Energy-transfer upconversion and excited-state
absorption in KGd
x
Lu
y
Er
1−x−y
(WO
4
)
2
waveguide
amplifiers
S
ERGIOA. V
ÁZQUEZ-C
ÓRDOVA,
1S
HANMUGAMA
RAVAZHI,
2A
LEXANDERM. H
EUER,
3C
HRISTIANK
RÄNKEL,
3,4Y
EAN-S
HENGY
ONG,
1S
ONIAM. G
ARCÍA-B
LANCO,
1J
ENNIFERL. H
EREK,
1 ANDM
ARKUSP
OLLNAU2,5,*1Optical Sciences Group, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
2Integrated Optical Micro Systems Group, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
3Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany 4Center for Laser Materials, Leibniz-Institut für Kristallzüchtung, Max-Born-Str. 2, 12489 Berlin, Germany 5Advanced Technology Institute, Department of Electrical and Electronic Engineering, University of Surrey, Guildford GU2 7XH, United Kingdom
*m.pollnau@surrey.ac.uk
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 the4I
13/2and4I11/2levels are analyzed and the probabilities of the
energy-transfer-upconversion (ETU) processes (4I
13/2,4I13/2) → (4I15/2,4I9/2) and (4I11/2,4I11/2) →
(4I
15/2,4F7/2) 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 the4I
13/2 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 × 1020cm−3and 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 theOSA 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−3are chosen, because energy-transfer upconversion (ETU) between neighboring active ions
#376406 https://doi.org/10.1364/OME.9.004782
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 × 1021cm−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 transitions4I15/2→4I13/2around 1480 nm and4I
15/2→4I11/2 around 980 nm, the ESA transition4I11/2→4F7/2around 980 nm, the ground-state luminescence (LUM) transitions, as well as stimulated-emission (SE) transitions4I
13/2→4I15/2and4I11/2→4I15/2around 1530 nm and 980 nm, respectively, non-radiative multiphonon decay (NR), and the ETU process ETU1 (4I13/2,4I13/2) →
(4I15/2,4I9/2). τiare 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,
4I 13/2).
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 the4I15/2 ↔4I13/2 and4I15/2 ↔4I11/2 transitions are
determined. Due to the rather high phonon energies of ∼904–935 cm−1present in potassium
double tungstates [22,23], leading to fast multiphonon relaxation and accordingly short lifetime [24] of the4I
11/2 level (τ2 ≈135 µs) and, particularly, the 4I9/2 level (τ3 ≈1 µs) [3], their excitation rapidly decays to the4I
13/2level. Decay curves and lifetimes of luminescence from
the4I
13/2and4I11/2levels are presented, from which microscopic parameters of migration and
ETU from the4I
13/2level are determined and the macroscopic ETU parameter is obtained. The
macroscopic parameter of ETU from the4I
11/2level is estimated. Pump excited-state absorption
(ESA) on the4I
11/2→4F7/2transition around 980 nm is measured. The influence of ETU and
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
Table1), were grown by liquid-phase epitaxy (LPE) onto undoped KY(WO4)2substrates [25,26].
Rib channel waveguides were microstructured by Ar+etching [21] parallel to the N
gaxis in the Nm−Ngplane of the crystalline layer, hence the optical modes propagate with a polarization of
either E||Nmor E||Np. Composition and channel thickness (t), width (w), rib height (d), and
length (`) of each investigated sample are shown in Table1.
Table 1. Optimized compositions of layers with different Er3+concentrations, and waveguide dimensions.
