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Pump-induced refractive index changes in Tb3+ doped glasses
Journal of Luminescence 169 (2016) 659–664
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Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Pump-induced refractive index changes in Tb3 þ doped glasses T.A. Vieira a, J.F.M. dos Santos a, Y.M Auad a, L.A.O. Nunes a, N.G.C Astrath b, M.L. Baesso b, T. Catunda a,n a b
Instituto de Física de São Carlos, Universidade de São Paulo, SP, Brazil Departamento de Física, Universidade Estadual de Maringá, PR, Brazil
art ic l e i nf o
a b s t r a c t
Article history: Received 15 October 2014 Received in revised form 14 July 2015 Accepted 21 July 2015 Available online 22 August 2015
It now well known in laser materials, that a refractive index change appears when the active ions are pumped from ground to excited state due to the polarizability difference between ground and excited states (metastable). In this paper this effect was investigated in Tb3 þ doped glasses: calcium alumino phosphate (CAP), low-silica calcium aluminosilicate (LSCAS) and calcium aluminosilicate (CAS). The measurements were performed using the time resolved Z-scan technique, with an Ar þ laser at 488 nm, close to the resonance of 7F6-5D4 absorption line, where 5D4 is a metastable state. We obtained for lowsilica calcium aluminosilicate glass Δαp 10 24 cm3 which is the highest value ever reported for a RE doped material. & 2015 Elsevier B.V. All rights reserved.
Keywords: Z-Scan Nonlinear refractive index Polarizability difference Tb3 þ
1. Introduction There has been a great interest in the study of nonlinear properties of ion doped materials due to spatial hole burning, which can induce both refractive-index and gain gratings, its implications in laser behavior (including bistability and instabilities), as well as applications such as phase conjugation of high power laser systems [1,2]. The observation of Q-switching behavior in Cr:LiSAF has been attributed to the effect of Refractive Index Changes (RIC) of the Cr ion due to the excited state population [3]. In addition, resonantly enhanced nonlinear phase shifts have been observed in optically pumped fibers (doped with Er3 þ , Nd3 þ , Sm3 þ and Yb3 þ ), motivated by applications such as all-optical switches, transient Bragg gratings, etc. The nonlinear properties of ion doped materials have also been applied to demonstration of interesting phenomena such as fast and slow light [4]. More recently, it was demonstrated in ruby that the effect of rotatory photon drag can be enhanced by the use of slowlight medium [5]. Usually, RIC are studied by populating the ion metastable state through the excitation of higher energy absorption bands, which nonradiatively decay to the metastable state. It is well known that RIC arises from the difference of ion excited state polarizability, αpex, compared to the ground state one, αpg. This polarizability difference, Δαp ¼ αpex αpg, is attributed mainly to the interaction with nonresonant transitions (in the UV) which are far from resonance of the laser transition. For rare-earth doped ions, it is n
Corresponding author. Tel.: þ 55 1633739861. E-mail address: [email protected] (T. Catunda).
http://dx.doi.org/10.1016/j.jlumin.2015.07.035 0022-2313/& 2015 Elsevier B.V. All rights reserved.
generally believed that the 4f-5d transitions give the main contribution to Δαp [6,7]. The energy of 4f-5d transitions in Tb3 þ are known to be very low compared to other rare earth ions. For instance, in Tb3 þ doped calcium aluminosilicate glasses, this transition was observed 35000 cm 1 in the excitation spectrum [8,9]. This ion have emissions from ultraviolet to infrared through metastable levels 5D3, 5D4 and 7F0. The intense green emission due transition 5D4-7F5 has potential application in green light emitters, scintillators, and lasers [10]. Z-scan is nowadays the most popular technique to determine n2 in different kinds of materials [11]. In ion doped solids with a slow nonlinearity, the time-resolved Z-scan method has been used because of its high sensitivity and its ability to investigate the nonlinearity's physical origin [4,12–16]. This method was also recently used to distinguish population lens from thermal lens contributions to the nonlinearity. The Z-scan method was successfully apply to ruby (Al2O3:Cr3 þ ) which is considered as a reference among the ion doped materials, since it was used to demonstrate many nonlinear effects such as bistability, degenerate and nearly degenerate four-wave-mixing, nearly degenerate twowave mixing, transverse phase modulation, interferometric measurements of RIC, etc. [17–19]. The Δαp 1.8 10 25 cm3 in the blue–green visible range (457–528 nm) is in very good agreement with all data available [14]. In this paper, time resolved Z-scan measurements were performed in Tb3 þ doped glasses, at 488 nm, close to the resonance of 7F6-5D4 transition, where 7F6 is the ground state. More details about the Tb þ 3 luminescence dynamics in this glass were recently published [9]. In this paper very high n2 and Δαp values were obtained and a strong host dependence. The values found in calcium
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aluminosilicate glasses are much larger than in phosphates. Among the aluminosilicate glasses, it was observed a larger Δαp in the sample with lower silica and consequently, lower band edge energy and refractive index [20].
