Rotation of the absorption frame as a function of the electronic transition in the
Nd3+:YCa4O(BO3)3 monoclinic crystal
Simon Joly 1, Patricia Segonds 1, Benoît Boulanger 1*, Yannick Petit 2, Alexandra Peña Revellez1, Corinne Félix 1, Bertrand Ménaert 1
1 Institut Néel CNRS/UJF, 25 rue des Martyrs, BP 166, F38402 Grenoble Cedex 9 France 2 Université de Genève, 20 rue de l’Ecole de Médecine, CH-1205, Genève Switzerland
Abstract: We report the first measurements of the angular distribution of absorption under polarized light corresponding to seven electronic transitions of Nd3+ ions in the monoclinic crystal Nd:YCOB, revealing a rotation of the symmetry axes of the different patterns.
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1. Introduction
It is well known that in monoclinic crystals the crystallographic axes (a, b, c) do not coincide with the orthonormal dielectric frame (X, Y, Z) that is defined as the frame in which the real part of the complex permittivity tensor is diagonal [1]. Only two axes are in common, usually the Y- and b-axes by convention, and the orientation of the X- and Z-axes may vary as a function of any dispersive parameters of the refractive index as the wavelength or the temperature for example, while the crystallographic frame remains unchanged [2]. In previous works devoted to the symmetry of the imaginary part of the complex permittivity of monoclinic crystals, it was showed that the angular distribution surface of the absorption
#130252 - $15.00 USD Received 16 Jun 2010; revised 6 Jul 2010; accepted 11 Jul 2010; published 25 Aug 2010(C) 2010 OSA 30 August 2010 / Vol. 18, No. 18 / OPTICS EXPRESS 19169
coefficient magnitude measured in polarized light exhibits two layers, which is valid for the three monoclinic crystal classes, i.e. CS, C2 and C2h [3,4]. The section of this surface in the XZ plane is composed of two patterns with different behaviors: a circle corresponding to the polarization parallel to the Y-axis, and a bi-lobar pattern relative to the polarization perpendicular to the Y-axis [4]. Furthermore, the symmetry axes of this angular distribution, labeled as (Xabs, Yabs, Zabs), do not correspond to the dielectric frame. For example in the case of Nd3+:YCa4O(BO3)3 (Nd:YCOB) belonging to crystal class CS (space group Cm, unit cell parameters a = 8.076 Å, b ∇=16.02 Å, c ∇=3.53 Å, β = 101.23° between the a and c axes [5]), it was shown that the XZ and XabsZabs planes are both in the mirror plane m perpendicular to the b-axis, but rotated one from each other [4]. Then the b-, Y- and Yabs-axes are collinear. This specific feature of monoclinic crystals had been demonstrated by studying the electronic transition 4I9/2 → (4F5/2 + 2H9/2) of Neodymium ions Nd3+ at 812 nm in a Nd:YCOB crystal cut as a sphere [4].
In the present paper we report the first study to the best of our knowledge devoted to the orientation of the absorption frame of a monoclinic crystal as a function of the electronic transition. We considered seven transitions ranging between 355 nm and 887 nm of Nd3+ in Nd:YCOB with a Neodynium concentration of 5%.
2. Selected electronic transitions
We measured the transmission spectrum in polarized light along the Z-axis of a Nd:YCOB crystal cut as a slab in order to choose the peak wavelengths prior to the study of the related absorption angular distributions. The corresponding spectrum is shown in Fig. 1.
Fig. 1. Polarized transmission spectrum of 5%Nd:YCOB between 350 nm and 1000 nm corresponding to a propagation along the Z-axis of the dielectric frame (X, Y, Z); the crystal length along the Z-axis is 4.11 mm ; the dashed spectrum refers to the (X)-polarization (//) and the continuous spectrum corresponds to the Y-polarization (⊥) ; the arrows denote the selected transitions for the angular distribution measurement of absorption.