Sample Stoichiometric formula Er3+[1020cm−3] t[µm] w[µm] d[µm] ` [mm]
I KGd0.4923Lu0.5002Er0.0075(WO4)2 0.48 6.4 5.6 1.48 5.07
II KGd0.4896Lu0.4955Er0.015(WO4)2 0.95 7.7 7.9 1.43 8.60
III KGd0.4850Lu0.4850Er0.03(WO4)2 1.90 7.1 7.8 1.27 6.75
IV KGd0.4756Lu0.4644Er0.06(WO4)2 3.81 8.5 7.5 1.55 0.75
V KGd0.4626Lu0.4374Er0.1(WO4)2 6.36 3.1 5.6 1.56 0.58
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 transitions4I13/2→4I15/2near 1.5 µm and4I11/2→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],
σe,q(λ) = 3λ 5 8πτrn2qc Iq(λ) ∫ λ[INg(λ) + INm(λ) + INp(λ)]dλ , (1)
where q stands for each of the principal axes of Np, Nm, or Ng, λ is the wavelength, τris the
radiative lifetime of the emitting level, nqis the material refractive index parallel to the axis q, cis the speed of light in vacuum, and Iq is the axis-respective intensity spectrum. Refractive
indexes were measured by use of the prism-coupling technique (Metricon 2010) at 633 nm, 830 nm, 1300 nm, and 1550 nm parallel to each optical axis, and the refractive index values at the pump and signal wavelength were interpolated using the single-term Sellmeier equation. For λP= 980 nm, we obtained ng= 2.067, nm= 2.021 and np= 1.989, and for λS= 1534 nm the
values are ng= 2.054, nm= 2.008, and np= 1.977. The radiative lifetime of the4I11/2 level,
τr,2= 2.137 ms [29] and the intrinsic luminescence lifetime of the4I
13/2level presented below,
τr,1≈τ1= 3.05 ms, were considered for the calculations. The resulting polarized emission cross sections on the transitions4I
13/2→4I15/2and4I11/2→4I15/2are displayed in Fig.2(a) and2(c),
respectively.
Using the reciprocity theorem [30], the related absorption cross sections on the transitions
4I
15/2→4I13/2, see Fig.2(b), and4I15/2→4I11/2, see Fig.2(d), were calculated from
σa,q(λ) = σe,q(λ) Zi Z0e
hc(λ−1−λ−1
Fig. 2.(a) Emission and (b) absorption cross sections of the4I13/2↔4I15/2transition. (c) Emission and (d) absorption cross sections of the4I
11/2↔4I15/2transition.
where h is the Planck constant, kBis the Boltzmann constant, λZL= 1535 nm for4I15/2↔4I13/2
or 981.5 nm for4I
15/2↔4I11/2is the wavelength of the zero-phonon-line transition, T = 300 K is
the temperature, and Z0= 4.5851, Z1= 4.5395, and Z2= 4.6606 are the partition functions of the 4I
15/2,4I13/2, and4I11/2levels, respectively. λZLand the energy levels of the manifolds used to
calculate Ziwere extracted from the literature [31–35].
2.2. Pump excited-state-absorption cross sections
The Er3+ion is known for its large number of ESA transitions from the4I
13/2,4I11/2, and4S3/2
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(WO
4)2bulk 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 the4I
13/2level.
With the tight mode confinement in our channel waveguides, a significantly higher excitation density is achieved in the4I
11/2level 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 ` = 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 the4I
9/2level, from which fast multiphonon relaxation populated the 4I
11/2level. 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
and detected by a silicon detector. The difference signal ∆I(λ) = Ip(λ) − Iu(λ) was amplified by a
double lock-in technique. The difference signal accounts for GSA (4I
15/2→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
ln ∆I(λ)
Iu(λ) + 1
= σa(λ)NeΓ` + (σe(λ) − σESA(λ))N2Γ`, (3)
where Neis the total averaged excitation density, N2 is the averaged excitation density of the 4I
11/2 level, Γ is the overlap factor of the signal mode with the active layer (calculated from
simulated mode profile), and σa(λ), σe(λ), and σESA(λ) are the GSA, emission, and signal ESA
cross sections, respectively. The results are presented in Fig.3(a) and3(b) for signal polarizations of E||Nmand E||Np, respectively. A rate-equation model [37], see later in Section4, was used
to determine the parameters Neand N2. Pump-GSA and emission cross sections (E||Nm) at
800 nm were taken from [9] and pump-ESA cross sections (E||a) at 800 nm from [3]. While the pump polarization was chosen as E||Nmduring the experiments, due to improved pump-coupling
conditions when realigning the experimental set-up between experiments different pump-coupling efficiencies were obtained during the two independent measurements for signal E||Nmand E||Np,
resulting in different launched pump powers, hence also different Neand N2 (averaged along
the entire length of the waveguide) for the two measurements (Table2). From Eq. (3) the ESA cross sections of Fig.3(c) and3(d) were then calculated. The resulting ESA cross sections are nominally independent of the amount of launched pump power.
Fig. 3. Experimental pump-probe spectra combining the contributions from ESA, GSA,
and SE parallel to the (a) Nmand (b) Npaxis. Comparison of GSA and ESA cross sections
for (c) E||Nmand (d) E||Np.
