Nonlinear spectroscopic properties of Yb3+-doped sesquioxides Lu2O3 and Sc2O3

doi:10.1364/OE.18.011173

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Nonlinear spectroscopic properties of Yb³⁺-doped sesquioxides Lu₂O₃ and Sc₂O₃

R. Soulard, R. Moncorgé, A. Zinoviev, K. Petermann, O. Antipov, and A. Brignon »View Author Affiliations

Optics Express, Vol. 18, Issue 11, pp. 11173-11180 (2010)
http://dx.doi.org/10.1364/OE.18.011173

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▸ Article Outline
– Abstract
1. Introduction
2. Interferometric measurements and associated refractive index changes
3. Excited-state absorption spectra and associated polarisability changes
4. Conclusion
– References and links

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Abstract

We report on the measurements of near-UV excited-state absorption (ESA) spectra and refractive index changes (RICs) in the two ytterbium doped laser crystals Yb:Lu₂O₃ and Yb:Sc₂O₃. ESA is assigned to ligand-to-metal charge transfer (LMCT) absorption transitions and RICs to the polarizability changes experienced by the Yb³⁺ ions due to these strong electric-dipole allowed absorption bands.

1. Introduction

It is now clearly recognized that the Yb-doped crystals and glasses have the most significant potential in the development of the present and future directly-diode-pumped high power and/or ultra-short pulse laser chains. This is due to their broad emission bands, enabling short-pulse generation, their long emission lifetimes, allowing large energy storage, and to the simple two-electronic energy-level structure of the Yb³⁺ lasing ions, which results in the absence of any excited-state absorption losses at the pump and the laser wavelengths and to limited thermal loads thanks to a reduced quantum defect (defined as the ratio of the laser emission over the excitation wavelengths).

In this context, an increased interest has appeared and many efforts have been dedicated in the last years to the particular properties and the development of crystals with a simple cubic structure, garnets and fluorides like YAG [1

J. Aus der Au, S. F. Schaer, R. Paschotta, C. Hönninger, U. Keller, and M. Moser, “High-power diode-pumped passively mode-locked Yb:YAG lasers,” Opt. Lett. 24(18), 1281–1283 (1999). [CrossRef]

–3

Y. Akahane, M. Aoyama, K. Ogawa, K. Tsuji, S. Tokita, J. Kawanaka, H. Nishioka, and K. Yamakawa, “High-energy, diode-pumped, picosecond Yb:YAG chirped-pulse regenerative amplifier for pumping optical parametric chirped-pulse amplification,” Opt. Lett. 32(13), 1899–1901 (2007). [CrossRef] [PubMed]

] and CaF₂ [4

A. Lucca, G. Debourg, M. Jacquemet, F. Druon, F. Balembois, P. Georges, P. Camy, J. L. Doualan, and R. Moncorgé, “High-power diode-pumped Yb3+:CaF2 femtosecond laser,” Opt. Lett. 29(23), 2767–2769 (2004). [CrossRef] [PubMed]

–6

M. Siebold, S. Bock, U. Schramm, B. Xu, J.L. Doualan, P. Camy, and R. Moncorgé, Appl. Phys. B – Lasers and Optics. 97(2), 327 (2009 [CrossRef]

], and the sesquioxides Y₂O₃, Sc₂O₃ and Lu₂O₃ [7

C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, T. Südmeyer, R. Peters, K. Petermann, G. Huber, and U. Keller, “Femtosecond Yb:Lu(2)O(3) thin disk laser with 63 W of average power,” Opt. Lett. 34(18), 2823–2825 (2009). [CrossRef] [PubMed]

–9

R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Broadly tunable high-power Yb:Lu(2)O(3) thin disk laser with 80% slope efficiency,” Opt. Express 15(11), 7075–7082 (2007). [CrossRef] [PubMed]

]. Indeed, these cubic crystalline structures present two main advantages: first, very good thermal properties [10

R. Gaumé, B. Viana, D. Vivien, J. P. Roger, and D. Fournier, “A simple model for the prediction of thermal conductivity in pure and doped insulating crystals,” Appl. Phys. Lett. 83(7), 1355 (2003). [CrossRef]

, 11

S. Chénais, F. Druon, S. Forget, F. balembois, and P. Georges, Progr. in Quant Electronics 30, 89–153 (2006). [CrossRef]

], with thermal conductivities on the order of 10 W/m/K for undoped crystals, second, the possibility to prepare them either in the form of large size and transparent bulk crystals and ceramics [8

M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped sub-100 fs Kerr-lens mode-locked Yb3+:Sc2O3 ceramic laser,” Opt. Lett. 32(23), 3382–3384 (2007). [CrossRef] [PubMed]

], with crystals already exceeding 30 cm diameter in the case of CaF₂ [12

http://www.schott.com/lithotec/english/products/calcium_Fluoride/calcium_fluoride.html

], for instance, or in the form of thin-disks [7

] by using the so-called “top-down” technique (thinned-down bulk crystals) or deposition techniques such as PLD (Pulsed Laser Deposition) and LPE (Liquid Phase Epitaxy).

