Abstract

We present a theoretical model to thermal (TL) and population (PL) lenses effects in the presence of Auger upconversion (AU) for analysis of Nd3+ doped materials. The model distinguishes and quantifies the contributions from TL and PL. From the experimental and theoretical results, the AU cannot be neglected because it plays an important role on the excited state population and therefore on the temperature and polarizability difference between excited and ground states. Considering the extensive use of these techniques, the model presented here could be useful for the investigation of materials and also to avoid misleading analysis of lenses transients.

© 2015 Optical Society of America

1. Introduction

Thermal lens (TL) spectrometry is a highly sensitive photothermal technique that is used for the thermal and optical analysis of materials [1,2 ]. It relies on the measurement of the laser-induced local heating in a sample by probing the change in the optical path, mainly by the radial refractive index gradient, known as the TL effect. The study of thermo-optical properties is generally done using the time resolved TL method. However, it is well known that some non-linear effects may also be present in the illuminated volume. One example is the photon-induced population change in the ground and excited states that can alter the refractive index according the excitation intensity profile [1,3,4 ]. This effect is referred to as population lens (PL), and it may mainly be important in rare-earth doped optical solids [1,3–6 ]. Indeed, the study of nonlinear properties of photonics materials is particularly important because standing waves, principally in laser cavities, produce self-focusing, temporal and spatial self-phase modulation, and light-induced gratings that cause effects like hole-burning [1,7,8 ].

The laser-induced optical path change produces lens-like optical elements into the sample. Each of these optical elements introduces an additional phase shift that can be probed by a laser beam that is passed through the illuminated volume of the sample and exhibits a corresponding on-axis intensity change. Both the PL and TL effects are generally present, appearing as a complex transient signal. Theoretical and experimental efforts have been made to describe properly and to discriminate these effects [1,8–11 ]. When the lifetime () of the excited state is so shorter than the TL formation time (tc), the transient, in principle, contains only TL effect. This occurs, for instance, with the Nd-doped NAB crystal that has a lifetime of ~20 µs [12]. The opposite occurs to Ruby crystal because tcτ [3,13 ]. However, when tc is of the same order of magnitude of τ both effects will be present in the transient. This situation occurs for many Nd3+ and mainly Yb3+ doped materials and when the PL and TL transients have the same sign (both either positive or negative), the interpretation could be difficult and mistakes can be made easily. Indeed, we have recently shown that, for Yb3+ doped systems, the population lens can be accounted in the framework of the TL transient [11].

Among the intrinsic processes that can relatively impact laser action is the energy transfer upconversion, also known as Auger upconversion (AU) [12,14–18 ]. It occurs when two neighbor ions, both at the same metastable level, interact non-radiatively such that one of them is transferred to a higher excited state while the other goes to a lower state. Since this process leads to a reduction of the excited state population and lifetime, and, therefore, changes the PL and the generated heat (TL), it has been evaluated using the PL and TL techniques [12,14,16–18 ]. In this way, it is also desirable to study the influence of the AU on the transient signal of the TL + PL spectrometry. In this letter, we present a theoretical model describing the cw laser induced time-resolved lens spectrometry with both TL and PL effects, and including the AU process, for Nd3+ doped systems.

2. Results

The modeling is based on the rate equation solution for the ion excited-state population Nex(g,z,t). In a conventional mode-mismatched TL experiment, a cw TEM00 Gaussian beam excites a sample of thickness L, producing a TL signal. A weak TEM00 Gaussian beam, collinear with the excitation beam, is used to probe the TL. The temporal dependency of the temperature gradient, T(r,z,t), is given by the diffusion equation [2,11 ]:

T(r,z,t)/tD2T(r,z,t)=Q0φe2r2/woe2eAez
with Q0=2Pe Ae/ρCπω0e2. ω0e is the excitation beam radius into the sample position, Pe is the excitation power, Ae is the linear absorption coefficient at the excitation wavelength, φ is the fraction of absorbed energy converted into heat, D = kT/ρC is the thermal diffusivity, ρ, C, and kT are the mass density, specific heat, and thermal conductivity, respectively. For Nd3+ ions, one can write φ=1η0  (λex/λem), with η0 being the fluorescence quantum efficiency, λex 800 nm and λem 1060 nm are excitation and average emission wavelengths, respectively [1]. In the presence of AU an additional decay rate (WAU) appears changing η0 of the emitter level to η(r,t)=η0/[1+β Ne (r,t)/NT], i.e., η presents spatial and temporal dependences [16], β is a dimensionless parameter that determines the strength of the AU process as shown below. Therefore, before we study the thermal contribution to the transient signal, we must first investigate the excited state population.

For Nd3+ doped systems, the excited-state population taking into account AU is given by the following rate equation [14]:

Net=RPNT(RP+1τ)NeγNe2
in which NT is the total ion concentration, τ is the 4F3/2 excited-state lifetime in absence of AU, RP=σabs I(r,z)/E is the pumping rate, σabs is the absorption cross-section, I(r,z) is the beam intensity profile, E is the energy of the excitation photon, and γ is the AU parameter.

The solution of Eq. (2), considering that Ne(r,z,t)=Ne(r,t) eAez, is given by:

Ne(r,z,t)=NT{2  S Tanh(Δ(S,β)2τt)(S+1)Tanh(Δ(S,β)2τt)+ Δ(S,β)}eAez
where S=RPτ=I(r,z=0)/Is=S0 e2r2/ω0e2  is the saturation parameter, in which S0=I0/Is, I0=2Pe/(πwoe2), and the saturation intensity Is=E/σabsτ; Δ=[(S+1)2+4βS] is a term used for simplification, and β=γ.τ.NT. Note that for t, Ne tends to the steady-state population, Ne(r,z,t)=[(S+1)+Δ]NT/2β. Therefore, without AU (γ=0), the solution to Eq. (2) is Ne(g,z,t)=NT{[S/(S+1)][1et(S+1)τ]}eAez.

