The spectroscopic properties of Tm3+/Yb3+ co-doped silica fibers under excitation at 980 nm are reported. Three distinct up-conversion fluorescence bands were observed in the visible to near infra-red regions. The blue and red fluorescence bands at 475 and 650 nm, respectively, were found to originate from the 1G4 level of Tm3+. A three step up-conversion process was established as the populating mechanism for these fluorescence bands. The fluorescence band at 800 nm was found to originate from two possible transitions in Tm3+; one being the transition from the 3H4 to 3H6 manifold which was found to dominate at low pump powers; the other being the transition from the 1G4 to 3H6 level which dominates at higher pump powers. The fluorescence lifetime of the 3H4 and 3F4 levels of Tm3+ and 2F5/2 level of Yb3+ were studied as a function of Yb3+ concentration, with no significant energy back transfer from Tm3+ to Yb3+ observed.
©2008 Optical Society of America
Over the past decade there has been a renewed interest in the spectroscopic properties of the thulium (Tm3+) ion, particularly in application areas such as optical communications, high power lasers, medicine and sensing. Of particular interest to this work is the application of thulium for optical amplification in the telecommunication S-band from 1460–1530 nm. Thulium doped fiber amplifiers (TDFAs) are amongst the leading candidates to bring the same effective means of optical amplification to the S-band as the erbium doped fiber amplifier (EDFA) has for the C-band and L-band.
To date, the only efficient TDFAs have been demonstrated in low phonon energy host materials (such as fluoride glasses) which are incompatible with existing silica based telecommunication infrastructure. For this technology to be a viable solution for S-band amplification efficient, robust and compatible amplifiers are required. TDFAs in a silica based host material are the preferred solution; however the spectroscopic properties of thulium result in silica being a poor host material for optical amplification. Various pumping techniques have been explored in the thulium system to improve the efficiency of the S-band transition [1–3], the most popular being the up-conversion pumping technique in which 1040–1060 nm pump photons are absorbed by the ground state and then the first excited state (3F4) to result in an excited ion in the upper amplifying 3H4 manifold (see Fig. 1.). Unfortunately, the energy level structure of the thulium supports a third absorption step from the upper amplifying manifold to a higher lying manifold (1G4) resulting in a quenching of the excited state population from the amplifying manifold , hence, research into other possible up-conversion pumping techniques is now under way. An alternate technique which is attracting considerable interest is co-doping thulium ions with other sensitising rare earth elements which can act to absorb and transfer energy. Ytterbium (Yb3+) is seen as a promising candidate due to its significant absorption cross section and favorable energy level structure.
Studies of Tm3+/Yb3+ co-doped systems date back to the 1960s and 70s where Hewes et al.  and Ostermayer et al.  carried out extensive studies on the up-conversion characteristics of Tm3+/Yb3+ in YF3 crystals. Researchers have since studied the properties of Tm3+/Yb3+ co-doped systems in a range of host materials [7–11], however limited work has been carried out on such systems in silica based glasses. Hanna et al.  reported on the up-conversion properties of Tm3+/Yb3+ co-doped silica glass under excitation at 1060 and 800–860 nm and found that the poor up-conversion efficiencies of the system were a result of the short excited state lifetimes of Tm3+. However, recent work has demonstrated a 3-fold increase in the fluorescence lifetimes of the 3H4 manifold through the incorporation of large amounts of Al2O3 into the silica glass network . This, coupled with the development of high-powered semi-conductor laser sources around 980 nm, which enables the peak absorption of Yb3+ to be optically pumped efficiently, suggests that an improvement in the up-conversion efficiencies in silica-based materials may now be realised.
In this work the up-conversion properties of Tm3+/Yb3+ co-doped alumino-silicate fibers under excitation at 980 nm are presented. The population mechanisms for the up-conversion processes are established and studied at three different Tm3+/Yb3+ concentration ratios. The lifetimes of the excited states of Tm3+ and Yb3+ are also reported and studied as a function of Yb2O3 concentration. By studying the population dynamics of the Tm3+/Yb3+ co-doped system in alumino-silicate glass, meaningful conclusions as to the system’s potential to produce optical amplification in the S-band can be drawn. These conclusions also have important implications for Tm3+ doped high power fiber lasers operating near 2 µm as the up-conversion mechanisms involved have been shown to reduce the performance of these devices [14–18].
