## Abstract

We report the first measurements of the angular distribution of absorption under polarized light corresponding to seven electronic transitions of Nd^{3+} ions in the monoclinic crystal Nd:YCOB, revealing a rotation of the symmetry axes of the different patterns.

© 2010 OSA

## 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 coefficient magnitude measured in polarized light exhibits two layers, which is valid for the three monoclinic crystal classes, *i.e. C _{S}*,

*C*and

_{2}*C*[3,4]. The section of this surface in the

_{2h}**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 (

**X**,

_{abs}**Y**,

_{abs}**Z**), do not correspond to the dielectric frame. For example in the case of Nd

_{abs}^{3+}:YCa

_{4}O(BO

_{3})

_{3}(Nd:YCOB) belonging to crystal class

*C*(space group

_{S}*Cm*, unit cell parameters

*a*= 8.076 Å,

*b*∇=16.02 Å,

*c*∇=3.53 Å,

*β*= 101.23° between the

**and**

*a***axes [5]), it was shown that the**

*c***XZ**and

**X**planes are both in the mirror plane

_{abs}Z_{abs}*m*perpendicular to the

**b**-axis, but rotated one from each other [4]. Then the

**b**-,

**Y**- and

**Y**-axes are collinear. This specific feature of monoclinic crystals had been demonstrated by studying the electronic transition

_{abs}^{4}I

_{9/2}→ (

^{4}F

_{5/2}+

^{2}H

_{9/2}) of Neodymium ions Nd

^{3+}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 Nd^{3+} 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
.

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 Nd^{3+} transitions. According to a Dieke diagram for rare earth ions, these seven transitions correspond to the same fundamental level, *i.e.*
^{4}I_{9/2}, and to the different excited levels shown in Fig. 2 [7].

## 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 ${{\displaystyle \alpha}}_{//,\perp}=-\frac{1}{L}\mathrm{ln}\left(\frac{{{\displaystyle T}}_{//,\perp}}{{{\displaystyle T}}_{//,\perp}^{F}}\right)$ where ${{\displaystyle T}}_{//,\perp}^{F}$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 (**X _{abs}**,

**Y**,

_{abs}**Z**) do not coincide with the dielectric frame. Indeed the

_{abs}**X**- and

_{abs}**X**-axes make an angle θ

_{abs}, the same as between the

**Z**- and

_{abs}**Z**-axes, the only common axes being

**Y**and

**Y**. All the values of θ

_{abs}_{abs}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].

Table 1
shows that the wavelength dependence of θ_{abs} 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 BiB_{3}O_{6} 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 (**X _{abs}**,

**Y**,

_{abs}**Z**) 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.

_{abs}## 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 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. C _{S}*,

*C*and

_{2}*C*, which is

_{2h}*a fortiori*valuable for the triclinic classes

*C*and

_{1}*C*since their degree of symmetry is lower.

_{i}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)Ca_{4}O(BO_{3})_{3} [7], Yb:KLu(WO_{4})_{2} [9], or Yb:LiGd_{6}O_{5}(BO_{3})_{3} [10], but also for several other optical materials: Pr:Lu_{2}SiO_{5} (photoluminescence) [11], Pr:Y_{2}SiO_{5} (slow light) [12], or Sn_{2}P_{2}O_{6} (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.

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