The ESA spectra are blue-shifted with respect to the GSA spectra, see the comparison in Fig.3(c) and3(d), thus a longer pump wavelength will evoke less ESA. On the other hand, the
Table 2. Parameters used in the determination of ESA cross sections
Parameter E | |Nm E | |Np
Γ 0.998 0.9995
N2[cm−3] 0.0465 Nd 0.214 Nd
Ne[cm−3] 0.352 Nd 0.726 Nd
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||Nmat 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 transitions4I 13/2→
4I
15/2at 1535 nm,4I11/2→4I15/2at 1010 nm, and4S3/2→4I15/2at 545 nm was measured. A fiber-coupled laser diode with λp= 1480 nm or 976 nm directly excited the4I13/2or4I11/2level,
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 from4I13/2
Normalized luminescence-decay curves at 1535 nm for the five different Er3+concentrations (see
Table1) were recorded for four different pump powers, see Fig.4(a)−4(d). The spectroscopic processes affecting luminescence decay on the4I
13/2→4I15/2transition are depicted in Fig.1.
After pump excitation into the4I
13/2level, this level is depleted via ETU1(4I13/2,4I13/2) → (4I15/2, 4I
9/2), thereby populating the4I9/2level, followed by a fast non-radiative multi-phonon relaxation
to4I
11/2. 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 the4I
13/2level 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)2layers, for which
concentration quenching of the Yb3+lifetime is usually expected in other host materials already
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 the4I13/2level versus Er3+concentration.
(f) Macroscopic ETU parameter WETU,1for 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]
N1(t)= N1(0)e −t/τ1 1 + N1(0)βπ32 q CDA τ0 τ1 q1 +τ0 τ1erf r tτ1 0 + 1 τ1 − e−t/τ1erfqτt 0 (4)
describes the excitation density N1, to which the luminescence intensity is proportional, as
a function of time t. In the original form of Eq. (4) [41], β = 2, which can be a reasonable approximation for materials where a large fraction of the4I
11/2 population density decays
investigation, β = 1 is chosen, thereby assuming that the upconverted ion quickly relaxes back to the 4I
13/2 level [10], which is a reasonable approximation for high-phonon oxides. A
detailed analysis considering measured luminescence lifetimes and Judd-Ofelt data for the radiative lifetimes would provide β = 1+ β20= 1.055 for our material (see Section4), close
to our approximation of β = 1. The migration mean time τ0and migration micro-parameter
CDDare related by 1/τ0 = CDDNd2[10,42], whereas the donor-acceptor micro-parameter CDA
quantifies the ETU1 process. The number of donors equals the number of active ions. N1(0)
is the average excitation in the geometrical cross section of the active layer where the pump intensity is > Ip(z = 0)e−2. This value was calculated for a thin (∼100 µm) longitudinal slab at the
beginning of the waveguide. By an iterative estimation of N1(0) from a three-level (4I15/2,4I13/2,
and4I
11/2) rate-equation system [10] considering the waveguide characteristics (Table1) and a
simultaneous least-squares fit of Eq. (4) to the 20 luminescence-decay curves of Fig.4(a)−4(d), micro-parameters of CDD,1= 5.43 × 10−39cm6/s for energy migration (4I13/2,4I15/2) → (4I15/2, 4I
13/2) and CDA,1= 4.94 × 10−40cm6/s for ETU1(4I13/2,4I13/2) → (4I15/2,4I9/2) were extracted.
The macroscopic ETU parameter [10] then amounts to
WETU=
π2
3 p
CDDCDANd = CETUNd, (5)
resulting in the concentration-independent micro-parameter of the ETU1process having a value
of CETU,1= 5.39 × 10−39cm6/s and WETU,1as displayed in Fig.4(f).