As mentioned before, if the change of η due to the additional decay rate is taken into account, using Eq. (3) we can now study the AU process effect on the temperature distribution. As the results presented in Fig. 1(a) , the exact numerical temperature profile can be well described by using in the diffusion equation the steady solution for Ne(r,z,t), and, in addition, by replacing, S(r)S0/2. This procedure gives the resulting approximated solution of the diffusion equation:

T(r,z,t)=2PeAeπρCω0e2φ(S0,β)eA_e z0te2r2/ωoe21+2ξ/tc1+2ξ/tc dξ
where, φ(S0,β)=1(2η0 (λex/λem  ))/[2+(Δ(S0/2,β) )(S0/2+1) ], and the characteristic thermal time is tc=ω0e2/4D. The AU process increases the thermal effects. This increasing is non-negligible as can be seen in Fig. 1(a). Therefore, it is necessary to include it in calculating the phase shift due to TL.

 figure: Fig. 1

Fig. 1 (a) Radial dependence of the laser induced temperature profile, T(r,0,t), for different exposure times. Dashed and solid lines are analytical solutions, Eq. (4), without and considering AU process, respectively. Open circle are the exact numerical solution from the diffusion Eq. (1) with AU process. β=10 and the other parameters listed in Table 1 (Part 1) were used in simulations. I(t) dependence on θel for (b) diverging TL (ZBLAN:Nd fluoride glass) and (c) converging TL (Q-98:Nd phosphate glass). θel was artificially varied from 0 to 4. All these results of the right figure are for β = 0 (without AU).

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The probe beam propagating through the illuminated volume of the sample has its wave front slightly distorted. This distortion can be expressed in terms of phase shifts. The total phase shift is the superposition of the individual phase shifts caused by the PL and TL effects:ϕ(g,t)=ϕPL(g,t)+ϕTL(g,t) . These phase shifts are expressed by:

ϕTL(g,t)=2πλp0L[S(r,z,t)S(0,z,t)]dz
where S(r,t) is the optical path change induced by thermoelastic effect [19]. The population lens contribution is given by:
ϕPL(g,t)=2πλpoLckNe(g,z,t)dz
here λp is the probe beam wavelength, ck=2πfL2Δαp/no, fL=(no2+2)/3 is the Lorentz local field correction factor, Δαp is the polarizability difference between the excited and ground states of Nd3+ ions [23]. Note that the r dependence of Ne(r,z,t) [Eq. (3)] is seen in S because I(r,z=0)=Ioe2r2/woe2. With the help of Eq. (3) and (4) , the TL and PL phase shifts can then be given respectively by [19]:
ϕTL=θthφ(S0,β)0χ(α,L)eω0e2α2/8×(1e14ωoe2α2ttc)[J0(αω0emg)1]α1dα
and
ϕPL=θel(2STanh(Δ(S,β)2τt)(S+1)Tanh(Δ(S,β)2τt)+Δ(S,β))
in which θth=Pe Ae Leff/(kTλP) and θel=2πck Leff NT/λP, with Leff=L(1Ae L/2) being the sample's effective length and L its thickness. The factor (1Ae L/2) accounts for the effect of moderated optical absorption. Jn(x) is the Bessel function of first kind. The function χ(α,L) is given by:
χ(α,L)=nT+4Lα(n1)(1+ν)αTh(α,L)+n3EαT4(1ν)[(q+q)(4[qν+q(2+ν)]h(α,L)Lα)]
where h(α,L)=[Cosh(Lα)1]/[Lα+Sinh(Lα)]. In Eq. (9) n/T is the temperature coefficient of refractive index,  kT is the thermal conductivity, ν is the Poisson's ration, Y is the Young's modulus, αT is the thermal expansion coefficient, q and q refer to the piezo-optic coefficients for stresses applied parallel and perpendicular to the polarization axis, respectively. In the limit of  L 0, χ(α,L) recovers the form for the temperature coefficient of the optical path length change in the plane-stress approximation, usually denoted by ds/dT [1,19 ].

The phase shifts due to the TL and PL effects can then be numerically integrated and the intensity on the center of the probe beam spot at the detector plane, which is positioned at the far field, can be written as I(t)=I(0)|0exp{(1+iV)giΦth(g,t)iΦPL(g,t)} dg|2, with V = Z1/Zc and I(0) as the intensity signal at t = 0. Zc is the confocal distance of the probe beam and Z1 the distance between the waist of the probe beam and the sample. The parameters from the setup are m = 13, V = 1.73, ω0e=40 μm, and λp=632.8nm. Table 1 (Part 1) presents the values of the physical properties for ZBLAN:Nd and Q-98:Nd glasses from the literature, which are fixed in this work.

Tables Icon

Table 1. Part 1: Physical properties of the samples. Parameters for ZBLAN and Q-98 are from references [1,17–22]. Part 2: Parameters obtained from the computational fits for ZBLAN:Nd and Q-98:Nd samples.

The contributions of the PL and TL effects on the transient, without AU (β = 0), can be seen in Fig. 1(b) and 1(c) for respectively a representative diverging TL (ZBLAN:Nd) and a converging TL (Q-98:Nd). All other parameters are kept fixed with exception of the strength of PL, that could be modified by increasing θel. Note that θel=0 represents a pure thermal contribution. Similarly to what we have found for the Yb3+ doped systems [24], the additional PL contributions appear as an overshoot of the initial signal at short times, tending to follow the TL transient afterwards in the converging TL effect. On the other hand, when a diverging TL is present, it appears more intensively modifying inclusive the PL response (at the short time). Indeed, it can be observed that both TL and PL effects could affect significantly the signal along all transient. However, the effect is more marked when one is positive and the other is negative. In order to study the influence of the AU on the TL + PL transient we consider both Eqs. (7) and (8) and compare the transients. Furthermore, we also investigate how the thermal diffusivity affects the transient. The notable influence of the AU shown in Fig. 2(a), 2(b), 2(c), and 2(d) only confirms what we expected, since, according to this Figure, the AU plays an important role in the temperature distribution. However, a detailed analysis is necessary to exactly evaluate the AU process on both effects, mainly when both are present in the same transient. Naturally the AU contribution to PL is more easily noted than to the TL when observing the Eq. (2), but it also makes itself present in the TL signal changing φ by means of η that now appears as a function of Ne. The question is: what are the AU contributions on the TL and PL transients?

 figure: Fig. 2

Fig. 2 [(a), (b), (c), and (d)] - Normalized TL signal transients for a typical value of θel=4, Auger upconversion parameter varying from β = 0 up to β = 20, and thermal diffusivity of [(a) and (b)] D=3×107m2/s and [(c) and (d)] D=3×107m2/s, typics of glasses and crystals, respectively. In [(a) and (c)] and [(b) and (d)] were used other representative parameters given in Table 1 (Part 1), which lead to positive and negative TL signals. [(e) and (f)] - Typical normalized experimental lensing signals for (e) ZBLAN:Nd (1.0 mol%) and (f) Q-98:Nd (1.0 wt.%) samples. Continuous lines denotes least-squares curves fit using I(t) equation. The excitation power for these transients was fixed at Pin = 200 mW. The obtained parameters are given in Table 1 (Part 2).

