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We have realized highly transparent Yb:fluorapatite (FAP) ceramics by use of slip casting under rotational magnetic field, even though the main crystal axis become a hard magnetization axis due to the enhancement of magnetic anisotropy by the total angular momentum of 4f electrons in doped rare-earth ions. We confirmed that our Yb:FAP ceramics reached to have a laser-grade quality: it did not interrupt laser oscillation when it was inserted into a lasing cavity. We also evaluate the absorption and the round-trip loss including Fresnel loss of our Yb:FAP ceramics, which were 3.7 cm−1 at 902 nm and 0.26 (11.5% by a single pass) at 1064 nm, respectively.
© 2014 Optical Society of America
1. Introduction
The progresses in laser ceramic technologies are indeed remarkable after the first experimental confirmation of their superiority to single-crystalline gain media [1], while people had been considering ceramic laser gain media are not practical for a long time since they are invented in 1964 [2]. Currently many researchers expect that laser ceramics are primary candidates for laser gain media of laser fusion drivers, laser igniters, laser accelerators, and so on [3]. Milestones in the research history of laser ceramics are (a) the high speed fabrication of laser grade ceramics [4], (b) the possibility of composite structure [5], (c) high doping of rare-earth ions [1, 6], (d) low cost and scalable fabrication [7], (e) the high fracture toughness [8], (f) the designability of composition [9], (g) over 100-kW laser generation [10], and (h) the anisotropic laser ceramics [11].
Before the final milestone of anisotropic ceramics, applicable gain media for laser ceramics had been limited to be isometric materials [12], and they were not able to appreciate many benefits of anisotropic laser gain media such as YVO4 [13] and apatite [14]. Although optical characteristics of Yb3+-doped apatite crystals are quite suitable for fusion drivers, it is difficult to scale-up Yb:apatite laser systems due to the difficulty in a fabrication of large sized crystals which could be solved by the technology of anisotropic laser ceramics. Thus, the invention of anisotropic laser ceramics is as important as the first laser oscillation of laser ceramics among these milestones.
We invented the orientation control of crystal axes in anisotropic laser ceramics [15], which was the micro-domain control based on the magnetic anisotropy enhancement of non-magnetic crystals by spin-orbit interactions of 4f electrons in doped rare-earth trivalent [16]. This enhancement of magnetic anisotropy shift anisotropic laser ceramics fabrications from the use of complicated superconductive magnets to easy electromagnets. Our anisotropic ceramics consists of well-aligned grains along the main crystal axis not only by magnetic orientation control but also by the preferential grain growth during sintering process [17]. Of course, there is another way to obtain transparent anisotropic ceramics where the grain growths in samples are suppressed by the fast consolidation process [18], where high transmittance in these samples are realized not by the orientation control in grains but mainly by the reduction of Rayleigh scattering caused by small sized grains. However, it is difficult for fast-consolidated samples to show efficient performances that are desired from benefits of anisotropic gain media such as highly polarized large cross sections [19]. Therefore, well-aligned anisotropic ceramics by the combination of the magnetic orientation control and the preferential grain growth should be the key to open the door of giant-micro photonics [3]. By means of anisotropic laser ceramics we can appreciate large cross sections of anisotropic gain media, the scalability and structural designability of ceramic gain media simultaneously.
Fluoroapatite (Ca5(PO4)3F, FAP) ceramics are our current target because the scale-up of FAP media can bring the fusion energy to human societies. Fortunately the easy magnetization axis of Nd:FAP is c-axis that is the main crystal axis of FAP, therefore crystal orientation of Nd:FAP powders are easily controlled by static magnetic field [11]. However, an easy magnetization axis of Nd3+-doped crystals become a hard magnetization axis when the crystal is doped with Yb3+ due to the difference in the crystal field potentials around rare earth trivalent determined by Stevens factors [16,20]. This is the reason why it is difficult to fabricate well-orientation controlled Yb:FAP ceramics by slip-casting under static magnetic field. The orientation control of hard magnetization axes by rotating magnetic fields was proposed in 2003 [21], and optimal process conditions were already established quantitatively [22]. However, this technique seemed to be not useful for the fabrication of Yb:FAP since it was assuming the use of 10-T class magnetic fields produced by superconductive magnet.
