1. Introduction

Waveguide structures that allow effective confinement and unidirectional propagation of optical signals are the most desirable building blocks for all-optical photonic circuits, including on-chip transceivers and receivers that are different from the corresponding bulk form [1–4]. However, most monolithic architectures have too large a footprint to be suitable for integrated photonic applications [5–8]. Fortunately, glass-based fibers have emerged as a basic matrix for a variety of fundamental optical components, such as lasers and optical amplifiers thanks to their light weight, better mode quality, and relatively low maintenance cost [9–11]. However, these glass-based schemes to date often suffer from the stringent requirement of scaling fiber lasers and amplifiers to high average powers in spite of poor heat dissipation, which has seriously limited their potential applications.

Single-crystal materials can offer some exceptionally outstanding properties that are unattainable with typical amorphous glasses, including higher thermal conductivity and mechanical hardness [12–15], relatively narrow Raman signals [16–18], stronger damage threshold [6,19,20], and better chemical inertness [21–23], as well as remarkable nonlinearity [7,24–26]. Among the variety of crystalline materials, the thermodynamically stable sapphire crystal with hexagonal close packing of oxygen finds widespread applications in science and industry because of the unique electronic structures of its Al-O clusters [27]. Stimulated by these versatile optical and material applications of bulk-type sapphire crystals, unclad sapphire crystal fibers have been shown to be useful in other diverse devices as high-temperature sensors [28–31], high-sensitivity Raman probes [32–34], and supercontinuum generators [35–37]. The main problems with these commercially available unclad sapphire fibers are their huge scattering losses due to the large refractive index contrast (Δn) between sapphire and air. This is because the scattering loss is proportional to Δn³ [38]. This drawback would be further exacerbated by the presence of ambient particulates and contaminants on the fiber surfaces as the light passes through.

A number of different strategies have been proposed for the fabrication of cladding layers onto bare sapphire fibers, such as (i) high-energy H ion implantation [39], in which high-dose energetic bombardment would induce severe degradation in crystal quality, resulting in a weak luminescence that makes its use for active fiber devices difficult; (ii) sol-gel Al₂O₃ deposition [40], in which complete water removal becomes problematic, seriously hindering its scalable applications; and (iii) spinel MgAl₂O₄ coating [41], in which a polycrystalline structure usually accompanies a great number of pores formed at the core/clad interface, leading to an unacceptably large scattering loss that cannot fully meet practical requirements. For high-power applications needing thermal and structural stability, even one degree of temperature variation can be significant. Under such constraints, many of those methods simply cannot meet the functional requirements; that is why researchers turn to glass. A key advantage of glass is that it has a low transition temperature compared to sol-gel Al₂O₃ and polycrystalline MgAl₂O₄. This means that the cladded glass can easily be molded or formed into a flexible shape at its transition point before the crystal core reaches its melting point during laser-heated pedestal growth (LHPG) growth. Recently, a desirable configuration, consisting of a YAG crystal core with a glass cladding has been developed because of its potential to overcome the aforementioned shortcomings and facilitate the realization of glass-clad crystal-core devices [42–44].

Despite the worldwide efforts devoted to this field during the past few years, up till now, no literature has reported on correlating sapphire-core/glass-clad interfacial roughness with device performance, especially at the atomic level. This is mainly because implementing cladding processes based on melting-crystallization techniques remains a challenging issue, even today. High-temperature treatment was found to be very effective in improving the luminescent efficiency (by favoring Ti³⁺ over Ti⁴⁺ ions [45–47]) as well as for defect relaxation. However, practically no research has been performed to date on the direct impact of annealing on the defect reduction, crystallinity, and enhanced luminescence, and hence on low-loss optical wave guiding.

Interfacial roughness is clearly important to our understanding of the light-matter interactions in this glass-clad crystal-core structure. To the best of our knowledge, our present work is the first experimental study of core/clad interfacial roughness at the atomic scale. Since we are able to resolve the atomically smooth roughness after annealing treatment, we can provide a contour guideline reflecting the interdependence of interfacial roughness and propagation loss, as well as detailed estimates for laser actions in these glass-clad Ti:sapphire-core fibers. We also show that excellent crystalline quality with low propagation loss was observed on a large scale along the core/clad interface of glass-clad Ti:sapphire-core fibers, revealing that they are attractive alternatives to bulk lasers with low-threshold, high-efficiency, and room-temperature lasing for future utility for all-optic integrations and high-power devices.