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It can also be noticed that as D increases, both the thermal and population lens formation times decrease (which is evident by the different scales used on the left and right sides of Fig. 2 [(a), (b)] and [(c), (d)]. Also, when β increases the peaks of the graph occur faster (see the diverging lens case in the inferior part). This tell us that, if β and D are large enough, thus we can make the population effects take action under a very short period of time. However, the AU effect is so strong that it could not be neglected in the transient analysis of both TL and PL.

In order to validate the theoretical model here developed, experimental results were obtained to Nd3+ doped glass samples of fluoride (ZBLAN) and phosphates (Q-98) doped respectively with 1.0 mol% and 1.0 wt.%. Two representative experimental transients are displayed in Fig. 2(e) and 2(f). As excitation laser, it was used a Ti:sapphire laser tuned at 792 nm and 802 nm for ZBLAN and Q-98 samples, respectively. A low power HeNe laser at 632.8 nm was used as probe beam. Note that the signal of the PL effect appears in both cases, following the same behavior presented in the simulations. As one can see, the non-linear adjusts based on the theoretical model presented here fits very well with the experimental data.

To estimate the magnitude of PL and TL contributions, including the AU effect, several transients with different pump powers were obtained and adjusted with the proposed model. As we can see in Eqs. (3)-(6) , the model allows the access to a large number of physical properties. However, in a multiparameter regression analysis the output could present large fluctuation, which can induces error in the results. To minimize this fluctuation, we kept fixed some parameters by using values obtained from the literature (see Table 1 – Part 1). The parameters obtained by the regression analysis were θth, θel, D and β, and by means of these kT and Δαp. As we can see from Eq. (7), the effects of the absorbed power and AU process appear as the product θthφ(S0,β) in the TL phase shift. This induces an additional difficult in the data fitting. As showed in Fig. 3 , the fitting of the experimental data with inappropriate values for β leads to a wrong nonlinear behavior of the curve θth versus Pe. The strategy used was thus to change the parameter β in order to obtain the best linear fit to the curve θth versus excitation power. Note that θel does not depend on Pe.

 figure: Fig. 3

Fig. 3 θth versus the excitation power Pe for ZBLAN:Nd sample obtained from the experimental data fitting with β = 0, 2, and 5. Dashed lines are guides for the eye. The fitting parameters obtained for β = 2 were θth/Pe = (810 ± 50) × 106 K/W, θel=(1.5±0.1), and D = (2.7 ± 0.3) × 10−7 m2/s.

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Figure 3 shows the results to θth versus Pe obtained with ZBLAN:Nd by means of experimental data fitting with different values of AU parameter β. The β=2 for ZBLAN:Nd glass, corresponds to the linear behavior of θth (R2=0.999. In this case, the constant values of θth/Pe proves its definition (θthPe=AeLeffkTλP). Neglecting the AU process (β=0) or an overestimation of the effect (β=5) induces nonlinearity in the curve. For the best value of β, the corresponding parameters D, θel, and θth were determined. Equivalent procedure was performed in the Q-98:Nd glass giving the best value of β1.2. Several tests were made, leading to a confidence of around 70% in the values of AU parameter. A small discrepancy with the literature, in which β=3.66 and 1.54 for ZBLAN:Nd and Q-98:Nd, respectively, could be justified by the fact that the PL contribution on the phase shift was neglected in previous works [1, 9, 14, 18 ]. The values for diffusivity are in good agreement with those reported in the literature [1,19–22 ]. Table 1 (Part 2) summarizes all the values obtained in the present work.

3. Conclusions

In this letter we present a theoretical model to distinguish between population and thermal contributions to the laser-induced optical path change, including the influence of the Auger Upconversion (AU) effect. From the results, it is evident that the AU cannot be so easily neglected and that it plays an important role on the temperature distribution and, therefore on the TL spectroscopy. Considering that the studied effects are usually present in ions doped optical materials and the combination of wide use of materials and lasers, the model presented here may be useful in the materials´ characterization as well as to avoid misleading analysis of lenses´ transients.

Acknowledgments

The authors gratefully acknowledge the financial support from Brazilian agencies: PRONEX/FAPEAL (Project 2009-09-006), FINEP (Financiadora de Estudos e Projetos), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico through the grants INCT NANO(BIO)SIMES and Project Universal no 483238/2013-9), CAPES (Coordenadoria de Aperfeiçoamento de Pessoal de Ensino Superior) – Project PVE A077/2013, and Fundação Araucária. The research of E. C. Ximendes is supported by CNPq. The Q-98:Nd phosphate sample was provided by the company Kingre Inc.

References and links

1. C. Jacinto, D. N. Messias, A. A. Andrade, S. M. Lima, M. L. Baesso, and T. Catunda, “Thermal lens and Z-scan measurements: thermal and optical properties of laser glasses - a review,” J. Non-Cryst. Solids 352(32–35), 3582–3597 (2006). [CrossRef]  

2. J. Shen, R. D. Lowe, and R. D. Snook, “A Model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. 165(2–3), 385–396 (1992). [CrossRef]  

3. S. M. Lima and T. Catunda, “Discrimination of resonant and nonresonant contributions to the nonlinear refraction spectroscopy of ion-doped solids,” Phys. Rev. Lett. 99(24), 243902 (2007). [CrossRef]   [PubMed]  

4. D. N. Messias, T. Catunda, J. D. Myers, and M. J. Myers, “Nonlinear electronic line shape determination in Yb3+-doped phosphate glass,” Opt. Lett. 32(6), 665–667 (2007). [CrossRef]   [PubMed]  

