Anisotropy of the thermal and laser output properties in Yb,Nd:Sc2SiO5 crystal

Yuqing Zhao; Qiangguo Wang; Lihua Meng; Yongping Yao; Shande Liu; Na Cui; Liangbi Su; Lihe Zheng; Huiyun Zhang; Yuping Zhang

doi:10.3788/COL202119.041405

Abstract

The anisotropy of thermal property in an

Yb, Nd : {Sc}_{2} {SiO}_{5}

crystal is investigated from the temperature of 293 to 573 K. Based on the systematical study of thermal expansion, thermal diffusivity, and specific heat, the thermal conductivity in

Yb, Nd : {Sc}_{2} {SiO}_{5}

crystals orientated at (100), (010), (001), and (406) is calculated to be 3.46, 2.60, 3.35, and

3.68 W / (m \cdot K)

, respectively. The laser output anisotropy of a continuous-wave (CW) and tunable laser is characterized, accordingly. A maximum output power of 6.09 W is achieved in the

Yb, Nd : {Sc}_{2} {SiO}_{5}

crystal with (010) direction, corresponding to a slope efficiency of 48.56%. The tuning wavelength range in the

Yb, Nd : {Sc}_{2} {SiO}_{5}

crystal orientated at (100), (010), and (001) is 68, 67, and 65 nm, separately. The effects of thermal properties on CW laser performance are discussed.

Keywords

anisotropy thermal property tunable laser Yb,Nd:Sc2SiO5 crystal

1. Introduction

Recently, studies on laser crystals have accelerated the developments of novel laser devices and technologies. ${Yb}^{3 +}$ -doped crystal lasers drew great attention in the 1 µm spectral region because of the quasi-three-level scheme of ${Yb}^{3 +}$ ions^[1–3], which could effectively avoid occurrence of up-conversion, excited-state absorption, concentration quenching, and cross relaxation. Besides, low quantum defects could increase laser efficiency and reduce generation of thermal effects. In particular, the broad absorption and emission bands of the ${Yb}^{3 +}$ -doped crystals make it suitable for ultrafast and tunable laser operations. Many researchers make great efforts on Yb-doped gain medium and obtain lots of encouraging achievements. A 25.6 MW, high peak power $Yb : Y_{3} {Al}_{5} O_{12}$ (Yb:YAG) femtosecond laser was reported by Saraceno et al.^[4]. In 2017, Toci et al. reported growth of a $Yb : {Gd}_{3} {Al}_{2} {Ga}_{3} O_{12}$ (Yb:GAGG) crystal, spectral properties, and laser output characteristics^[5]. Nevertheless, the main defect of the ${Yb}^{3 +}$ -doped crystal is that the laser threshold is relatively high. The large crystal field strength in oxy-orthosilicate crystals could increase the manifold splitting of energy states in ${Yb}^{3 +}$ ions, which could partly overcome the shortage of high pump power threshold^[6]. Due to the unique property of negative thermo-optical coefficient $d n / d T$ , the ${Sc}_{2} {SiO}_{5}$ crystal is regarded as a promising laser crystal for ultrafast and high-power laser applications^[7–9]. The mode-locked $Yb : {Sc}_{2} {SiO}_{5}$ laser with a pulse width of 2.3 ps was first reported by Li et al.^[10]. Wentsch et al. reported an $Yb : {Sc}_{2} {SiO}_{5}$ thin-disk laser with a output power of 9.4 W in 2012^[11]. However, the low emission cross section of the $Yb : {Sc}_{2} {SiO}_{5}$ crystal limits the power extraction. Benefiting from energy transfer between ${Nd}^{3 +}$ ions and ${Yb}^{3 +}$ ions, an ${({Yb}_{0.05} {Nd}_{0.03} {Sc}_{0.947})}_{2} {SiO}_{5}$ ( $Yb, Nd : {Sc}_{2} {SiO}_{5}$ ) single crystal was grown in order to augment the gain cross section of the $Yb : {Sc}_{2} {SiO}_{5}$ crystal. Compared with the $Yb : {Sc}_{2} {SiO}_{5}$ crystal, the emission cross section of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal increases by 18.9%^[12]. A 3 W continuous-wave (CW) laser and a ultrafast laser with pulse width of 367 fs were achieved in a b-cut $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal^[13]. It is noticed that the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal possesses anisotropy properties due to the characterization of the monoclinic crystal structure. It is of significance in understanding the anisotropy of thermal and laser properties to design $Yb, Nd : {Sc}_{2} {SiO}_{5}$ laser devices.