2. Experimental

2.1 Hybrid crystal-glass fiber fabrications

All the sapphire crystal fibers and the corresponding cladding processes were performed by the LHPG technique [42–44,48]. A commercially available c-axis sapphire rod with a 0.5 mm × 0.5 mm cross section was used as the starting material. In the first step of LHPG, a c-axis Czochralski-grown rod was heated and a molten zone was created at the top end. A CO₂ laser (firestar-v40, SYNRAD) was used for heating the rods. The oriented seed was then dipped into the molten zone and slowly withdrawn in an ambient atmosphere, producing a 40-μm-diameter sapphire crystalline core. This single crystalline fiber core was grown by pulling the seed rod and feeding the raw material upward simultaneously at a constant growth ratio. The growth rates of the 40-μm sapphire crystal core and glass cladding are 6.5 and 3 mm/min, respectively. The corresponding diameter of the as-grown sapphire core is primarily determined by controlling the growth rate and CO₂ laser power. The growth rates do not affect the interface structure because of the repeatable and well-controlled growth procedures. The as-grown core and cladding maintain single crystal and amorphous structures, respectively. Apart from the growth rate, the crucial parameter most strongly affecting the density of structural defects at the interface is the thermal treatment process, as demonstrated in the experimental results.

Subsequently, high-temperature treatment at 1650 °C in a strongly reducing atmosphere of 5% H₂ and 95% Ar was applied for 3 h. The sapphire crystalline core was annealed prior to its cladding in the borosilicate capillary (VitroCom company). Next, both the annealed and non-annealed crystalline cores were sleeved into borosilicate glass capillaries with inner and outer diameters of 50 and 320 μm, respectively, and they were grown again at 10⁻³ torr using the same LHPG technique to form a borosilicate-glass-clad sapphire-crystalline-core fiber [49]. The transition temperature of the borosilicate glass capillary was ~525 °C, which is much lower than the melting point of the sapphire core at 2040 °C. In this case, the crystal-fiber-inserted capillary was heated so that the glass capillary became pliable and attached to the unmelted sapphire crystal core. As a result of this, glass cladding was formed as shown in Fig. 1. Borosilicate glass has a low transition temperature and softening point, and that this could be problematic in high-power applications. On the other hand, this same borosilicate-glass-clad structure has proven feasible under watt-level pumping without any active cooling [50]. We therefore speculate that borosilicate glass cladding could be sustainable at high power with active cooling. Ultimately, it is hoped that a desirable configuration consisting of a doped crystalline core with an undoped crystal cladding can offer a truly viable architecture for high-power operations. Investigations are currently underway toward this end goal.

 

Fig. 1 (a) Schematic of the glass cladding process. (b) Optical images of polished end view of a borosilicate-glass-clad sapphire-crystal-core fiber. (c) Enlarged image of (b). (d) Corresponding as-grown side view of (b). (e) Schematic of the c-axis sapphire, manifesting a hexagonal close packing arrangement of sapphire crystalline core, as shown in (c).

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2.2 Nanostructural and spectroscopic inspections

Atomic-scale investigation was accomplished by combing a scanning electron microscope (SEM, JXA-8900R, JEOL) and a field-emission high-resolution transmission electron microscope (HRTEM, Tecnai G² F20, FEI). HRTEM specimens were prepared by focused ion beam (FIB, SMI3050, Seiko) milling, which allows a precisely controlled nanomachining of the fiber end. Electron beam evaporation was used to coat the fiber end with a thin layer of Pt to avoid electrostatic charging during FIB milling. The optical bright-field end view of an as-grown fiber was imaged by a metallographic microscope (LV100ND, Nikon). Spectral measurements of the fiber samples were carried out in a back-scattering mode at room temperature by using a 325-nm He-Cd laser (IK3802R-G, Kimmon Koha) under a 40X objective lens with a numerical aperture of 0.50 (LMU-40X-NUV, OFR) and analyzed by a confocal Raman spectrometer (LabRAM HR 800, JOBIN-YVON) equipped with an 1800 mm⁻¹ grating and a liquid-nitrogen-cooled charge-coupled-device detector. The propagation losses of the annealed and non-annealed crystal fibers were measured using the cutback method [51].

3. Results and discussion

3.1 Macro-scale observations

Figures 1(a)–1(d) show the schematic of glass cladding process, optical microscopic cross section, and side view of a typical as-grown glass-clad sapphire crystal-core fiber, along which no flaws are observed; these are readily available in lengths up to 50 cm. Note that the occurrence of bubbles or voids are commonly observed during the micropulling-down growth of sapphire crystal fibers [52,53], and it is unfortunately already problematic in high-power fiber applications. This is because the micropulling-down growth is typically performed at ambient environment, i.e., positive pressure. In contrast, as mentioned in the Experimental section, the cladding process in the LHPG system is conducted at 10⁻³ torr, i.e., negative pressure. This low-pressure condition not only creates a strongly reduction that favors the conversion of Ti into its luminescent 3 + valence state, but also produces a pliable state of the cladded glass, and it is attached to the sapphire crystalline core without bubble forming.