2. Experimental details
Three Tm3+/Yb3+ co-doped alumino-silicate fibers were fabricated for this study using the MCVD and solution doping techniques. The core concentrations of the fibers are listed in Table 1 along with the Tm3+/Yb3+ concentration ratios.
The Tm2O3 and Yb2O3 concentrations given in Table 1 were estimated from the absorption peaks at 786 and 920 nm, respectively. The refractive index profiles of the fiber samples were measured, using a York S14 index profiler and used to obtain the Al2O3 concentrations since it has been shown that Al2O3 increases the refractive index of silica by 2.3×10-3 per mol %; it was assumed that the concentration of Tm3+ and Yb3+ did not contribute significantly to the index difference. Al2O3 was used to modify the core region of the fiber, as it has been established that it has a lengthening effect on the fluorescence lifetime of the excited state manifolds. The Al2O3 also helps to distribute the rare earth ions homogeneously throughout the glass host. High Tm2O3 concentrations were avoided in this study as the cross relaxation processes between Tm3+ ions may mask the energy transfer properties from the energy exchange between Yb3+ and Tm3+ ions. No other standard modifiers of silica, such as germanium, phosphorus or fluorine were used in the fabrication process.
The fluorescence intensity and lifetime measurements presented in the following sections were conducted by collecting the fluorescence immediately after the splice to the excitation source with a 0.5 NA aspheric lens transverse to the doped fibre. Sample lengths were kept to 50 mm to minimise the effects of amplified spontaneous emission and re-absorption. Table 2 summarises the experimental configuration for each energy manifold. Note: for the fluorescence lifetime measurements the pump laser decay time was around 50 ns.
3. Fluorescence intensity measurements
The approach taken in this investigation was to use a double energy transfer process between Yb3+ and Tm3+ ions to further enhance the quantum efficiency of the S-band transition in Tm3+. The proposed double energy transfer process has the added advantage of populating the upper amplifying 3H4 manifold of Tm3+ whilst depopulating the lower amplifying 3F4 manifold, as shown in Fig. 1.
The double energy transfer mechanism involves the energy transfer of an excited ion in the 2F5/2 manifold of Yb3+ with a nearby ground state Tm3+ ion, which excites the ground state Tm3+ ion to the 3H5 manifold. Due to the close proximity of the 3F4 manifold, multi-phonon decay quickly relaxes any population in the 3H5 manifold to the relatively long lived 3F4 manifold. A second energy transfer from another excited Yb3+ ion can then populate the 3F2 and 3F3 manifolds of Tm3+. Again, multi-phonon decay quickly relaxes any population in the 3F2 and 3F3 manifolds to the 3H4 manifold. The non-resonant nature of each energy transfer step necessitates the assistance of phonons. The energy mismatch for each up-conversion step is given below for Tm3+/Yb3+ in YF3 :
Yb3+(2F5/2)+Tm3+(3H6)→Yb3+(2F7/2)+Tm3+(3H5) ΔE~1650 cm-1
Yb3+(2F5/2)+Tm3+(3F4)→Yb3+(2F7/2)+Tm3+(3F2,3) ΔE~1000 cm-1
From the absorption spectra of the fiber samples used in this investigation these mismatches are estimated to be 1124±4 and 822±33 cm-1, respectively. The reduction in the energy mismatches in silica glass may be attributed to the energy level broadening caused by the amorphous nature of the glass. The positive energy mismatch associated with these processes requires the emission of phonons to conserve energy.
3.1 Up-conversion pumping at 980 nm
When excited optically at 980 nm the fibers were found to emit blue luminescence that was clearly visible with the naked eye. The counter-propagating up-conversion luminescence spectrum for each fiber sample, between the wavelength range of 450 and 900 nm is shown in Fig. 2. It should be noted that the side fluorescence up-conversion spectrum was too weak to detect.
