Composition and structure analysis

In order to monitor the composition and quality of crystal fiber after growth, the EPMA (JXA-8900R, JEOL) method and X-ray diffractometer (D5000, Siemens) were used. EPMA is a qualitative and quantitative method for μm-sized elemental analysis on the surface of material. Figure 3.3 (a) shows the typical line scanning marks on the cross section of crystal fiber by electron beam. The composition of perfect YAG crystal comprises three Y₂O₃ and five Al₂O₃ in mole percentage, which are equivalent to 57.06 and 42.94 in weight percentage (wt.%), respectively. In Fig. 3.3 (b), the distributions of Y₂O₃ and Al₂O₃ show the average concentrations of 57.05 wt.% and 42.71 wt.% in YAG crystal fiber. It is in good agreement with perfect YAG crystal.

The tiny variation is attributed to the doping ions of Cr₂O₃ and CaO in YAG crystal fiber.

Fig. 3.3 (a) Photograph of line scanning marks on the cross section of crystal fiber. (b) The distribution of Y₂O₃ and Al₂O₃ in YAG crystal fiber.

In addition, the refractive index profile of crystal fiber was measured by normal incident Fresnel reflection. This technique, as devised by Eickhoff and Weidel [3.12], relies on the Fresnel relation between the refractive index of material and its reflectivity. At normal incidence we have

2

Figure 3.4 shows the refractive index profile of crystal fiber with Pyrex glass

cladding. It can clearly be seen that the refractive index between Cr:YAG crystal fiber and Pyrex glass cladding is sharp, which indicates that the Cr:YAG and Pyrex glass did not melt into each other while fused by gas torch. The refractive index of Cr:YAG crystal fiber was measured to be 1.82 when the index of Pyrex glass cladding (n=1.47) was used as a reference for calibration. In the refractive index measurement, the power fluctuation of the single mode DFB laser is 0.3% during an hour period, as shown in Fig. 3.5. We can estimate the sensitivity of refractive index according to the power fluctuation, as shown below.

n R

where the Δn is sensitivity of refractive index, n is refractive index of material, and ΔR is power fluctuation.

For the YAG crystal, the refractive index is 1.82 and its sensitivity of refractive index is about 0.02 by using this DFB laser.

0 10 20 30 40 50 60 70 80 90 100

Fig. 3.4 Refractive index profile of crystal fiber with Pyrex glass cladding.

0 5 10 15 20 25 30 35 40 45 50 55 60 1.241

1.242 1.243 1.244 1.245 1.246 1.247 1.248

DFB laser power (a.u.)

Time (min)

DFB laser power fluctuation (0.3%)

Fig. 3.5 The power fluctuation of DFB laser.

After measuring the composition and refractive index profile of crystal fiber, the crystal quality is also an important issue to be considered. It may affect both electrical and optical properties of the material and devices performance. We adopt the X-ray powder diffractometer to measure diffraction pattern of crystal fiber. By examining the full width half maximum (FWHM) of 2θ angle, the crystal quality can be examined. The use of X-ray source is kα1 and kα2 of copper. Figure 3.6 shows the normalized X-ray diffraction patterns of the raw material grown by the Czochralski method and the 400-μm diameter crystal fiber grown by LHPG method under 0.5 mm/min. The higher peak is caused by kα1, while the lower peak is caused by kα2.

The solid points are measured data with 0.02^o scanning step, and the curve lines were fitted to find out the peak positions and their FWHM values. The FWHM values of kα1 are 0.049^o and 0.065^o for the crystal grown by LHPG and CZ methods. The peak differences between kα1 and kα2 of LHPG and CZ methods are 0.071^o and 0.111^o, respectively.

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Fig. 3.6 The normalized X-ray diffraction patterns of Cr⁴⁺:YAG crystal grown by CZ and LHPG methods.