Such high power laser developments raise however a number of fundamental and technological questions concerning the behaviour of the considered laser materials under intense optical pumping and emission conditions. From this point of view, several works have been recently published [13

R. Moncorgé, O. N. Eremeykin, J. L. Doualan, and O. L. Antipov, “Origin of athermal refractive index changes observed in Yb3+ doped YAG and KGW,” Opt. Commun. 281(9), 2526–2530 (2008). [CrossRef]

–16

A. A. Fotiadi, O. L. Antipov, and P. Mégret, “Dynamics of pump-induced refractive index changes in single-mode Yb-doped optical fibers,” Opt. Express 16(17), 12658–12663 (2008). [PubMed]

] about the existence in these materials of strong near-UV absorption bands which might be responsible for significant refractive index changes (RICs) when the lasing ions are pumped into their metastable emitting level, and for non-negligible multi-photon absorption losses at very high excitation pump powers.

After having recently discussed the case of Yb:YAG, Yb:YVO₄ and Yb:KGW [13

, 14

E. V. Ivakin, A. V. Sukhadolau, O. L. Antipov, and N. V. Kuleshov, “Transient grating measurements of refractive-index changes in intensively pumped Yb-doped laser crystals,” Appl. Phys. B 86(2), 315–318 (2007). [CrossRef]

], we concentrate here in this communication on the case of the two important laser crystals (and ceramics) Yb:Lu₂O₃ and Yb:Sc₂O₃. These crystals are indeed grown and conditioned nowadays, more particularly in the “thin-disk” configuration, to develop both high peak power and high repetition rate laser chains for different applications.

Our study is made in two steps. The first step deals with excited-state absorption (ESA) measurements performed in the near-UV spectral domain by using a specifically dedicated pump-probe experimental set-up. The second one deals with measurements of pump induced refractive index changes by using a transient interferometric technique based on a Jamin-Lebedev interferometer.

2. Interferometric measurements and associated refractive index changes

Details on the interferometric experimental set-up and on the procedure which is used to analyse the data can be found, respectively, in a paper dedicated to Yb:YAG [15

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, E. V. Ivakin, A. P. Savikin, A. V. Sukhodolov, and K. A. Fedorova, “Quant. Electr. QE 36 (5), 418 (2006) and Opt,” Lett. 31(6), 763 (2006).

] and in a very recent one concerning a series of well-known Nd-doped laser materials [17

R. Soulard, A. Zinoviev, J. L. Doualan, E. Ivakin, O. Antipov, and R. Moncorgé, “Detailed characterization of pump-induced refractive index changes observed in Nd:YVO(4), Nd:GdVO(4) and Nd:KGW,” Opt. Express 18(2), 1553–1568 (2010). [CrossRef] [PubMed]

]. In the present experiment, however, pumping was realized by using a QCW (500 µs pulses at 10Hz repetition rate) fiber-coupled diode laser operating around 969 nm. Such an excitation wavelength was not optimized for Yb:Lu₂O₃ or Yb:Sc₂O₃ but it was efficient enough to obtain good transient signals. The probe beam, as in the works performed previously, was provided by an He-Ne laser operating at 632.8 nm.

As explained in Ref [17

], pump-induced refractive index changes lead to phase-shift variations which can be evaluated from the observed relative intensity modulation of the interference signal

{\bar{Δ I (t) / 2 I_{0}}}^{x, y}

through the expression (in case of small modulations):

{\bar{Δ I (t) / 2 I_{0}}}^{x, y} \approx {\bar{Δ ϕ (t)}}^{x, y} = 2 π {\bar{Δ n (t)}}^{x, y, z} (2 l) / λ_{0}

(1)

where z stands for the propagation direction, x and y the transverse axes and λ₀ = 632.8nm is the wavelength of the probe beam. On the other hand, the transient interferometric signals, measured after QCW pulse excitation, can be satisfactorily described by such an expression as:

{\bar{Δ n (t)}}^{x, y, z} \approx {\bar{Δ n_{e l}}}^{x, y, z} \times \exp (- t / τ_{e l}) + {\bar{Δ n_{t h}}}^{x, y, z} \times \exp (- t / τ_{t h})

(2)

where the first and the second terms stand for the purely electronic and thermal contributions to the refractive index changes. These contributions indeed correspond to short- and long-lived exponential decays associated with the time-constant

τ_{e l} = τ_{F}

, the fluorescence lifetime of the Yb³⁺ emitting level, and the time-constant

τ_{t h}

associated with the dissipation of the generated thermal load in the crystal.

Figure 1 displays what was found in the case of the 0.85 mm thick 2.5%Yb:Sc₂O₃ single crystal used in the experiments. As illustrated, the electronic and thermal contributions with the time-constants

τ_{e l} = τ_{F} = 0.82 m s

and

τ_{t h} = 9.8 m s

, respectively, can be unambiguously deconvoluted and these contributions at time t = 0 (at the end of the pump pulse) amount to about 69 and 31%, respectively. In these conditions, at time t = 0, the calibration of these transient signals have allowed to estimate the electronic refractive index change (RIC)

{\bar{Δ n_{e l}}}^{x, y, z} \approx 6.5 \times 10^{- 6}

Fig. 1 Total refractive index changes Δn_total found in the case of Yb:Sc₂O₃, as measured (○○○) and as resulting (—) from the sum of the deconvoluted electronic and thermal contributions Δn_el and Δn_th, respectively.