In this work, we proved that magnetic anisotropy enhancement of non-magnetic crystals by spin-orbit interactions in doped rare-earth trivalent was applicable to the orientation control of the hard magnetization axis of grains in laser grade ceramics. Well-aligned Yb:FAP ceramics were fabricated by use of slip-casting under rotating magnetic field produced not by a superconductive magnet but by an electromagnet. We also evaluated the optical characteristics of our Yb:FAP ceramics in order to show its quality as laser grade.
2. Guideline for the orientation control of hard magnetization axes
At first, we consider the orientation control of a micro-domain that contains N rare-earth ions. Under magnetic flux density B, spin-orbit interaction in 4f-electrons brings the magnetic energy G of this particle that is given by
where M, mB, gJ, and <JB> are the magnetization of the particle, Bohr magneton, Lande g-factor for total angular momentum J, and, the average value of the direction cosine of total angular momentum in rare-earth ion along the direction of magnetic field, respectively. If doped rare-earth ions have Kramers degeneracy, the direction cosine of total angular momentum can be + |JB| or -|JB|. Therefore, <JB> is mainly contributed by Zeeman shift of |JB|. Here we introduce Je and Jh that are |JB| under the magnetic field parallel to the easy magnetization axis and the hard magnetization axis of the micro-domain, respectively. By use of Je and Jh, <JB> is expressed approximately bywhere k, T, and ψ are Boltzmann constant, temperature, and the angle between directions of the easy magnetization axis and magnetic field, respectively. In Eq. (2) we assumed that magnetic moments of rare-earth ions are much smaller than kT, and neglected over second order perturbation of Zeeman effect. From the definition of magnetic susceptibility χ, we can derive magnetic anisotropy Δχ to bewhere μ0 and V are permeability of vacuum and the volume of the particle. Equation (3) shows that higher doping concentration can enhance the magnetic anisotropy directly. Unfortunately, there is an upper limit for the doping concentration of Nd3+ ions into laser gain media: heavily Nd3+-doping cause a drastic degradation of emission performances due to the concentration quenching. However, there is no concentration quenching of Yb3+ ions, which indicates that Yb3+-doped anisotropic laser gain media are promising candidates for anisotropic laser ceramics. In YVO4 single crystals, magnetic anisotropy in undoped YVO4 is only 1.5 × 10−7 that is due to Larmor diamagnetism [16]: this Δχ is too small to apply orientation control by a simple electromagnet. However, Δχ can be designed by rare-earth doping. In the case of Yb:YVO4, VΔχ/N is 5.2 × 10−33 m3. This implies that 10at.% Yb:YVO4 has Δχ of 6.7 × 10−6 that is 44 times larger than pure YVO4.The magnetic anisotropy expressed by Eq. (3) allows us to apply the magnetic orientation control technology for fabrication process of rare-earth doped anisotropic laser ceramics. In the case that there is only one easy magnetization axis of raw powders, we can align this easy magnetization axis along the direction of static magnetic field. The kinetics of the orientation control under static magnetic field were discussed in our previous work [17], where the processing time τS of the orientation control under static magnetic field was expressed by Δχ. When the micro-domain is a particle with the shape of micro-sphere, from Eq. (3) τS is described as
where η is a viscosity of slurry for slip-casting under magnetic field. In the slurry with the viscosity of 300 × 10−3 Pa·s under room temperature (T = 280K) and 1.4 T of magnetic flux density generated by a electromagnet, τS of 10at.% Yb:YVO4 and pure YVO4 are estimated to be 0.17 s and 7.7 s, respectively.However, if two easy magnetization axes exist in the target material, we have to align one hard magnetization axis in order to suppress scatterings due to its birefringence. In this case, we can apply rotating magnetic field with the angular velocity ω, and an easy magnetization axis of the particle will be aligned perpendicular to the plane to which rotating magnetic field parallel. According to [22], the processing time τR for the orientation control under rotating magnetic field is expressed by
