1. Introduction

Deposition is the opposite of sublimation, however, both of these phenomena are used in tandem to create thin films and nanoparticles on substrates. In particular, the deposition of rare-earth ion doped silica (SiO$_{2}$) glass has a wide range of applications in many fields from telecommunications and biosensing to nonlinear and quantum optics. Probably the most well-known and commonly used method is pulsed laser deposition [1–5]. A doped target material is ablated by irradiation with a pulsed laser and the resulting plume emanating from the target is intercepted by a substrate. The particles in the plume deposit on the substrate where they can form a thin film. The doping concentration and thickness of the film can be partially controlled by the laser power and number of pulses [3,6]. Inductively coupled plasma-optical emission spectrometry and laser ablation inductively coupled plasma mass spectrometry are methods used to determine the elemental constituent of glass materials [7] and the relative concentrations of any dopants. Laser ablation was used to examine historical glass [8–15] as well as in forensic studies [9]. These analytical methods use ablation but do not reveal any information about the evaporation kinetics of the individual components.

Vaporization of glass materials is also a well-studied effect with a number of papers presenting vapor pressures and evaporation coefficients for SiO$_2$ and Si mixes [10,11] as well as pure erbium [12] and other rare-earth ions [13]. There is a nonlinear relationship between vapor pressure/evaporation and temperature which is traditionally measured using a Knudsen effusion cell and a thermogravimetric balance [12,13]. Continuous wave and pulsed lasers can be used to create evaporation from glass targets for such studies; CO$_2$ lasers are particularly well-suited for heating glass materials, with several studies on evaporation rates reported in the literature [14–16]. Due to the properties of silica, the rare-earth ion concentration in doped silica materials is usually very low [17,18]. Therefore, the change of ion concentration due to the evaporation process of doped silica is difficult to measure simply and directly. One method used is Rutherford backscattering spectrometry after the pulsed laser deposition, to determine substrate Er³⁺ concentration dependence on the number of pulses [19]. Surprisingly, there seems to be little information on the evaporation of rare-earth ion doped glass, particularly the evaporation ratio of the dopant to the glass host. To the best of our knowledge, the characteristics of SiO$_2$ doped with trace rare-earth ions during evaporation have not been studied. Therefore, we present a measurement of the evaporation rate of Er³⁺ to SiO$_2$ in a doped glass using a novel method based on whispering gallery spectroscopy and volumetric evaporation analysis that does not require any knowledge of the temperature.

In this work, we use whispering gallery resonators (WGRs) as a tool to determine the number of Er³⁺ ions lost for every cubic micron of SiO$_2$ evaporated. The combination of an ultrahigh quality (Q-) factor and small mode volume in WGRs significantly enhances the light-matter interactions, giving them excellent detection/sensing capabilities [20–25]. To determine the evaporation characteristics, sections of doped fiber were spliced to sections of undoped fiber, then melted and evaporated to form microspheres. Using different ratios of doped and undoped fiber lengths provides us with a way to estimate the volumes evaporated and to reach a critical doping concentration during the tests. The results show that, for a given CO$_2$ laser power, it is possible to control the doping concentration (by a factor of 20) in the microsphere by adjusting the volumes of fiber evaporated. We also discuss the possible physical mechanism behind the observed evaporation ratio.

As an application of our findings, a method to deterministically prepare active microsphere resonators using commercially available doped fiber is presented. To date, sol-gel coatings are commonly used method to add rare-earth ions to WGRs, but this method requires careful chemical preparation. In the scenarios where different doped samples need to be prepared, sol-gel method becomes more complicated [26–29]. Other methods for preparing doped WGRs include doping by ion implantation [30], coating the WGR with a doped glass layer of lower melting temperature [31] or etching the cladding of commercial doped fiber [32]. These methods have been proven to be effective, but have not been widely used because of their complex processes and low efficiency. The method of directly melting the end of undoped fiber is an ideal platform to prepare passive silica microspheres [33], but this method is generally not suitable for the preparation of active microspheres from commercial doped fiber. It is noted that there are some reports that the doped fibers used were originally pulled from bulk doped glass, and are not commercial doped fibers [34]. Since the rare-earth ions of the commercial doped fiber are primarily deposited in the core (and not in the cladding), microspheres prepared directly from such fiber often cannot meet the requirements for lasing due to the low doping concentration in the bulk microsphere material. In the method proposed in this paper, the different evaporation rates of Er³⁺ and SiO$_{2}$ during heating effectively increase the concentration of Er³⁺ distributed in the bulk microspheres. This boil-down or reduction method is not only simple and economical, but can also be used to control and calculate the doping concentration and size of the resulting microspheres. It ensures that any volume of doped fiber can be used to produce a microspherical WGR with sufficient concentration of gain material to achieve lasing.