5. O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorobev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003). [CrossRef]  

6. A. Rodenas, C. Jacinto, L. R. Freitas, D. Jaque, and T. Catunda, “Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal,” Phys. Rev. B 79(3), 033108 (2009). [CrossRef]  

7. R. C. Powell, Physics of Solid-State Laser Materials (Springer, 1998).

8. L. R. Freitas, C. Jacinto, A. Rodenas, D. Jaque, and T. Catunda, “Time-resolved study electronic and thermal contributions to the nonlinear refractive index of Nd3+:SBN laser crystals,” J. Lumin. 128(5–6), 1013–1015 (2008). [CrossRef]  

9. A. A. Andrade, E. Tenorio, T. Catunda, M. L. Baesso, A. Cassanho, and H. P. Jenssen, “Discrimination between electronic and thermal contributions to the nonlinear refractive index of SrAlF5:Cr+3,” J. Opt. Soc. Am. B 16(3), 395–400 (1999). [CrossRef]  

10. O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006). [CrossRef]   [PubMed]  

11. J. R. Silva, L. C. Malacarne, M. L. Baesso, S. M. Lima, L. H. C. Andrade, C. Jacinto, M. P. Hehlen, and N. G. C. Astrath, “Modeling the population lens effect in thermal lens spectrometry,” Opt. Lett. 38(4), 422–424 (2013). [PubMed]  

12. C. Jacinto, T. Catunda, D. Jaque, and J. G. Sole, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3(BO3)4,” Phys. Rev. B 72(23), 235111 (2005). [CrossRef]  

13. S. M. Lima, H. Jiao, L. A. O. Nunes, and T. Catunda, “Nonlinear refraction spectroscopy in resonance with laser lines in solids,” Opt. Lett. 27(10), 845–847 (2002). [CrossRef]   [PubMed]  

14. C. Jacinto, S. Oliveira, T. Catundab, A. Andrade, J. Myers, and M. Myers, “Upconversion effect on fluorescence quantum efficiency and heat generation in Nd3+-doped materials,” Opt. Express 13(6), 2040–2046 (2005). [CrossRef]   [PubMed]  

15. V. Ostroumov, T. Jensen, J. P. Meyn, G. Huber, and M. A. Noginov, “Study of luminescence concentration quenching and energy transfer upconversion in Nd-doped LaSc3(BO3)4 and GdVO4 laser crystals,” J. Opt. Soc. Am. B 15(3), 1052–1060 (1998). [CrossRef]  

16. A. S. S. de Camargo, C. Jacinto, T. Catunda, A. O. Nunes, D. Garcia, and J. A. Eiras, “Thermal lens and Auger upconversion losses' effect on the efficiency of Nd3+-doped lead lanthanum zirconate titanate transparent ceramics,” J. Opt. Soc. Am. B 23(10), 2097–2106 (2006). [CrossRef]  

17. V. Pilla, T. Catunda, H. P. Jenssen, and A. Cassanho, “Fluorescence quantum efficiency measurements in the presence of Auger upconversion by the thermal lens method,” Opt. Lett. 28(4), 239–241 (2003). [CrossRef]   [PubMed]  

18. C. Jacinto, D. N. Messias, A. A. Andrade, and T. Catunda, “Energy transfer upconversion determination by thermal-lens and Z-scan techniques in Nd3+-doped laser materials,” J. Opt. Soc. Am. B 26(5), 1002–1007 (2009).

19. T. P. Rodrigues, V. S. Zanuto, R. A. Cruz, T. Catunda, M. L. Baesso, N. G. C. Astrath, and L. C. Malacarne, “Discriminating the role of sample length in thermal lensing of solids,” Opt. Lett. 39(13), 4013–4016 (2014). [PubMed]  

20. J. M. Jewell and I. D. Aggarwal, “Thermal lensing in heavy-metal fluoride glasses,” J. Non-Crystal. Solids 142(1–3), 260–268 (1992).

21. L. G. Hwa, “Rayleigh-Brillouin scattering in calcium aluminosilicate glasses,” J. Raman Spectrosc. 29(4), 269–272 (1998). [CrossRef]  

22. http://kigre.com/files/q98data.pdf, (In January 2015).

23. R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index-of-refraction change in optically pumped solid-state laser materials,” Opt. Lett. 14(21), 1204–1206 (1989). [CrossRef]   [PubMed]  

24. J. R. Silva, L. C. Malacarne, M. L. Baesso, S. M. Lima, L. H. C. Andrade, C. Jacinto, M. P. Hehlen, and N. G. C. Astrath, “Modeling the population lens effect in thermal lens spectrometry,” Opt. Lett. 38(4), 422–424 (2013). [CrossRef]   [PubMed]  

