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Abstract
Rare-earth-doped on-chip microlasers are of great significance in both fundamental research and engineering. To the best of our knowledge, this is the first report of Yb3+-doped and Er3+/Yb3+-codoped on-chip microsphere lasers fabricated via sol-gel synthesis. Laser emissions were observed in a band around 1040 nm in both Yb3+-doped and Er3+/Yb3+-codoped resonators pumped at 980 nm and had measured ultralow thresholds of 5.2 µW and 0.6 µW, respectively. Both single-mode and multi-mode emissions were recorded around 1040 nm in these lasers. Single-mode and two-mode emissions were obtained at 1550 nm in the Er3+/Yb3+-codoped lasers when pumped at 980 nm and 1460 nm, respectively. Furthermore, quality factors induced by different loss mechanisms in the microsphere lasers are theoretically estimated. These resonators are expected to contribute to the high-density integration of on-chip silica-based microlasers.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical microcavities, containing microspheres [1], microtoroids [2–4], and photonic waveguides [5], have attracted global interest from researchers in various fields, such as quantum information processing [6–8], sensing [9,10], nonlinear optics [11], non-Hermitian physics [12] and optomechanics [13–15]. Among them, silica microspheres possess extremely high optical quality factor $\sim$10$^{10}$ [16]. As the gain media in whispering-gallery-mode (WGM) microresonators, rare-earth ions, such as Yb$^{3+}$, Er$^{3+}$, Nd$^{3+}$, and Tm$^{3+}$, interact strongly with the light field, because of the high quality factor and small mode volume of WGM [17–20]. These doped resonators can be used for low-threshold and narrow-linewidth lasers [21,22].
Ytterbium ions absorb 980 nm pump and lase at 1040 nm, where the water absorption is extremely low [23]. Furthermore, Yb$^{3+}$ is also a dopant for high efficiency laser devices. Ytterbium lasers have been achieved in microtoroids and fiber-based microspheres and the upconversion luminescence of Yb$^{3+}$ was also reported [24,25]. Erbium doped lasers are of great significance for telecommunication and they have been achieved based on microtoroid and fiber-based microspheres [26–29]. Ytterbium can be used as a sensitizer for more efficient erbium emission. Erbium and ytterbium codoped lasers have been demonstrated in fiber-based microspheres and on-chip microtoroids [30–32].
Compared with fiber-based microsphere lasers, on-chip microsphere lasers are easier to be integrated and the doping concentrations are more controllable. Furthermore, smaller diameters are easier to be achieved with on-chip microspheres, which enables a higher density of microlaser integration and increases the spatial resolution for relative sensing applications. On-chip microspheres doped with Yb$^{3+}$ may generate laser emissions in water, which can be potentially utilized for high-spatial-resolution biosensing in microfluidics applications [33,34]. Erbium-doped and neodymium-doped on-chip microspheres have been demonstrated in Ref. [35,36]. However, it is challenging to achieve an on-chip microsphere laser with diameters around 20 µm due to radiation leakage [20,37,38]. To the best of our knowledge, Yb$^{3+}$-doped and Er$^{3+}$/Yb$^{3+}$-codoped on-chip microsphere lasers have never been reported.
In this work, we first achieve Yb$^{3+}$-doped and Er$^{3+}$/Yb$^{3+}$-codoped on-chip microsphere lasers with diameters approximately 20 µm based on the sol-gel synthesis method. As far as we know, these may be the sol-gel silica WGM lasers ever reported with the smallest diameters. Laser emissions in the 1040 nm band are demonstrated with the Yb$^{3+}$-doped and Er$^{3+}$/Yb$^{3+}$-codoped microcavities when pumped at 980 nm. And laser emissions in the 1550 nm band are observed with the Er$^{3+}$/Yb$^{3+}$-codoped on-chip microspheres when pumped at 980 nm and 1460 nm, separately. Furthermore, the material, water absorption, and radiative quality factors of the on-chip microspheres are discussed.