On the other hand, the average pump power absorbed in the crystal was of the order of 9.1 mW which means, at a 10Hz repetition rate, an absorbed pump energy E_abs of about 910µJ per pulse. In such conditions, knowing the wavelength λ_p = 969nm of the pump photons, the average waist-radii

ϖ_{p} = 300 µ m

and

ϖ_{s} = 150 µ m

of the pump and probe beams inside the crystal, and the time-duration

τ_{p} = 500 µ s

of the QCW pump pulses, it is possible to determine the average density of excited ions

{\bar{N_{e x}}}^{x, y, z}

by writing:

{\bar{N_{e x}}}^{x, y, z} = \frac{2}{π (ϖ_{p}^{2} + ϖ_{s}^{2})} \frac{1}{l} \frac{E_{a b s} . λ_{p}}{h c} \frac{τ_{F}}{τ_{p}} [1 - \exp (- \frac{τ_{p}}{τ_{F}})]

(3)

Knowing this excited state ion density and assuming, as it is now generally admitted, that the observed RIC is coming from a variation of polarisability

Δ α_{p}

of the Yb³⁺ ions when they are brought into their emitting state, we have the now well-know expression:

{\bar{Δ n_{e l}}}^{x, y, z} = \frac{2 π}{n_{0}} f_{L}^{2} Δ α_{p} {\bar{N_{e x}}}^{x, y, z}

(4)

where

n_{0}

is the refractive index of the host material (1.96 and 1.91 around 1µm in the case of Sc₂O₃ and Lu₂O₃, respectively) and

f_{L} = \frac{n_{0}^{2} + 2}{3} \approx 1.94

is the usual Lorenz correction factor.

Using the above expressions, it was found for Yb:Sc₂O₃ the polarisability change:

Δ α_{p}^{Y b : S c_{2} 0_{3}} (633 n m) = (1.9 \pm 0.6) \times 10^{- 26} c m^{3}

The indicated error bar is a rough estimation (upper limit) resulting from the measurement uncertainties on the excited-ion density (15%) and on the electronic refractive index change (15%).

Figure 2 displays what was found in the case of the 1.05mm thick 2.5%Yb:Lu₂O₃ sample.

Fig. 2 Total refractive index changes Δn_total found in the case of Yb:Lu₂O₃, as measured (○○○) and as resulting (—) from the sum of the deconvoluted electronic and thermal contributions Δn_el and Δn_th, respectively.

With the same pumping conditions as above, the crystal absorbed about 5.3 mW, thus 533µJ per pulse, and the relative amount of the purely electronic contribution to the observed total refractive index change was about 83% with an absolute value

{\bar{Δ n_{e l}}}^{x, y, z} \approx 3.8 \times 10^{- 6}

. Such a value led in turn to the polarisability change:

Δ α_{p}^{Y b : L u_{2} 0_{3}} (633 n m) = (2.3 \pm 0.6) \times 10^{- 26} c m^{3}

It is also worth noting at this point that the measured thermal contributions to the registered overall refractive index changes in the two materials should be related in some way to their respective thermal properties. For instance, our RICs measurements, with a stronger thermal contribution in the case of Yb:Sc₂O₃ than in the case of Yb:Lu₂O₃ (about 31% against 17%) perfectly agree with the thermal conductivities of these doped materials with values about 8 and 12 W/m.K, respectively, as measured for the considered Yb³⁺ dopant concentration of about 7.25 x 10²⁰ ions/cm³ [9

3. Excited-state absorption spectra and associated polarisability changes

Details on the pump-probe ESA experimental set-up and on the procedure which is used to extract the data can be found in Refs 13

and 18

J. Margerie, R. Moncorgé, and P. Nagtegaele, “Spectroscopic investigation of variations in the refractive index of a Nd:YAG laser crystal: Experiments and crystal-field calculations,” Phys. Rev. B 74(23), 235108 (2006). [CrossRef]

. Pumping is realized with a standard (1cm⁻¹ bandwidth, 5ns pulse length) GWU model C355 OPO (Optical Parametric Oscillator) pumped by a 10Hz repetition rate, 10ns pulse duration Q-switched Nd-YAG laser frequency-tripled at 355 nm, and the probe is a synchronized pulsed xenon arc-lamp with a 5µs pulse duration. In the case of Yb:Lu₂O₃ and Yb:Sc₂O₃, the crystals were pumped around 975 and 976 nm, respectively, which correspond to the most intense “zero-line” absorption peaks [9

], and the time-resolved ESA spectra were registered between about 190nm (which is the spectral limit of the grating and reflecting mirrors) and 500 nm.

Figure 3 displays the ESA “difference” spectra of our 2.5%Yb doped Sc₂O₃ and Lu₂O₃ samples, as registered in the same near-UV spectral domain. It also displays their regular absorption spectra in terms of optical density (O.D). The ESA “difference” spectra are given by the logarithmic intensity ratio ln(I_u/I_p ) where I_p and I_u stand for the intensity of the probe beam transmitted by the crystals when they are respectively pumped and unpumped by the OPO.