In Al2O3:Er3+, the concentration-independent micro-parameter of the ETU1process has a
value of CETU,1= 2.5 × 10−39cm6/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,
CDD= 6c (2π)4n2 ∫ σe(λ)σa(λ)dλ, (6) CDA= 6c (2π)4n2 ∫ σe(λ)σESA(λ)dλ, (7)
respectively, and apply Eq. (6) to the spectral overlap between the emission and absorption cross sections on the4I
13/2↔4I15/2transition for E||Nm, see Fig.2a and2b, respectively, a value of CDD,1= 5.91 × 10−39cm6/s is calculated for energy migration (4I13/2,4I15/2) → (4I15/2,4I13/2),
which is only slightly higher than the value of CDD,1= 5.43 × 10−39cm6/s extracted from the
luminescence-decay curves. In contrast, there is no direct spectral overlap between the emission
4I
13/2→4I15/2at 1470−1630 nm, see Fig.2(a), and the ESA4I13/2→4I9/2which appears only at
wavelengths longer than 1650 nm in KY(WO4)2[3]. Consequently, the value of CDA,1calculated
from the overlap integral of Eq. (7) for ETU1(4I13/2,4I13/2) → (4I15/2,4I9/2) is several orders of
magnitude smaller than the value of CDD,1calculated from the overlap integral of Eq. (6) for
energy migration (4I13/2,4I15/2) → (4I15/2,4I13/2) and the macroscopic parameter W
ETU,1which
is subsequently calculated from Eq. (5) has an extremely low value. Nevertheless, ETU1is a
strong, albeit phonon-assisted process. However, it cannot be quantified by the overlap integral of the Förster-Dexter theory but can only be described correctly by a theory that takes into account assistance by a phonon to bridge the energy gap between the two transitions involved in the ETU1
process.
3.2. Luminescence decay and energy-transfer upconversion from4I11/2 Luminescence decay on the4I
11/2 →4I15/2 transition was measured at 1010 nm after direct
excitation into the4I
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 coupled2H
11/2and4S3/2levels, 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 suggest4I
11/2and4S3/2intrinsic
lifetimes of τ2= 135 ± 8 µs and τ5= 25 ± 2 µs, respectively.
Fig. 5. Luminescence decay curves recorded at (a) 1010 nm on the transition4I11/2→
4I
15/2and (b) 550 nm on the transition4S3/2→4I15/2after 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 the4I
11/2level in the higher-doped samples exhibits a
more complex temporal dynamics. Figure6displays 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 τ2of the emitting level, whereas the second component
arises, because the ETU1 process re-populates the4I11/2 level (Fig.1), and has a decay time
similar to half the decay time of the4I
13/2level in which the ETU process originates [37,44]. The
first component of the4I
11/2decay 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 from4I
13/2 by the process ETU1 to4I9/2 relax to 4I11/2 via multiphonon
relaxation, and ions upconverted from4I
11/2by the process ETU2return to4I11/2via multiphonon
relaxation, in a simplified way the population densities N2(t) and N1(t) can be approximated by
the rate equations [37]
dN2 dt = WETU,1N 2 1 −τ1 2N2− WETU,2N 2 2, (8) dN1 dt = β21 τ2 N2− 1 τ1N1−2WETU,1N12. (9)
From the fits to the luminescence decay curves of Fig. 6, we estimate the concentration-independent macroscopic ETU parameter as CETU,2= 9.81 × 10−39cm6/s. This value is a rather
rough estimation, because Eqs. (8) and (9) assume infinitely fast relaxation of the energy upconverted by the ETU2process back to the4I11/2level and neglect the finite migration time.