It is known that the crystal quality can be described by the ratio of width of random fluctuation (δd) to lattice constant (d). The calculated formula is shown below:

where the δθ is FWHM of fluctuation and the θ is the peak positions between kα1 and kα2.

The calculated result shows the crystal grown by CZ method is better than that by LHPG method. But it should be noted that the growth speed by CZ method is quite slow, which is typically about few hours for 1 mm in length. Therefore, the crystal fiber grown by LHPG method can maintain high quality under higher growth speed.

3.3 Oxidation states of Cr ion in Cr:YAG single crystal fiber

In this section, the concentrations of Cr2O3 and CaO in crystal fiber after growing by LHPG system were measured by EPMA method. The oxidation states of Cr ions were discriminated by LSCM measurement. In addition, the evolution of Cr³⁺

and Cr⁴⁺ distributions during diameter-reduction steps are obtained with high sensitivity. Combining the EPMA and LSCM techniques, a quantitative analysis in charge compensation efficiency was achieved.

3.3.1 Doping concentrations in single crystal fiber

Since the doping concentration is critical to the device performance, it should be well monitored at every diameter-reduction steps. Figure 3.7 shows the doping profiles of Cr2O3 and CaO by EPMA measurement with crystal fibers of various diameter, which are grown from a 2-mm-diameter raw material (α = 4.5 cm^-1). The concentrations of Cr2O3 and CaO in raw material are quite uniform. In Fig. 3.7 (a), the concentration of Cr2O3 shows the gradient distributions in crystal fibers with diameters of 920, 530, and 300 μm. The concentration of Cr2O3 at the fiber center is lower than that at the edge. After multiple regrowth steps to size down the crystal fiber to 66 μm in diameter, the concentration of Cr2O3 is becoming uniform again. In Fig. 3.7 (b), the distribution of CaO is contrary to that of Cr2O3. It tends to aggregate at the center during growth. The distribution difference between Cr2O3 and CaO is attributed to the signs of the segregation coefficient. The average concentrations of doping ions in crystal fibers are shown in Fig. 3.8. It reveals only slight change in the average concentration of CaO, but that of Cr2O3 decreases quickly when reducing the diameter of crystal fiber. It is estimated that the concentrations of Cr2O3 are 20-fold lower from 2000 μm to 66 μm. It is due to that Cr ions tend to diffuse outward and evaporate during the growth.

Figure 3.9 (a) shows the side view of crystal fiber. Micron-sized particles formed on the circumference of crystal fiber were observed, as shown in Figure 3.9 (b). It is interest that some compositions precipitate during the growth. For the detailed analysis, the surface feature was examined by scanning electron microscopy (SEM, JSM6400, JEOL) in secondary electron image (SEI) mode coupled with point-count

energy dispersive X-ray (EDX) analysis at 20 kV. In Fig. 3.10, SEI side view and EDX mappings of Cr:YAG crystal fiber show wide distribution of micron-sized Cr-rich particles on the surface. It is in consistent with that the decrease of the concentration of Cr ions is due to the Cr ions like to diffuse outward and precipitate on the circumference of crystal fiber.

0 10 20 30 40 50 60 70 80 90 100

2250 2000 1750 1500 1250 1000 750 500 250 0 0.00

0.05 0.10 0.15 0.20 0.25 0.30

C o nce n tr at ion ( w t. % )

Diameter ( μ m)

Cr

₂

O

₃

CaO

Fig. 3.8 The average concentrations of Cr2O3 and CaO in fiber with various diameters.

(a) (b)

Fig. 3.9 (a) Side view of Cr:YAG crystal fiber. (b) The micron-sized particles formed at the surface of crystal fiber.

Fig. 3.10 SEM side view SEI and EDX mappings of Cr:YAG crystal fiber showing wide distribution of micron-sized Cr-rich particles on the surface.