2. Theoretical background In ion doped materials, such as rare earth and transition metal ions, the redistribution changes the overall optical susceptibility, χ, and therefore the refractive index. Here we consider that the system has only one metastable state in the stationary state which is the case of most ion doped laser materials in the cw regime. If the pump beam has a Gaussian intensity profile, the excited state population will follow the same radial profile. This makes the refractive index variation, Δn, to acquire a lens-like profile. Consequently, this phenomenon is known as the Population Lens (PL) effect. Since the excited state population is, in first order, proportional to pump intensity, the PL is equivalent to Kerr nonlinearity, where Δn ¼n2I. The electronic refractive index changes due to the active ion can be analyzed considering in the PL effect the susceptibility, which is given by [4,12]:
χ = χm +
1 (Ng χg + Nex χex ) Nt
(1)
where χm represents the host matrix's susceptibility, Nt is the ion concentration (cm 3), Ng and Nex are the ion concentration in the ground and excited state, respectively, and χg, χex are the complex susceptibilities of the dopand ion in the ground and excited state, respectively. We are assuming that the medium has only one metastable excited level, whose lifetime is much longer compared to the other excited states. Therefore, in the CW regime only the ground state and the metastable excited state are significantly populated, so that Nt∼Ng þNex. We are interested in the refractive index change produced by the excited state population, so the local field effect should be introduced as
⎤ n2 − 1 4π ⎡ Nex . χex − χg ⎥ = ⎢ χ + χg + ⎦ 3 ⎣ m Nt n2 + 1
(
)
(2)
with the refractive index given by n ¼n0 þ Δn, where n0 the refractive index of the unpumped glass, n02 ¼1 þ4πfL(χm þNt.χg) and fL ¼ (n02 þ 2)/3 is the Lorenz local field correction factor. The refractive index change Δn is proportional to the susceptibility change due to the excited state population is given by
∆n =
2π 2 Nex (χ − χg ) f n0 L Nt ex
(3)
where Δn is a complex quantity which real part is proportional to ∆αp = Re {(χex − χg ) /Nt }, the polarizabilities difference of the ion in excited and ground states. The imaginary part of ∆n is proportional to Δs ¼(sex sg), the difference between ion excited state absorption (ESA) and ground state absorption cross sections. We'll first consider the unsaturated pump regime, where Nex∼Nt.I/Is, approximation valid for Nex o o Nt, with the pump saturation intensity given by
Is =
hv σg τ
Fig. 1. Partial energy level diagram of Tb3 þ ions in low silica aluminosilicate glasses. The arrows indicate the excitation at 488 nm and main green emission at 544 nm.
(4)
Where hν is the pump photon energy and τ the lifetime of the metastable excited state. Therefore, Δn is proportional to the intensity and can be written similarly to the Kerr nonlinear effect, n ¼n0 þn2I, with a complex, n2 ¼n2′ in2′′, given by [14]
n2 =
⎞ Nt ⎛ 2π 2 λ fL ∆αp − i ∆σ ⎟ ⎜ Is ⎝ n0 4π ⎠
(5)
Supposing that the pump laser is turned on at t¼ 0, the excited state population Nex(t) can be calculated by rate equations as [12]
Nex (t ) = Nt
I (1 − e−t/ τ ) Is
(6)
where I is the laser incident intensity. Eq. (6) is valid only for Io oIs since it does not include the effect of depletion of ground state population. In this paper, time resolved Z-scan measurements were performed in three different Tb3 þ doped glass. An Ar þ laser was used at 488 nm, close to the resonance of 7F6-5D4 transition, where 7F6 is the ground state. As depicted in Fig. 1, several emission lines 5 D4-7Fj are observed and Tb3 þ is known for its strong green emission at 544 nm. The quantum efficiency is typically high due to the large energy gap (15000 cm 1) below the 5D4 state. In most materials, this level is not significantly affected by concentration quenching, as oppose to the of 5D3 state.