2. Experimental setup

To study the evaporation characteristics of doped silica, Er³⁺-doped (custom made) and undoped fibers (SMF-28, Thorlabs) were fused together and microspheres were fabricated from the fused fiber. The Er³⁺-doped fiber used in this experiment was prepared via a low-temperature chelate gas phase deposition technique [35]. The percentage of Er³⁺ in the doped fiber core (p$_{mpc}$) was about 0.05 mol${\% }$ (calculated from the external doping method, i.e., the molar amount of Er³⁺ in the core was 0.05 mol${\% }$ of SiO$_{2}$). The core radius (r$_{c}$) was 1.6 $\mu$m and the fiber radius (r$_{f}$) was 62.5 $\mu$m. This is the same as the radius of the undoped fiber used, hence r$_{f}$ is used to denote the radius for both types of fiber.

The microsphere preparation process is illustrated in Fig. 1(a) (i)-(iv). The fusion splicer was set to continue a slight tapering operation after the splicing process to mark the splicing position between the doped and undoped fiber sections. Figure 1(b) is an image of the sample under a microscope, the center of the depression is the splicing point of the two fibers. Next, the fused fiber was placed vertically, so that the undoped section was at the top and the doped section was at the bottom, and a weight was hung on the end. The undoped fiber section (at the top) was irradiated by a CO$_{2}$ laser, at a distance l$_{u}$ above the splice mark, until the glass softened and stretched to form a thin rod. Figure 1(c) shows an image of the resulting thin rod. Next, at high power ($\sim$7 W), the CO$_{2}$ laser was used to irradiate the doped fiber section at a distance, l$_{d}$ + l$_{u}$, below the thin rod, and any material below this point dropped off thereby removing any excess fiber material in this section. Then, by continuously moving the fiber downward, the bottom tip of the l$_{d}$ and l$_{u}$ section was constantly evaporated by the CO$_{2}$ laser.

 

Fig. 1. (a) Sample preparation. (i) A section of undoped fiber is fused to a section of doped fiber. (ii) A thin rod is formed in the undoped fiber region by CO$_{2}$ laser heating. Then, the region of the doped fiber is cut off by a CO$_{2}$ laser to form a fiber region composed of l$_{u}$ and l$_{d}$. (iii) By continuously moving the fused fiber downward, the bottom tip of the l$_{d}$ and l$_{u}$ section was constantly evaporated by the CO$_{2}$ laser. (iv) Finally, a microsphere was formed. l$_{u}$ is the length of the undoped fiber section. l$_{d}$ is the length of the erbium-doped fiber section. (b) The fused point is marked by the microtapering process. (c) A thin rod prepared by SiO$_{2}$ heating. (d) Fiber being heated by a 7 W CO$_{2}$ laser. (e) Image of a microsphere produced by evaporation of the fused fiber.

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The laser spot size full-width-half-maximum (FWHM) was measured to be $\sim$700 $\mu$m, yielding an intensity of $\sim$5 kW/cm$^{2}$. This intensity was sufficient to increase the temperature of the glass to near its boiling point of $2,230 ^\circ \text {C}$ and produce rapid evaporation [14,15]. Figure 1(d) is an image of the fused fiber under $\sim$7 W CO$_{2}$ laser irradiation. Laser heating was stopped once there was essentially no more fiber remaining below the very thin rod. This overall process resulted in the formation of a microsphere at the end of the thin rod (see inset of Fig. 1(e)).