Fig. 3 Optical density and excited-state “absorption difference” spectra of 0.85 mm thick 2.5%Yb:Sc₂O₃ and 1.05 mm thick 2.5%Yb:Lu₂O₃ single crystals

Because of the absorption edge of the crystal hosts, ESA measurements made below 240 nm were rather delicate. In fact, they were made points by points by allowing more and more light going through the pin-holes located along the pathway of the probe beam, by opening the slits of the spectrometer and by increasing the voltage on the detector (photomultiplier).

The measured transmitted intensities are related to the ground- and excited-state absorption cross-sections σ_gsa and σ_esa of the Yb³⁺ ions and to their ground- and excited-state ion densities N_g and N_ex by the usual expressions:

I_{u} = I_{0} T^{2} \exp [- σ_{g s a} N l] a n d I_{p} = I_{0} T^{2} \exp [- σ_{g s a} N_{g} l - σ_{e s a} N_{e x} l]

(5)

where

T = \frac{4 n}{{(1 + n)}^{2}}

is the Fresnel transmission coefficient, l the thickness of the crystals, and

N_{g} + N_{e x} = N

is the total Yb³⁺ ion density.

The above expressions thus lead to the relation:

σ_{e s a} - σ_{g s a} = \frac{\ln (I_{u} / I_{p})}{N_{e x} l}

(6)

The registered ln(I_u/I_p ) “absorption difference” spectra occur in fact in a spectral domain where there is no or negligible GSA coming from the Yb³⁺ ions. Indeed, the very steep absorption occurring around 240 nm (see in the Fig. 3) is due to the absorption edge of the crystal host and has nothing to do with an Yb³⁺ ground-state absorption. Moreover, even though this absorption tail was related to Yb³⁺ ions, the corresponding “GSA” cross section would be much smaller than the ESA one. Let us estimate for instance the cross sections which could be involved, with such an hypothesis, in the case of Yb:Sc₂O₃ and around 248 nm. Around that wavelength, which corresponds to a maximum of ln(I_u/I_p ), the “GSA” optical density is about 0.38, which means an absorption coefficient

α = \frac{0.38 \times \ln 10}{l} = 10.3 c m^{- 1}

, thus a “GSA” cross-section (for 2.5%Yb ≈7.25 × 10²⁰ ions/cm³) σ_gsa ≈1.4 × 10⁻²⁰ cm². Now, let us determine the value of σ_esa - σ_gsa from ln(I_u/I_p ) at the considered probe wavelength, by using Expr. (6) and by estimating N_ex. As the crystals are positioned immediately behind a pin-hole of calibrated diameter and the pump and probe beams propagate collinearly throughout this pin-hole and the crystals, the Yb³⁺ excited ion density N_ex is determined by measuring first the incident and transmitted pump intensities I_inc and I_trans , thus the absorbed intensity

I_{a b s} = I_{i n c} \times T - I_{t r a n s} / T

, then the average beam waist radius

ϖ_{p}

of the pump beam inside the crystal, by writing:

N_{e x} \approx \frac{I_{a b s} λ_{p}}{h c π ϖ_{p}^{2} l}

(7)

Doing so, the σ_esa - σ_gsa values derived around 248 nm in the case of Yb:Sc₂O₃ and around 261 nm in the case of Yb:Lu₂O₃ are approximately equal to 6.4 × 10⁻¹⁹ cm² and 7.5 × 10⁻¹⁹ cm², respectively, thus more than one order of magnitude larger the above “GSA” cross section σ_gsa .

This means that we can safely estimate, whatever is the origin of the absorption tail between about 220 and 330 nm, that:

σ_{e s a}^{Y b : S c_{2} O_{3}} (248 n m) \geq 6.4 \times 10^{- 19} c m^{2} a n d σ_{e s a}^{Y b : L u_{2} O_{3}} (261 n m) \geq 7.5 \pm 0.5 \times 10^{- 19} c m^{2}

This also means that the final ESA spectra have the same shape as the directly registered spectra Ln(I_u/I_p ). The ESA spectra of Yb:Sc₂O₃ and Yb:Lu₂O₃ thus extend from about 220 and 330 nm. Both spectra are probably made of two overlapping broad bands and it is so whatever is the time delay between the pump and probe beams. In the case of Yb:Sc₂O₃, the bands are peaking around 248 and 287 nm and the former is about twice more intense than the latter. In the case of Yb:Lu₂O₃, the bands have about the same intensity and they are peaking around 261 and 291 nm, thus closer to each other and slightly red-shifted by about 10nm.

Now, as already realized in the case of the other Yb³⁺ doped laser crystals Yb:YAG, Yb:YVO4 and Yb:KGW [13

, 14

], some comments can be made concerning the above derived ESA cross sections. Such high cross-sections indeed indicate very strong optical transitions, probably with oscillator strengths of about two orders of magnitude larger than the usual ff intraconfigurational near-IR absorption and laser transitions of the Yb³⁺ ions in these materials. After having initially assigned these strong near-UV absorption bands [15

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, E. V. Ivakin, A. P. Savikin, A. V. Sukhodolov, and K. A. Fedorova, “Quant. Electr. QE 36 (5), 418 (2006) and Opt,” Lett. 31(6), 763 (2006).