3. Experimental 3.1. Preparation of samples Calcium Aluminosilicate glass: two different matrix compositions were studied, the Low Silica Calcium Aluminosilicate (LSCAS) and the Calcium Aluminosilicate (CAS). The silica content is the main difference in these compositions: LSCAS nominal composition of (47.4 x/2)% CaOþ (41.5 x/2)% Al2O3 þ 4.1% MgOþ7.0%SiO2 þx% Tb4O7 with x¼0.5% and 0.2%; CAS with nominal composition is 33.25% CaOþ 27.65%Al2O3 þ 4.1% MgOþ34%SiO2 þ0.5% Tb4O7. Both mixtures were melted under vacuum atmosphere at 1600 °C for two hours. The fact that the samples are prepared in a vacuum furnace has eliminated the radicals OH and increases the transmission window (0.3–6 μm). Calcium Aluminophosphate (CAP) nominal composition: 58%(NaPO3)3 þ40%Al(PO3)3 þ2%Tb4O7 prepared with reagent (NaPO3)3 and Al(PO3)3 using conventional melt at temperatures between 750
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and 1150 °C. More details about CAS and CAP sample preparation can be found in Refs. [20,21]. Under 488 nm cw excitation, all samples presented nearly exponential decays (5D4-7Fj(j ¼ 3–6)) with lifetimes: 1.9 ms (LSCAS), 3.4 ms (CAS) and 2.9 ms (CAP). It was previously observed that these decays times are nearly independent of Tb3 þ concentration up to 5 wt% [8–10]. 3.2. Z-scan technique Among the techniques applied to characterize the n2 material, Z-scan is the most popular one [9]. In addition to the simplicity of the experimental setup, a Z-scan measurement provides a sensitive method for determination of the signal and value of the real and imaginary part of χ(3). The technique relies on the basic idea of relating the beam center intensity variation with the refractive index variation. This can be done, monitoring the normalized transmittance as a function of sample path along the incident beam. The transmittance variation between peak and valley position is proportional to the induced phase shift, ΔΦ0, given by [9]
ΔTp − v ≈ 0. 406ΔΦo
(7)
with
ΔΦo = kL eff n2‵ I0
(8)
where k is the pump wavenumber, Leff is the effective length, and I0 is the beam waist incident intensity. Moreover, the separation between the peak and valley position is related to the Rayleigh range through ΔZp v E 1.7zc. When all light is focused in the detector, the maximum transmittance variation is related with the imaginary part of n2 as
Tp − 1 ≈ kL eff n2‵‵ I0
(9)
where Tp is the transmittance with the sample at the beam waist position. τ In slow absorbers, where Δn(t)∝Ne(t)∝Nt.(1 e t/ ) and τ Z100 μs, it is possible to apply the time resolved Z-scan procedure [12]. In this case, a chopper modulates the beam and the transmittance is defined as the ratio between the intensity at a time ti o o τ, where there is only linear effects, and at a time tf 4 4 τ, where both linear and nonlinear effects are present. The main advantage of this technique is to eliminate linear parasitic effects due to unparallel faces of the sample, polish imperfections, etc.; enhancing the sensitivity. In this way, the signal-to-noise ratio achieved is much better than the one obtained in the standard Z-scan set-up Fig. 2. Fig. 3 shows a typical Z-scan signal, obtained with 500 averages for each z position. The fit of Fig. 3(a) resulted in zc ¼ 0.24 cm and ΔΦ0 ¼ 0.012.
4. Results and discussion Calcium AluminoPhosphate (CAP) – the Z-scan measurements were performed in CAP sample with Tb3 þ concentration, Nt ¼2.15 1020 cm 3. Fig. 4(a) shows typical data obtained in CAP at 488 nm with chopper frequency f¼ 32 Hz and ti ¼40 ms, tf ¼ 10 ms. The measurements were performed in low intensity to avoid saturation effect (I0 o oIs ¼1.5 106 W/cm2). By Eq. (8) we found the real nonlinear refractive index n2’¼1.6 10 11 cm2/W and, from Eq. (5), the polarizability difference Δαp 1.6 10 26 cm3 is obtained from the linear fit of Fig. 5. We did not observe any signal in open aperture (S¼100%) photodetector, even for the maximum power available. The transient signal, Fig. 4(b) was obtained at peak position of z-scan curve and fitted by exponential function Eq. (6), give us a response time 2.86 ms, in good agreement with
Fig. 2. Experimental setup for the nonlinear laser spectroscopy. The closed aperture (S¼ 30%) and open aperture (S¼100%) signals are proportional to the real and imaginary parts of n2, respectively, where S is the aperture factor as defined in Ref. [11].
luminescence lifetime (2.9 ms). Fig. 6 shows a linear dependence of peak and valley transmittance ΔΤpv with excitation power, as expected by Eq. (8). Calcium Aluminosilicate (LSCAS and CAS) – the 0.5 wt% LSCAS sample has a Tb3 þ concentration Nt ¼ 4.7 1019 cm 3 (0.5 wt%) and Is ¼2.3 106 W/cm2 is obtained using s ¼9.8 10 23 cm2 (at 488 nm) and τ ¼1.9 ms. Typical Z-scan data are shown in Fig. 6, resulting in n2 ¼(4.3 þ0.004i) 10 10 cm2/W. The 0.5 wt% CAS glass presented n2’ ¼1.4 10 10 cm2/W. No open aperture signal was observed even at maximum available power (n2’’E0). Fig. 7 shows the power dependence of the Z-scan signal amplitude for both CAS and LSCAS, samples. Differently than observed in CAP (Fig. 5), Fig. 7 indicates a nonlinear increase of ΔTpv versus P. This behavior may be interpreted considering the higher order contributions to susceptibility: χ(3), χ (5), χ(7)… which would correspond to complex refractive index changes given by n2I, n4I2, n6I6… respectively as observed, for instance in colloidal solutions by [22]. In this paper, these high order terms might represent the effect of highly excited states (above the 5D4), which population depends on higher power of pump intensity. It should be noticed that the open aperture Z-scan signs, Tp 1, was much weaker than the close aperture. They could only be measured at intensities about one order of magnitude higher than the ones used for the closed aperture measurements, as shown in Fig. 3(b) and Fig. 4(b). It is remarkable that these curves are very narrow, with a width 60% narrower than expected by the standard Z-scan theory, which assumes Δn ¼n2I, for both real and imaginary parts of n2. However, in the high intensity regime the closed aperture signal, ΔTpv, is nearly proportional to the intensity square, so it is dominated by the n4, term. Therefore, we attribute the very narrowness of the curves shown in Fig. 3(b) and Fig. 6(b), to the influence of n4,, (the imaginary part of n4). In fact, the theory considering only the n4,, term predicts curves narrower by a 0.64 factor close to the observed factor 0.6. A similar interpretation was recently given for strong nonlinear behavior observed in a photothermal experiment in Tb3 þ doped LSCAS [23]. Using Eq. (5), from the n2’, Δαp ¼ 4.1 10 25 cm3 and 8.0 10 26 cm3 were obtained for LSCAS and CAS, respectively. In principle, the polarizability of a certain state can be calculated as summation over the contribution of all possible transitions. Powell and Payne [6], estimated Δαp 8 10 26 cm 3 for the free Nd3 þ ion, considering only the contribution of the lowest 4f-5d transition at energy 80,000 cm 1. The oscillator strength of 4f-5d transitions are typically 4–5 orders of magnitude higher than 4f4f transitions which are dipole forbidden, so they should give the
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Fig. 3. Z-scan results in LSCAS glass (0.2 wt% of Tb3 þ ). (a) Closed aperture signal with I0 ¼ 4.38 103 W/cm2, zc ¼0.24 cm (b) open aperture signal with I0 ¼4.4 104 W/cm2, zc ¼0.13 cm.