Investigations in amorphous Al2O3:Er3+[37] have shown that the microscopic parameters of
migration within the4I
11/2level determined from the spectral-overlap integral of the resonant
transitions (4I
11/2→4I15/2,4I15/2→4I11/2) and of ETU determined from the spectral-overlap
integral of the resonant transitions (4I
11/2 → 4I15/2, 4I11/2 → 4F7/2) provide similar results
for the concentration-independent macroscopic ETU parameter CETU,2as the evaluation from
luminescence-decay curves from the4I
Fig. 6.Luminescence decay curves recorded at 1010 nm on the transition4I11/2→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). Fig.3(c) and3(d), it is possible to calculate the strength of the resonant ETU2process using the
ESA, GSA, and emission cross sections from Figs.3(c) and3(d),2(c), and2(d), respectively. With Eq. (6), the microscopic parameters of migration and ETU are determined as CDD,2= 2.98 × 10−39
cm6/s and C
DA,2= 2.98 × 10−39cm6/s, respectively, which coincidentally are the same until
the third digit. With these CDD,2and CDA,2values and Eq. (5), the concentration-independent
macroscopic ETU parameter is then determined as CETU,2= 9.81 × 10−39cm6/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 ETU1on the achievable optical gain. The channel-waveguide amplifier model is based on a set
of rate equations describing the excitation densities of4I15/2,4I13/2,4I11/2, and4S3/2energy levels,
accounting for the relevant processes that populate/depopulate these levels:
dN5 dt = RESA− 1 τ5N5, (10) dN2 dt = RP+ WETU,1N 2 1 + β52 τ5 N5− 1 τ2N2− RESA, (11) dN1 dt = β21 τ2 N2+ β51 τ5 N5− Rs−τ1 1N1−2WETU,1N 2 1, (12) Nd = N0+ N1+ N2+ N5. (13)
The pump, ESA, and signal-amplification rate are given by
RP= λP hcIP(σa,PN0−σe,PN2), (14) RESA= λP hcIPσESAN2, (15) RS = λS hcIS(σe,SN1−σa,SN0). (16)
The evolution of pump power PPand signal power PSwithin the channel waveguide is considered
as dPP dz = PP ∫ ∫ AEr
ΦP(σe,PN2−σa,PN0−σESAN2)dxdy −αloss,P
, (17)
dPS dz = PS ∫ ∫ AEr ΦS(σe,SN1−σa,SN0)dxdy −αloss,S . (18)
AEr is the area of the active region and ΦP and ΦS are the normalized pump and signal
mode-profile distribution simulated with the PhoeniX software Field Designer [45]. The branching ratios, in which we consider fast multiphonon-relaxation processes4F
9/2→4I9/2→ 4I
11/2in the intermediate levels, are calculated from the electric-dipole radiative-transition rate
constants, radiative lifetimes, and branching ratios given in [29] and the luminescence lifetimes of τ1= 3.05 ms, τ2= 135 µs, and τ3= 25.5 µs determined above: β50= 0.056, β51= 0.022,
β52= 0.922, β20= 0.055, and β21= 0.945. The macroscopic energy-transfer parameter WETU,1
was calculated for each doping concentration from Eq. (5) and the obtained concentration-independent parameter CETU,1= 5.39 × 10−39cm6/s. A launched pump power of 300 mW at a
pump wavelength of λP= 984.5 nm, a signal power of 0.1 µW, and typical propagation losses
in buried channel waveguides of αloss,P= 0.34 dB/cm near 1.0 µm [21] and αloss,S= 0.2 dB/cm
at 1.5 µm (estimated from experimental data of 0.34 dB/cm at 1.0 µm [21] and 0.11 dB/cm at 1.84 µm [46]) are assumed. From the measurements above, the transition cross sections at the chosen pump and signal wavelengths are derived as σa,P= 1.03 × 10−20 cm2, σe,P= 1.18 ×
10−20cm2, σ
ESA= 1.0 × 10−20cm2, σa,S= 2.51 × 10−20cm2, and σe,S= 2.52 × 10−20cm2. The
waveguide length and cross-sectional dimensions are fixed to ` = 0.75 mm, t = 5 µm, w = 6.3 µm, and d = 1.22 µm. The attainable gain for the polarization E||Nm(TE-polarization in the waveguide)
at the peak-gain wavelength of λS= 1534.8 nm is then calculated.
The results are shown in Fig.7. Figure7(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 ETU2and 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
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).
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.
Figure7(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 ETU1which substantially
reduces the excitation density of the4I
13/2level with increasing doping concentration. Although it
was predicted that ETU could strongly affect the gain at ∼1.5 µm in Er3+,Yb3+-doped KY(WO 4)2,
only rough estimations on the magnitude of the macroscopic ETU parameter were reported [14]. Pump ESA from the4I
11/2pump 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. ETU2from the4I11/2
pump level and the CR process from the4I
11/2level have only a small influence.
5. Summary
Spectroscopic investigations of a set of KGLW:Er3+channel waveguide samples with five different
Er3+concentrations ranging from 0.45–6.36 × 1020cm−3have been performed. Investigation
of the temporal dynamics of luminescence decay from the4I
13/2and4I11/2levels has provided
probabilities of the energy-transfer processes ETU1(4I13/2,4I13/2) → (4I15/2,4I9/2) and ETU2
(4I
11/2,4I11/2) → (4I15/2,4F7/2). The micro-parameters CDD,1= 5.43 × 10−39cm6/s for migration
and CDA,1= 4.94 × 10−40cm6/s for upconversion from4I13/2were 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 × 10−39cm6/s and CETU,2= 9.81 × 10−39cm6/s. The concentration-dependent
quenching of the4I13/2 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, ETU1from the4I13/2level 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.