The up-conversion luminescence spectra shows three distinct fluorescence bands centred around 475, 650 and 780 nm, which are attributed to the transitions from the 1G4→3H6, 1G4→3F4, and (1G4→3H5 & 3H4→3H6) manifolds, respectively. Unfortunately, low fluorescence intensity levels prevented the counter propagating spectrum from the 3H4→3F4 and 3F4→3H6 transitions from being obtained. The three visible luminescence bands were found to increase with increasing Yb3+ concentration and since these bands are not observed in Tm3+ doped silica fibers under 980 nm excitation  it can be concluded that energy transfer is occurring between Yb3+ and Tm3+ ions.
To understand the origin of the luminescent bands the power dependencies of the up-conversion luminescence bands were studied as a function of the Yb3+ excited state population for a range of incident pump powers. The number of pump photons, n, required to produce a up-converted photon in the Tm3+/Yb3+ co-doped system can be determined easily, as the up-conversion intensity is proportional to the power, n, on the density of excited atoms in the 2F5/2 manifold of Yb3+. Since the fluorescence intensity at 1060 nm is directly proportional to the density of excited atoms in the 2F5/2 manifold of Yb3+, the number of pump photons required for a particular up-conversion process is readily obtained from the slope of the up-conversion intensity versus the fluorescence intensity at 1060 nm.
3.1.1 3F4 manifold of Tm3+
To establish the first energy transfer step, the fluorescence intensity at 1800 nm from the 3F4 manifold of Tm3+ was studied as a function of the fluorescence intensity at 1060 nm from Yb3+. Figure 3 shows the log/log plot of the 1800 nm luminescence versus the 1060 nm luminescence for the three fibers.
The equation used to fit the measured data in Fig. 3 was obtained by solving the rate equations describing the excited state populations of the 2F5/2 and 3F4 manifolds. These rate equations are given below, along with the energy manifold labeling which is shown in Fig. 4, where NYi represents the population of the i th Yb3+ manifold and NTj represents the population of the j th Tm3+ manifold. It should be noted that the populations of the 3H5 and 3F2,3 manifolds of Tm3+ have been ignored in this analysis due to the close spacing to the next lowest energy manifold; any population in these manifolds will decay non-radiatively to the longer lived 3F4 and 3H4 manifolds, respectively. τY1 represents the fluorescence lifetime of the 2F5/2 manifold of Yb3+, whilst τTj represents the fluorescence lifetime of the j th excited manifold of Tm3+. Wi represents the energy transfer co-efficient describing the interaction between Yb3+ and Tm3+ ions for steps i=1 to 3 and σTi,j represents the excited state absorption cross sections for transitions from the i th to jth manifold in Tm3+. Finally, σY01 is the absorption cross section of the ground to excited state transition of Yb3+ when excited at 980 nm by pumping intensity I. The rate equations describing the populations of the 2F5/2 manifold of Yb3+ and the 3F4 manifold of Tm3+ can be written as:
with the additional condition that:
where cY and cT represent the concentration of Yb3+ and Tm3+ ions, respectively.
It should be noted that Eq. (1) takes into account the assumption that the energy transfer up-conversion terms (i.e. W1NY1NT0, W2NY1NT1 and W3NY1NT2) are significantly less than the spontaneous decay term NY1/τY1. This assumption is verified by fluorescence decay results from the 2F5/2 manifold, reported in a later section. The second assumption made in this analysis is that, since only a small fraction of ground state Tm3+ ions are excited by the up-conversion mechanisms, NT0≈cT. The validity of this assumption is discussed further in the text. Equations (1) and (2) can be solved in the steady state, i.e. when dNY1/dt and dNT1/dt=0, to obtain an expression for NT1 as a function of NY1:
The solution shows that in the limit that W2NY1≪τT1 -1, a linear relationship exists between the population of the 3F4 and 2F5/2 manifolds. To test the validity of this solution, the measured data were fit to a linear expression in the form of y=Ax+B, where A and B were the fitting parameters. The excellent agreement, as shown in Fig. 3, between the fit and measured data over the entire pump power range for all fiber samples verifies that under 980 nm excitation, the 3F4 manifold of Tm3+, is populated by the energy transfer process:
It can also be concluded from the analysis that the energy transfer up-conversion rate, W2NYi, which depopulates the 3F4 manifold is much less than the spontaneous decay, τT1 -1.