References

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  1. C. Jacinto, D. N. Messias, A. A. Andrade, S. M. Lima, M. L. Baesso, and T. Catunda, “Thermal lens and Z-scan measurements: thermal and optical properties of laser glasses - a review,” J. Non-Cryst. Solids 352(32–35), 3582–3597 (2006).
    [Crossref]
  2. J. Shen, R. D. Lowe, and R. D. Snook, “A Model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. 165(2–3), 385–396 (1992).
    [Crossref]
  3. S. M. Lima and T. Catunda, “Discrimination of resonant and nonresonant contributions to the nonlinear refraction spectroscopy of ion-doped solids,” Phys. Rev. Lett. 99(24), 243902 (2007).
    [Crossref] [PubMed]
  4. D. N. Messias, T. Catunda, J. D. Myers, and M. J. Myers, “Nonlinear electronic line shape determination in Yb3+-doped phosphate glass,” Opt. Lett. 32(6), 665–667 (2007).
    [Crossref] [PubMed]
  5. O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorobev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
    [Crossref]
  6. A. Rodenas, C. Jacinto, L. R. Freitas, D. Jaque, and T. Catunda, “Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal,” Phys. Rev. B 79(3), 033108 (2009).
    [Crossref]
  7. R. C. Powell, Physics of Solid-State Laser Materials (Springer, 1998).
  8. L. R. Freitas, C. Jacinto, A. Rodenas, D. Jaque, and T. Catunda, “Time-resolved study electronic and thermal contributions to the nonlinear refractive index of Nd3+:SBN laser crystals,” J. Lumin. 128(5–6), 1013–1015 (2008).
    [Crossref]
  9. A. A. Andrade, E. Tenorio, T. Catunda, M. L. Baesso, A. Cassanho, and H. P. Jenssen, “Discrimination between electronic and thermal contributions to the nonlinear refractive index of SrAlF5:Cr+3,” J. Opt. Soc. Am. B 16(3), 395–400 (1999).
    [Crossref]
  10. O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
    [Crossref] [PubMed]
  11. J. R. Silva, L. C. Malacarne, M. L. Baesso, S. M. Lima, L. H. C. Andrade, C. Jacinto, M. P. Hehlen, and N. G. C. Astrath, “Modeling the population lens effect in thermal lens spectrometry,” Opt. Lett. 38(4), 422–424 (2013).
    [PubMed]
  12. C. Jacinto, T. Catunda, D. Jaque, and J. G. Sole, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3(BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
    [Crossref]
  13. S. M. Lima, H. Jiao, L. A. O. Nunes, and T. Catunda, “Nonlinear refraction spectroscopy in resonance with laser lines in solids,” Opt. Lett. 27(10), 845–847 (2002).
    [Crossref] [PubMed]
  14. C. Jacinto, S. Oliveira, T. Catundab, A. Andrade, J. Myers, and M. Myers, “Upconversion effect on fluorescence quantum efficiency and heat generation in Nd3+-doped materials,” Opt. Express 13(6), 2040–2046 (2005).
    [Crossref] [PubMed]
  15. V. Ostroumov, T. Jensen, J. P. Meyn, G. Huber, and M. A. Noginov, “Study of luminescence concentration quenching and energy transfer upconversion in Nd-doped LaSc3(BO3)4 and GdVO4 laser crystals,” J. Opt. Soc. Am. B 15(3), 1052–1060 (1998).
    [Crossref]
  16. A. S. S. de Camargo, C. Jacinto, T. Catunda, A. O. Nunes, D. Garcia, and J. A. Eiras, “Thermal lens and Auger upconversion losses' effect on the efficiency of Nd3+-doped lead lanthanum zirconate titanate transparent ceramics,” J. Opt. Soc. Am. B 23(10), 2097–2106 (2006).
    [Crossref]
  17. V. Pilla, T. Catunda, H. P. Jenssen, and A. Cassanho, “Fluorescence quantum efficiency measurements in the presence of Auger upconversion by the thermal lens method,” Opt. Lett. 28(4), 239–241 (2003).
    [Crossref] [PubMed]
  18. C. Jacinto, D. N. Messias, A. A. Andrade, and T. Catunda, “Energy transfer upconversion determination by thermal-lens and Z-scan techniques in Nd3+-doped laser materials,” J. Opt. Soc. Am. B 26(5), 1002–1007 (2009).
  19. T. P. Rodrigues, V. S. Zanuto, R. A. Cruz, T. Catunda, M. L. Baesso, N. G. C. Astrath, and L. C. Malacarne, “Discriminating the role of sample length in thermal lensing of solids,” Opt. Lett. 39(13), 4013–4016 (2014).
    [PubMed]
  20. J. M. Jewell and I. D. Aggarwal, “Thermal lensing in heavy-metal fluoride glasses,” J. Non-Crystal. Solids 142(1–3), 260–268 (1992).
  21. L. G. Hwa, “Rayleigh-Brillouin scattering in calcium aluminosilicate glasses,” J. Raman Spectrosc. 29(4), 269–272 (1998).
    [Crossref]
  22. http://kigre.com/files/q98data.pdf , (In January 2015).
  23. R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index-of-refraction change in optically pumped solid-state laser materials,” Opt. Lett. 14(21), 1204–1206 (1989).
    [Crossref] [PubMed]
  24. J. R. Silva, L. C. Malacarne, M. L. Baesso, S. M. Lima, L. H. C. Andrade, C. Jacinto, M. P. Hehlen, and N. G. C. Astrath, “Modeling the population lens effect in thermal lens spectrometry,” Opt. Lett. 38(4), 422–424 (2013).
    [Crossref] [PubMed]

2014 (1)

2013 (2)

2009 (2)

A. Rodenas, C. Jacinto, L. R. Freitas, D. Jaque, and T. Catunda, “Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal,” Phys. Rev. B 79(3), 033108 (2009).
[Crossref]

C. Jacinto, D. N. Messias, A. A. Andrade, and T. Catunda, “Energy transfer upconversion determination by thermal-lens and Z-scan techniques in Nd3+-doped laser materials,” J. Opt. Soc. Am. B 26(5), 1002–1007 (2009).

2008 (1)

L. R. Freitas, C. Jacinto, A. Rodenas, D. Jaque, and T. Catunda, “Time-resolved study electronic and thermal contributions to the nonlinear refractive index of Nd3+:SBN laser crystals,” J. Lumin. 128(5–6), 1013–1015 (2008).
[Crossref]

2007 (2)

S. M. Lima and T. Catunda, “Discrimination of resonant and nonresonant contributions to the nonlinear refraction spectroscopy of ion-doped solids,” Phys. Rev. Lett. 99(24), 243902 (2007).
[Crossref] [PubMed]

D. N. Messias, T. Catunda, J. D. Myers, and M. J. Myers, “Nonlinear electronic line shape determination in Yb3+-doped phosphate glass,” Opt. Lett. 32(6), 665–667 (2007).
[Crossref] [PubMed]

2006 (3)

2005 (2)

C. Jacinto, S. Oliveira, T. Catundab, A. Andrade, J. Myers, and M. Myers, “Upconversion effect on fluorescence quantum efficiency and heat generation in Nd3+-doped materials,” Opt. Express 13(6), 2040–2046 (2005).
[Crossref] [PubMed]

C. Jacinto, T. Catunda, D. Jaque, and J. G. Sole, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3(BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
[Crossref]

2003 (2)

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorobev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[Crossref]

V. Pilla, T. Catunda, H. P. Jenssen, and A. Cassanho, “Fluorescence quantum efficiency measurements in the presence of Auger upconversion by the thermal lens method,” Opt. Lett. 28(4), 239–241 (2003).
[Crossref] [PubMed]

2002 (1)

1999 (1)

1998 (2)

1992 (2)

J. M. Jewell and I. D. Aggarwal, “Thermal lensing in heavy-metal fluoride glasses,” J. Non-Crystal. Solids 142(1–3), 260–268 (1992).