2. Fabrication of on-chip microsphere lasers
Yb$^{3+}$-doped and Er$^{3+}$/Yb$^{3+}$-codoped on-chip microspheres were fabricated in this study, starting with the preparation of rare-earth-ion-doped silica films by sol-gel synthesis [26,39]. Isopropanol, tetraethoxysilane, water solution and concentrated hydrochloric acid were firstly mixed in a Teflon beaker. Ytterbium(III) nitrate pentahydrate (Yb(NO$_3$)$_3\cdot$5H$_2$O) was dissolved in the water solution to obtain Yb$^{3+}$-doped on-chip microspheres, while both Yb(NO$_3$)$_3\cdot$5H$_2$O and erbium(III) nitrate pentahydrate (Er(NO$_3$)$_3\cdot$5H$_2$O) were added to water solution for Er$^{3+}$/Yb$^{3+}$-codoped on-chip microspheres. The mixed solution was heated on a hotplate at a temperature of 70 $^{\circ }$C and an agitation rate of 500 rpm. The solution was then aged at room temperature for 24 h to form sol-gel solution. Subsequently, a sol-gel layer was spin coated on a silicon wafer and annealed at 1000 $^{\circ }$C to deposit the ytterbium or erbium/ytterbium ion-doped silica film. A film thickness of approximately 1.5 µm was obtained after four deposition cycles. A specific doping concentration of Er$^{3+}$ or Yb$^{3+}$ in silica film could be prepared with a proper mass ratio of tetraethoxysilane and rare-earth nitrate hydrate in the mixed solution.
In the following process, the silica film was used to fabricate the on-chip microspheres. Round silica patterns with diameters of 120 µm were defined by photolithography and hydrofluoric acid (HF) etching. Then, xenon difluoride (XeF$_2$) dry etching was utilized to undercut the silicon below the silica to produce microdisks with silicon microneedles. Finally, the microdisks were reflowed using a carbon dioxide (CO$_2$) laser. The scales at the top of the microneedles were of the order of 5 µm. Smaller top scales contribute to higher quality factor, but lead to easier collapse of the microdisk and more obvious thermal asymmetries as well [35,40].
The doping concentration was crucial to realize on-chip microsphere lasers. Higher concentration might result in luminescence quenching of rare-earth ions [41], stronger stress in sol-gel film and consequent surface roughness, while lower ions concentration could not provide sufficient gain for laser generation. An Yb$^{3+}$ concentration of approximately 4$\times$10$^{18}$ ions$\cdot$cm$^{-3}$, which could be utilized to fabricate WGM lasers with a relatively low threshold [25], was utilized to achieve Yb$^{3+}$-doped on-chip microsphere lasers. However, we experimentally found that an Er$^{3+}$/Yb$^{3+}$ concentration of about 4$\times$10$^{18}$/8$\times$10$^{18}$ ions$\cdot$cm$^{-3}$, which could achieve WGM lasers with a relatively low threshold [32], might not be able to provide sufficient gain for on-chip microspheres lasers with a diameter of around 20 µm at 1550 nm. And we finally achieved Er$^{3+}$/Yb$^{3+}$ co-doped on-chip microsphere lasers with a concentration of around 1$\times$10$^{19}$/1$\times$10$^{19}$ ions$\cdot$cm$^{-3}$. The equivalent concentration of Yb$^{3+}$ and Er$^{3+}$ made it easier to compare lasing performance of the two kinds of ions.
Fig. 1(a) and 1(b) show scanning electron microscope (SEM) images of the Yb$^{3+}$-doped and Er$^{3+}$/Yb$^{3+}$-codoped on-chip microsphere lasers, respectively. These microspheres have shape deformation [42]. The Yb$^{3+}$-doped microsphere had a diameter $D$ of around 19 µm, a thickness $d$ of about 14 µm and an ytterbium ion concentration of approximately 4$\times$10$^{18}$ ions$\cdot$cm$^{-3}$. The diameter $D$ and thickness $d$ of Er$^{3+}$/Yb$^{3+}$-codoped on-chip microsphere were around 21 µm and 13 µm, separately. The erbium and ytterbium ion concentration were both about 1$\times$10$^{19}$ ions$\cdot$cm$^{-3}$ in the Er$^{3+}$/Yb$^{3+}$-codoped on-chip microspheres. These on-chip microspheres supported more azimuthal modes than microtoroid with the same diameter because of the comparable diameter and thickness of them [43].
Fig. 1. Side view scanning electron microscope (SEM) images of on-chip microsphere lasers. The $D$ ($d$) is the diameter (thickness) of an on-chip microsphere. The Yb$^{3+}$-doped microsphere (a) has a diameter of around 19 µm and a thickness about 14 µm. The diameter and thickness of Er$^{3+}$/Yb$^{3+}$-codoped microsphere (b) are about 21 µm and 13 µm, respectively.