3. Results

The microfiber-micosphere coupling setup is shown in Fig. 2. A tapered fiber with a waist diameter of $\sim$3 $\mu$m was prepared by heating and stretching method, which was used to couple the pump light into the microsphere resonator [36]. In the experiment, the tapered fiber is contact-coupling with the microsphere resonator to ensure stability. The input end of the tapered fiber was connected to a 980 nm laser, and its output end was connected to an optical spectrum analyzer (OSA, AQ6375, YOKOGAWA) for signal collection. The coupling between the tapered fiber and the microsphere was monitored through an optical microscope, and the inset in Fig. 2 demonstrates the green upconversion luminescence of the Er³⁺-doped microsphere at the coupled state. Figure 3(a) shows the spectra obtained from two different samples when using the same pump power (20 mW) and tapered fiber coupler. Note that the pump power was measured at the input of the tapered fiber. The microsphere radius, r$_{s}$, and the lengths of the undoped sections l$_{u}$ used in the fabrication were the same for both samples but the lengths of the doped sections, l$_{d}$, were different. Whispering gallery lasing (WGL) and fluorescence from the Er³⁺ doped spheres were observed for both samples.

 

Fig. 2. Schematic diagram of the coupling setup. The inset is a photomicrograph of a microsphere with green upconversion luminescence at the coupled state.

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Fig. 3. (a) Spectra from two microspheres prepared by fused fibers with different doped lengths. Parameters of Sample 1 are r$_{s}$=71 $\mu$m, l$_{d}$=1.0 cm, l$_{u}$=0.4 cm and the parameters of Sample 2 are r$_{s}$=70 $\mu$m, l$_{d}$=3.0 cm, l$_{u}$=0.4 cm. (b) Spectra from microspheres prepared by fused fibers with different undoped lengths. Parameters of Sample 3 are r$_{s}$=74 $\mu$m, l$_{d}$=1.0 cm, l$_{u}$=0.2 cm; parameters of Sample 4 are r$_{s}$=71 $\mu$m, l$_{d}$=1.0 cm, l$_{u}$=0.6 cm; parameters of Sample 5 are r$_{s}$=70 $\mu$m, l$_{d}$=1.0 cm, l$_{u}$=0.8 cm; parameters of Sample 6 are r$_{s}$=74 $\mu$m, l$_{d}$=1.0 cm, l$_{u}$=0.9 cm.

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In these experiments, the bulk of the material used to form a microsphere was from the undoped fiber section, with the only possible source of Er³⁺ coming from the doped section, which was evaporated during the fabrication process. The fact that both microspheres emitted light shows that, during the evaporation of the doped fiber, some of the Er³⁺ ions were retained and continuously deposited in the undoped section that formed the microsphere. Notably, the microsphere made by evaporating the longer length of doped fiber (Sample 2) had stronger fluorescence and laser signals, see Fig. 3(a), indicating that evaporation of longer doped sections leads to more ions being retained, as would be expected. Unlike the fluorescence spectrum, the lasing is more sensitive to various factors and relatively hard to control. In the spectrum from Sample 2, the increased presence of rare-earth ions not only increases the laser intensity, but also leads to more laser modes. From these results, we hypothesize that fixing the length of the undoped section and the sphere size, while varying the length of the doped section, allows one to control the concentration of Er³⁺ in the microsphere.

A second experiment was designed to study whether all or only some of the Er³⁺ ions were retained during evaporation. The same method as described above was used, but this time the length of the doped section was fixed and the length of the undoped section was varied. The result of this second experiment is shown in Fig. 3(b) for four different microspheres labeled sequentially as Sample 3 to Sample 6. As evident from Fig. 3(b), for microspheres with equal diameter, the fluorescence is weaker for longer sections of undoped fiber. This indicates that Er³⁺ ions were also lost during the evaporation of the undoped section. The longer undoped sections resulted in lower ion concentrations because a larger volume of glass must be evaporated (compared to the shorter undoped section) to achieve the same size sphere. This longer evaporation process resulted in more ions being lost and a lower final concentration in the microsphere.

From this set of spectra, the loss rate of Er³⁺ can be estimated. As shown in Fig. 3(b), the fluorescence reduces as the undoped fiber section is increased to 0.9 cm (in steps of $l_d=0.1$ cm). Assuming a high Q-factor for the WGM microspheres combined with the large 980 nm pump power used in the experiment, we can infer that the Er³⁺ concentration in Sample 6 was extremely low. For all practical purposes, we can surmise that the Er³⁺ concentration in this microsphere is zero. Sample 6 appears to be the boundary situation between the observation of fluorescence and no fluorescence. Hence, the parameters for this sample could be regarded as the critical values for a complete loss of Er³⁺. Monitoring the loss rate of rare-earth ions in real-time is challenging and beyond the scope of this work. However, we can estimate an average loss rate of rare-earth ions when laser evaporating doped glass, L$_{mv}$. The number of Er³⁺ ions lost by evaporation per unit volume from the fiber during the microsphere fabrication can be defined as:

Equation (3) corresponds to Sample 6 in Fig. 3 with $l_d=1.0$ cm and $l_u=0.9$ cm. The corresponding values of the other parameters are: $p_{mvc}=1.83 \times 10^{-17}$ mol/$\mu$m$^3$, $r_c=1.6$ $\mu$m, $r_s=74$ $\mu$m, and $r_f=62.5$ $\mu$m. By substituting these values, we get $L_{mv}=6.36 \times 10^{-21}$ mol/$\mu$m$^{3}$. From another approach, we can express the ratio of the amount of Er³⁺ lost to the amount of SiO$_{2}$ evaporated in the fabrication process as $R_{mm}$ where

Using the values for from Sample 6 in Fig. 3, $R_{mm}=1.74 \times 10^{-7}$. Hence, $1.74 \times 10^{-7}$ mol of Er³⁺ was lost for each mol of SiO$_{2}$ evaporated. The experimental observations and our calculations show that there was a trace loss of Er³⁺ in the high-temperature evaporation process of the Er³⁺-doped SiO$_{2}$ glass. This is an approximate ratio with the accuracy mainly limited by the step size ($\sim$0.1 cm) of $l_d$ in the experiment, the sensitivity of the OSA to very low signal levels, and the influence of a small amount of other metal ions in the doped fiber that could lead to a variation in the refractive index. In the experiment, the pulling down of the fiber was controlled by manually adjusting the displacement stage. During the fiber evaporation process, no significant effect of pulling rate on the experimental results was observed.

4. Application and discussion

The evaporation of Er³⁺-doped fiber using a high-power laser can be used to adjust the ratio between the size and doping concentration of the microspheres. A section of doped fiber was tapered to a thin rod and cut as described in Section 2. However, this time no undoped fiber section was used in the microsphere fabrication process. After cutting the fiber with the laser, the remaining fiber length was recorded as $l_d$. The CO$_{2}$ laser was set to 7 W and kept on as the fiber was slowly moved downward and fed into the focus of the laser, during which the glass melted and formed a microsphere. When the thin rod region was reached, the sphere was held in the focus until it evaporated down to the desired size.

The amount of Er³⁺ lost ($n_{loss}$ in moles) can be calculated from the amount of SiO$_{2}$ lost when evaporating the volume of the fiber down to the volume of the sphere:

The molar amount of Er³⁺ in the core (n$_{Er core}$) is:

The molar amount of SiO$_{2}$ in the microsphere is:

The molar percentage of Er³⁺ in the doped microspheres (p$_{mps}$) formed by the evaporation of the doped fiber can be calculated from

From Eq. (8), one can see that, for a given sphere size, the doping concentration scales linearly with $l_d$. However, for a fixed $l_d$, the concentration of erbium scales nonlinearly with sphere size, as shown in Fig. 4(a) and (b). Therefore, one needs to consider the length of the doped fiber section for a given sphere size to arrive at the final desired concentration. It should be possible to increase the final erbium concentration in the sphere to three or four times the original concentration in the doped fiber by choosing $l_d$ appropriately. For a 3 cm length of fiber, as used in these experiments, evaporated to form a sphere with a 20 $\mu$m radius, the volume of material reduces by a factor of 11,000, while the erbium concentration increases by a factor of 3.4 from 0.05${\% }$ to 0.17${\% }$. The fiber used was the same as that for the results in Fig. 3, hence $L_{mv}=6.36 \times 10^{-21}$ mol/$\mu$m$^{3}$ and $R_{mm}=1.74 \times 10^{-7}$.

 

Fig. 4. Esimtated molar percentage Er³⁺ concentration for microspheres with different parameters. (a) Effect of doped fiber length on concentration for microsphere radii ranging from 20 $\mu$m to 60 $\mu$m. (b) Effect of microsphere radius on concentration for doped fiber lengths ranging from 0.1 cm to 3.0 cm.

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We prepared 5 microspheres, labeled from Sample A to Sample E, directly from doped fiber of different lengths, $l_d$, while the radius of the spheres was kept constant at $\sim$50 $\mu$m. Figure 5(a) shows the spectrum from each sample under near identical excitation conditions. Each sample was excited by a 980 nm laser with a power of $\sim$20 mW using a $\sim$3 $\mu$m diameter tapered fiber. The fluorescent bandwidth and power are, respectively, wider and stronger for microspheres made from longer lengths of doped fiber as would be expected for higher final concentrations [38].