J. Shen, R. D. Lowe, and R. D. Snook, “A Model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. 165(2–3), 385–396 (1992).
[Crossref]

1989 (1)

Aggarwal, I. D.

J. M. Jewell and I. D. Aggarwal, “Thermal lensing in heavy-metal fluoride glasses,” J. Non-Crystal. Solids 142(1–3), 260–268 (1992).

Andrade, A.

Andrade, A. A.

Andrade, L. H. C.

Antipov, O. L.

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
[Crossref] [PubMed]

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorobev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[Crossref]

Astrath, N. G. C.

Baesso, M. L.

Bredikhin, D. V.

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
[Crossref] [PubMed]

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorobev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[Crossref]

Cassanho, A.

Catunda, T.

T. P. Rodrigues, V. S. Zanuto, R. A. Cruz, T. Catunda, M. L. Baesso, N. G. C. Astrath, and L. C. Malacarne, “Discriminating the role of sample length in thermal lensing of solids,” Opt. Lett. 39(13), 4013–4016 (2014).
[PubMed]

C. Jacinto, D. N. Messias, A. A. Andrade, and T. Catunda, “Energy transfer upconversion determination by thermal-lens and Z-scan techniques in Nd3+-doped laser materials,” J. Opt. Soc. Am. B 26(5), 1002–1007 (2009).

A. Rodenas, C. Jacinto, L. R. Freitas, D. Jaque, and T. Catunda, “Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal,” Phys. Rev. B 79(3), 033108 (2009).
[Crossref]

L. R. Freitas, C. Jacinto, A. Rodenas, D. Jaque, and T. Catunda, “Time-resolved study electronic and thermal contributions to the nonlinear refractive index of Nd3+:SBN laser crystals,” J. Lumin. 128(5–6), 1013–1015 (2008).
[Crossref]

S. M. Lima and T. Catunda, “Discrimination of resonant and nonresonant contributions to the nonlinear refraction spectroscopy of ion-doped solids,” Phys. Rev. Lett. 99(24), 243902 (2007).
[Crossref] [PubMed]

D. N. Messias, T. Catunda, J. D. Myers, and M. J. Myers, “Nonlinear electronic line shape determination in Yb3+-doped phosphate glass,” Opt. Lett. 32(6), 665–667 (2007).
[Crossref] [PubMed]

C. Jacinto, D. N. Messias, A. A. Andrade, S. M. Lima, M. L. Baesso, and T. Catunda, “Thermal lens and Z-scan measurements: thermal and optical properties of laser glasses - a review,” J. Non-Cryst. Solids 352(32–35), 3582–3597 (2006).
[Crossref]

A. S. S. de Camargo, C. Jacinto, T. Catunda, A. O. Nunes, D. Garcia, and J. A. Eiras, “Thermal lens and Auger upconversion losses' effect on the efficiency of Nd3+-doped lead lanthanum zirconate titanate transparent ceramics,” J. Opt. Soc. Am. B 23(10), 2097–2106 (2006).
[Crossref]

C. Jacinto, T. Catunda, D. Jaque, and J. G. Sole, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3(BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
[Crossref]

V. Pilla, T. Catunda, H. P. Jenssen, and A. Cassanho, “Fluorescence quantum efficiency measurements in the presence of Auger upconversion by the thermal lens method,” Opt. Lett. 28(4), 239–241 (2003).
[Crossref] [PubMed]

S. M. Lima, H. Jiao, L. A. O. Nunes, and T. Catunda, “Nonlinear refraction spectroscopy in resonance with laser lines in solids,” Opt. Lett. 27(10), 845–847 (2002).
[Crossref] [PubMed]

A. A. Andrade, E. Tenorio, T. Catunda, M. L. Baesso, A. Cassanho, and H. P. Jenssen, “Discrimination between electronic and thermal contributions to the nonlinear refractive index of SrAlF5:Cr+3,” J. Opt. Soc. Am. B 16(3), 395–400 (1999).
[Crossref]

Catundab, T.

Chase, L. L.

Cruz, R. A.

de Camargo, A. S. S.

Eiras, J. A.

Eremeykin, O. N.

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
[Crossref] [PubMed]

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorobev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[Crossref]

Freitas, L. R.

A. Rodenas, C. Jacinto, L. R. Freitas, D. Jaque, and T. Catunda, “Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal,” Phys. Rev. B 79(3), 033108 (2009).
[Crossref]

L. R. Freitas, C. Jacinto, A. Rodenas, D. Jaque, and T. Catunda, “Time-resolved study electronic and thermal contributions to the nonlinear refractive index of Nd3+:SBN laser crystals,” J. Lumin. 128(5–6), 1013–1015 (2008).
[Crossref]

Garcia, D.

Hehlen, M. P.

Huber, G.

Hwa, L. G.

L. G. Hwa, “Rayleigh-Brillouin scattering in calcium aluminosilicate glasses,” J. Raman Spectrosc. 29(4), 269–272 (1998).
[Crossref]

Ivakin, E. V.

Jacinto, C.

J. R. Silva, L. C. Malacarne, M. L. Baesso, S. M. Lima, L. H. C. Andrade, C. Jacinto, M. P. Hehlen, and N. G. C. Astrath, “Modeling the population lens effect in thermal lens spectrometry,” Opt. Lett. 38(4), 422–424 (2013).
[PubMed]

J. R. Silva, L. C. Malacarne, M. L. Baesso, S. M. Lima, L. H. C. Andrade, C. Jacinto, M. P. Hehlen, and N. G. C. Astrath, “Modeling the population lens effect in thermal lens spectrometry,” Opt. Lett. 38(4), 422–424 (2013).
[Crossref] [PubMed]

C. Jacinto, D. N. Messias, A. A. Andrade, and T. Catunda, “Energy transfer upconversion determination by thermal-lens and Z-scan techniques in Nd3+-doped laser materials,” J. Opt. Soc. Am. B 26(5), 1002–1007 (2009).