By comparison of the transmission spectrum of Fig. 1with that of pure YCOB crystal [6], we can clearly assign the seven selected absorption peaks to Nd3+ transitions. According to a Dieke diagram for rare earth ions, these seven transitions correspond to the same fundamental level, i.e. 4I9/2, and to the different excited levels shown in Fig. 2 [7].
#130252 - $15.00 USD Received 16 Jun 2010; revised 6 Jul 2010; accepted 11 Jul 2010; published 25 Aug 2010(C) 2010 OSA 30 August 2010 / Vol. 18, No. 18 / OPTICS EXPRESS 19170
Fig. 2. Energy levels of Nd3+ in Nd:YCOB and electronic transitions and corresponding wavelengths selected for the study of the absorption angular distribution.
3. Angular distribution of absorption
We considered the same method and experimental setup than that used in the previous study devoted to the angular distribution of absorption at 812 nm [4]. We took the same Nd:YCOB sphere with a diameter of 7.44 mm, placed at the center of an Euler circle and illuminated by a properly focused tunable polarized laser beam. It was possible to propagate the beam parallel inside the sphere, successively over θ = 360° in the XZ plane of the dielectric frame by steps of 5°, and to determine the magnitude of the corresponding absorption coefficient α//,⊥ from a transmission coefficient measurement T//,⊥ relative to the two orthogonal polarization states of
the light, (//) in the XZ plane and (⊥) along the Y-axis, according to //,
//,//,
1ln
F
T
L Tα
⊥⊥
⊥
= −
where
//,F
T ⊥ is the Fresnel transmission of the sphere, and L the sphere diameter.
The patterns corresponding to the seven selected transitions are given in Fig. 3. The fit of the experimental data of Fig. 3 were performed by using a propagation equation written in the dielectric frame (X,Y,Z) with a non diagonal tensor of the imaginary part of the complex dielectric permittivity as required by the monoclinic symmetry [3]. Notice that some aberrant experimental data points are due to a diffusion increase due to slightly damaged surface areas of the studied sample. Figure 3 well shows that the symmetry axes of the angular distribution of absorption (Xabs,Yabs,Zabs) do not coincide with the dielectric frame. Indeed the Xabs- and X-axes make an angle θabs, the same as between the Zabs- and Z-axes, the only common axes being Y and Yabs. All the values of θabs are reported in Tab. 1 as a function of the absorption peak wavelength. It clearly appears that the relative orientation between the dielectric and absorption frames strongly depend on the considered electronic transition, that is to say on the excited level since the fundamental one is common to all the transitions. It is important to notice that the orientation of the dielectric frame of Nd:YCOB does not depend on wavelength as in the case of undoped YCOB [6,8].
#130252 - $15.00 USD Received 16 Jun 2010; revised 6 Jul 2010; accepted 11 Jul 2010; published 25 Aug 2010(C) 2010 OSA 30 August 2010 / Vol. 18, No. 18 / OPTICS EXPRESS 19171
Fig. 3. Perpendicular (⊥, Y-axis) (dots) and parallel (//, XZ plane) (squares) components of the absorption coefficient measured as a function of the angle θ in the mirror plane m of 5%Nd:YCOB for seven electronic transitions of Nd3+: 4I9/2 → (2I11/2 + 4D5/2) at λ = 355 nm (a), 4I9/2 → 2K13/2 at λ = 534 nm (b), 4I9/2 → (2G7/2 + 4G5/2) at λ = 595 nm (c), 4I9/2 → 4F9/2 at λ = 686 nm (d), 4I9/2 → 4F7/2 at λ = 742 nm (e), 4I9/2 → 4F5/2 + 2H9/2 at λ = 812 nm (f), and 4I9/2 → 4F3/2 at λ = 887 nm (g). The continuous lines stand for the fit of the experimental data. (X, Y, Z) is the dielectric frame and (Xabs,Yabs,Zabs) the absorption frame. θabs is the oriented angle between the X- and Xabs-axes; the dashed radii and concentric circles at 1, 2, 3, 4 and 6 cm−1 stand for the polar scale.