3.1.2 3H4 manifold of Tm3+
The second energy transfer step from the 3F4 to the 3F2,3 manifolds could not be determined from the luminescence at 810 nm in this sample set as, upon inspection of the Tm3+ energy level diagram, see Fig. 1, luminescence from the 1G4→3H5 and 3H4→3H6 transitions both result in fluorescence bands around 810 nm. Since blue luminescence has been observed in these fiber samples it can be concluded that excited ions have been promoted to the 1G4 manifold of Tm3+. With this in mind, the 810 nm luminescence should show the properties associated with the populating mechanisms for both energy manifolds and hence an independent measurement of the 3H4 manifold population cannot be obtained. This complication could be avoided by studying the luminescence properties of the 1480 nm transition; unfortunately the luminescence in this wavelength region was too weak to be detected, due to the low Tm2O3 concentrations and limited pump powers available. A short discussion of the 810 nm luminescence is given following the exploration of the 1G4 manifold. This order has been chosen to aid understanding.
3.1.3 1G4 manifold of Tm3+
The populating mechanism responsible for the blue luminescence from the 1G4 manifold can be established by studying its dependence on the 1060 nm luminescence from Yb3+. The fluorescence at 650 nm from the 1G4→3F4 transition could also be used to study the mechanism populating the 1G4 manifold. However the branching ratio in silica glass for the 475 nm luminescence is 0.51 compared to 0.069 for the 650 nm luminescence , therefore the luminescence intensity of the 475 nm luminescence is at least 7 times stronger. Figure 5 shows the log/log plot of the 475 nm luminescence as a function of the Yb3+ luminescence at 1060 nm for a range of input pump powers.
The equation used to fit the measured data in Fig. 5 was determined from the solution to the rate equation describing the population of the 1G4 manifold. Since the populating mechanism of the 3H4 manifold could not be determined from the 810 nm luminescence data, it was assumed that a second energy transfer up-conversion process, involving the energy exchange between an excited Yb3+ ion and an excited Tm3+ ion in the 3F4 manifold, populates the 3H4 manifold under 980 nm excitation, as shown in Fig. 1. Based on this assumption the rate equation describing the population of the 3H4 manifold and 1G4 manifold of Tm3+ can be written as:
Equation (7) assumes that the 1G4 manifold is populated by a third energy transfer up-conversion process involving an excited Yb3+ ion and an excited Tm3+ ion in the 3H4 manifold. This assumption was made on the basis of the significant body of work which attributes blue luminescence to the successive 3 step energy transfer up-conversion process [7, 9, 20–22].
By solving the rate equations for the respective manifolds in the steady state, expressions for the population of the 3H4 and 1G4 manifolds can be obtained as a function of Yb3+ population. These solutions are:
Both expressions contain a saturation term, which plays a role only when the energy transfer up-conversion rate is comparable to the spontaneous decay rate from the 3H4 manifold. It has been established that the energy transfer rate of the second energy transfer up-conversion (ETU) step (W2 NY1) is much less than the spontaneous decay of the 3F4 manifold; since the decay rate of the 3H4 manifold is an order of magnitude greater than the 3F4 manifold, it is suggested that the ETU rate of the third step from 3H4→1G4 (W3 NY1) is much less than the spontaneous rate from the 3H4 manifold (τT2 -1). Therefore the steady state solutions for the 3H4 and 1G4 manifolds can simplify to:
This results in the population of the 3H4 manifold being dependent on the square of the 2F5/2 population whilst, the 1G4 manifold population is dependent on the cube of the 2F5/2 population. Equation (11) was used to fit the measured data shown in Fig. 5. The fit describes the data accurately at low pump powers, but fails to describe the data at higher pump powers, for all three fiber samples. Figure 5 shows that the 475 nm luminescence continues to grow after the 1060 nm fluorescence begins to saturate. This behaviour cannot be described solely by the successive three step ETU process. The ETU process is inherently linked to the population of the excited states; hence as the 2F5/2 manifold begins to saturate, so too will the other successive excited states of Tm3+. The fact that the 475 nm luminescence continues to grow indicates that another populating mechanism is occurring within the co-doped system which is not simply dependent on the excited state populations, but also the incident pump power. The only energy transfer process which fulfils this criterion is excited state absorption (ESA), as it involves the energy exchange of a pump or fluorescent photon with an ion in an excited state. Since ESA requires only one accepting ion, the process is concentration independent and scales with incident pump or fluorescence power, which is an important difference when compared to ETU. Although ESA of Tm3+ ions has been frequently reported in the literature [23–25], this has not been the case for Tm3+/Yb3+ co-doped systems. For ESA to occur in the Tm3+/Yb3+ co-doped system, excited Tm3+ ions are required to absorb incident pump photons at 980 nm and/or fluorescing photons at 1060 nm. Of the possible ESA transitions which can occur in Tm3+, only two are possible in the Tm3+/Yb3+ co-doped system under 980 nm excitation, namely the 3F4→3F2,3 and 3H4→1G4 transitions. The ESA cross sections for these two transitions have been calculated  and are shown in Fig. 6, with the 3F4→3F2,3 transition exhibiting stronger absorption strengths compared to the 3H4→/1G4 transition. However, of most interest, is the location of these absorption peaks in regard to the energy available from the incident pump and fluorescing photons. Included in Fig. 6 is the emission spectrum of Yb3+ under 980 nm excitation; the position of this fluorescence band indicates which ESA transition of Tm3+ has the greatest spectral overlap with the energy available from the pump and fluorescing photons.
The 3F4→3F2,3 transition is found to have the greatest overlap with the Yb3+ fluorescence but, more importantly, it is found to have a larger absorption cross section at the pump wavelength, 980 nm. The absorption cross section at the pump wavelength is the most critical parameter in this case as the number of incident pump photons is many orders of magnitude greater than the number of fluorescent photons. The ESA cross section of the 3F4→3F2,3 transition at 980 nm in silica glass is estimated to be 5.2×10-28 m2, compared with 5.4×10-36 m2 for the 3H4→1G4 transition. This comparison suggests that the 3F4→3F2,3 transition is the most favourable ESA transition in the co-doped system under 980 nm excitation.
If the 3F4→3F2,3 ESA transition is now considered in the populating dynamics of the Tm3+/Yb3+ co-doped system, the rate equation describing the population of the 3H4 manifold would be given by Eq. (12); bearing in mind that the previous analysis determined that the energy transfer rates W1 NY1, W2 NY1, and W3 NY1 are much less than the spontaneous decay rates from the 3F4 and 3H4 manifolds, respectively.
Since ESA from the 3H4→1G4 manifold is extremely unlikely under 980 nm pumping, the rate equation describing the population of the 1G4 manifold would remain the same as that stated in Eq. (7). It should be noted that the inclusion of the (3F4→3F2,3) ESA term in the analysis also has implications on the rate equation describing the population of the 3F4 manifold. However the linear dependence of the 1800 nm luminescence on the 1060 nm luminescence indicates that the ESA term is much less than the spontaneous decay rate from the 3F4 manifold. Equations (12) and (7) can be solved in the steady state to obtain an expression for NT3 as a function of NY1, namely:
Equation (13) is similar to the expression obtained for the successive three step ETU process except for the additional term which results from the inclusion of ESA. The measured 475 nm versus 1060 nm luminescence data were then fitted with the new expression in the form of y=Ax 3+Bx 3/(1 - Cx), where A, B and C were the fitting parameters. The resulting fits are shown in Fig. 7 along with the R2 value which provides an indication of the quality of the fit. The A, B and C fitting parameters are listed in Table 3 for each fiber sample along with their uncertainty.