 

Fig. 5. (a) Spectra from five microspheres prepared by evaporation under identical excitation conditions. (b) Peak fluorescence intensity as a function of the calculated Er³⁺ concentration for the five microspheres (triangles) and the variation of the peak fluorescence intensity for Sample C for five different coupling positions (dots).

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From Fig. 5(a), we see that the laser emission tends toward longer wavelengths possibly due to increasing Er³⁺ concentration, which would reduce the distance between individual Er³⁺ ions, thereby enhancing the inter-ion energy transfer and excited state absorption [39]. Comparing the known absorption and emission cross-sections of Er³⁺ ions in the $\sim$ 1550 nm band [40,41], shorter emission wavelengths may be re-absorbed by nearby Er³⁺ ions. This could lead to an apparent increase in the laser emission signal at longer wavelengths.

In general, lasing in WGRs is very dependent on the coupling condition, but the fluorescence signal is less so. For the lasing signal, we can expect competition between different whispering gallery modes [42,43], hence the exact relationship between laser intensity and Er³⁺ concentration in microspheres is still not obvious. To quantify the effect of the fiber length on the Er³⁺ concentration dependent emission from the WGR, the peak power of the fluorescence band rather than the lasing peak power is plotted (triangles in Fig. 5(b)) against the calculated Er³⁺ concentration for the five microspheres. If the assumption about evaporation leading to the appearance of a critical minimum concentration is correct then, for a given final sphere size, the concentration should be positively correlated with fiber length and also with the fluorescence peak power as shown in Fig. 5(b). The linear relationship predicted in Fig. 3(a) is reflected in the linear trend in Fig. 4(a), at the low concentration range calculated here one can expect a linear relationship between the fluorescence and Er³⁺ concentration [44]. These experimental results indicate the ability of our fabrication method to control the Er³⁺ concentration in a microsphere.

To highlight the independence of the fluorescence peak power to the coupling position on the tapered fiber, the orange dots in Fig. 5(b) represent the fluorescence peak power of Sample C in Fig. 5(a) at different coupling positions labeled as i to v. The change in coupling position was achieved by uncoupling the microsphere and rotating it by an angle along the equator before coupling again. The peak power of the fluorescence remains constant for many different coupling positions, demonstrating that the linear variation in the peak power is consistent with increasing fiber length and is not strongly affected by the coupling condition.

5. Conclusion

Active microsphere resonators were directly prepared from Er³⁺-doped fiber such that the final erbium concentration in the microsphere could be increased or decreased relative to the initial concentration in the fiber. This is a study and demonstration of controlled doping concentration in WGM resonators that does not require chemical processing such as sol-gel or the fabrication of specifically doped fibers to achieve the desired concentration. The loss rate of Er³⁺ ions in doped silica fiber during evaporation was estimated by studying the fluorescence emission from the whsipering gallery resonators. By controlling the volume of fiber evaporated and determining the glass volume when fluorescence emissions disappear, we hypothesize that Er³⁺ was lost during the evaporation process at a rate of $6.36 \times 10^{-21}$ mol of Er³⁺ for every cubic micron of silica fiber. This can also be expressed as ratio of $1.74 \times$ 10$^{-7}$ mol of Er³⁺ lost for each mol of SiO$_{2}$ evaporated. This work provides us with a method to estimate evaporation in the low doping concentration range (10$^{-4}$ to 10$^{-2}$ mol). Again it is noted that the absence of fluorescence does not mean there are no erbium ions remaining in the glass, rather the ion concentration is so low that emission could not be detected with the present measurement method. However, the absence of emission at high pump powers (>20 mW) and the high sensitivity of the OSA (−70 dBm) makes the concentration effectively zero for practical purposes. To claim the actual absence of ions, more suitable detection methods would be needed, such as laser confocal fluorescence imaging, X-ray photoelectron spectroscopy or energy-dispersive X-ray spectroscopy, all of which are beyond the scope of this work and could be the focus of future studies. The technique herein could be used to study other rare-earth ions, the loss of doped ions in multi-component glass fiber or luminescent materials and should be helpful in the preparation and characterization of doped-glass photonic devices. In addition, the method proposed in this investigation is expected to be extended to polymer and multicomponent fiber based lasers [45].