A. Rodenas, C. Jacinto, L. R. Freitas, D. Jaque, and T. Catunda, “Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal,” Phys. Rev. B 79(3), 033108 (2009).
[Crossref]

L. R. Freitas, C. Jacinto, A. Rodenas, D. Jaque, and T. Catunda, “Time-resolved study electronic and thermal contributions to the nonlinear refractive index of Nd3+:SBN laser crystals,” J. Lumin. 128(5–6), 1013–1015 (2008).
[Crossref]

C. Jacinto, D. N. Messias, A. A. Andrade, S. M. Lima, M. L. Baesso, and T. Catunda, “Thermal lens and Z-scan measurements: thermal and optical properties of laser glasses - a review,” J. Non-Cryst. Solids 352(32–35), 3582–3597 (2006).
[Crossref]

A. S. S. de Camargo, C. Jacinto, T. Catunda, A. O. Nunes, D. Garcia, and J. A. Eiras, “Thermal lens and Auger upconversion losses' effect on the efficiency of Nd3+-doped lead lanthanum zirconate titanate transparent ceramics,” J. Opt. Soc. Am. B 23(10), 2097–2106 (2006).
[Crossref]

C. Jacinto, T. Catunda, D. Jaque, and J. G. Sole, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3(BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
[Crossref]

C. Jacinto, S. Oliveira, T. Catundab, A. Andrade, J. Myers, and M. Myers, “Upconversion effect on fluorescence quantum efficiency and heat generation in Nd3+-doped materials,” Opt. Express 13(6), 2040–2046 (2005).
[Crossref] [PubMed]

Jaque, D.

A. Rodenas, C. Jacinto, L. R. Freitas, D. Jaque, and T. Catunda, “Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal,” Phys. Rev. B 79(3), 033108 (2009).
[Crossref]

L. R. Freitas, C. Jacinto, A. Rodenas, D. Jaque, and T. Catunda, “Time-resolved study electronic and thermal contributions to the nonlinear refractive index of Nd3+:SBN laser crystals,” J. Lumin. 128(5–6), 1013–1015 (2008).
[Crossref]

C. Jacinto, T. Catunda, D. Jaque, and J. G. Sole, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3(BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
[Crossref]

Jensen, T.

Jenssen, H. P.

Jewell, J. M.

J. M. Jewell and I. D. Aggarwal, “Thermal lensing in heavy-metal fluoride glasses,” J. Non-Crystal. Solids 142(1–3), 260–268 (1992).

Jiao, H.

Kuznetsov, M. S.

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorobev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[Crossref]

Lima, S. M.

Lowe, R. D.

J. Shen, R. D. Lowe, and R. D. Snook, “A Model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. 165(2–3), 385–396 (1992).
[Crossref]

Malacarne, L. C.

Messias, D. N.

Meyn, J. P.

Myers, J.

Myers, J. D.

Myers, M.

Myers, M. J.

Noginov, M. A.

Nunes, A. O.

Nunes, L. A. O.

Oliveira, S.

Ostroumov, V.

Payne, S. A.

Pilla, V.

Powell, R. C.

Rodenas, A.

A. Rodenas, C. Jacinto, L. R. Freitas, D. Jaque, and T. Catunda, “Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal,” Phys. Rev. B 79(3), 033108 (2009).
[Crossref]

L. R. Freitas, C. Jacinto, A. Rodenas, D. Jaque, and T. Catunda, “Time-resolved study electronic and thermal contributions to the nonlinear refractive index of Nd3+:SBN laser crystals,” J. Lumin. 128(5–6), 1013–1015 (2008).
[Crossref]

Rodrigues, T. P.

Savikin, A. P.

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
[Crossref] [PubMed]

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorobev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[Crossref]

Shen, J.

J. Shen, R. D. Lowe, and R. D. Snook, “A Model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. 165(2–3), 385–396 (1992).
[Crossref]

Silva, J. R.

Snook, R. D.

J. Shen, R. D. Lowe, and R. D. Snook, “A Model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. 165(2–3), 385–396 (1992).
[Crossref]

Sole, J. G.

C. Jacinto, T. Catunda, D. Jaque, and J. G. Sole, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3(BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
[Crossref]

Sukhadolau, A. V.

Tenorio, E.

Vorobev, V. A.

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorobev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[Crossref]

Wilke, G. D.

Zanuto, V. S.

Chem. Phys. (1)

J. Shen, R. D. Lowe, and R. D. Snook, “A Model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. 165(2–3), 385–396 (1992).
[Crossref]

IEEE J. Quantum Electron. (1)

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorobev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[Crossref]

J. Lumin. (1)

L. R. Freitas, C. Jacinto, A. Rodenas, D. Jaque, and T. Catunda, “Time-resolved study electronic and thermal contributions to the nonlinear refractive index of Nd3+:SBN laser crystals,” J. Lumin. 128(5–6), 1013–1015 (2008).
[Crossref]

J. Non-Cryst. Solids (1)

C. Jacinto, D. N. Messias, A. A. Andrade, S. M. Lima, M. L. Baesso, and T. Catunda, “Thermal lens and Z-scan measurements: thermal and optical properties of laser glasses - a review,” J. Non-Cryst. Solids 352(32–35), 3582–3597 (2006).
[Crossref]

J. Non-Crystal. Solids (1)

J. M. Jewell and I. D. Aggarwal, “Thermal lensing in heavy-metal fluoride glasses,” J. Non-Crystal. Solids 142(1–3), 260–268 (1992).