3.3.2 Fluorescence mappings of Cr

³⁺

and Cr

⁴⁺

ions in single crystal fiber

The crystal fiber after sized down to 66 μm in diameter, the concentration of Cr ions is significantly decreased. For the application of Cr⁴⁺:YAG crystal, the active ion is Cr ion in 4+ oxidation state. Although EPMA can measure the concentration of Cr ion, it cannot distinguish its oxidation states. Several ways to discriminate Cr³⁺ and Cr⁴⁺ ions have been studied, such as electron paramagnetic resonance (EPR) [3.13]

and X-ray absorption near-edge structure (XANES) [3.14]. The millimeter spatial resolution is not suitable to measure the 100-μm-sized crystal fiber. Besides, the sample preparation for these two techniques is quite complicated. We utilized the property of the different spectral characteristics of 3+ and 4+ oxidation states of Cr ions to construct a LSCM for distinguishing Cr³⁺ and Cr⁴⁺ ions.

The Cr³⁺ and Cr⁴⁺ fluorescence mappings of crystal fibers with various diameters are shown in Fig. 3.11. The Cr³⁺ and Cr⁴⁺ fluorescence mappings reflect the concentration distributions of Cr³⁺ and Cr⁴⁺ ions in the crystal fiber. In the 920 μm sample, the Cr³⁺ and Cr⁴⁺ fluorescence mappings reveal the stress striation in the center of crystal fiber. This stress striation is three {211} facet planes [3.15] which are formed by radius distributed three <111> facets separate the crystal cross section. This stress striation will cause crystal optical heterogeneity. It is clearly seen that the crystal fibers below 530 μm in diameter are free from the stress striation. Therefore, after down-sizing the crystal fiber to 66 μm in diameter, the high-optical homogeneity crystal was obtained.

A comparison between LSCM and EPMA measurements is shown in Fig. 3.12.

The EPMA curve shows the total concentration of Cr ions, but the Cr³⁺ fluorescence curve only reflects the concentration of Cr³⁺ ions. For the measurements of the 920 μm crystal fiber, as shown in Fig. 3.12 (a), the two curves are in good agreement because most of the Cr ions are Cr³⁺ ions. In Fig. 3.12 (b), it shows these two measurements of a 300 μm crystal fiber sample. The signal-to-noise ratio of LSCM is higher than that of EPMA measurement. The Cr³⁺ ion sensitivity by LSCM measurement was determined to be 1.6×10¹⁷ cm^-3, which is equal to 4.4×10^-4 wt.%

with a 0.3-sec/pixel measurement rate. However, the Cr2O3 sensitivity by EPMA measurement was determined to be 0.01 wt.% with a 240-sec-per-spot measurement time. The LSCM measurement exhibits 20-fold better in sensitivity and 800-fold faster in acquisition speed than EPMA measurement.

0 20 40 60 80 100

Cr

³⁺

fluorescence

Cr

3+

co n cen tr atio n ( w t.%)

Cr

³⁺

fluorescence

Cr

3+

co ncen tratio n ( w t.%)

Fig. 3.12 Comparison between LSCM and EPMA measurements for (a) 920 μm and (b) 300 μm crystal fibers.

For the calibration of Cr⁴⁺ concentration, a bulk material with absorption coefficient ( ) of 4.5 cm

α

^-1 at 1064 nm was used. Its absorption spectrum from 500 nm to 1400 nm was shown in Fig. 3.13. It is known that

× N

= σ

_a

α

(3.4)

∝ α

∝ N

I

_e (3.5) where is the absorption coefficient of Cr

α

⁴⁺ ion,

σ

_a is absorption cross section of Cr⁴⁺ ion, N is number of Cr⁴⁺ ion, and I is Cr_e ⁴⁺ fluorescence emission intensity.

The absorption coefficient of Cr⁴⁺ ion is the product of absorption cross section and number of Cr⁴⁺ ion, while the Cr⁴⁺ fluorescence intensity is direct proportional to the number of Cr⁴⁺ ion, which is also directly proportional to absorption coefficient.