], as in the case of most of the Nd³⁺ doped materials [17

, 18

], to electric-dipole allowed fd interconfigurational transitions, it is now admitted in the case of Yb³⁺ doped materials [13

] that they predominantly come from electric-dipole allowed ligand-to-metal charge transfer (LMCT) transitions, thus, here, in the case of Yb-doped sesquioxides, to O^2-→Yb³⁺ electronic transitions. This is confirmed both by previous UV emission and excitation experimental data [19

L. van Pieterson, M. Heeroma, E. De Heer, and A. Meijerink, “Charge transfer luminescence of Yb3+,” J. Lumin. 91(3-4), 177–193 (2000). [CrossRef]

, 20

N. V. Guerassimova, L. A. Kamenskikh, D. N. Krasikov, V. V. Mikhailin, K. Petermann, D. F. de Sousa, G. Zimmerer “Charge transfer luminescence of Yb³⁺ in sesquioxides” HASYLAB Annual Report 2004.

] and by Hartree-Fock and DFT calculations [21

D. N. Krasikov, A. V. Scherbinin, A. N. Vasil’ev, I. A. Kamenskikh, and V. V. Mikhailin, “Model of Y2O3–Yb charge-transfer luminescence based on ab initio cluster calculations,” J. Lumin. 128(11), 1748–1752 (2008). [CrossRef]

]. According to UV excitation and emission data, the excitation spectrum of the considered LMCT luminescence is complex and made of two broad bands located around 6.2 eV (200nm) and 5.5eV (220 nm). According to the ab-initio cluster calculations, the center of the direct LMCT excitation band is located around 5.5-5.6 eV for both types of possible Yb³⁺ centres with C₂ and C_3i symmetry. On the other side, when considering the ESA data, for instance in the case of Yb:Sc₂O₃, there are two broad bands peaking around 248 nm (40300 cm⁻¹) and 288 nm (34700 cm⁻¹). Namely, with a metastable ²F_5/2 energy level around 1000 nm (10000cm⁻¹), it means two excited states around 50300 cm⁻¹ (199 nm) and 44700 cm⁻¹ (223 nm), thus in perfect agreement with the above LMCT excitation bands.

Assuming, in the end, that the position of the lowest absorption energy levels associated with these ESA bands is approximately given by the energy of the peaks located around 290 nm (thus

{\bar{υ}}_{e s a}^{C T} \approx 34480 c m^{- 1}

) added to the energy corresponding to the “zero-line” position (975nm) of the Yb³⁺ infrared emitting state (thus

{\bar{υ}}_{Z L} \approx 10260 c m^{- 1}

), it is possible to determine up to what extent these bands can account for the refractive index and polarizabilitiy changes observed when the Yb³⁺ ions are brought into this excited emitting state, by using the “spectroscopic” expression [22

R. C. Powell, Physics of Solid State Laser Materials, Springer, NY, Berlin, Heidelberg, 1998.

Δ α_{p}^{s p e c} (\bar{υ}) = 7.1 \times 10^{- 15} [\frac{f_{e s a}}{{\bar{υ}}_{e s a}^{2} - {\bar{υ}}^{2}} - \frac{f_{g s a}}{{({\bar{υ}}_{e s a} + {\bar{υ}}_{Z L})}^{2} - {\bar{υ}}^{2}}]

(8)

with [23

B. Di Bartolo, Optical Interactions in Solids, John Wiley and Sons Inc., NY, 1968.

f_{e s a} = \frac{1.13 \times 10^{19}}{λ^{2}} \int σ_{e s a} (λ) d λ

(9)

and by assuming that the GSA and ESA transitions to the considered charge transfer (CT) states have about the same oscillator strengths, i.e.

f_{e s a} \approx f_{g s a}

Using the above reported ESA data, the following results were then found:

f_{e s a}^{Y b : S c_{2} O_{3}} \approx 0.0054 a n d Δ α_{p}^{Y b : S c_{2} O_{3}} (633 n m) = (1.9 \pm 0.5) \times 10^{- 26} c m^{3}

f_{e s a}^{Y b : L u_{2} O_{3}} \approx 0.0073 a n d Δ α_{p}^{Y b : L u_{2} O_{3}} (633 n m) = (2.6 \pm 0.6) \times 10^{- 26} c m^{3}

thus in perfect agreement with the values found via interferometric measurements.

4. Conclusion

In conclusion, pump-probe interferometric and ESA experiments show unambiguously that the main contribution to the pump-induced electronic refractive index change observed in the Yb-doped sesquioxide laser crystals comes from a polarizability variation of the Yb³⁺ ions due to the non-resonant effect of broad and intense near-UV absorption bands associated with ligand-to-metal charge transfer transitions. With the experimental conditions of our interferometric set-up, thermally induced refractive index variations were also observed and could reach about 30% of the overall signal. This thermal contribution was found to be lower in the case of Yb:Lu₂O₃ that in the case of Yb:Sc₂O₃. Such a result can be probably related to the respective thermal properties of these two materials.