References
1. M. Pollnau, Y. E. Romanyuk, F. Gardillou, C. N. Borca, U. Griebner, S. Rivier, and V. Petrov, “Double tungstate lasers: from bulk toward on-chip integrated waveguide devices,”IEEE J. Sel. Top. Quantum Electron.13(3), 661–671
(2007).
2. A. A. Kaminskii, J. B. Gruber, S. N. Bagaev, K. Ueda, U. Hömmerich, J. T. Seo, D. Temple, B. Zandi, A. A. Kornienko, E. B. Dunina, A. A. Pavlyuk, R. F. Klevtsova, and F. A. Kuznetsov, “Optical spectroscopy and visible stimulated emission of Dy3+ions in monoclinic α-KY(WO4)2and α-KGd(WO4)2crystals,”Phys. Rev. B65(12),
3. N. V. Kuleshov, A. A. Lagatsky, A. V. Podlipensky, V. P. Mikhailov, A. A. Kornienko, E. B. Dunina, S. Hartung, and G. Huber, “Fluorescence dynamics, excited-state absorption, and stimulated emission of Er3+in KY(WO
4)2,”J. Opt.
Soc. Am. B15(3), 1205–1212 (1998).
4. N. V. Kuleshov, A. A. Lagatsky, V. G. Shcherbitsky, V. P. Mikhailov, E. Heumann, T. Jensen, A. Diening, and G. Huber, “CW laser performance of Yb and Er,Yb doped tungstates,”Appl. Phys. B: Lasers Opt.64(4), 409–413
(1997).
5. D. Geskus, S. Aravazhi, S. M. García-Blanco, and M. Pollnau, “Giant optical gain in a rare-earth-ion-doped microstructure,”Adv. Mater.24(10), OP19–OP22 (2012).
6. D. Geskus, S. Aravazhi, K. Wörhoff, and M. Pollnau, “High-power, broadly tunable, and low-quantum-defect KGd1−xLux(WO4)2:Yb3+channel waveguide lasers,”Opt. Express18(25), 26107–26112 (2010).
7. K. van Dalfsen, S. Aravazhi, C. Grivas, S. M. García-Blanco, and M. Pollnau, “Thulium channel waveguide laser with 1.6 W of output power and ∼80% slope efficiency,”Opt. Lett.39(15), 4380–4383 (2014).
8. J. D. B. Bradley and M. Pollnau, “Erbium-doped integrated waveguide amplifiers and lasers,”Laser Photonics Rev.
5(3), 368–403 (2011).
9. M. Rico, M. C. Pujol, F. Díaz, and C. Zaldo, “Green up-conversion of Er3+in KGd(WO4)2crystals. Effects of sample
orientation and erbium concentration,”Appl. Phys. B: Lasers Opt.72(2), 157–162 (2001).
10. L. Agazzi, K. Wörhoff, and M. Pollnau, “Energy-transfer-upconversion models, their applicability and breakdown in the presence of spectroscopically distinct ion classes: a case study in amorphous Al2O3:Er3+,”J. Phys. Chem. C 117(13), 6759–6776 (2013).
11. E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,”IEEE Photonics Technol. Lett.5(1), 73–75 (1993).
12. E. Maurice, G. Monnom, B. Dussardier, and D. B. Ostrowsky, “Clustering-induced nonsaturable absorption phenomenon in heavily erbium-doped silica fibers,”Opt. Lett.20(24), 2487–2489 (1995).
13. P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy transfer processes in Er3+-doped and Er3+,
Pr3+-codoped ZBLAN glasses,”Phys. Rev. B62(2), 856–864 (2000).
14. S. Bjurshagen, J. E. Hellström, V. Pasiskevicius, M. C. Pujol, M. Aguiló, and F. Díaz, “Fluorescence dynamics and rate equation analysis in Er3+and Yb3+doped double tungstates,”Appl. Opt.45(19), 4715–4725 (2006).
15. J. D. B. Bradley, L. Agazzi, D. Geskus, F. Ay, K. Wörhoff, and M. Pollnau, “Gain bandwidth of 80 nm and 2 dB/cm peak gain in Al2O3:Er3+optical amplifiers on silicon,”J. Opt. Soc. Am. B27(2), 187–196 (2010).