Although the physical parameters associated with the A, B and C terms cannot be obtained from the fitting parameters due to the coupling of several unknown parameters and proportionality constants, the uncertainty in the fitting parameters validates the model and the quality of the fit for all fiber samples. This establishes for the first time the 3F4→3F2,3 ESA process as a populating mechanism in Tm3+/Yb3+ co-doped silica glasses under 980 nm excitation. It can therefore be concluded that the populating mechanisms involved in promoting Tm3+ ions to the 1G4 manifold in Tm3+/Yb3+ co-doped silica glass under 980 nm excitation are:
Step 1 - Yb3+(2F5/2) + Tm3+(3H6)→Yb3+ (2F7/2)+Tm3+ (3H5→3F4)
Step 2 - Yb3+(2F5/2)+Tm3+(3F4)→Yb3+(2F7/2)+Tm3+(3F2,3→3H4) & (980 nm photons)+Tm3+(3F4)→Tm3+ (3F2,3→3H4)
Step 3 - Yb3+(2F5/2)+Tm3+(3H4)→Yb3+(2F7/2)+Tm3+(1G4)
Although the quantum efficiency of the S-band transition cannot be quantified in this sample set, the spectroscopic study of the system has established two energy transfer processes that act to populate the upper amplifying 3H4 manifold whilst depopulating the lower amplifying 3F4 manifold, under 980 nm excitation.
3.1.4 810 nm luminescence
As discussed previously, the up-conversion luminescence at 810 nm is attributed to the presence of two overlapping luminescence bands, one from each of the 1G4 and 3H4 manifolds. In this case, the luminescence at 810 nm should exhibit the characteristics of both excited manifolds with the 3H4 manifold dominating over the 1G4 manifold at low excitation powers. Figure 8 shows the log/log plot of the 810 nm luminescence as a function of the Yb3+ luminescence at 1060 nm over a range of input pump powers for each fiber sample.
The non-linear nature of the log-log plot suggests the presence of more than one up-conversion process. At low pump powers the measured data exhibits a slope of 2, as seen in Fig. 8, whilst at high pump powers >50 mW the slope exceeds 3. The non-linear behaviour is greatest in the TmYb-3 sample which has the highest 1G4 manifold population. This provides further evidence of the two overlapping transitions from the 1G4 and 3H4 manifold and is consistent with the rate equation model proposed here. Unfortunately, the large number of unknown parameters prevents the rate equation model from being fitted to the measured data with any degree of certainty. A more accurate account of the population dynamics involved in this luminescence band can be obtained by studying the fluorescence decay characteristics after the pump excitation has been removed.
4. Fluorescence lifetime measurements
The final stage in the spectroscopic study of the Tm3+/Yb3+ co-doped system was to investigate the fluorescence lifetimes of the excited states of Tm3+ and Yb3+. The fluorescence lifetimes of the 2F5/2, 3F4, and 3H4 manifolds were studied under direct excitation at the appropriate wavelength. In addition, the 3F4, 3H4 and 1G4 manifolds of Tm3+ were studied under in-direct pumping at 980 nm.
4.1 Direct pumping
4.1.1 2F5/2 manifold of Yb3+
The decay characteristics of the 2F5/2 manifold of Yb3+ were studied in the Tm3+/Yb3+ -co-doped fibers by directly exciting Yb3+ ions to the 2F5/2 manifold at 980 nm. Figure 9 shows the normalised measured decay waveform from the 2F5/2 manifold under 980 nm excitation. The fluorescence decay was measured using 50 ms pulses at a repetition rate of 10 Hz.
The solid line shown in Fig. 9 was obtained by fitting a single exponential function to the measured data. The single exponential fit is in excellent agreement with the measured waveform. The 1/e lifetimes obtained from the single exponential fit are listed in Table 4 for the three Tm3+/Yb3+ -co-doped fibers.
The measured lifetimes of the three alumino-silicate samples reported in Table 4 are consistent with those reported for Yb3+-doped alumino-silicate glass , which provides strong evidence that the assumption used in the rate equation analysis that the energy transfer terms W1NY1NT0, W2NY1NT1, and W3NY1NT2 are much less than NY1/τY1 is valid. This is also supported by the lack of lifetime dependence on the Yb2O3 concentration.