Figure 1(b) shows that the uniform sapphire crystal core is bounded quite well within the surrounding glass cladding matrix. For the above-mentioned polycrystalline-cladded method [39–41], in contrast, it is very hard to avoid the formation of voids at the core/clad interface where the surface roughness is the dominant loss factor. As shown in Figs. 1(b) and 1(c), the cross section of the 40-μm sapphire core is hexagonal as a result of the c-axis structural nature of the corundum, as illustrated in Fig. 1(e). The corners of the core are rather rounded, and their radius of curvature can be tuned by controlling the fiber-drawing condition. Compared with sharp corners, these blunt corners could be an effective alternative that provide superior performance in whispering gallery mode lasing in terms of enhanced photon confinement and low-threshold operation [54, 55].

3.2 Nano-scale crystal-core glass-clad interfacial analyses

Although atomic force microscopy (AFM) can provide good spatial resolution [56–60] and rapid scanning, it is rather difficult to precisely measure the device roughness along the specific crystal orientation. In addition, in rib-waveguide cases [57,59,60], directly imaging the real sidewall by AFM is still extremely challenging because of the limited sharpness of the AFM probes and the requirement of the routine complicated calibrations. On the other hand, as waveguide dimensions are scaled down, the capability of AFM becomes unqualified, while the importance of nanometer-sized defects, such as misfit dislocations and stacking faults, for the optical properties of waveguide devices becomes even more dominant. Alternatively, in this study, a relatively reliable and promising technique of electron microscopy has been applied to study the interface morphology with atomic resolution by HRTEM. The atomically-imaged nature of HRTEM allows for direct imaging and quantitative roughness analysis on any types of waveguide structures as well as the preferable crystal orientations.

Now we look closely at the core/clad interface at the atomic scale and delve into the impact of annealing on defect relaxation related to core crystallinity. Figure 2(a) shows HRTEM images from the sapphire-core/borosilicate-clad interface without annealing treatments. As seen in Fig. 2(a), the sapphire core acts as a thermodynamically stable substrate to suppress interfacial reactions between the crystal core and the glass cladding, leading to an atomically manifest interface yet corrugated boundary due to growth of the structural defects. In fact, the rapid nature of heating and cooling in such a laser-based drawing process introduced significant residual stress in the crystalline core [44], which can be expected to result in a high density of misfit dislocations. Each specimen containing a core/clad interface was carefully examined, and showed no detectable large nano-sized pores or voids as compared to other cladding methods [39–41].

 

Fig. 2 HRTEM (a) lattice image of the sapphire-crystal-core/borosilicate-glass-clad interface without annealing treatment, showing the abundant defects nearby the interface (marked by arrows). The inset in (a) presents a magnified view of the defective region denoted by the square. The inset scale bar is 1 nm. (b), (c) Fourier transform and inverse Fourier transform, respectively, from the square region in (a) showing several (0002) misfit dislocations (marked by ⊥). Note that the double diffractions are denoted by D in (b). The scale bar in (c) is 1 nm. (d) Shows the atomically smooth core/clad interface due to effective annihilation of structural defects after thermal treatment at 1650 °C for 3 h, in contrast to the rather corrugated interface in (a). (e) False-colored high-magnification HRTEM image of the annealed core/clad interface. The scale bar is 2 nm.

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It is also noteworthy that, in Fig. 2(a) viewed along sapphire [2$\overline{1}$$\overline{1}$0], the non-annealed sample presents considerable amounts of misfit dislocations and stacking faults, as evidenced by the undulated stripes marked with arrows; this is further confirmed by the Fourier transform shown in Fig. 2(b). The streaks at the diffraction spots along [0002] are an indication of the presence of planar defects in the {0001} basal plane of the sapphire core. Figure 2(c) shows a Fourier-filtered image of the rectangular region in Fig. 2(a) using (0002) and (000$\overline{2}$) reflections exhibiting several dislocation half planes indicated by ⊥. The defect formation was substantially driven by the local strain fields due to the rapid cooling in the LHPG process, analogous to the case of the growth of YAG crystal fibers [44,61]. In this regard, the cooling rate can be estimated to be ~10⁹ K/s, similar to the case of pulsed laser ablation, which is well-known to result in the formation of faults, dislocations, and twinning [62,63].