16. S. A. Vázquez-Córdova, M. Dijkstra, E. H. Bernhardi, F. Ay, K. Wörhoff, J. L. Herek, S. M. García-Blanco, and M. Pollnau, “Erbium-doped spiral amplifiers with 20 dB of net gain on silicon,”Opt. Express22(21), 25993–26004
(2014).
17. T. Zayarnyuk, M. T. Borowiec, V. P. Dyakonov, H. Szymczak, E. Zubov, A. A. Pavlyuk, and M. Baranski, “Optical properties of potassium erbium double-tungstate KEr(WO4)2,”Proc. SPIE4412, 280–283 (2001).
18. M. C. Pujol, X. Mateos, R. Solé, J. Massons, J. Gavaldà, X. Solans, F. Díaz, and M. Aguiló, “Structure, crystal growth and physical anisotropy of KYb(WO4)2, a new laser matrix,”J. Appl. Crystallogr.35(1), 108–112 (2002).
19. I. M. Krygin, A. D. Prokhorov, V. P. D’yakonov, M. T. Borowiec, and H. Szymczak, “Spin-spin interaction of Dy3+
ions in KY(WO4)2,”Phys. Solid State44(8), 1587–1596 (2002).
20. K. Petermann, D. Fagundes-Peters, J. Johannsen, M. Mond, V. Peters, J. J. Romero, S. Kutovoi, J. Speiser, and A. Giesen, “Highly Yb-doped oxides for thin-disc lasers,”J. Cryst. Growth275(1-2), 135–140 (2005).
21. D. Geskus, S. Aravazhi, C. Grivas, K. Wörhoff, and M. Pollnau, “Microstructured KY(WO4)2:Gd3+, Lu3+, Yb3+
channel waveguide laser,”Opt. Express18(9), 8853–8858 (2010).
22. L. Macalik, J. Hanuza, and A. A. Kaminskii, “Polarized Raman spectra of the oriented NaY(WO4)2and KY(WO4)2
single crystals,”J. Mol. Struct.555(1-3), 289–297 (2000).
23. J. Hanuza and L. Macalik, “Polarized infra-red and Raman spectra of monoclinic α-KLn(WO4)2single crystals
(Ln = Sm-Lu, Y),”Spectrochim. Acta, Part A43(3), 361–373 (1987).
24. H. W. Moos, “Spectroscopic relaxation processes of rare-earth ions in crystals,”J. Lumin.1-2, 106–121 (1970).
25. F. Gardillou, Y. E. Romanyuk, C. N. Borca, R. P. Salathé, and M. Pollnau, “Lu, Gd codoped KY(WO4)2:Yb epitaxial
layers: towards integrated optics based on KY(WO4)2,”Opt. Lett.32(5), 488–490 (2007).
26. S. Aravazhi, D. Geskus, K. van Dalfsen, S. A. Vázquez-Córdova, C. Grivas, U. Griebner, S. M. García-Blanco, and M. Pollnau, “Engineering lattice matching, doping level, and optical properties of KY(WO4)2:Gd, Lu, Yb layers for a
cladding-side-pumped channel waveguide laser,”Appl. Phys. B: Lasers Opt.111(3), 433–446 (2013).
27. G. Huber, W. W. Krühler, W. Bludau, and H. G. Danielmeyer, “Anisotropy in the laser performance of NdP5O14,”J.
Appl. Phys.46(8), 3580–3584 (1975).
28. F. Mougel, K. Dardenne, G. Aka, A. Kahn-Harari, and D. Vivien, “Ytterbium-doped Ca4GdO(BO3)3: an efficient
infrared laser and self-frequency doubling crystal,”J. Opt. Soc. Am. B16(1), 164–172 (1999).
29. J. Martínez de Mendívil, G. Lifante, M. C. Pujol, M. Aguiló, F. Díaz, and E. Cantelar, “Judd-Ofelt analysis and transition probabilities of Er3+doped KY
1−x−yGdxLuy(WO4)2crystals,”J. Lumin.165, 153–158 (2015).
30. D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,”Phys. Rev.136(4A),
A954–A957 (1964).