We can measure the absorption coefficient of Cr⁴⁺ ion to estimate the number of Cr⁴⁺

ion. However, the absorption cross section is needed to be known first. In the study by Borodin et al. [3.16], the absorption cross section of 5×10^-18 cm² was reported. The number of Cr⁴⁺ ion with α of 4.5 cm^-1 is calculated to be 9×10¹⁷ (#/cm³), which is 2.5×10^-3 wt.%. Using this bulk material as reference, the measured Cr⁴⁺ fluorescence intensity can be converted to the number of Cr⁴⁺ ion. Two another bulk materials with α of 0.5 and 2.5 cm^-1 were tested for this method. The measured α are 0.47 and 2.55 cm^-1, which are calculated by their Cr⁴⁺ fluorescence intensities. By this fluorescence intensity method to quantify the number of Cr⁴⁺ ion is quite accurate and easy, and the measured deviation is less than 6%. The Cr⁴⁺ measurement sensitivity was also determined to be 7.5×10¹⁵ cm^-3, which is equal to 2.1×10^-5 wt.% with a 0.3-sec/pixel measurement rate.

5 10 15 20

coefficient (cm

-1

)

α

1064=4.5 cm^-1

In Fig. 3.14, the distributions of Cr³⁺ and Cr⁴⁺ with various crystal fiber diameters are shown. The line distribution is extracted from the Cr³⁺ and Cr⁴⁺

mappings. In Fig. 3.14 (a), the distribution of Cr³⁺ is getting smoother from 920 μm to 66 μm. It is also verified from the distribution of Cr2O3 by EPMA measurement. In Fig. 3.14 (b), it shows the concentration of Cr⁴⁺ is decreased with reducing the crystal fiber diameter. However, the distribution of Cr⁴⁺ is getting peaked at the fiber center when the core diameter is less than 300 μm. This will be explained in section 3.3.3. In Fig. 3.15, it shows the measured average concentrations of Cr³⁺ and Cr⁴⁺ in different diameter crystal fibers. The concentrations of Cr³⁺ and Cr⁴⁺ are 10-fold and 11-fold decreased from 2000 μm to 66 μm, respectively. In addition, the concentration of Cr⁴⁺

is less than 1% when comparing to that of Cr³⁺.

Fig. 3.14 The distributions of (a) Cr³⁺ and (b) Cr⁴⁺ with various diameter crystal fibers measured by LSCM.

2100 1800 1500 1200 900 600 300 0 0.00

0.05 0.10 0.15 0.20 0.25 0.30

Concentration (wt.%)

Diameter ( μ m)

Cr³⁺ concentration

Cr⁴⁺ concentration (x100)

Fig. 3.15 The concentrations of Cr³⁺ and Cr⁴⁺ ions in various diameter crystal fibers.

3.3.3 The dependency between normalized Cr

⁴⁺

and Ca

²⁺

It is known that the 4+ oxidation state of Cr ion in YAG is generated by Ca²⁺ ion with charge compensation. To explain the phenomenon of the distribution difference between of Cr³⁺ and Cr⁴⁺ ions, the distribution of Ca²⁺ needs to be taken into account.

In Fig. 3.16, the distributions of Cr⁴⁺, Cr2O3, and CaO in 920-μm- and 66-μm-diameter crystal fibers are shown. In the 920 μm sample, the distribution of Cr⁴⁺ ion is flatter than that of Cr2O3. The reason is that the concentration of Cr⁴⁺ ion depends on both the concentrations of Cr2O3 and CaO. Although the concentration of Cr2O3 at fiber center is lower than that at the edge, the concentration of CaO tends to accumulate near the fiber center, which results in the flatter distribution of Cr⁴⁺ ion. In the 66 μm diameter sample, the distribution of Cr2O3 is quite flat, while that of CaO gathers near the fiber center. Therefore, the concentration of Cr⁴⁺ ion peaks at the fiber center.