Figure 2(d) shows the HRTEM image of the annealed sample taken edge-on in the [01$\overline{1}$1] direction; there are no obvious defects. The lattice contrast becomes more consistent in the long-range order after annealing. As demonstrated by the high crystallinity in Figs. 2(d) and 2(e), it can be deduced that during such thermodynamic transformation, the dislocation half planes and planar defects disappeared and the resultant defect-free sapphire crystal core was achieved after prolonged thermal treatment at 1650 °C for 3 h. Another striking difference between Figs. 2(a) and 2(d) is that the high-temperature treatment causes a drastic decrease of interfacial roughness; this will be discussed in detail later. Hence, it appears to be most likely that the uneven core/clad interface serves as the initial stage in the LHPG growth, further migrating toward atomically smooth interface through Brownian motion to reach a low surface energy. This leads to a completely coherent, nearly perfect single-crystal core without structural defects.

3.3 Raman spectroscopic analyses

Raman scattering is sensitive to the crystalline quality. Therefore, a comparative Raman study was conducted at the fiber core edge to evaluate the effects of thermal treatment on the optical properties. Raman excitation at 325 nm was employed instead of the more commonly used wavelengths of 532 or 405 nm to minimize the background fluorescence because it is difficult to completely exclude Cr³⁺ impurities from raw sapphire rods [64], and their strong absorption band falls in the blue-green region [46,47]. Figure 3(a) shows the representative full-range Raman spectra collected from LHPG-grown fiber samples between 200 and 1000 cm⁻¹, together with the spectrum of a Czochralski-grown source rod for comparison. As predicted by the factor group analysis, the Raman spectrum of corundum sapphire is composed of 7 phonon modes: 2A_1g + 5E [18]. All the observed Raman signals of these three samples are well-defined, sharp, intense peaks, as expected for a high degree of crystallinity, whilst the signal at 649.92 cm⁻¹ is a broader, less intense peak, indicative of an unequivocal c-axis sapphire signature.

 

Fig. 3 Representative Raman spectra. (a) Full-range spectra of glass-clad sapphire-core fibers with and without annealing, together with a bulk sapphire rod for comparison, showing seven phonon modes at ~385, 422, 435, 454, 583, 650, and 755 cm⁻¹. (b) Close-up spectra of (a) showing the linewidth narrowing characteristics, indicating the improvement of crystalline core quality with thermal annealing.

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Another salient conclusion is that the Raman linewidth presents defect-induced broadening, as shown in the close-up spectra in Fig. 3(b). The spectral resolution (~1.5 cm⁻¹) of the confocal Raman spectroscope employed is not enough to reflect the real crystallinity of the sapphire crystal core. Therefore we choose just one of the Raman peaks at ~755 cm⁻¹ for Raman linewidth analysis. The linewidths of the three test samples (annealed and non-annealed fibers, and bulk source rod) are all around 12 cm⁻¹. After fitting the Raman spectra of Fig. 3(b), the peak of the annealed glass-clad fiber sample was found at 754.34 cm⁻¹ with a full width at half maximum (FWHM) of ~12.32 cm⁻¹, which was the narrowest of the three. The obtained FWHM values for non-annealed glass-clad fiber and bulk source rod are ~13.11 cm⁻¹ at 754.09 cm⁻¹ and ~12.74 cm⁻¹ at 756.09 cm⁻¹, respectively. This ~6.0% decrease of Raman linewidth with subsequent preferential annealing treatment agrees satisfactorily with the HRTEM investigations in Fig. 2 and corroborates the improvement of crystalline core quality. On the other hand, the blue-shift of the Raman peak in the non-annealed glass-clad fiber relative to the peak in the bulk source rod suggests that the LHPG-fabricated glass cladding imposes some strain on the sapphire crystal core [65] due to thermal expansion coefficient difference between the crystal core and glass cladding. The thermal expansion coefficients of the c-axis sapphire core and borosilicate glass cladding are 4.5 × 10⁻⁶ °C⁻¹ [66] and 3.8 × 10⁻⁶ °C⁻¹ [67], respectively.

3.4 Correlation between atomic-scale roughness and optical guiding loss

To quantitatively understand the effect of the core/clad interfacial roughness on the guiding properties, the propagation loss α related to the interfacial roughness σ and correlation length L_c can be reasonably estimated by the following expression [68]:

 

Fig. 4 Corresponding autocorrelation functions (a) before annealing and (b) after annealing. The extracted values for σ and L_c derived from the fitted exponential curves are 5.350 Å and 2.4938 nm in (a) and 1.933 Å and 1.0660 nm in (b), respectively. Both small σ and small L_c are necessary to obtain very low propagation losses in glass-clad crystal-core fibers, reflecting the obvious superiority of the LHPG-based fiber drawing technique.