In this Letter, thermal anisotropy in the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal was investigated. The thermal properties including thermal expansion, thermal diffusivity, and specific heat of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal were systematically studied from the temperature of 293 to 573 K. The thermal conductivity was determined accordingly. The CW and tuning characteristics of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal lasers along different principal directions were investigated.

2. Experimental Setup

The buoyancy method was used to measure density of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal at room temperature. The whole process is carried out without the crystal touching the bottom of the beaker. Specific heat of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal was measured by using a differential scanning calorimeter (DSC, Perkin-Elmer Diamond model DSC-ZC). A laser pulse method was applied to measure thermal diffusion coefficient of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal (apparatus: Netzsch Nano-flash model LFA 447). A thermal–mechanical analyzer (Diamond TMA, Perkin-Elmer Co.) was employed to measure thermal expansion coefficient of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal. The measuring temperature range was from 299 to 772 K with a heating step of 5 K/min.

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Figure 1 shows a schematic of the laser experiments. A 976 nm laser diode was selected as a pump source with a maximum pump power of 30 W. The pump light was delivered into the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal with an imaging system. The pump waist in the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal was about 200 µm. The uncoated $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystals cut along the principal axis (X, Y, and Z) were employed as laser medium. All of the laser crystals were wrapped by indium and mounted in a copper block in order to efficiently reduce the influence of the thermal effect. The cooling temperature for the copper block was maintained at 16°C. Mirrors $M_{1}$ , $M_{3}$ , and $M_{4}$ were all processed with antireflection (AR) coating around 976 nm and high-reflection coating (HR, $R > 99.9 %$ ) at 1030–1100 nm. The mirror radii of curvature were $r = 200$ , $r = \infty$ , and $r = 200 mm$ , respectively. The output mirrors $M_{2}$ and $M_{5}$ were both partial transmittance ( $T_{oc} = 1 %$ , 3%, 10%, and 25%) coated at 1030–1100 nm. As shown in Fig. 1(b), a quartz birefringent filter (BF) was employed in the tunable laser experiment to achieve laser tuning operation. The size of the BF was $Φ 25 \times 3 mm$ . A laser power meter (Fieldmax-II, Coherent) was employed to measure laser power. The laser output spectra were measured by a spectrometer (Avantes, AcaSpec-3468-NIR256-2.2).

Figure 1.Experimental setup of $Yb, Nd : {Sc}_{2} {SiO}_{5}$ lasers. (a) CW laser; (b) tunable laser.

3. Results and Discussion

The thermal expansion coefficient tensor of the monoclinic $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal in the conventional orientation can be expressed by Eq. (1): $(\begin{matrix} α_{11} & 0 & α_{13} \\ 0 & α_{22} & 0 \\ α_{31} & 0 & α_{33} \end{matrix}) .$ (1)

As can be seen, $α_{11}$ , $α_{31} (= α_{13})$ , $α_{22}$ , and $α_{33}$ are four independent thermal components. Therefore, thermal expansion coefficients of four different crystal orientations are required to determine $α_{i j}$ . In our experiment, four $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal samples cut along (100), (010), (001), and (406) orientations are prepared. By calculation, the four independent principal thermal components in Eq. (1) could be diagonalized in Eq. (2): $(\begin{matrix} 1.781 & 0 & 0 \\ 0 & 11.864 & 0 \\ 0 & 0 & 16.137 \end{matrix}) .$ (2)

Density of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal could be calculated by Eq. (3): $ρ = \frac{ρ_{0}}{(1 + \frac{Δ a}{a_{0}}) (1 + \frac{Δ b}{b_{0}}) (1 + \frac{Δ c}{c_{0}})} .$ (3)