In the end, compared to the other already investigated Yb-doped laser crystals, the polarizability change occurring in the Yb-doped sesquioxides would be comparable to that found in the case of Yb:YAG (

Δ α_{p}^{Y b : Y A G} (633 n m) = (1.9 \pm 0.8) \times 10^{- 26} c m^{3}

) but substantially smaller than in the case of the Yb-doped tungstate and vanadate Yb:KGW and Yb:YVO₄ (

Δ α_{p}^{Y b : K G W} (633 n m) \approx (1.1 \pm 0.2) \times 10^{- 25} c m^{3}

and

Δ α_{p}^{Y b : Y V O_{4}} (633 n m) = (8.1 \pm 0.4) \times 10^{- 26} c m^{3}

Then, let us determine whether, in Yb-doped sesquioxides, phase gratings will dominate over absorption/gain gratings at the usual pump and laser wavelengths, by comparing the real and imaginary parts of the dielectric susceptibility, as given by the usual expression:

β = \frac{Δ χ_{R}}{Δ χ_{Im}} = \frac{8 π^{2} f_{L}^{2} \bar{υ}}{n} . \frac{Δ α_{p}}{Δ σ}

(10)

Δ σ

measures the cross section at the considered absorption or laser wavelength and

Δ α_{p}

measures the polarizability change estimated at these wavelengths by using the above expressions and the values obtained at 633nm.

Using the data reported in Ref. 9 for Yb:YAG and Yb:Lu₂O₃, and assuming, as in the case of the high power Yb:YAG laser chains, that pumping occurs around 945nm (secondary absorption peak), it is found

β (948 n m) =

3.4 for Yb:Lu₂O₃ against

β (940 n m) =

3.7 in the case of Yb:YAG, and

β (1030 n m) =

2.6 for Yb:Lu₂O₃ against 1.4 in the case of Yb:YAG. Thus phase grating is more important in the case of Yb:Lu₂O₃ than in the case of Yb:YAG. This can be used advantageously, for instance via two-wave mixing [24

O. L. Antipov, S. I. Belyaev, A. S. Kuzhelev, and D. V. Chausov, “Resonant two-wave mixing of optical beams by refractive-index and gain gratings in inverted Nd:YAG,” J. Opt. Soc. Am. B 15(8), 2276 (1998). [CrossRef]

], for high power laser operation with improved beam quality.

Acknowledgements

Authors acknowledge DGA for providing the PhD scholarship of one of us (R.S.), Mr. V. Ménard for preparing the samples and Drs P. Camy and J.L. Doualan for their help in setting-up the interferometric experiment.