Fig. 4. Z-scan results in CAP glass (2.0 wt% of Tb3 þ ). (a) Closed and open aperture signal Pexc ¼300 mW, zc ¼ 0.24 cm (b) transient measurement with sample fixed at peak position of the Z-scan curve with Pexc ¼ 360 mW. The single exponential fit of the data results in τ ¼ 2.86 ms.
main contribution to oscillator model [6,7]:
Δαp (ω) =
Fig. 5. Dependence of amplitude of the Z-scan signal (ΔTpv) with incident power for CAP glass, where open circle is experimental data.
Δαp. Therefore, according to this single-
⎤ fg fex e2 ⎡ ⎢ ⎥ − 2 m ⎣ (ωo − Δ)2 − ω2 ωo − ω2 ⎦
(10)
where e is the electron charge, m the electron mass, ℏω0 the energy of the 4f-5d transition, ℏΔ the excited state energy and fex (fg) is the oscillator strength of the transition from excited (ground) state to 5d level. For Nd3 þ , Powell and Payne [6] observed a strong host dependence of Δαp, which varies one order of magnitude. This variation was attributed to the sensitivity of radial integral ⟨4f r 5d⟩ with the host character. The 4f-5d transitions of Tb3 þ doped materials are well known to be presented in relative low energies (35000–50000 cm 1), as observed in the absorption and excitation spectra [8,9]. For CAS and LSCAS, these transitions were observed at about the same energy ( 35,000 cm 1). However, the corresponding peak at the excitation spectra is much larger in LSCAS compared to CAS, in qualitative agreement with the observation that Δαp is larger in
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Fig. 6. Z-scan results in LSCAS glass (0.5 wt% of Tb3 þ ). (a) Closed aperture signal with Pexc ¼32 mW, I0 ¼ 6.2 103 W/cm2, zc ¼ 0.24 cm and (b) open aperture signal with Pexc ¼202 mW, I0 ¼ 3.6 104 W/cm2, zc ¼0.14 cm.
probably due to the lower energy of the 4f-5d transitions of Tb3 þ ( 35,000 cm 1) compared to Nd3 þ (50,000–80,000 cm 1) and other rare earths ions [8,9,23]. Our results indicate that the investigation in Tb3 þ doped glasses is very promising for a better understanding of the physical origin of Δαp and the role of the 4f-5d transitions. The nonlinear refractive index 10 9 cm2/W is very high for a material with low absorption coefficient (αabs). Consequently, the figure of merit (n2/αabs) 10 7 cm3/W is high for a material with miliseconds response time, much faster than photorefractive materials [1,4]. As a drawback, a strong excited state absorption strongly depletes its population and consequently the refractive index change, an effect that also prevents efficient cw laser action at 545 nm in Tb3 þ doped materials [9,10].
Acknowledgments Fig. 7. Dependence of amplitude signal in Z-scan with incident power: LSCAS (0.5 wt% of Tb3 þ ) in open circles and CAS (0.5 wt% of Tb3 þ ) in close circles. The lines are guides to the eyes.
LSCAS. These indicate that the oscillator strengths fex and fg are sensitive to the amount of SiO2 in the matrix as observed for the UV transparence, which is much higher in CAS compared to LSCAS. The Δαp observed in CAP is 1 order of magnitude lower than observed in CAS and LSCAS, probably because of the higher energy of the 5d levels in phosphate glasses ( 48000 cm 1) [24,25]. However, this point should be further investigated in the specific CAP composition used in this paper.
5. Conclusions The Δαp 10 24 cm3 value measured in Tb3 þ low concentration doped LSCAS is the highest value ever reported for a RE. It is typically 2 order of magnitude larger than the values reported in most of Er3 þ , Nd3 þ [4,6,7], Yb3 þ [16] doped materials. The Δαp origin has been attributed to mainly nonresonant transitions in the UV, particularly the 4f-5d transitions of RE ions. Although far from resonance, 4f-5d are dipole electric allowed, so they have oscillator strength 5 orders of magnitude larger than resonant f-f transitions. Therefore, the high Δαp observed in Tb3 þ is
We are thankful to the Brazilian Agencies Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for the financial support of this work.