Cr⁴⁺ fluorescence

Cr

4+

c onc en tra tio n (x10

-3

wt.%)

Cr⁴⁺ fluorescence

Cr

4+

co ncentr a tion ( x 1 0

-3

wt.%)

diameter and (b) 66-μm-diameter crystal fibers.

To find out the relation between Cr⁴⁺, total Cr, and Ca²⁺, the ratio of Cr⁴⁺/total Cr with different Ca²⁺/total Cr was investigated. The dependence between normalized Cr⁴⁺ and Ca²⁺ concentration can be seen in Fig. 3.17. There is no Cr⁴⁺ in a YAG host without charge compensator. The ratio of Cr⁴⁺/total Cr is increased with Ca²⁺/total Cr.

In addition, only less than 1% of the Ca²⁺ becomes active in charge compensation when Ca and total Cr ions are in the same quantity. The low compensation efficiency may be explained by large lattice mismatch (i.e. +8.7%) with Ca²⁺ ions incorporated into the dodecahedrally coordinated Y³⁺ sites. The large lattice mismatch is also accompanied by the production of oxygen vacancies, which result in the de-activation of Ca²⁺ charge compensation.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Cr 4+ / total C r (%)

Ca ²⁺ / total Cr

Fig. 3.17 The dependence between normalized Cr⁴⁺ and Ca²⁺ concentrations.

3.4 Oxidation states in Cr:YAG double-clad fiber

In order to reduce the propagation loss of crystal fiber for delivering the light, fused-silica and borosilicate were used as cladding. In the previous study, it is known that the borosilicate-clad fiber can produce a strong Cr⁴⁺ fluorescence in the core area, but it is very difficult to fabricate the core with less than 30-μm in diameter using LHPG technique. When using fused-silica as cladding, it possible to obtain core diameter below 30 μm. However, there is almost no Cr⁴⁺ fluorescence in the core area due to complete mixing of SiO2 into YAG [1.10]. With well controlled growth conditions, the fused silica only partially diffused into Cr:YAG to form a double-clad fiber. In this section, we describe the growth method for DCF and measure its optical property.

3.4.1 Growth of double-clad fiber

The fused-silica capillary was used as cladding and its physical properties were listed in Table 3.3. With properly controlled growth parameters of co-drawing LHPG (CDLHPG) method, the double-clad fiber was grown successfully. The

<111>-oriented single crystal with diameter of 68 μm was inserted into a fused silica capillary tube with 76- and 320-μm inner and outer diameters, respectively. A crateriform molten zone for downward growth is shown schematically in the left part of Fig. 3.18. The side view of the grown fiber with a three-layer structure is shown in the right part of Fig. 3.18. The core diameter can be controlled by adjusting the CO2

laser power and growth speed.

Table 3.3 Physical properties of fused-silica glass [3.17].

Compositions (wt.%)

SiO₂: 99.9 %, Na₂O: 0.03 %, Al₂O₃: 0.02 %, TiO₂: 0.01 %, K₂O: 0.01 %,...

Refractive index 1.459

Softening point (^oC) 1600

Annealing point (^oC) 1075

Thermal expansion coefficient (m/m-^oC) 0.55x 10^-6 Thermal conductivity (W/m-K) 1.38

Hardness (Knoop) 500

Fig. 3.18 Left: Schematic diagram of the molten zone during growth, right:

photograph of the side view of the grown double-clad Cr⁴⁺:YAG fiber.