4.1.2 3F4 and 3H4 manifolds of Tm3+
The decay characteristics of the 3F4 and 3H4 manifolds of Tm3+ were studied by exciting the manifolds directly at 1586 and 780 nm, respectively. The luminescence decay from both excited manifolds was characterised by a single exponential function. A more rigorous treatment of the decay characteristics of these manifolds in Tm3+doped silica glass has been done in . In that work the decay from the 3H4 and 3F4 manifolds under direct excitation was shown to exhibit a degree of non-exponentiality which was attributed to the distribution of possible multi-phonon decay rates in the glass matrix. The measured decay waveforms in this work were found to exhibit similar degrees of non exponentiality than those observed in Tm3+ doped silica fibers. Hence, the non exponential nature of the decay can be attributed to the host matrix rather than possible energy transfer processes between Yb3+ and Tm3+ ions. The single exponential fits applied in this work allow comparisons to be made between each fiber sample and aid comparison between the measured lifetimes reported the literature. The 1/e lifetime of the 3F4 and 3H4 manifolds are listed in Table 5, respectively.
The fluorescence lifetimes of both excited manifolds are consistent with those reported in Tm3+-doped alumino-silicate fibers . Sample TmYb-3 did however exhibit a considerable reduction when compared to the other Tm3+/Yb3+ samples. This reduction is attributed to the glass host rather than potential energy back transfer processes and cross relaxation effects. Previous work on singly doped Tm3+ alumino-silicate has shown that the lifetime of the 3F4 and 3H4 manifolds are dependent on the amount of Al2O3 present in the fiber core . In that work the fluorescence lifetime of both excited manifolds were found to decrease with decreasing amounts of Al2O3. This is consistent with results presented in Table 5 as the TmYb-3 sample contains ~15% less Al2O3 in the core when compared to the other two co-doped samples.
4.2 In-direct pumping
The in-direct excitation of the 3F4, 3H4 and 1G4 manifolds of Tm3+ has been demonstrated in the previous section under continuous wave excitation at 980 nm. In this section, the fluorescence decay characteristics of the excited manifolds are studied under pulsed excitation. The time dependent rate equation model established in the previous section for continuous wave pumping can be carried over into the fluorescence decay analysis to describe the excited state population over time, allowing the validity of the model to be tested under two energy excitation regimes.
4.2.1 3F4 manifold of Tm3+
The fluorescence decay of the 3F4 manifold under in-direct excitation at 980 nm is shown in Fig. 10 for the TmYb-3 sample. The decay characteristics of the 3F4 manifold showed considerable differences to those obtained under direct excitation.
The fluorescence decay was described well by a single exponential function, as seen in Fig. 10. The characteristic lifetime of the manifold was found to increase by a factor of two on average, when compared to the lifetimes obtained under direct pumping and were comparable to the fluorescence lifetime of the 2F5/2 manifold of Yb3+ (see Table 6).
The considerably large error associated with the single exponential fit was a result of the poor signal to noise ratio of the 1800 nm luminescence under in-direct pumping, rather than the inability of the fit to describe the waveform accurately. The effective doubling of the fluorescence lifetime of the 3F4 manifold under in-direct pumping provides strong evidence that efficient energy transfer is occurring from the 2F5/2 manifold of Yb3+ to the 3F4 manifold of Tm3+, as the decay of the 3F4 manifold of Tm3+ is being dictated by the longer lived fluorescence lifetime of the Yb3+ excited state. It also reaffirms the conclusions draw in Section 3.1.1 that the decay rates associate with ETU and ESA are much less than the spontaneous decay rate of the 3F4 manifold.
4.2.2 1G4 manifold of Tm3+
The in-direct excitation of the 1G4 manifold of Tm3+ can be achieved by the series of successive energy transfer processes as discussed in the previous section. The fluorescence decay from the 1G4 manifold under in-direct pumping at 980 nm is shown in Fig. 11 for the TmYb-1 sample. The measured waveforms for all samples were described adequately by a single exponential fit. The characteristic lifetimes obtained from the single exponential fits are listed in Table 7 for the three co-doped samples.