31. S. Bjurshagen, P. Brynolfsson, V. Pasiskevicius, I. Parreu, M. C. Pujol, A. Peña, M. Aguiló, and F. Díaz, “Crystal growth, spectroscopic characterization, and eye-safe laser operation of erbium- and ytterbium-codoped KLu(WO4)2,”
32. A. A. Kaminskii, Crystalline Lasers: Physical Processes and Operating Schemes (Taylor & Francis, 1996). 33. B. Z. Malkin, A. A. Kaminskii, N. R. Agamalyan, L. A. Bumagina, and T. I. Butaeva, “Spectra of rare-earth ions in
the crystal fields of double tungstates and molybdates,”Phys. Status Solidi B110(2), 417–422 (1982).
34. X. Mateos, M. C. Pujol, F. Güell, M. Galán, R. M. Solé, J. Gavaldà, M. Aguiló, J. Massons, and F. Díaz, “Erbium spectroscopy and 1.5-µm emission in KGd(WO4)2:Er,Yb single crystals,”IEEE J. Quantum Electron.40(6), 759–770
(2004).
35. M. C. Pujol, M. Rico, C. Zaldo, R. Sole, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2single crystals,”Appl. Phys. B: Lasers Opt.68(2), 187–197 (1999).
36. M. Pollnau, E. Heumann, and G. Huber, “Time-resolved spectra of excited-state absorption in Er3+doped YAlO3,”
Appl. Phys. A54(5), 404–410 (1992).
37. L. Agazzi, K. Wörhoff, A. Kahn, M. Fechner, G. Huber, and M. Pollnau, “Spectroscopy of upper energy levels in an Er3+-doped amorphous oxide,”J. Opt. Soc. Am. B30(3), 663–667 (2013).
38. J. Koetke and G. Huber, “Infrared excited-state absorption and stimulated-emission cross sections of Er3+-doped
crystals,”Appl. Phys. B: Lasers Opt.61(2), 151–158 (1995).
39. W. J. Miniscalco, “Erbium-doped glasses for fiber amplifiers at 1500 nm,”J. Lightwave Technol.9(2), 234–250
(1991).
40. F. Auzel, F. Bonfigli, S. Gagliari, and G. Baldacchini, “The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity,”J. Lumin.94-95, 293–297 (2001).
41. D. A. Zubenko, M. A. Noginov, V. A. Smirnov, and I. A. Shcherbakov, “Different mechanisms of nonlinear quenching of luminescence,”Phys. Rev. B55(14), 8881–8886 (1997).
42. L. Palatella, F. Cornacchia, A. Toncelli, and M. Tonelli, “Microscopic treatment of upconversion in Nd3+-doped
samples,”J. Opt. Soc. Am. B20(8), 1708–1714 (2003).
43. J. A. Caird, A. J. Ramponi, and P. R. Staver, “Quantum efficiency and excited-state relaxation dynamics in neodymium-doped phosphate laser glasses,”J. Opt. Soc. Am. B8(7), 1391–1403 (1991).
44. J. Rubin, A. Brenier, R. Moncorge, and C. Pedrini, “Excited-state absorption and energy transfer in Er3+doped
LiYF4,”J. Lumin.36(1), 39–47 (1986).
45.http://www.phoenixbv.com.
46. K. van Dalfsen, S. Aravazhi, D. Geskus, K. Wörhoff, and M. Pollnau, “Efficient KY1−x−yGdxLuy(WO4)2:Tm3+
channel waveguide lasers,”Opt. Express19(6), 5277–5282 (2011).
47. S. A. Vázquez-Córdova, S. Aravazhi, C. Grivas, Y. S. Yong, S. M. García-Blanco, J. L. Herek, and M. Pollnau, “High optical gain in erbium-doped potassium double tungstate channel waveguide amplifiers,”Opt. Express26(5),
6260–6266 (2018).
48. Y. S. Yong, S. Aravazhi, S. A. Vázquez-Cordova, J. J. Carjaval, F. Díaz, J. L. Herek, S. M. García-Blanco, and M. Pollnau, “Temperature-dependent absorption and emission of potassium double tungstates with high ytterbium content,”Opt. Express24(23), 26825–26837 (2016).
49. Y. S. Yong, S. Aravazhi, S. A. Vázquez-Córdova, J. L. Herek, S. M. García-Blanco, and M. Pollnau, “Gain dynamics in a highly ytterbium-doped potassium double tungstate epitaxial layer,”J. Opt. Soc. Am. B35(9), 2176–2185 (2018).