3.4.2 Composition analysis and refractive index profile

In Fig. 3.19, it shows the polished end face of double-clad fiber by SEM. A slight crack after polishing by diamond powder is observed. The three layers of double-clad fiber are denoted as core, inner cladding, and outer cladding with diameters of 25 μm, 100 μm, and 320 μm, respectively. In order to find out the compositions of double-clad fiber, EPMA method was used, as shown in Fig. 3.20. It shows that the compositions of core and outer cladding are almost YAG and SiO2, respectively. But the composition of the inner cladding is a mixture of SiO2 and YAG. The concentration of Y2O3 is almost 36.2 wt.%, but that of Al2O3 and SiO2 are dependent on functions of position with average concentrations of 34.6 wt.% and 29.2 wt.%, respectively. The distribution of Al2O3 is increased near the core, while that of SiO2 is on the contrary. In addition, slight increase of the SiO2 concentration near the core is due to the softening point of fused silica is much lower than the melting point of YAG so that the in-diffusion of SiO2 is blocked at the inner cladding-core boundary. The corresponding refractive index profile was also shown in Fig. 3.20. The core and outer cladding are wholly YAG and SiO2 with 1.82 and 1.46 in refractive indices, respectively. In the inner cladding region, due to the SiO2 diffusion into YAG, the concentrations of SiO2 are from 43% to 27% toward the core, the corresponding refractive indices are from 1.58 to 1.66.

Fig. 3.19 The SEM image of double-clad fiber end view.

-100 -75 -50 -25 0 25 50 75 100 0

20 40 60 80 100

Outer cladding

Outer cladding Inner

cladding

Inner cladding

Refractive index

SiO

₂

Y

₂

O

₃

Al

₂

O

₃

Concentration (wt.%)

Position ( μ m)

Core

1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85

Fig. 3.20 Compositions of double-clad fiber and its refractive index profile.

3.4.3 Fluorescence mappings of Cr

³⁺

and Cr

⁴⁺

ions in double-clad fiber

Figure 3.21 shows the Cr³⁺ fluorescence mapping by LSCM measurement. Its line scan of Cr³⁺ fluorescence intensity and concentration of Cr2O3 by EPMA measurement are shown in Fig. 3.22. It is found that Cr2O3 spreads in the region of core and inner cladding. The Cr³⁺ fluorescence was also detected from these two structures, but the emission intensity in the inner cladding is five-fold weaker than that in core. It may be attributed to the fact that the emission cross section in the inner cladding is smaller than that in YAG. The corresponding Cr³⁺ fluorescence spectra are shown in Fig. 3.23. In the core, it shows a typical Cr³⁺:YAG emission spectrum, which is a sharp R-line (689 nm from ²E→⁴A₂ transition) associate with three phonon sidebands (675, 707, and 726 nm). In addition, a broad ⁴T₂→⁴A₂ emission band (approximated with the dash curve) as a result of thermal population of the ⁴T2 state at room temperature was also observed. The Cr³⁺ fluorescence spectrum of inner cladding shows broadband emission from 650 nm to 950 nm as a result of its weaker crystal-field strength compared to YAG (Dq/B=2.6) [2.18]. The crystal-field strength of Cr³⁺-doped glasses has been reported in the range of 1.8 < Dq/B < 2.3 with compositions chosen systematically for fluoride, phosphate, silicate, telluride, and borate glasses [3.18]. The measured Cr³⁺ fluorescence in the inner cladding is similar to that in glass hosts with broad emission from 675 to 900 nm.

Fig. 3.21 Cr³⁺ fluorescence intensity mapping.

-100 -75 -50 -25 0 25 50 75 100 Cr

³⁺

fluorescence

Fig. 3.22 Distribution of Cr2O3 concentration and Cr³⁺ fluorescence intensity.

600 650 700 750 800 850 900 950

0.0 DCF inner cladding (x5 times)

Fig. 3.23 Cr³⁺ fluorescence spectra at DCF core and inner cladding.

In Fig. 3.24, it shows the Cr⁴⁺ fluorescence mapping. The corresponding line scan of Cr⁴⁺ fluorescence intensity and concentration of CaO are shown in Fig. 3.25.

It is apparent that CaO distributes over the core and inner cladding. It should be noted that CaO tends to diffuse outward in the inner cladding, whereas it is contrary to that

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