References and links

1.	J. Aus der Au, S. F. Schaer, R. Paschotta, C. Hönninger, U. Keller, and M. Moser, “High-power diode-pumped passively mode-locked Yb:YAG lasers,” Opt. Lett. 24(18), 1281–1283 (1999). [CrossRef]
2.	D. J. Ripin, J. R. Ochoa, R. L. Aggarwal, and T. Y. Fan, “300-W cryogenically cooled Yb:YAG laser,” IEEE J. Quantum Electron. 41(10), 1274–1277 (2005). [CrossRef]
3.	Y. Akahane, M. Aoyama, K. Ogawa, K. Tsuji, S. Tokita, J. Kawanaka, H. Nishioka, and K. Yamakawa, “High-energy, diode-pumped, picosecond Yb:YAG chirped-pulse regenerative amplifier for pumping optical parametric chirped-pulse amplification,” Opt. Lett. 32(13), 1899–1901 (2007). [CrossRef] [PubMed]
4.	A. Lucca, G. Debourg, M. Jacquemet, F. Druon, F. Balembois, P. Georges, P. Camy, J. L. Doualan, and R. Moncorgé, “High-power diode-pumped Yb3+:CaF2 femtosecond laser,” Opt. Lett. 29(23), 2767–2769 (2004). [CrossRef] [PubMed]
5.	M. Siebold, M. Hornung, R. Boedefeld, S. Podleska, S. Klingebiel, C. Wandt, F. Krausz, S. Karsch, R. Uecker, A. Jochmann, J. Hein, and M. C. Kaluza, “Terawatt diode-pumped Yb:CaF2 laser,” Opt. Lett. 33(23), 2770–2772 (2008). [CrossRef] [PubMed]
6.	M. Siebold, S. Bock, U. Schramm, B. Xu, J.L. Doualan, P. Camy, and R. Moncorgé, Appl. Phys. B – Lasers and Optics. 97(2), 327 (2009 [CrossRef]
7.	C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, T. Südmeyer, R. Peters, K. Petermann, G. Huber, and U. Keller, “Femtosecond Yb:Lu(2)O(3) thin disk laser with 63 W of average power,” Opt. Lett. 34(18), 2823–2825 (2009). [CrossRef] [PubMed]
8.	M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped sub-100 fs Kerr-lens mode-locked Yb3+:Sc2O3 ceramic laser,” Opt. Lett. 32(23), 3382–3384 (2007). [CrossRef] [PubMed]
9.	R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Broadly tunable high-power Yb:Lu(2)O(3) thin disk laser with 80% slope efficiency,” Opt. Express 15(11), 7075–7082 (2007). [CrossRef] [PubMed]
10.	R. Gaumé, B. Viana, D. Vivien, J. P. Roger, and D. Fournier, “A simple model for the prediction of thermal conductivity in pure and doped insulating crystals,” Appl. Phys. Lett. 83(7), 1355 (2003). [CrossRef]
11.	S. Chénais, F. Druon, S. Forget, F. balembois, and P. Georges, Progr. in Quant Electronics 30, 89–153 (2006). [CrossRef]
12.	http://www.schott.com/lithotec/english/products/calcium_Fluoride/calcium_fluoride.html
13.	R. Moncorgé, O. N. Eremeykin, J. L. Doualan, and O. L. Antipov, “Origin of athermal refractive index changes observed in Yb3+ doped YAG and KGW,” Opt. Commun. 281(9), 2526–2530 (2008). [CrossRef]
14.	E. V. Ivakin, A. V. Sukhadolau, O. L. Antipov, and N. V. Kuleshov, “Transient grating measurements of refractive-index changes in intensively pumped Yb-doped laser crystals,” Appl. Phys. B 86(2), 315–318 (2007). [CrossRef]
15.	O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, E. V. Ivakin, A. P. Savikin, A. V. Sukhodolov, and K. A. Fedorova, “Quant. Electr. QE 36 (5), 418 (2006) and Opt,” Lett. 31(6), 763 (2006).
16.	A. A. Fotiadi, O. L. Antipov, and P. Mégret, “Dynamics of pump-induced refractive index changes in single-mode Yb-doped optical fibers,” Opt. Express 16(17), 12658–12663 (2008). [PubMed]
17.	R. Soulard, A. Zinoviev, J. L. Doualan, E. Ivakin, O. Antipov, and R. Moncorgé, “Detailed characterization of pump-induced refractive index changes observed in Nd:YVO(4), Nd:GdVO(4) and Nd:KGW,” Opt. Express 18(2), 1553–1568 (2010). [CrossRef] [PubMed]
18.	J. Margerie, R. Moncorgé, and P. Nagtegaele, “Spectroscopic investigation of variations in the refractive index of a Nd:YAG laser crystal: Experiments and crystal-field calculations,” Phys. Rev. B 74(23), 235108 (2006). [CrossRef]
19.	L. van Pieterson, M. Heeroma, E. De Heer, and A. Meijerink, “Charge transfer luminescence of Yb3+,” J. Lumin. 91(3-4), 177–193 (2000). [CrossRef]
20.	N. V. Guerassimova, L. A. Kamenskikh, D. N. Krasikov, V. V. Mikhailin, K. Petermann, D. F. de Sousa, G. Zimmerer “Charge transfer luminescence of Yb³⁺ in sesquioxides” HASYLAB Annual Report 2004.
21.	D. N. Krasikov, A. V. Scherbinin, A. N. Vasil’ev, I. A. Kamenskikh, and V. V. Mikhailin, “Model of Y2O3–Yb charge-transfer luminescence based on ab initio cluster calculations,” J. Lumin. 128(11), 1748–1752 (2008). [CrossRef]
22.	R. C. Powell, Physics of Solid State Laser Materials, Springer, NY, Berlin, Heidelberg, 1998.
23.	B. Di Bartolo, Optical Interactions in Solids, John Wiley and Sons Inc., NY, 1968.
24.	O. L. Antipov, S. I. Belyaev, A. S. Kuzhelev, and D. V. Chausov, “Resonant two-wave mixing of optical beams by refractive-index and gain gratings in inverted Nd:YAG,” J. Opt. Soc. Am. B 15(8), 2276 (1998). [CrossRef]

OCIS Codes
(160.3380) Materials : Laser materials
(140.3615) Lasers and laser optics : Lasers, ytterbium

ToC Category:
Materials

History
Original Manuscript: March 15, 2010
Revised Manuscript: April 27, 2010
Manuscript Accepted: April 28, 2010
Published: May 12, 2010

Citation
R. Soulard, R. Moncorgé, A. Zinoviev, K. Petermann, O. Antipov, and A. Brignon, "Nonlinear spectroscopic properties of Yb³⁺-doped sesquioxides Lu₂O₃ and Sc₂O₃," Opt. Express 18, 11173-11180 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-11-11173