Here, $ρ_{0}$ is density at room temperature. $Δ a / a_{0}$ , $Δ b / b_{0}$ , and $Δ c / c_{0}$ denote the thermal expansion coefficients of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal along crystallographic axes of (100), (010), and (001), respectively. Thermal conductivity $k$ of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal was calculated through Eq. (4), where $λ$ , $C_{p}$ , and $ρ$ denote the thermal diffusion coefficient, specific heat, and density of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal, respectively: $k = λ ρ C_{p} .$ (4)

Figure 2(a) shows the relationship between specific heat and temperature. The specific heat is enhanced linearly from 0.641 to $0.999 J \cdot g^{- 1} \cdot K^{- 1}$ with temperature increasing from 293 to 573 K. The experimental data presents that the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal possesses the advantage of tolerating more thermal energy. Figure 2(b) displays thermal diffusion coefficients of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal along the (100), (010), (001), and (406) directions at the temperatures ranging from 299 to 522 K. The achieved thermal diffusion coefficients were 1.486, 1.359, 1.336, and $1.553 {mm}^{2} / s$ in $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystals along crystallographic axes of (100), (010), (001), and (406) at room temperature. Figure 2(c) displays the thermal expansion coefficient as a function of temperature. It can be observed that the thermal expansion coefficient variation is almost linear over the entire temperature range. Figure 2(d) presents density values at different temperatures. Density of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal is $3.51 g \cdot {cm}^{- 3}$ at room temperature.

Figure 2.Thermal properties of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal versus temperature. (a) Specific heat; (b) thermal diffusion coefficient; (c) thermal expansion coefficient; (d) density.

Figure 3 depicts the relationship between the thermal conductivity and temperature. Thermal conductivity of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal decreases with the increasing temperature.

Figure 3.Calculated thermal conductivity in a single $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal.

Thermal conductivity of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal at room temperature is 3.46, 2.60, 3.35, and 3.68 W/(m·K) along the (100), (010), (001), and (406) axes, respectively.

The monoclinic structure of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal belongs to the crystal system of $C_{2 / c}$ , which indicates an anisotropy performance of the laser output property. Thus, the orientation of the principal axis was determined. The angles between crystallographic axes ( $a$ , $b$ , $c$ ) in the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal are $β_{a b} = β_{b c} = 90 °$ and $β_{a c} = 103.8 °$ . In the monoclinic structure of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal, crystallographic axis $b$ is one of the principal axes that are collinear with the two-fold axis. The other two principal axes locating in the (010) face are at an angle to the crystallographic axes $a$ and $c$ , respectively. A $b$ -cut $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal sample with thickness of 1 mm was measured by an XPT-6-type polarized microscope to determine the angle relationship. Figure 4 shows the relationship between the principal axis and the crystallographic axis. The (010) face is perpendicular to the crystallographic axis $b$ . The angle between crystallographic axis $a$ and principal axis Z is measured to be 21.2°. Besides, that between crystallographic axis $c$ and principal axis Y is 35°.

Figure 4.Relationship between the principal axis and crystallographic axis (a, b, c) in the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal.

A linear laser cavity is designed to investigate anisotropy of the CW laser output properties of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystals. The CW output power versus absorbed pump power is shown in Fig. 5. As can be seen, the effect of anisotropy on laser output power was observed obviously. The maximum average output power of 6.09 W is generated in the X-cut $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal, corresponding to a slope efficiency of 48.56%. The anisotropy of laser output power may be partly attributed to the anisotropy of thermal properties. The expansion coefficients and thermal conductivities along the $a$ axis and $c$ axis are similar to and higher than that of the $b$ axis. In our experiment, the maximum absorbed pump power is 15.3 W in the ( $b$ axis) X-cut $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal, which is higher than that of the Y-cut and Z-cut $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystals. It clarifies that the X-cut $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal possesses relatively uniform thermal expansion and better heat dissipation along the radial direction. Meanwhile, it is worth noting that Fresnel reflection loss in the uncoated $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal is above 10%, which increases the lasing threshold and limits the output power.