3. Characterization setup of the on-chip microsphere lasers
Fig. 2 depicts the experimental setup used to characterize the two types of on-chip microsphere lasers. A tunable diode laser of 980 nm was used to pump the Yb$^{3+}$-doped and Er$^{3+}$/Yb$^{3+}$ co-doped on-chip microspheres, separately. Further, a 1460 nm tunable laser was utilized to pump the Er$^{3+}$/Yb$^{3+}$ co-doped on-chip microspheres. A fiber taper with a diameter of around 1 µm was used to couple the pump into and out of the on-chip microspheres as well as collect the generated laser emissions from the resonators. The gap between the cavity and fiber taper was adjusted using nanopositioning stages. A variable optical attenuator (VOA) and polarization controller (PC) were also used to adjust the intensity and polarization of the pump light, respectively. The first fiber coupler (FC-1) splits the pump input to the power meter for pump power measurements. The light output comprising the pump and laser emission was divided into two beams using the second fiber coupler (FC-2). One optical output was measured by an optical spectrum analyzer (OSA). The pump and the generated laser in the other beam were isolated by a wavelength division multiplexer (WDM) and separately monitored with two photon detectors. A triangle wave signal produced by an arbitrary function generator (AFG) drives tunable laser for fine frequency scanning. A servo controller (SC) was used along with the AFG to flexibly adjust the offset and amplitude of the triangle wave.
Fig. 2. Experimental setup to characterize the on-chip microsphere lasers. AFG, arbitrary function generator; SC, servo controller; OSA, optical spectrum analyzer; VOA, variable optical attenuator; WDM, wavelength division multiplexer; FC, fiber coupler; PC, polarization controller; PD, photon detector; OSC, oscilloscope; OMSL, on-chip microsphere laser; PM, power meter.
Chip-based microspheres are resonantly pumped to excite Er$^{3+}$ or Yb$^{3+}$ ions. Fig. 3(a) illustrates the transmission spectrum of the Yb$^{3+}$-doped on-chip microspheres at 972.08 nm, which has a loaded quality factor of 3.0$\times$10$^6$. Fig. 3(b) and 3(c) illustrate the transmission spectrums of the Er$^{3+}$/Yb$^{3+}$-codoped on-chip microsphere at 970.89 nm and 1456.94 nm, respectively. The corresponding loaded quality factors were 8.2$\times$10$^5$ and 1.6$\times$10$^6$. Thermal broadening can be obviously observed under a high pump power. These transmission spectrums were recorded under an output power of the order of 3 µW.
Fig. 3. Fine scan transmission spectrums (blue dots) and Lorenz fitting (red curves) of the on-chip microsphere lasers. (a) Yb$^{3+}$-doped on-chip microsphere has a loaded quality factor of 3.0$\times$10$^6$ at a wavelength of 972.08 nm. The Er$^{3+}$/Yb$^{3+}$-codoped on-chip microsphere possesses loaded quality factors of 8.2$\times$10$^5$ and 1.6$\times$10$^6$ at wavelengths of (b) 970.89 nm and (c) 1456.94 nm, respectively.
Laser emissions arouse only when the pump light is coupled into the cavity. Thus, the generated laser signals are not continuous because the fine frequency scan repeats linearly. The OSA works in the hold max mode to record optical spectrums with the maximum power for each wavelength. The peak–peak amplitude of the triangle wave can be adjusted to a relatively small value (such as $\sim$1 V) to broaden the Lorenz curve in the time domain, thereby enhancing the possibility of capturing lasing signals in the OSA. During the threshold measurements, the pump laser still works in the fine frequency scan mode, and the coupling condition of the resonator and fiber taper remains almost unchanged. The power meter indicates the pump intensity and the OSA records optical power of the lasing mode. The insertion losses of the fiber couplers are compensated in both optical spectrum and laser threshold measurements.
4. Characterization of the Yb$^{3+}$-doped lasers
Yb$^{3+}$-doped on-chip microsphere lasers are characterized under the pump of 980 nm. An isolated ytterbium ion has a simple energy diagram with a ground-state manifold ${}^{2}{{F}_{7/2}}$ and an excited-state manifold ${}^{2}{{F}_{5/2}}$ in the optical waveband. Doping ytterbium ions into a solid host broadens these energy levels to energy bands. The absorption of the ytterbium ions is typically peaked at around 975 nm and the emissions are relatively higher from about 1020 nm to 1060 nm [44]. Fig. 4(a) shows the optical spectrums of the Yb$^{3+}$-doped on-chip microsphere at a pump wavelength of 973 nm. The two-mode laser emission is first observed at 1026 nm and 1039 nm at a low pump power. With the increase in pump power, the losses induced by the material, coupling, surface roughness, etc are compensated by the optical gain, thereby producing more laser modes. The two-mode laser thus changes to a multi-mode laser at 1026 nm, 1028 nm, 1036 nm, 1039 nm, and 1043 nm when the pump power is approximately increased by a factor of 20. These laser emissions are in the range centered at 1040 nm with a span of 40 nm. Each lasing mode corresponds to a specific cavity resonance mode. The free spectrum range (FSR) of the on-chip microsphere with 19 µm diameter was theoretically predicted to be 12 nm at emissions centered about 1040 nm. The effective refractive index $n_{eff}$ of silica is assumed to be 1.46 in the calculation. The minimum spacing between two adjacent lasing modes was approximately 2 nm in the experiment, which was obviously smaller than the FSR. Therefore, the excitation of the azimuthal modes contributes to the multi-mode lasing.