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References

J. Aus der Au, S. F. Schaer, R. Paschotta, C. Hönninger, U. Keller, and M. Moser, “High-power diode-pumped passively mode-locked Yb:YAG lasers,” Opt. Lett. 24(18), 1281–1283 (1999). [CrossRef]
D. J. Ripin, J. R. Ochoa, R. L. Aggarwal, and T. Y. Fan, “300-W cryogenically cooled Yb:YAG laser,” IEEE J. Quantum Electron. 41(10), 1274–1277 (2005). [CrossRef]
Y. Akahane, M. Aoyama, K. Ogawa, K. Tsuji, S. Tokita, J. Kawanaka, H. Nishioka, and K. Yamakawa, “High-energy, diode-pumped, picosecond Yb:YAG chirped-pulse regenerative amplifier for pumping optical parametric chirped-pulse amplification,” Opt. Lett. 32(13), 1899–1901 (2007). [CrossRef] [PubMed]
A. Lucca, G. Debourg, M. Jacquemet, F. Druon, F. Balembois, P. Georges, P. Camy, J. L. Doualan, and R. Moncorgé, “High-power diode-pumped Yb3+:CaF2 femtosecond laser,” Opt. Lett. 29(23), 2767–2769 (2004). [CrossRef] [PubMed]
M. Siebold, M. Hornung, R. Boedefeld, S. Podleska, S. Klingebiel, C. Wandt, F. Krausz, S. Karsch, R. Uecker, A. Jochmann, J. Hein, and M. C. Kaluza, “Terawatt diode-pumped Yb:CaF2 laser,” Opt. Lett. 33(23), 2770–2772 (2008). [CrossRef] [PubMed]
M. Siebold, S. Bock, U. Schramm, B. Xu, J.L. Doualan, P. Camy, and R. Moncorgé, Appl. Phys. B – Lasers and Optics. 97(2), 327 (2009 [CrossRef]
C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, T. Südmeyer, R. Peters, K. Petermann, G. Huber, and U. Keller, “Femtosecond Yb:Lu(2)O(3) thin disk laser with 63 W of average power,” Opt. Lett. 34(18), 2823–2825 (2009). [CrossRef] [PubMed]
M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped sub-100 fs Kerr-lens mode-locked Yb3+:Sc2O3 ceramic laser,” Opt. Lett. 32(23), 3382–3384 (2007). [CrossRef] [PubMed]
R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Broadly tunable high-power Yb:Lu(2)O(3) thin disk laser with 80% slope efficiency,” Opt. Express 15(11), 7075–7082 (2007). [CrossRef] [PubMed]
R. Gaumé, B. Viana, D. Vivien, J. P. Roger, and D. Fournier, “A simple model for the prediction of thermal conductivity in pure and doped insulating crystals,” Appl. Phys. Lett. 83(7), 1355 (2003). [CrossRef]
S. Chénais, F. Druon, S. Forget, F. balembois, and P. Georges, Progr. in Quant Electronics 30, 89–153 (2006). [CrossRef]
http://www.schott.com/lithotec/english/products/calcium_Fluoride/calcium_fluoride.html
R. Moncorgé, O. N. Eremeykin, J. L. Doualan, and O. L. Antipov, “Origin of athermal refractive index changes observed in Yb3+ doped YAG and KGW,” Opt. Commun. 281(9), 2526–2530 (2008). [CrossRef]
E. V. Ivakin, A. V. Sukhadolau, O. L. Antipov, and N. V. Kuleshov, “Transient grating measurements of refractive-index changes in intensively pumped Yb-doped laser crystals,” Appl. Phys. B 86(2), 315–318 (2007). [CrossRef]
O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, E. V. Ivakin, A. P. Savikin, A. V. Sukhodolov, and K. A. Fedorova, “Quant. Electr. QE 36 (5), 418 (2006) and Opt,” Lett. 31(6), 763 (2006).
A. A. Fotiadi, O. L. Antipov, and P. Mégret, “Dynamics of pump-induced refractive index changes in single-mode Yb-doped optical fibers,” Opt. Express 16(17), 12658–12663 (2008). [PubMed]
R. Soulard, A. Zinoviev, J. L. Doualan, E. Ivakin, O. Antipov, and R. Moncorgé, “Detailed characterization of pump-induced refractive index changes observed in Nd:YVO(4), Nd:GdVO(4) and Nd:KGW,” Opt. Express 18(2), 1553–1568 (2010). [CrossRef] [PubMed]
J. Margerie, R. Moncorgé, and P. Nagtegaele, “Spectroscopic investigation of variations in the refractive index of a Nd:YAG laser crystal: Experiments and crystal-field calculations,” Phys. Rev. B 74(23), 235108 (2006). [CrossRef]
L. van Pieterson, M. Heeroma, E. De Heer, and A. Meijerink, “Charge transfer luminescence of Yb3+,” J. Lumin. 91(3-4), 177–193 (2000). [CrossRef]
N. V. Guerassimova, L. A. Kamenskikh, D. N. Krasikov, V. V. Mikhailin, K. Petermann, D. F. de Sousa, G. Zimmerer “Charge transfer luminescence of Yb3+ in sesquioxides” HASYLAB Annual Report 2004.
D. N. Krasikov, A. V. Scherbinin, A. N. Vasil’ev, I. A. Kamenskikh, and V. V. Mikhailin, “Model of Y2O3–Yb charge-transfer luminescence based on ab initio cluster calculations,” J. Lumin. 128(11), 1748–1752 (2008). [CrossRef]
R. C. Powell, Physics of Solid State Laser Materials, Springer, NY, Berlin, Heidelberg, 1998.
B. Di Bartolo, Optical Interactions in Solids, John Wiley and Sons Inc., NY, 1968.
O. L. Antipov, S. I. Belyaev, A. S. Kuzhelev, and D. V. Chausov, “Resonant two-wave mixing of optical beams by refractive-index and gain gratings in inverted Nd:YAG,” J. Opt. Soc. Am. B 15(8), 2276 (1998). [CrossRef]

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