#130252 - $15.00 USD Received 16 Jun 2010; revised 6 Jul 2010; accepted 11 Jul 2010; published 25 Aug 2010(C) 2010 OSA 30 August 2010 / Vol. 18, No. 18 / OPTICS EXPRESS 19172
Table 1 shows that the wavelength dependence of θabs is completely hieratic and does not follow a dispersion law. Note that when the orientation of the dielectric frame (X,Y,Z) of a monoclinic crystal has a variation as a function of the wavelength, which is the case of BiB3O6 for example, this variation exhibits a continuous behavior linked to the dispersion of the refractive indices [2].
The absorption axes are also those allowing the imaginary part of the complex dielectric permittivity tensor to be diagonalized [3]. Thus (Xabs,Yabs,Zabs) is the frame in which can be defined the principal values of the absorption coefficient. The corresponding values are given in Table 1. It is important to notice that they are completely different from those that would be measured in the directions of the dielectric frame, as can be easily seen in Fig. 3. Thus Table 1 provides essential tool to properly optimize absorption in devices that involve Nd:YCOB.
Table 1. Rotation angle between the dielectric and absorption frames, θabs, and principal values of the absorption coefficient (αXabs, αYabs, αZabs) in the monoclinic crystal
5%Nd:YCOB, as a function of the excited energy levels of the Nd3+ electronic transitions with 4I9/2 as the common fundamental level.
Fig. 4. Evolution of the oriented rotation angle θabs between the dielectric and absorption frames as a function of the different wavelengths corresponding to the excited energy levels of the seven electronic transitions studied in the monoclinic crystal 5%Nd:YCOB.
5. Conclusion
For the first time to the best of our knowledge, we demonstrated that the orientation of the angular distribution of the absorption coefficient of a monoclinic crystal depends on the considered electronic transition. This unexpected fundamental feature will find an explanation
#130252 - $15.00 USD Received 16 Jun 2010; revised 6 Jul 2010; accepted 11 Jul 2010; published 25 Aug 2010(C) 2010 OSA 30 August 2010 / Vol. 18, No. 18 / OPTICS EXPRESS 19173
from a microscopic quantum model taking into account the symmetry of the wave functions of the considered energy levels as well as the symmetry of the ions host crystallographic sites. Then the present work constitutes a suited experimental basis for further theoretical studies that are essential for a predictive approach of this phenomenon. They may concern crystals belonging to any monoclinic crystal class, i.e. CS, C2 and C2h, which is a fortiori valuable for the triclinic classes C1 and Ci since their degree of symmetry is lower.
The present work also reveals the necessity to reconsider all the values of absorption coefficients of monoclinic crystals tabulated in Handbooks, since they systematically had been measured in the dielectric frame instead of the absorption frame. Such revision of tabulated values is indeed of prime importance for future optimized exploitation of the numerous monoclinic crystals for optics. It is not only important in the case of laser materials such as Nd:(Gd,Y)Ca4O(BO3)3 [7], Yb:KLu(WO4)2 [9], or Yb:LiGd6O5(BO3)3 [10], but also for several other optical materials: Pr:Lu2SiO5 (photoluminescence) [11], Pr:Y2SiO5 (slow light) [12], or Sn2P2O6 (photorefractivity) [13].
Aknowledgment
The authors wish to thank Prof. Gérard Aka from Ecole Nationale Supérieure de Chimie de Paris (ENSCP) who grew the studied Nd:YCOB crystal.
#130252 - $15.00 USD Received 16 Jun 2010; revised 6 Jul 2010; accepted 11 Jul 2010; published 25 Aug 2010(C) 2010 OSA 30 August 2010 / Vol. 18, No. 18 / OPTICS EXPRESS 19174