Fig. 4. Lasing characterization of the Yb$^{3+}$-doped on-chip microsphere under a pump of 980 nm. (a) Two-mode lasing changes to multi-mode lasing with the increasing of pump power at a pump wavelength of 973 nm. The dark blue, red, orange, purple, green, and light blue spectrums correspond to pump powers of 8.02 µW, 31.92 µW, 73.88 µW, 111.30 µW, 131.76 µW, and 161.08 µW, respectively. Their lasing modes are 1026 nm, 1039 nm (dark blue); 1026 nm, 1039 nm (red); 1026 nm, 1028 nm, 1039 nm (orange); 1026 nm, 1028 nm, 1036 nm, 1039 nm (purple); 1026 nm, 1028 nm, 1039 nm, 1043 nm (green); 1026 nm, 1028 nm, 1036 nm, 1039 nm, 1043 nm (light blue). (b) A typical single-mode lasing at a wavelength of 1039 nm. The pump wavelength is at 976 nm. (c) Lasing power (blue circles) at 1046 nm versus pump power at 973 nm. A lasing threshold of around 5.2 µW can be obtained through linear fitting (red curve).
Single-mode lasing was also achieved by adjusting the power, wavelength, polarization of the pump light, and coupling between the resonator and fiber taper. Fig. 4(b) illustrates a single lasing spectrum at 1039 nm with a pump at 976 nm. The relationship between lasing power at 1046 nm and pump power at 973 nm is shown in Fig. 4(c). The slope efficient is in the order of 0.4%. The threshold of the lasing mode is approximately 5.2 µW, as estimated by linear fitting, which is comparable to the previously reported Yb$^{3+}$-doped microtoroid laser [25]. The threshold is related to the coupling condition between microsphere and fiber taper. The condition slowly changes due to the instability of the nanopositioning stage during laser threshold measurement, leading to systematic error. We believe the magnitude order of the threshold is reliable.
5. Characterization of the Er$^{3+}$/Yb$^{3+}$-codoped lasers
Er$^{3+}$/Yb$^{3+}$-codoped on-chip microspheres were first characterized at a 980 nm pump. Fig. 5(a) illustrates an optical spectrum when pumped by a 970 nm laser. Lasing modes were observed at both 1040 nm and 1550 nm. The ytterbium ions could work as an active medium and its lasers still existed after introducing erbium ions in the microresonators. The mechanism of the 1040 nm lasers involves transition of ytterbium ions from ${}^{2}{{F}_{5/2}}$ to ${}^{2}{{F}_{7/2}}$, which is the same as that of the Yb$^{3+}$-doped on-chip microsphere lasers. Single-mode and multi-mode ytterbium lasers in 1040 nm band were obtained as shown in Fig. 5(b) and 5(c), respectively. The optical power of 1035 nm mode versus the pump power at 970 nm is shown in Fig. 5(d). The slope efficiency is in the order of 0.7%. The threshold of the lasing mode is calculated as 0.6 µW, which was comparable with the Yb$^{3+}$-doped on-chip microsphere lasers. Furthermore, under a 980 nm pump, the erbium ions undergo two-photon upconversion and exhibit green luminescence, as can be clearly seen in the inset of Fig. 5(d).
Fig. 5. Lasing characterization of the Er$^{3+}$/Yb$^{3+}$-codoped on-chip microsphere laser under 980 nm pump. (a) Optical spectrum of the Er$^{3+}$/Yb$^{3+}$-codoped on-chip microsphere laser at a pump wavelength of 970 nm. Both 1040 nm and 1550 nm lasing emissions are observed. The pump is coupled into the cavity with a fiber taper. (b) and (c) are typical single-mode and multi-mode lasings at 1040 nm for pump wavelengths of 981 nm and 971 nm, respectively. (d) Optical power of a 1035 nm lasing mode depends on the pump power at 970 nm. The laser threshold is approximately 0.6 µW through linear fitting. The inset is a photograph of green upconversion luminescence from the Er$^{3+}$/Yb$^{3+}$-codoped on-chip microsphere under the pump of 980 nm.