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A propagation loss contour at 800 nm against σ and L_c via Eq. (1) is mapped in Fig. 5(a). It should be noted that, to prevent the propagation losses from being underestimated, all the guided modes are taken into consideration in Fig. 5, with the exception of only the fundamental mode being included at 800 nm (see Appendix A). The propagation loss for our glass-clad sapphire crystal-core fiber with σ of 5.350 (non-annealed) and 1.933 Å (annealed) and L_c of 2.4938 (non-annealed) and 1.0660 nm (annealed) are calculated to be 1.236 and 0.069 dB/cm at 800 nm, respectively, as overlaid by “*” in the contour map of Fig. 5(b). This very low loss of 0.069-dB/cm is in satisfactory agreement with the experimentally determined value of < 0.1 dB/cm. Furthermore, according to the favorable match between the experimental result and the theoretical analysis on the correlation between the propagation loss and the interfacial nanostructure, the model can be elucidated in depth showing the dependence of loss on roughness in crystal-fiber-based waveguides. As depicted in Fig. 5, it can be concluded that the criterion for fabricating glass-clad crystal-core fiber with low propagation loss less than 0.1 dB/cm is that σ and L_c should be < 0.23 nm and < 2.10 nm, respectively. This result suggests that an accurately controlled fabrication process plays a key factor in obtaining a good quality core surface because a larger interfacial variation results in a stronger scattering loss. Furthermore, in view of the LP₀₁ fundamental mode at 800 nm (see Appendix A), it appeared that, with a given σ ranging from 1 nm to a few nm, α linearly increases by increasing L_c, whereas α is inversely proportional to L_c for L_c larger than 400 nm and reaches a maximum loss when L_c is ~300 nm. On the contrary, for a given L_c, α increases rapidly as σ increases, since the light interacts more with a larger surface fluctuation.

 

Fig. 5 Contour of propagation loss (α) for (a) all the guided modes at 800 nm calculated against the correlation length (L_c) and roughness (σ), showing a dependence of α on L_c is more severe for a larger σ. (b) Magnified view of (a) showing the effectiveness of high-temperature treatment that reduces the propagation loss from 1.236 to 0.069 dB/cm.

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The above result obviously indicates that such a dependence of loss on L_c has a more prominent effect than on σ, as is the case for all the guided modes shown in Fig. 5. Moreover, the non-monotonic dependence of loss on L_c is valid for all waveguides [70–72] and is further evident from the following [68]:

Fig. 6(a) shows the contour of propagation loss for a 532-nm excitation calculated against correlation length and roughness. All the guided modes are taken into account for the loss estimation. Referring to LP₀₁ fundamental mode at 532 nm, see Appendix B. A comparison with Fig. 5(a), which was calculated at 800 nm, shows that α increases rapidly as λ decreases; this is to be expected, since the overall wavelength dependence of the Rayleigh scattering and Mie scattering losses are proportional to be λ^-4 and λ^-2 [73], respectively. Additionally, for a multi-mode fiber, the number of supported modes at 532 nm is larger than those at 800 nm, and this also results in an increased scattering loss at the core/clad interface. Figure 6(b) is a close-up map of Fig. 6(a) of the propagation loss corresponding to all the guided modes at 532 nm of the non-annealed and annealed fibers. The obtained results (denoted by “*”) were employed in the numerical simulation for the laser action.

 

Fig. 6 Contour of propagation loss (α) for (a) all the guided modes at 532 nm calculated against the correlation length (L_c) and roughness (σ). As expected, α increases rapidly as λ decreases when compared to Fig. 5. (b) Magnified view of (a) showing the effectiveness of high-temperature treatment that reduces the propagation loss from 10.015 to 0.560 dB/cm.

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Figure 7 shows the propagation loss estimations against different wavelengths for both non-annealed and annealed crystal fibers. The corresponding extracted values are listed in Table 1 (see Appendix C). In view of annealed case in Figs. 7(a) and 7(b), it presents similar measured results over the two typically used excitation (532 nm) and signal (800 nm) wavelengths, as marked with the error bars. The calculated and the experimental values are in good agreement. At this stage, one can conclude in the annealed fiber that the loss results for both all guided modes and LP₀₁ mode are in the same trend, that is, at least an order of magnitude lower than those of non-annealed fibers. In addition, all loss curves in Figs. 7(a) and 7(b) exhibit the same dispersion-like behaviors, indicating that these obtained results confirm predictions based on the two approximate expressions of α in Eqs. (1) and (2). The above results clearly demonstrate that the atomically smooth core/clad interface of our LHPG-grown annealed fiber ensures an order of magnitude improvement in the roughness, giving rise to a low propagation loss over the ultrafast-laser-inscribed waveguides and Ti:sapphire channel waveguides that have large values from 1 to a few dB/cm [74–77].