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Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Pump-induced refractive index changes in Tb3 þ doped glasses T.A. Vieira a, J.F.M. dos Santos a, Y.M Auad a, L.A.O. Nunes a, N.G.C Astrath b, M.L. Baesso b, T. Catunda a,n a b
Instituto de Física de São Carlos, Universidade de São Paulo, SP, Brazil Departamento de Física, Universidade Estadual de Maringá, PR, Brazil
art ic l e i nf o
a b s t r a c t
Article history: Received 15 October 2014 Received in revised form 14 July 2015 Accepted 21 July 2015 Available online 22 August 2015
It now well known in laser materials, that a refractive index change appears when the active ions are pumped from ground to excited state due to the polarizability difference between ground and excited states (metastable). In this paper this effect was investigated in Tb3 þ doped glasses: calcium alumino phosphate (CAP), low-silica calcium aluminosilicate (LSCAS) and calcium aluminosilicate (CAS). The measurements were performed using the time resolved Z-scan technique, with an Ar þ laser at 488 nm, close to the resonance of 7F6-5D4 absorption line, where 5D4 is a metastable state. We obtained for lowsilica calcium aluminosilicate glass Δαp 10 24 cm3 which is the highest value ever reported for a RE doped material. & 2015 Elsevier B.V. All rights reserved.
Keywords: Z-Scan Nonlinear refractive index Polarizability difference Tb3 þ
1. Introduction There has been a great interest in the study of nonlinear properties of ion doped materials due to spatial hole burning, which can induce both refractive-index and gain gratings, its implications in laser behavior (including bistability and instabilities), as well as applications such as phase conjugation of high power laser systems [1,2]. The observation of Q-switching behavior in Cr:LiSAF has been attributed to the effect of Refractive Index Changes (RIC) of the Cr ion due to the excited state population [3]. In addition, resonantly enhanced nonlinear phase shifts have been observed in optically pumped fibers (doped with Er3 þ , Nd3 þ , Sm3 þ and Yb3 þ ), motivated by applications such as all-optical switches, transient Bragg gratings, etc. The nonlinear properties of ion doped materials have also been applied to demonstration of interesting phenomena such as fast and slow light [4]. More recently, it was demonstrated in ruby that the effect of rotatory photon drag can be enhanced by the use of slowlight medium [5]. Usually, RIC are studied by populating the ion metastable state through the excitation of higher energy absorption bands, which nonradiatively decay to the metastable state. It is well known that RIC arises from the difference of ion excited state polarizability, αpex, compared to the ground state one, αpg. This polarizability difference, Δαp ¼ αpex αpg, is attributed mainly to the interaction with nonresonant transitions (in the UV) which are far from resonance of the laser transition. For rare-earth doped ions, it is n
Corresponding author. Tel.: þ 55 1633739861. E-mail address: [email protected] (T. Catunda).
http://dx.doi.org/10.1016/j.jlumin.2015.07.035 0022-2313/& 2015 Elsevier B.V. All rights reserved.
generally believed that the 4f-5d transitions give the main contribution to Δαp [6,7]. The energy of 4f-5d transitions in Tb3 þ are known to be very low compared to other rare earth ions. For instance, in Tb3 þ doped calcium aluminosilicate glasses, this transition was observed 35000 cm 1 in the excitation spectrum [8,9]. This ion have emissions from ultraviolet to infrared through metastable levels 5D3, 5D4 and 7F0. The intense green emission due transition 5D4-7F5 has potential application in green light emitters, scintillators, and lasers [10]. Z-scan is nowadays the most popular technique to determine n2 in different kinds of materials [11]. In ion doped solids with a slow nonlinearity, the time-resolved Z-scan method has been used because of its high sensitivity and its ability to investigate the nonlinearity's physical origin [4,12–16]. This method was also recently used to distinguish population lens from thermal lens contributions to the nonlinearity. The Z-scan method was successfully apply to ruby (Al2O3:Cr3 þ ) which is considered as a reference among the ion doped materials, since it was used to demonstrate many nonlinear effects such as bistability, degenerate and nearly degenerate four-wave-mixing, nearly degenerate twowave mixing, transverse phase modulation, interferometric measurements of RIC, etc. [17–19]. The Δαp 1.8 10 25 cm3 in the blue–green visible range (457–528 nm) is in very good agreement with all data available [14]. In this paper, time resolved Z-scan measurements were performed in Tb3 þ doped glasses, at 488 nm, close to the resonance of 7F6-5D4 transition, where 7F6 is the ground state. More details about the Tb þ 3 luminescence dynamics in this glass were recently published [9]. In this paper very high n2 and Δαp values were obtained and a strong host dependence. The values found in calcium
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aluminosilicate glasses are much larger than in phosphates. Among the aluminosilicate glasses, it was observed a larger Δαp in the sample with lower silica and consequently, lower band edge energy and refractive index [20].