Figure 5.Average output power versus absorbed pump power along different principal axes in the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal.

As shown in Fig. 1(b), a BF was inserted into the laser cavity at a Brewster angle to achieve laser tuning. Figures 6(a)–6(c) depict the relationship between output power and absorbed pump power with the V-type cavity. Compared with the linear cavity, output power achieved with V-type cavity was relatively lower because of the polarization and insertion loss. Under an absorbed pump power of 11.9 W, the maximum average output power of 3.9 W was obtained with the X-cut $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal, corresponding to a slope efficiency of 43.2%. Laser polarization was measured by guiding the laser beam passing through a half-waveplate and a polarizing beam splitter (PBS). The polarization is parallel to the Y direction of the X-cut crystal, to Z direction of the Y-cut crystal, and to X direction of the Z-cut crystal. The laser wavelength could be flexibly tuned in the emission band by carefully varying the BF. Figures 6(d)–6(f) present the tuning wavelength versus the corresponding output power at different transmittances. The CW tuning coverage is 68, 67, and 65 nm in X-, Y-, and Z-cut $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystals, corresponding to tuning ranges of 1031–1099, 1031–1098, and 1032–1097 nm, respectively. The CW and tunable laser parameters including laser threshold, output power, and tuning coverage of $Yb, Nd : {Sc}_{2} {SiO}_{5}$ are listed in Table 1. The multi-wavelength laser is achieved by adjusting the insertion angle of the BF. The emergence of gain competition between various wavelengths led to the occurrence of simultaneous multi-wavelength oscillation. Figures 7(a)–7(c) record the multi-wavelength spectra of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal with $T_{oc} = 1 %$ .

Figure 6.Tunable characteristics of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystals. (a), (d) X-cut crystal; (b), (e) Y-cut crystal; (c), (f) Z-cut crystal.

Crystal Orientation	$T_{oc}$ (%)	CW		Tunable			Tuning Coverage (nm)
Crystal Orientation	$T_{oc}$ (%)	$P_{\max}$ (W)	$η$ (%)	$P_{thr}$ (W)	$P_{\max}$ (W)	$η$ (%)	Tuning Coverage (nm)
X-cut (E $∥$ Y)	1	2.05	29.78	1.82	0.12	14.42	1040–1099 (59)
	3	3.48	42.80	1.97	2.33	29.27	1037–1092 (55)
	10	6.09	48.56	2.49	3.90	43.20	1031–1088 (57)
Y-cut (E $∥$ Z)	1	1.44	19.60	2.05	0.63	11.98	1038–1098 (60)
	3	2.82	35.52	2.06	2.04	27.64	1035–1096 (61)
	10	3.60	40.56	2.62	3.06	32.83	1031–1088 (57)
Z-cut (E $∥$ Z)	1	1.49	21.96	2.10	1.02	14.57	1040–1096 (56)
	3	3.46	41.81	2.23	2.35	27.59	1032–1097 (65)
	10	4.62	50.43	2.50	3.30	39.18	1033–1088 (55)

Table 1. Anisotropy of Output Parameters in an Yb,Nd:Sc₂SiO₅ Crystal Laser

View all Tables

Figure 7.Multi-wavelength laser output spectra. (a) X-cut crystal; (b) Y-cut crystal; (c) Z-cut crystal.

4. Conclusions

In conclusion, the anisotropy of the thermal and laser output properties in the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal was fully studied. The room temperature thermal conductivity is 3.46, 2.60, 3.35, and 3.68 W/(m· K) along crystallographic axes of (100), (010), (001), and (406), respectively. Due to relatively uniform thermal expansion along the radial direction and better heat conduction along the X direction of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal, the maximum output power of 6.09 W was generated in the X-cut $Yb, Nd : {Sc}_{2} {SiO}_{5}$ crystal. The tuning ranges of the $Yb, Nd : {Sc}_{2} {SiO}_{5}$ tunable laser are 68 nm, 67 nm, and 65 nm for X-, Y-, and Z-cut crystals, respectively.

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