 

Fig. 7 Propagation loss as functions of optical wavelength and annealing effect for (a) all guided modes and (b) LP₀₁ fundamental mode. Loss increases significantly as the wavelength is decreased, since the L_c of the interfacial roughness is more comparable to the wavelength. The error bars in (a) represent standard deviations of quintuplicate measurements. The propagation losses of the annealed and non-annealed crystal fibers were measured using the cutback method [51].

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3.5 Correlation among interfacial roughness, optical loss, and device performance

Because the core/clad interfacial roughness is extremely sensitive to scattering losses, reduction of interfacial roughness to values as low as possible in these glass-clad sapphire-core fibers, is critically needed for the development of active fiber components—especially for extending our understanding of the fundamental interrelations among interfacial roughness, propagation loss, and device performance. To verify this conclusion, a four-energy-level simulation of a glass-clad Ti:sapphire-core fiber laser was carried out, as shown in Figs. 8(a) and 8(b), for designing the crystal fiber length L and output coupler reflectance R₂. Although many distribution-based algorithms for Ti:sapphire bulk lasers have been developed [77], the optimizations are usually time-consuming and the data are typically piecewise-defined results. Herein, a simple yet efficient lumped model was adopted in our systematic analyses. By combing the two major time-dependent rate equations, dN₂/dt and dI_c/dt, governing the steady-state coupling between the upper-level population density N₂ and the intracavity photon intensity I_c (see Appendix D), one can derive the threshold P_th and the slope efficiency η_s. This relation can be described as follows [78]:

 

Fig. 8 Numerical simulations of the Ti:sapphire crystalline core fiber laser. The performance of an 8-cm Ti:sapphire crystal fiber with a coated output reflectance of 30% is computed for (a) the slope efficiency of 42.3% with (b) a threshold of ~770 mW at room temperature.

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In Eqs. (3)–(6), λ_p, λ_L, σ_a, σ_e, N_g, and P_in are the pump and lasing wavelengths, the absorption and emission cross sections at λ_p and λ_L, the electron density of the ground state, and the incident pump power, respectively. ${\alpha }_{p0}$, ${\alpha }_{PL}^{pump}$, and ${\alpha }_{PL}^{sig}$ are the small-signal absorption coefficient at λ_p, and the modal propagation losses at λ_p and λ_L, respectively. η_in, η_out, M, and r stand for the input and output pump coupling efficiencies, the laser-to-pump mode matching ratio, and the mode radius of the crystalline core, respectively. Moreover, h, c, τ_f are Planck’s constant, the speed of light in vacuum, and the fluorescent lifetime, respectively; while n, L, R₁, R₂, and FOM represent the refractive index of the Ti:sapphire crystal core, the crystal fiber length, the input and output coupler reflectances, and the figure of merit, respectively. The values of the parameters employed for evaluation are as follows: λ_p, λ_L, σ_a, and σ_e are 532 nm, 800 nm, 6.5 × 10⁻²⁴ m², and 2.7 × 10⁻²³ m², respectively [79]; ${\alpha }_{p0}$, ${\alpha }_{PL}^{pump}$, and ${\alpha }_{PL}^{sig}$ are 1.0 cm⁻¹, 0.560 dB/cm, and 0.069 dB/cm, respectively; η_in, η_out, and R₁ are 70, 5, and 99%, respectively; r, n, M, FOM, and τ_f at room temperature are 10 μm, 1.7522 (for o-ray at 800 nm), 0.6, 100, and 3.1 μs [69,79], respectively. Note that the values of ${\alpha }_{PL}^{pump}$ at λ_p for annealed and non-annealed fibers are also computed based on Eq. (1), as shown in Fig. 6(b).