2. Theoretical background In ion doped materials, such as rare earth and transition metal ions, the redistribution changes the overall optical susceptibility, χ, and therefore the refractive index. Here we consider that the system has only one metastable state in the stationary state which is the case of most ion doped laser materials in the cw regime. If the pump beam has a Gaussian intensity profile, the excited state population will follow the same radial profile. This makes the refractive index variation, Δn, to acquire a lens-like profile. Consequently, this phenomenon is known as the Population Lens (PL) effect. Since the excited state population is, in first order, proportional to pump intensity, the PL is equivalent to Kerr nonlinearity, where Δn ¼n2I. The electronic refractive index changes due to the active ion can be analyzed considering in the PL effect the susceptibility, which is given by [4,12]:
χ = χm +
1 (Ng χg + Nex χex ) Nt
(1)
where χm represents the host matrix's susceptibility, Nt is the ion concentration (cm 3), Ng and Nex are the ion concentration in the ground and excited state, respectively, and χg, χex are the complex susceptibilities of the dopand ion in the ground and excited state, respectively. We are assuming that the medium has only one metastable excited level, whose lifetime is much longer compared to the other excited states. Therefore, in the CW regime only the ground state and the metastable excited state are significantly populated, so that Nt∼Ng þNex. We are interested in the refractive index change produced by the excited state population, so the local field effect should be introduced as
⎤ n2 − 1 4π ⎡ Nex . χex − χg ⎥ = ⎢ χ + χg + ⎦ 3 ⎣ m Nt n2 + 1
(
)
(2)
with the refractive index given by n ¼n0 þ Δn, where n0 the refractive index of the unpumped glass, n02 ¼1 þ4πfL(χm þNt.χg) and fL ¼ (n02 þ 2)/3 is the Lorenz local field correction factor. The refractive index change Δn is proportional to the susceptibility change due to the excited state population is given by
∆n =
2π 2 Nex (χ − χg ) f n0 L Nt ex
(3)
where Δn is a complex quantity which real part is proportional to ∆αp = Re {(χex − χg ) /Nt }, the polarizabilities difference of the ion in excited and ground states. The imaginary part of ∆n is proportional to Δs ¼(sex sg), the difference between ion excited state absorption (ESA) and ground state absorption cross sections. We'll first consider the unsaturated pump regime, where Nex∼Nt.I/Is, approximation valid for Nex o o Nt, with the pump saturation intensity given by
Is =
hv σg τ
Fig. 1. Partial energy level diagram of Tb3 þ ions in low silica aluminosilicate glasses. The arrows indicate the excitation at 488 nm and main green emission at 544 nm.
(4)
Where hν is the pump photon energy and τ the lifetime of the metastable excited state. Therefore, Δn is proportional to the intensity and can be written similarly to the Kerr nonlinear effect, n ¼n0 þn2I, with a complex, n2 ¼n2′ in2′′, given by [14]
n2 =
⎞ Nt ⎛ 2π 2 λ fL ∆αp − i ∆σ ⎟ ⎜ Is ⎝ n0 4π ⎠
(5)
Supposing that the pump laser is turned on at t¼ 0, the excited state population Nex(t) can be calculated by rate equations as [12]
Nex (t ) = Nt
I (1 − e−t/ τ ) Is
(6)
where I is the laser incident intensity. Eq. (6) is valid only for Io oIs since it does not include the effect of depletion of ground state population. In this paper, time resolved Z-scan measurements were performed in three different Tb3 þ doped glass. An Ar þ laser was used at 488 nm, close to the resonance of 7F6-5D4 transition, where 7F6 is the ground state. As depicted in Fig. 1, several emission lines 5 D4-7Fj are observed and Tb3 þ is known for its strong green emission at 544 nm. The quantum efficiency is typically high due to the large energy gap (15000 cm 1) below the 5D4 state. In most materials, this level is not significantly affected by concentration quenching, as oppose to the of 5D3 state.
3. Experimental 3.1. Preparation of samples Calcium Aluminosilicate glass: two different matrix compositions were studied, the Low Silica Calcium Aluminosilicate (LSCAS) and the Calcium Aluminosilicate (CAS). The silica content is the main difference in these compositions: LSCAS nominal composition of (47.4 x/2)% CaOþ (41.5 x/2)% Al2O3 þ 4.1% MgOþ7.0%SiO2 þx% Tb4O7 with x¼0.5% and 0.2%; CAS with nominal composition is 33.25% CaOþ 27.65%Al2O3 þ 4.1% MgOþ34%SiO2 þ0.5% Tb4O7. Both mixtures were melted under vacuum atmosphere at 1600 °C for two hours. The fact that the samples are prepared in a vacuum furnace has eliminated the radicals OH and increases the transmission window (0.3–6 μm). Calcium Aluminophosphate (CAP) nominal composition: 58%(NaPO3)3 þ40%Al(PO3)3 þ2%Tb4O7 prepared with reagent (NaPO3)3 and Al(PO3)3 using conventional melt at temperatures between 750
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and 1150 °C. More details about CAS and CAP sample preparation can be found in Refs. [20,21]. Under 488 nm cw excitation, all samples presented nearly exponential decays (5D4-7Fj(j ¼ 3–6)) with lifetimes: 1.9 ms (LSCAS), 3.4 ms (CAS) and 2.9 ms (CAP). It was previously observed that these decays times are nearly independent of Tb3 þ concentration up to 5 wt% [8–10]. 3.2. Z-scan technique Among the techniques applied to characterize the n2 material, Z-scan is the most popular one [9]. In addition to the simplicity of the experimental setup, a Z-scan measurement provides a sensitive method for determination of the signal and value of the real and imaginary part of χ(3). The technique relies on the basic idea of relating the beam center intensity variation with the refractive index variation. This can be done, monitoring the normalized transmittance as a function of sample path along the incident beam. The transmittance variation between peak and valley position is proportional to the induced phase shift, ΔΦ0, given by [9]