Equation (5) indicates that higher rotation brings earlier orientation control. If ω is equal to or higher than 1/2τS, the processing time τR become equal to 2τS, which is inversely proportional to Δχ. Therefore heavily doping of rare-earth ions can directly contribute to the alignment performance. Under magnetic flux density of 1.4 T with 17 rpm of rotation (1.8 rad/s), τR for the micro-domain with Δχ of 6.7 × 10−6 and 1.5 × 10−7 (this difference is equivalent to the difference between 10at.% Yb:YVO4 and pure YVO4) are estimated to be 2.1 s and 15.4 s, respectively. Thus we can conclude that rare earth ion doping is quite effective for the orientation control of a micro-domain with both of a static magnetic field and a rotating magnetic field.Figure 1 illustrates the schematic diagram for the spheroidal of magnetic energy G described Eq. (1) under the rotating magnetic field. In the case of Yb:FAP there are two easy magnetization axes (a- and b-axis of FAP) and one hard magnetization axis (c-axis of FAP), therefore magnetic spheroidal is an oblate spheroid as in Fig. 1. On the contrary, magnetic energy spheroidal for Nd:FAP is a prolate spheroid. Active Yb3+-ions occupy 6h site in FAP structure, where there is only one mirror symmetry, and this site has seven ligand ions of six oxygen ions and one fluorine ion [23]. We define z-axis as the specific axis for the orientation control under rotating magnetic field, and magnetic field is always perpendicular to z-axis. There is arbitrariness in the definition of the direction of x- and y-axes, and here x-axis is set along the magnetic field at process start time. Angles θ and φ are determined to be the angle between z-axis and c-axis of a processed particle, and the angle between x-axis and the direction cosine of c-axis to the magnetic-field rotating plane (xy-plane), respectively. In this situation, θ will be reduced with the time constant of τR defined by Eq. (5).
Fig. 1 Schematic diagram for the spheroidal of magnetic energy G of the processed particle under the rotating magnetic field. This particle is made of FAP doped with Yb3+. Doped Yb3+ ions are surrounded by O2- (illustrated by red sphere) and F- (gray sphere). c-axis of this particle is parallel to the symmetric reflection plane including a F- and RE3+ or Ca3+ ions. When ω is equal to or higher than 1/2τS, the alignment torque TM that is emerged by the applied magnetic field is simply proportional to Δχ.
3. Experimental setups
3.1 Fabrication of transparent Yb:FAP ceramics
In the real process for synthesizing anisotropic laser ceramics, it is difficult to rotate the direction of magnetic field. Therefore, we rotate the casting mold with slurry instead of the direction of magnetic field.
Yb:FAP powder was synthesized by ion substitutions between commercial FAP powder and commercial ytterbium nitrate powder in buffer solutions. Slurry containing Yb:FAP powders and distilled water was mixed with a deflocculant, and the resulting mixture was mechanically ground to convert aggregate particles to single crystals. The slurry containing grounded particles was then poured into a porous mold for casting. Slip casting was carried out under a horizontal static magnetic field of 1.4 T at room temperature, where mold containing slurry was rotated at 17 rpm speed. This magnetic field was generated by electric magnet (JER-3XG, JEOL). After casting, the samples were pre-sintered for 2 hours within 1600 °C in air. Post-sintering was carried out by use of hot isostatic pressing under 1600 °C for 1 hour at 190 MPa and in Ar. Figure 2 shows a schematic flow of the fabrication process for Yb:FAP ceramics. Our samples were cut out from sintered body. After polishing for optical inspections, sample size was 3.0 mm × 3.0 mm × 0.6 mm, where the direction of 1.0 mm was perpendicular to applied magnetic field.
Fig. 2 Schematic process flow of anisotropic ceramics fabrication that is illustrated into three stages. a) Raw powder of Yb:FAP of which magnetic energy is shown in Fig. 1. b) Slip-casting process under the rotating magnetic field generated by a electromagnet. θ will be fluctuated thermally around zero. c) Casted green body of anisotropic laser ceramics. After preferential grain growth during sintering by HIP, this powder compact will become transparent.