The single exponential nature of the 1G4 decay provides information regarding the mechanisms dominating the 1G4 manifold population after the pump excitation has been removed. The time dependent rate equation describing the population of the 1G4 manifold is given by:
Although the solution to Eq. (14) cannot be obtained without the knowledge of NT2(t), it is clear that the solution will contain several exponential components each with their own amplitude and characteristic time constant, resulting in a non-exponential decay waveform. However, the experimentally observed fluorescence decay waveforms were sufficiently single exponential in nature with characteristic time constants consistent with the 1G4 manifold lifetime reported in Tm3+-doped silica fibers [30, 31]. It can therefore be concluded that the energy transfer rate into the 1G4 manifold is much less than the spontaneous decay. Therefore, the 1G4 manifold decay can be described by the single exponential function:
This is not a surprising result; the lifetime of the 3H4 manifold is relatively short and hence the likelihood of an excited (3H4) Tm3+ ion interacting with an excited (2F5/2) Yb//3+ ion after the pump excitation has been removed is extremely low. The other important point is that the lifetime of the 1G4 manifold remains constant over the Yb2O3 concentration range studied here, providing further evidence that the energy transfer rate is negligible compared to the spontaneous decay. This also suggests that there is negligible energy back transfer from the 1G4 manifold of Tm3+ to the 2F5/2 manifold of Yb3+.
4.2.3 810 nm luminescence
The fluorescence decay properties of the 810 nm luminescence were studied in an effort to verify the existence of the two overlapping transitions from the 3H4 and 1G4 manifolds. The fluorescence decay of the 3H4 manifold under in-direct pumping at 980 nm is shown in Fig. 12 for the TmYb-1 sample.
The decay waveforms at 810 nm were described accurately by a double exponential function in the form of y=(1-A) exp(-x/B) + A exp(-x/C), where A was the fitting parameter describing the amplitude of the second exponential and B and C were the fitting parameters used to obtain the two characteristic lifetimes. The two characteristic lifetimes obtained from the double exponential fit are listed in Table 8 for the three co-doped fibers.
The cause of the double exponential decay is attributed to the presence of two overlapping transitions in the 810±10 nm window. It has been proposed throughout this paper that the 1G4→3H5 transition spectrally overlaps the 3H4→3H6 transition. The fluorescence decay in such a case would exhibit the characteristics from each energy manifold. It was established in the previous section, that the 1G4 manifold decays in a single exponential form with a characteristic lifetime around ~300 µs. Assuming the 3H4 manifold exhibits similar characteristics to the 1G4 manifold, i.e. the energy transfer rates which populate and depopulate the manifold are much less than the spontaneous decay, the resultant decay would be a double exponential with two characteristic time constants equivalent to the lifetimes of the 3H4 and 1G4 manifolds. The slow component of the 810 nm luminescence decay is in excellent agreement with the measured 1G4 manifold lifetime, whilst the fast component of the 810 nm decay is of the order of the 3H4 manifold lifetime. The 1G4 manifold contribution to the 810 nm luminescence may explain the increase in the amplitude of the slow component of the decay with increasing Yb2O3 concentration. The 1G4 luminescence intensity was found to increase at a greater rate than the 3H4 luminescence with increasing Yb2O3 concentration (refer to Fig. 2), and hence the contribution the 1G4 manifold makes to the overall luminescence at 810 nm increases with increasing Yb2O3 concentration.
The spectroscopic study of the Tm3+/Yb3+-co-doped system in alumino-silicate glass identified up-conversion luminescence in the visible and near infra-red regions under 980 nm excitation. The steady state rate equation analysis established two energy transfer processes capable of depleting the 3F4 manifold and populating the 3H4 manifold. A double energy transfer up-conversion process and an excited state absorption process were identified as populating mechanisms in the co-doped system under 980 nm excitation. These two processes are the key to the Tm3+/Yb3+-co-doped system becoming an efficient S-band amplifying source. The other significant result to come from the analysis was that there was little evidence of energy back transfer from Tm3+ to Yb3+ ions under the direct pumping of the 3F4 and 3H4 manifolds.
A drawback of the Tm3+/Yb3+-co-doped system is the presence of a third energy transfer up-conversion process which transfers population from the upper amplifying 3H4 manifold to the 1G4 manifold. The rate of quenching of the 3H4 manifold has not been identified in this analysis; however from the fluorescence lifetime results it is considered to be significantly less than the ~3257 s-1 decay rate of the 1G4 manifold.
This work was supported by the Australian Research Council, and Centre National de la Recherche Scientifique, in France.
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