ΔTp − v ≈ 0. 406ΔΦo
(7)
with
ΔΦo = kL eff n2‵ I0
(8)
where k is the pump wavenumber, Leff is the effective length, and I0 is the beam waist incident intensity. Moreover, the separation between the peak and valley position is related to the Rayleigh range through ΔZp v E 1.7zc. When all light is focused in the detector, the maximum transmittance variation is related with the imaginary part of n2 as
Tp − 1 ≈ kL eff n2‵‵ I0
(9)
where Tp is the transmittance with the sample at the beam waist position. τ In slow absorbers, where Δn(t)∝Ne(t)∝Nt.(1 e t/ ) and τ Z100 μs, it is possible to apply the time resolved Z-scan procedure [12]. In this case, a chopper modulates the beam and the transmittance is defined as the ratio between the intensity at a time ti o o τ, where there is only linear effects, and at a time tf 4 4 τ, where both linear and nonlinear effects are present. The main advantage of this technique is to eliminate linear parasitic effects due to unparallel faces of the sample, polish imperfections, etc.; enhancing the sensitivity. In this way, the signal-to-noise ratio achieved is much better than the one obtained in the standard Z-scan set-up Fig. 2. Fig. 3 shows a typical Z-scan signal, obtained with 500 averages for each z position. The fit of Fig. 3(a) resulted in zc ¼ 0.24 cm and ΔΦ0 ¼ 0.012.
4. Results and discussion Calcium AluminoPhosphate (CAP) – the Z-scan measurements were performed in CAP sample with Tb3 þ concentration, Nt ¼2.15 1020 cm 3. Fig. 4(a) shows typical data obtained in CAP at 488 nm with chopper frequency f¼ 32 Hz and ti ¼40 ms, tf ¼ 10 ms. The measurements were performed in low intensity to avoid saturation effect (I0 o oIs ¼1.5 106 W/cm2). By Eq. (8) we found the real nonlinear refractive index n2’¼1.6 10 11 cm2/W and, from Eq. (5), the polarizability difference Δαp 1.6 10 26 cm3 is obtained from the linear fit of Fig. 5. We did not observe any signal in open aperture (S¼100%) photodetector, even for the maximum power available. The transient signal, Fig. 4(b) was obtained at peak position of z-scan curve and fitted by exponential function Eq. (6), give us a response time 2.86 ms, in good agreement with
Fig. 2. Experimental setup for the nonlinear laser spectroscopy. The closed aperture (S¼ 30%) and open aperture (S¼100%) signals are proportional to the real and imaginary parts of n2, respectively, where S is the aperture factor as defined in Ref. [11].
luminescence lifetime (2.9 ms). Fig. 6 shows a linear dependence of peak and valley transmittance ΔΤpv with excitation power, as expected by Eq. (8). Calcium Aluminosilicate (LSCAS and CAS) – the 0.5 wt% LSCAS sample has a Tb3 þ concentration Nt ¼ 4.7 1019 cm 3 (0.5 wt%) and Is ¼2.3 106 W/cm2 is obtained using s ¼9.8 10 23 cm2 (at 488 nm) and τ ¼1.9 ms. Typical Z-scan data are shown in Fig. 6, resulting in n2 ¼(4.3 þ0.004i) 10 10 cm2/W. The 0.5 wt% CAS glass presented n2’ ¼1.4 10 10 cm2/W. No open aperture signal was observed even at maximum available power (n2’’E0). Fig. 7 shows the power dependence of the Z-scan signal amplitude for both CAS and LSCAS, samples. Differently than observed in CAP (Fig. 5), Fig. 7 indicates a nonlinear increase of ΔTpv versus P. This behavior may be interpreted considering the higher order contributions to susceptibility: χ(3), χ (5), χ(7)… which would correspond to complex refractive index changes given by n2I, n4I2, n6I6… respectively as observed, for instance in colloidal solutions by [22]. In this paper, these high order terms might represent the effect of highly excited states (above the 5D4), which population depends on higher power of pump intensity. It should be noticed that the open aperture Z-scan signs, Tp 1, was much weaker than the close aperture. They could only be measured at intensities about one order of magnitude higher than the ones used for the closed aperture measurements, as shown in Fig. 3(b) and Fig. 4(b). It is remarkable that these curves are very narrow, with a width 60% narrower than expected by the standard Z-scan theory, which assumes Δn ¼n2I, for both real and imaginary parts of n2. However, in the high intensity regime the closed aperture signal, ΔTpv, is nearly proportional to the intensity square, so it is dominated by the n4, term. Therefore, we attribute the very narrowness of the curves shown in Fig. 3(b) and Fig. 6(b), to the influence of n4,, (the imaginary part of n4). In fact, the theory considering only the n4,, term predicts curves narrower by a 0.64 factor close to the observed factor 0.6. A similar interpretation was recently given for strong nonlinear behavior observed in a photothermal experiment in Tb3 þ doped LSCAS [23]. Using Eq. (5), from the n2’, Δαp ¼ 4.1 10 25 cm3 and 8.0 10 26 cm3 were obtained for LSCAS and CAS, respectively. In principle, the polarizability of a certain state can be calculated as summation over the contribution of all possible transitions. Powell and Payne [6], estimated Δαp 8 10 26 cm 3 for the free Nd3 þ ion, considering only the contribution of the lowest 4f-5d transition at energy 80,000 cm 1. The oscillator strength of 4f-5d transitions are typically 4–5 orders of magnitude higher than 4f4f transitions which are dipole forbidden, so they should give the
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Fig. 3. Z-scan results in LSCAS glass (0.2 wt% of Tb3 þ ). (a) Closed aperture signal with I0 ¼ 4.38 103 W/cm2, zc ¼0.24 cm (b) open aperture signal with I0 ¼4.4 104 W/cm2, zc ¼0.13 cm.
