5), the concentration-independent macroscopic ETU parameter is then determined as CETU,2 = 9.81 × 10−39 cm6/s.
4. Influence of ETU and ESA on optical gain at 1.5 µm
By use of the obtained spectroscopic parameters, we investigate the influence of pump ESA and ETU1 on the achievable optical gain. The channel-waveguide amplifier model is based on a set of rate equations describing the excitation densities of 4I15/2, 4I13/2, 4I11/2, and 4S3/2 energy levels, accounting for the relevant processes that populate/depopulate these levels:
The results are shown in Fig. 7. Figure 7(a) displays the simulated internal net gain per unit length as a function of dopant concentration. For an optimum dopant concentration of ∼4 × 1020 cm−3 ( = 6.3at.%), a maximum gain of ∼15 dB/cm is calculated, slightly depending on the assumed value of the propagation loss. The simulation overestimates the experimentally achieved gain of ∼12 dB/cm [47] by approximately 25%, which may be due to (i) a non-negligible influence of the ETU2 and CR processes, (ii) errors in the approximation of the relevant parameter values, and most likely (iii) heating of the waveguide when pumping in the experiment, which leads to a temperature increase and, consequently, a reduction of transitions cross sections. This reduction, which leads to line broadening, is a fundamental process in rare-earth ions. It also impacts the performance of Yb3+-doped waveguide amplifiers [48,49], which typically generate less heat, temperature increase, and a consequent reduction of transition cross sections than comparable Er3+-doped devices. Nevertheless, the optimum dopant concentration is rather well predicted. Figure 7(b) indicates the influence of the processes ETU1 and ESA as a function of dopant concentration. The strongest detrimental effect on gain is caused by ETU1 which substantially reduces the excitation density of the 4I13/2 level with increasing doping concentration. Although it was predicted that ETU could strongly affect the gain at ∼1.5 µm in Er3+,Yb3+-doped KY(WO4)2, only rough estimations on the magnitude of the macroscopic ETU parameter were reported [14]. Pump ESA from the 4I11/2 pump level has a significantly smaller influence, partly because the pump wavelength has been chosen carefully to diminish the influence of ESA on the achievable gain. At shorter pump wavelengths the influence of pump ESA increases. ETU2 from the 4I11/2 pump level and the CR process from the 4I11/2 level have only a small influence.
Fig. 7. (a) Simulated internal net gain per unit length (equalling the stimulated-emission coefficient γ minus the propagation loss coefficient αloss) versus Er3+ concentration in potassium double tungstate channel waveguides at the peak gain wavelength for three different propagation losses (lines). Comparison with experimental results (data points) from [47]. (b) Simulated internal gain assuming a high propagation loss (αloss = 4 dB/cm), including ESA and ETU (black continuous line), excluding ESA and including ETU (red dashed line), and including ESA and excluding ETU (blue dotted line).
5. Summary
Spectroscopic investigations of a set of KGLW:Er3+ channel waveguide samples with five different Er3+ concentrations ranging from 0.45–6.36 × 1020 cm−3 have been performed. Investigation of the temporal dynamics of luminescence decay from the 4I13/2 and 4I11/2 levels has provided probabilities of the energy-transfer processes ETU1 (4I13/2, 4I13/2) → (4I15/2, 4I9/2) and ETU2 (4I11/2, 4I11/2) → (4I15/2, 4F7/2). The micro-parameters CDD,1 = 5.43 × 10−39 cm6/s for migration and CDA,1 = 4.94 × 10−40 cm6/s for upconversion from 4I13/2 were extracted by use of Zubenko’s model. These values are rather high, because the reduction of ETU probability by the long interionic distances between neighboring active ions is over-compensated by the large transition cross sections in these double tungstates. The concentration-independent macro-parameters are CETU,1 = 5.39 × 10−39 cm6/s and CETU,2 = 9.81 × 10−39 cm6/s. The concentration-dependent quenching of the 4I13/2 intrinsic lifetime observed in other Er3+-doped materials was found to be absent in KGLW:Er3+ for doping concentrations up to 10at.%. A pump-probe study of ESA for the tentative pump wavelengths between 960 and 990 nm has been performed. The pump wavelength of 984.5 nm (E||Nm) is predicted to be most suitable for the amplification of ∼1.5 µm signals. In a rate-equation simulation, ETU1 from the 4I13/2 level appears to have the strongest detrimental effect on optical gain at 1535 nm in these Er3+-doped channel waveguides. Measured values of internal net gain are over-estimated by ∼25%, partly because pump heating and the temperature dependence of transition cross sections are neglected in the simulation. The optimum dopant concentration for achieving the highest gain is confirmed in the simulation.
Funding
Stichting voor de Technische Wetenschappen (11689); H2020 European Research Council (648978).
Acknowledgment
The other authors of this paper dedicate this work to our colleague and co-author Yean-Sheng Yong who, sadly, deceased shortly after submission of this paper.
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