3.2 X-ray observations
In order to confirm the alignment condition, X-ray diffraction (XRD) patterns of Yb:FAP ceramics were observed by diffractometer (RINT-UltimaIII, Rigaku), where detected diffractions were from the surface parallel to the direction of applied magnetic field. The doping concentration of Yb3+ in these ceramics was examined by XRF (X-ray fluorescence analyzer: JSX-3400RII, JEOL).
3.3 Absorption measurement
Aiming to the confirmation of high linear transmission realized by orientation control, transmittance of Yb:FAP ceramics was measured by a spectrometer (U-3500: Hitachi Co.) from 850 nm to 1100 nm, where optical path is perpendicular to the surface of 3.0 mm × 3.0 mm. The probe source and the detector in this measurement were a tungsten lamp and a PbS detector, respectively. The upper limit of an absorption measurement under this experimental setup was 2.2 in optical density, and the resolution of this measurement was 2.0 nm.
3.4 Confirmation of laser grade quality
The optical quality of Yb:FAP ceramics was evaluated by inserting into the resonator of Nd:YVO4 microchip laser. We can speculate that our sample has the quality of laser grade if the laser oscillation can be maintained even after the sample insertion.
Figure 3 shows the structure of Nd:YVO4 microchip laser resonator. 880 nm output from a fiber-coupled laser diode (LIMO180-F400-DL880EX1288, LIMO) was delivered through a optical fiber with a core of 400-μm in diameter, and collimated by a lens with the focal length of 50 mm before focused onto a Nd:YVO4 microchip by a lens with the focal length of 150 mm. Nd:YVO4 microchip with thickness of 1.0 mm contained 1at.% Nd, and its surfaces were optically coated: high transmittance at 880 nm and total reflection at 1064 nm for the pumping surface, and anti-reflection at 1064 nm and total reflection at 880 nm for an opposite surface. The total reflection coating at 1064 nm on Nd:YVO4 microchip and flat output coupler consisted 10 mm plane–plane optical resonator. Optical couplings from 3% to 40% were used for this evaluation.
Fig. 3 Experimental arrangement of the confirming of laser grade quality. This setup included a 880-nm laser diode as a pump source, a delivering fiber, collimating and focusing lens, Nd:YVO4 microchip, flat output coupler, and a Yb:FAP ceramic sample.
4. Results
XRD patterns of Yb:FAP ceramics from the surfaces parallel to the direction of the imposed magnetic field and of FAP powder were shown in Fig. 4. In the diffraction pattern of Yb:FAP ceramics, diffraction peaks of (00l) corresponding to the c-plane were mainly observed. The relative intensity of diffractions from other planes in Yb:FAP ceramics are considerably lower than (00l). On the contrary, contributions from various planes can be detected in the diffraction pattern from FAP powder where they coincide to the pattern of fluoroapatite in ICDD #00-015-0876. Therefore, the c-axis in most of grains in our Yb:FAP ceramics have aligned perpendicular to flat surfaces of Yb:FAP ceramics. XRF measurement revealed that 2at.% of Yb3+-ions were detected in our Yb:FAP ceramics.
Fig. 4 X-ray diffraction pattern of FAP powder as a raw material for Yb:FAP ceramics and Yb:FAP ceramics. Diffraction from Yb:FAP ceramics were from the surface of 3 mm × 3mm.
Figure 5 shows transmission and absorption spectra of Yb:FAP ceramics, where over 84% of in-line transmittance was observed at wide wavelength range where there is no absorption due to Yb3+. From XRD data in Fig. 4, the sample is nearly the same as c-cut, therefore no dependence of incident polarization. The main absorption peak for pumping was measured to be 3.7 cm−1 at 902 nm with a bandwidth of 4 nm in FWHM. Zero-phonon line was observed at 981 nm with a bandwidth of 2 nm, which is the limit of spectral resolution in the experimental setup.