In Figs. 8(a) and 8(b), the performance of an 8-cm-long glass-clad Ti:sapphire crystal-core fiber with a 30% output reflectance is computed for the maximum η_s of 42.3% with a ~770-mw threshold at room temperature. The simulation results indicate that the crystal fiber length has a significant impact on the laser efficiency. Since the gain saturation increases with increasing σ_e, in our case with a large value of σ_e at a fixed R₂, the longer crystal fiber length is required in order to extract the maximum slope efficiency and the output power from the Ti:sapphire crystal core. Larger σ_e ensures higher maximum output powers. However, an increase in crystal fiber length gives rise to a greater round-trip loss introduced by ${\alpha }_{p0}$, ${\alpha }_{PL}^{pump}$, and ${\alpha }_{PL}^{sig}$, namely, a higher threshold pump power, as presented in Fig. 8(b).

Another important characteristic deduced from these results is that the large σ_e and small ${\alpha }_{PL}^{pump}$ are responsible for the optimized R₂ being as low as 30%. In contrast, in the non-annealed case involving a large propagation loss at λ_p, and λ_L, no laser action is observed over the entire region. All the parameters used in Figs. 8(a) and 8(b) are employed for the annealed case, with the exceptions of ${\alpha }_{PL}^{pump}$ and ${\alpha }_{PL}^{sig}$ being 10.015 and 1.236 dB/cm, respectively, for the non-annealed fiber.

The numerical analyses offer insights into how one might design Ti:sapphire crystal fiber lasers as a next step. As indicated in Fig. 8, the fiber-based waveguide geometry features a high pump intensity and stronger intracavity photon energy, meaning that the Ti:sapphire crystal fiber laser can potentially provide high quantum efficiency with a rather large output coupler transmittance, all while maintaining a low-threshold no bulk-type Ti:sapphire laser (including rib and channel waveguide lasers) can achieve. For example, with output couplings of 0.5 and 3%, a 5.2-mm-long bulk Ti:sapphire laser exhibits slope efficiencies of 3.7 and 11.1% with thresholds of 252 and 500 mW [5], respectively. In the case of a 5-mm-long rib waveguide laser [80], a rather low slope efficiency of 5.3% was obtained with a threshold of 500 mW using an output coupling of 4.6%. With a 4-mm-long channel waveguide laser [77], a slope efficiency of only ~0.1% was achieved by using high-reflection mirrors (R > 99.6%), which corresponds to a launched threshold of ~210 mW. In contrast, as shown in Fig. 8, a maximum slope efficiency of ~29% was achieved with a threshold of only 400 mW using a coated 5.0-cm-long Ti:sapphire crystal fiber with an output transmittance of 25%.

The above exceptional features make the near-infrared broadband tunability viable even with certain amounts of losses caused by the intracavity tuning components. The analytical simulations demonstrate that the high slope efficiency and low threshold are better than any previously reported Ti:sapphire bulk lasers as expected for the large emission cross section, low propagation loss, and high crystallinity of the core of the glass-clad Ti:sapphire crystal-core fiber lasers.

4. Conclusion

We demonstrated an alternative strategy to realize a glass-clad high-quality crystalline sapphire-core fiber by the LHPG technique with subsequent high-temperature treatment. Our simple method offers an efficient and more cost-effective approach to developing high-power fiber devices, when compared with conventional techniques such as ultrafast-laser inscription and the use of polycrystalline cladding. We have also directly observed at atomic resolution a roughness of only ~1.9 Å along the core/clad interface of the annealed fibers. The achieved propagation losses are below 0.1 dB/cm, which is an order of magnitude lower than the losses of non-annealed fibers (1.236 dB/cm vs. 0.069 dB/cm) and previously reported Ti:sapphire channel waveguides (1 to a few dB/cm). In addition, we theoretically predicted that such a high-crystallinity core with low-loss wave confinement can be utilized for realizing low-threshold lasing with high quantum efficiency that differs from existing bulk Ti:sapphire lasers. All these features make the crystalline-core-based fiber waveguides an attractive candidate as a building block for all-optic integrations and high-power devices.

Appendix A Propagation loss against correlation length and roughness @ 800 nm

Figure 9 shows the contour of propagation loss (α) for an 800-nm signal calculated against correlation length (L_c) and roughness (σ). The indicator “*” in the lower-left corner of the map (Fig. 9(a)) denotes the loss corresponding to the annealed fiber with L_c=1.07 nm and σ=0.1933 nm. Note that a value of L_c of around 300 nm has a physical significance in that it is nearly one-quarter wavelength of an 800-nm signal in a gain medium with an effective index of 1.75, as shown in Fig. 9 (b).

 

Fig. 9 (a) Calculated propagation loss for a fundamental mode LP₀₁ in a 40-μm-diameter sapphire crystalline core. (b) Dependency of α on L_c for σ = 0.1933 nm showing a maximum value at L_c ≈300 nm (marked by the dashed lines) followed by a decrease as L_c increases.