J. Opt. Soc. Am. B (4)

J. Raman Spectrosc. (1)

L. G. Hwa, “Rayleigh-Brillouin scattering in calcium aluminosilicate glasses,” J. Raman Spectrosc. 29(4), 269–272 (1998).
[Crossref]

Opt. Express (1)

Opt. Lett. (8)

S. M. Lima, H. Jiao, L. A. O. Nunes, and T. Catunda, “Nonlinear refraction spectroscopy in resonance with laser lines in solids,” Opt. Lett. 27(10), 845–847 (2002).
[Crossref] [PubMed]

T. P. Rodrigues, V. S. Zanuto, R. A. Cruz, T. Catunda, M. L. Baesso, N. G. C. Astrath, and L. C. Malacarne, “Discriminating the role of sample length in thermal lensing of solids,” Opt. Lett. 39(13), 4013–4016 (2014).
[PubMed]

V. Pilla, T. Catunda, H. P. Jenssen, and A. Cassanho, “Fluorescence quantum efficiency measurements in the presence of Auger upconversion by the thermal lens method,” Opt. Lett. 28(4), 239–241 (2003).
[Crossref] [PubMed]

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
[Crossref] [PubMed]

J. R. Silva, L. C. Malacarne, M. L. Baesso, S. M. Lima, L. H. C. Andrade, C. Jacinto, M. P. Hehlen, and N. G. C. Astrath, “Modeling the population lens effect in thermal lens spectrometry,” Opt. Lett. 38(4), 422–424 (2013).
[PubMed]

D. N. Messias, T. Catunda, J. D. Myers, and M. J. Myers, “Nonlinear electronic line shape determination in Yb3+-doped phosphate glass,” Opt. Lett. 32(6), 665–667 (2007).
[Crossref] [PubMed]

R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index-of-refraction change in optically pumped solid-state laser materials,” Opt. Lett. 14(21), 1204–1206 (1989).
[Crossref] [PubMed]

J. R. Silva, L. C. Malacarne, M. L. Baesso, S. M. Lima, L. H. C. Andrade, C. Jacinto, M. P. Hehlen, and N. G. C. Astrath, “Modeling the population lens effect in thermal lens spectrometry,” Opt. Lett. 38(4), 422–424 (2013).
[Crossref] [PubMed]

Phys. Rev. B (2)

C. Jacinto, T. Catunda, D. Jaque, and J. G. Sole, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3(BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
[Crossref]

A. Rodenas, C. Jacinto, L. R. Freitas, D. Jaque, and T. Catunda, “Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal,” Phys. Rev. B 79(3), 033108 (2009).
[Crossref]

Phys. Rev. Lett. (1)

S. M. Lima and T. Catunda, “Discrimination of resonant and nonresonant contributions to the nonlinear refraction spectroscopy of ion-doped solids,” Phys. Rev. Lett. 99(24), 243902 (2007).
[Crossref] [PubMed]

Other (2)

R. C. Powell, Physics of Solid-State Laser Materials (Springer, 1998).

http://kigre.com/files/q98data.pdf , (In January 2015).

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Figures (3)

Fig. 1
Fig. 1 (a) Radial dependence of the laser induced temperature profile, T ( r , 0 , t ) , for different exposure times. Dashed and solid lines are analytical solutions, Eq. (4), without and considering AU process, respectively. Open circle are the exact numerical solution from the diffusion Eq. (1) with AU process. β = 10 and the other parameters listed in Table 1 (Part 1) were used in simulations. I(t) dependence on θ e l for (b) diverging TL (ZBLAN:Nd fluoride glass) and (c) converging TL (Q-98:Nd phosphate glass). θ e l was artificially varied from 0 to 4. All these results of the right figure are for β = 0 (without AU).
Fig. 2
Fig. 2 [(a), (b), (c), and (d)] - Normalized TL signal transients for a typical value of θ e l = 4 , Auger upconversion parameter varying from β = 0 up to β = 20, and thermal diffusivity of [(a) and (b)] D = 3 × 10 7 m 2 / s and [(c) and (d)] D = 3 × 10 7 m 2 / s , typics of glasses and crystals, respectively. In [(a) and (c)] and [(b) and (d)] were used other representative parameters given in Table 1 (Part 1), which lead to positive and negative TL signals. [(e) and (f)] - Typical normalized experimental lensing signals for (e) ZBLAN:Nd (1.0 mol%) and (f) Q-98:Nd (1.0 wt.%) samples. Continuous lines denotes least-squares curves fit using I(t) equation. The excitation power for these transients was fixed at P i n = 200 mW. The obtained parameters are given in Table 1 (Part 2).
Fig. 3
Fig. 3 θth versus the excitation power Pe for ZBLAN:Nd sample obtained from the experimental data fitting with β = 0, 2, and 5. Dashed lines are guides for the eye. The fitting parameters obtained for β = 2 were θth/Pe = (810 ± 50) × 106 K/W, θ e l = ( 1.5 ± 0.1 ) , and D = (2.7 ± 0.3) × 10−7 m2/s.

Tables (1)

Tables Icon

Table 1 Part 1: Physical properties of the samples. Parameters for ZBLAN and Q-98 are from references [1,17–22 ]. Part 2: Parameters obtained from the computational fits for ZBLAN:Nd and Q-98:Nd samples.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

T ( r , z , t ) / t D 2 T ( r , z , t ) = Q 0 φ e 2 r 2 / w o e 2 e A e z
N e t = R P N T ( R P + 1 τ ) N e γ N e 2
N e ( r , z , t ) = N T { 2     S   Tan h ( Δ ( S , β ) 2 τ t ) ( S + 1 ) Tan h ( Δ ( S , β ) 2 τ t ) +   Δ ( S , β ) } e A e z
T ( r , z , t ) = 2 P e A e π ρ C ω 0 e 2 φ ( S 0 , β ) e A _ e   z 0 t e 2 r 2 / ω o e 2 1 + 2 ξ / t c 1 + 2 ξ / t c   d ξ
ϕ T L ( g , t ) = 2 π λ p 0 L [ S ( r , z , t ) S ( 0 , z , t ) ] d z
ϕ P L ( g , t ) = 2 π λ p o L c k N e ( g , z , t ) d z
ϕ T L = θ t h φ ( S 0 , β ) 0 χ ( α , L ) e ω 0 e 2 α 2 / 8 × ( 1 e 1 4 ω o e 2 α 2 t t c ) [ J 0 ( α ω 0 e m g ) 1 ] α 1 d α
ϕ P L = θ e l ( 2 S Tan h ( Δ ( S , β ) 2 τ t ) ( S + 1 ) Tan h ( Δ ( S , β ) 2 τ t ) + Δ ( S , β ) )
χ ( α , L ) = n T + 4 L α ( n 1 ) ( 1 + ν ) α T h ( α , L ) + n 3 E α T 4 ( 1 ν ) [ ( q + q ) ( 4 [ q ν + q ( 2 + ν ) ] h ( α , L ) L α ) ]

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