Figure 6 shows the input / output characteristics of the Nd:YVO4 microchip laser where the Yb:FAP ceramic sample was inserted. We experimentally observed that our Yb:FAP sample did not interrupt lasing, therefore it is clearly shown that our orientation controlled Yb:FAP ceramics has an optical quality as laser grade. This is the first confirmation of the laser grade quality of not only Yb:apatite ceramics but also of the highly aligned hard magnetization axis in non-magnetic materials without a superconductive magnet by means of the enhancement of magnetic anisotropy by rare-earth doping.
Fig. 6 Dependence of the output power on the incident pump power for Nd:YVO4 microchip laser with the insertion of Yb:FAP ceramics.
5. Discussions
5.1 Lotgering factor of Yb:FAP ceramics
The degree of the crystal orientation can be evaluated quantitatively in terms of the Lotgering factor f [24]. f shows the value from 0 for randomly oriented samples to 1 for samples with perfect alignment of domain orientation, thus f is normalized by the branching ratio ρi(hkl) defined by
where the subscript i indicates “r” or “s”, and are related to the peak intensity corresponding to (hkl) plane in XRD patterns from surfaces of an uncontrolled reference with random orientation and the sample for evaluation, respectively. S is a certain subset of (hkl)-planes and in this case it means (00l). By use of ρi(hkl), f is given byThe f value of our Yb:FAP ceramic was estimated to be 0.90, and it was smaller than our previously reported Nd:FAP processed by the magnetic field of 1.4 T which was same as this work [17]. Therefore, The orientation control in our Yb:FAP is inferior to Nd:FAP ceramics processed under static magnetic field. It means we have to construct more detailed process principles for the orientation control technology with the rotating magnetic field.5.2 Optical loss of Yb:FAP ceramics in laser cavity
The dependence of the slope efficiency ηs on output coupling TOC described in Fig. 6 enables us to evaluate the round trip-loss Li of laser cavity in Fig. 3. According to [15], this dependence can be described as
where η0 is the maximum efficiency determined as a fitting parameter. As shown in Fig. 7, internal round trip-loss Li of Nd:YVO4 microchip laser is determined to 0.26 (11.5% of incident power will be scattered by a single pass). It contains not the scattering loss of Yb:FAP ceramics but the total cavity loss including surface Fresnel losses, lower-level absorptions by Yb3+, and so on. Therefore, we are not able to directly compare this result to our reported scattering loss of 15% in Nd:FAP ceramics [15].Fig. 7 Slope efficiency of Nd:YVO4 laser as a function of output coupling. 2at.% Yb:FAP ceramics with the thickness of 0.6 mm was placed in the resonator.
More simply, we can roughly estimate the scattering coefficient of our Yb:FAP ceramics. From 1.62 of the refractive index of Yb:FAP single crystal for the light polarized to a-axis [25], we can calculate the ideal Fresnel loss during pass through Yb:FAP crystal should be 10.9%. Since the background of transmittance in Fig. 5 at 1080 nm is 83.8%, loss coefficient in our Yb:FAP ceramics can be utmost 1.0 cm−1.
6. Conclusion
We fabricated highly transparent Yb:FAP fluorapatite (FAP) ceramics by use of slip casting under rotational magnetic field of 1.4T from a electromagnet, even though the main crystal axis become a hard magnetization axis. This means that the enhancement of magnetic anisotropy by rare-earth doping is also useful for the orientation control even under the rotating magnetic field, and considerably reduced the minimum intensity of the applying magnetic field. X-ray and optical evaluations clearly give the first evidence that our Yb:FAP ceramics has a laser-grade quality in the world. Currently well-aligned anisotropic laser ceramics have been produced by only the orientation control by slip-casting under the magnetic field, therefore only our methods can be a solution for appreciating the advantage of anisotropic laser gain media and ceramic gain media.
Acknowledgments
This work was partially supported by Genesis Research Institute Inc., the Japan Science and Technology Agency, and the Special Coordination Funds for Promoting Science and Technology of the Ministry of Education, Culture, Sports, Science, and Technology of Japan. Authors also thanks to Mr. A. Kausas.
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