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Appendix B Propagation loss against correlation length and roughness @ 532 nm

Figure 10 shows the contour of propagation loss (α) for a 532-nm signal calculated against correlation length (L_c) and roughness (σ). The indicator “*” in the lower-left corner of the map (Fig. 10(a)) denotes the loss corresponding to the annealed fiber with L_c=1.07 nm and σ=0.1933 nm. Note that a value of L_c of around 200 nm has a physical significance in that it is nearly one-quarter wavelength of a 532-nm signal in a gain medium with an effective index of 1.75, as shown in Fig. 10 (b).

 

Fig. 10 (a) Calculated propagation loss for a fundamental mode LP₀₁ in a 40-μm-diameter sapphire crystalline core. (b) Dependency of α on L_c for σ = 0.1933 nm showing a maximum value at L_c ≈200 nm (marked by the dashed lines) followed by a decrease as L_c increases.

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Appendix C Comparison of propagation losses

Table 1. Summary of Propagation Loss Dependence on Optical Wavelength and Annealing Effect

View Table

Appendix D Numerical simulations of Ti:sapphire crystal fiber laser below and above threshold

To verify the effectiveness of the proposed model for glass-clad Ti:sapphire crystal fiber laser, the numerical results of the time-dependent N₂ evolution and I_c evolution for laser (Fig. 11) and amplified spontaneous emissions (ASE) (Fig. 12) are presented for comparison. It should be mentioned that the parameters used in Figs. 11(a) and 11(b) are all employed for the ASE case shown in Figs. 12(a) and 12(b), with the exceptions of R₁ and R₂ being 99 and 90%, respectively, for the Ti:sapphire crystal fiber laser. Both R₁ and R₂ are 7.4% (i.e., Fresnel reflection) for Ti:sapphire crystal fiber ASE. The parameters computed in Figs. 11 and 12 are as follows: λ_p, λ_L, σ_a, and σ_e are 532 nm, 800 nm, 6.5×10⁻²⁴ m², and 3.8×10⁻²³ m², respectively [79]; ${\alpha }_{p0}$, ${\alpha }_{PL}^{pump}$, ${\alpha }_{PL}^{sig}$, and L are 1.0 cm^-1, 0.560 dB/cm, 0.069 dB/cm, and 8 cm, respectively; η_in, η_out, and R₁ are 70, 5, and 99%, respectively; r, n, M, and τ_f at room temperature are 10 μm, 1.7522, 0.65, and 3.1 μs [79], respectively.

 

Fig. 11 Numerical simulations of time-dependent (a) N₂ and (b) I_c evolutions for the Ti:sapphire crystal fiber laser.

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Fig. 12 Numerical simulations of time-dependent (a) N₂ and (b) I_c evolutions for the Ti:sapphire crystal fiber ASE.

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It is evident from the lasing efficiency in Eq. (4) that ${\alpha }_{p0}$ depends explicitly on σ_a ×(N_T–N₂), where ${\alpha }_{PL}^{pump}$ is a constant. In this connection, the η_s is dominated by σ_a ×(N_T–N₂) because the steady-state clamped N₂ is inherently smaller than N_T during laser action. As shown in Fig. 11(a), taking 1.5 W incident pump power as an example, σ_a ×(N_T–N₂)= 99.5 m⁻¹ for the Ti:sapphire crystal fiber laser. This results from a clamped N₂ of 7.82×10²² #/m³. But for ASE, the steady-state N₂ is as high as 2.39×10²³ #/m³, which results in σ_a ×(N_T–N₂)= 84.5 m⁻¹. The above discrepancy clearly indicates the effectiveness of our numerical model for the glass-clad Ti:sapphire crystal-core fiber laser. Since the crystal fiber length L and output coupler reflectance R₂ are easy to control in experiments, one can obtain reasonably accurate estimations for P_th and η_s by tuning these crucial factors of L and R₂.

Funding

Work presented here has received funding from the Ministry of Science and Technology (MOST) of Taiwan under the grant MOST 104-2112-M-259-003-MY2.

Acknowledgments

The authors are grateful to Mrs. L. C. Wang for assistance with the HRTEM experiments at the facilities at National Sun Yat-Sen University, Kaohsiung, Taiwan. C. C. Lai conceived, designed, and led the project. C. Y. Lo carried out the fiber growths. C. C. Lai performed the experiments, simulations, and data analysis. D. H. Nguyen and J. Z. Huang assisted with some of the data processing. C. C. Lai wrote the manuscript. W. S. Tsai and Y. R. Ma contributed to the scientific discussion. All authors reviewed the manuscript.

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