Fig. 4. Z-scan results in CAP glass (2.0 wt% of Tb3 þ ). (a) Closed and open aperture signal Pexc ¼300 mW, zc ¼ 0.24 cm (b) transient measurement with sample fixed at peak position of the Z-scan curve with Pexc ¼ 360 mW. The single exponential fit of the data results in τ ¼ 2.86 ms.
main contribution to oscillator model [6,7]:
Δαp (ω) =
Fig. 5. Dependence of amplitude of the Z-scan signal (ΔTpv) with incident power for CAP glass, where open circle is experimental data.
Δαp. Therefore, according to this single-
⎤ fg fex e2 ⎡ ⎢ ⎥ − 2 m ⎣ (ωo − Δ)2 − ω2 ωo − ω2 ⎦
(10)
where e is the electron charge, m the electron mass, ℏω0 the energy of the 4f-5d transition, ℏΔ the excited state energy and fex (fg) is the oscillator strength of the transition from excited (ground) state to 5d level. For Nd3 þ , Powell and Payne [6] observed a strong host dependence of Δαp, which varies one order of magnitude. This variation was attributed to the sensitivity of radial integral ⟨4f r 5d⟩ with the host character. The 4f-5d transitions of Tb3 þ doped materials are well known to be presented in relative low energies (35000–50000 cm 1), as observed in the absorption and excitation spectra [8,9]. For CAS and LSCAS, these transitions were observed at about the same energy ( 35,000 cm 1). However, the corresponding peak at the excitation spectra is much larger in LSCAS compared to CAS, in qualitative agreement with the observation that Δαp is larger in
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Fig. 6. Z-scan results in LSCAS glass (0.5 wt% of Tb3 þ ). (a) Closed aperture signal with Pexc ¼32 mW, I0 ¼ 6.2 103 W/cm2, zc ¼ 0.24 cm and (b) open aperture signal with Pexc ¼202 mW, I0 ¼ 3.6 104 W/cm2, zc ¼0.14 cm.
probably due to the lower energy of the 4f-5d transitions of Tb3 þ ( 35,000 cm 1) compared to Nd3 þ (50,000–80,000 cm 1) and other rare earths ions [8,9,23]. Our results indicate that the investigation in Tb3 þ doped glasses is very promising for a better understanding of the physical origin of Δαp and the role of the 4f-5d transitions. The nonlinear refractive index 10 9 cm2/W is very high for a material with low absorption coefficient (αabs). Consequently, the figure of merit (n2/αabs) 10 7 cm3/W is high for a material with miliseconds response time, much faster than photorefractive materials [1,4]. As a drawback, a strong excited state absorption strongly depletes its population and consequently the refractive index change, an effect that also prevents efficient cw laser action at 545 nm in Tb3 þ doped materials [9,10].
Acknowledgments Fig. 7. Dependence of amplitude signal in Z-scan with incident power: LSCAS (0.5 wt% of Tb3 þ ) in open circles and CAS (0.5 wt% of Tb3 þ ) in close circles. The lines are guides to the eyes.
LSCAS. These indicate that the oscillator strengths fex and fg are sensitive to the amount of SiO2 in the matrix as observed for the UV transparence, which is much higher in CAS compared to LSCAS. The Δαp observed in CAP is 1 order of magnitude lower than observed in CAS and LSCAS, probably because of the higher energy of the 5d levels in phosphate glasses ( 48000 cm 1) [24,25]. However, this point should be further investigated in the specific CAP composition used in this paper.
5. Conclusions The Δαp 10 24 cm3 value measured in Tb3 þ low concentration doped LSCAS is the highest value ever reported for a RE. It is typically 2 order of magnitude larger than the values reported in most of Er3 þ , Nd3 þ [4,6,7], Yb3 þ [16] doped materials. The Δαp origin has been attributed to mainly nonresonant transitions in the UV, particularly the 4f-5d transitions of RE ions. Although far from resonance, 4f-5d are dipole electric allowed, so they have oscillator strength 5 orders of magnitude larger than resonant f-f transitions. Therefore, the high Δαp observed in Tb3 þ is
We are thankful to the Brazilian Agencies Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for the financial support of this work.
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