Energy transfer from the ytterbium ions and ground-state absorption excite the erbium ions to the energy state $^{4}{{I}_{11/2}}$. Non-radiative relaxation then populates the metastable state $^{4}{{I}_{13/2}}$. Finally, transition from the energy state $^{4}{{I}_{13/2}}$ to the ground state $^{4}{{I}_{15/2}}$ of the erbium ions emit photon at 1550 nm waveband. Fig. 6(a) shows a single-mode laser at 1539 nm under a pump wavelength of 981 nm. Only two-mode lasing was observed at 1550 nm band because of the limited pump power. Fig. 6(b) illustrates a two-mode laser spectrum with peaks at 1537 nm and 1539 nm when pumped at 981 nm. The threshold of the 1537 nm lasing mode was estimated to be 219 µW when pumped at 982 nm.
Fig. 6. Erbium lasing characterization of the Er$^{3+}$/Yb$^{3+}$-codoped on-chip microsphere. (a) and (b) are typical single-mode and two-mode lasings at 1550 nm for a pump wavelength of 981 nm. (c) and (d) are typical single-mode and two-mode lasing at 1550 nm under the pump wavelength of 1457 nm. The inset in (c) shows the green upconversion luminescence of the Er$^{3+}$/Yb$^{3+}$-codoped resonator at a pump wavelength of 1460 nm.
The Er$^{3+}$/Yb$^{3+}$-codoped microspheres were also characterized under a pump at 1460 nm, and lasing modes at 1550 nm were observed through the excitation and de-excitation between energy bands broadened from $^{4}{{I}_{13/2}}$ and $^{4}{{I}_{15/2}}$ of the erbium ions. Fig. 6(c) illustrates a single-mode laser at 1553 nm under the 1457 nm pump. The erbium ions work separately as a gain medium for the lasers. The inset in Fig. 6(c) depicts the three-photon upconversion luminescence of the erbium ions. This green light is weaker than that of the two-photon upconversion process (see inset in Fig. 5(d)). Fig. 6(d) illustrates two-mode lasing at 1539 nm and 1553 nm at a pump wavelength of 1457 nm. The threshold of the 1537 nm mode was approximately 576 µW when pumped at 1456 nm.
The FSRs of the codoped microspheres with a diameter of 21 µm were estimated to be 11 nm and 25 nm at 1040 nm and 1550 nm, respectively, under the assumption of $n_{eff}$=1.46. The minimum measured spacing between these lasing modes was 2 nm. Thus, the excitation of azimuthal modes contributed to the two-mode lasing of Er$^{3+}$/Yb$^{3+}$-codoped microspheres.
6. Discussion
The loaded quality factor ${{Q}_{load}}$ of a WGM is determined by the intrinsic quality factor (${{Q}_{0}}$) and the external quality factor (${{Q}_{ex}}$): $Q_{load}^{-1}=Q_{0}^{-1}+Q_{ex}^{-1}$. The intrinsic loss $Q_{0}^{-1}$ contains material ($Q_{mat}^{-1}$), water absorption ($Q_{water}^{-1}$), and radiative ($Q_{rad}^{-1}$) losses: $Q_{0}^{-1}=Q_{mat}^{-1}+Q_{water}^{-1}+Q_{rad}^{-1}$, where ${{Q}_{mat}}$ and ${{Q}_{water}}$ can be theoretically calculated from the following equations [45,46]:
The absorption cross section of Yb$^{3+}$ in silica is around 1$\times$10$^{-24}$ m$^2$ at 970 nm [44]. The absorption cross section of Er$^{3+}$ in silica are 1.0$\times$10$^{-25}$ m$^2$, 7.5$\times$10$^{-26}$ m$^2$, 7.5$\times$10$^{-26}$ m$^2$ at 970 nm, 1460 nm, 1550 nm, respectively [41,48]. The absorption loss of silica can be neglected because it is relatively much smaller [49]. Furthermore, we assume pump light is absorbed by erbium and ytterbium ions individually in Er$^{3+}$/Yb$^{3+}$-codoped on-chip microspheres under the pump wavelength of 970 nm. The theoretically estimated ${{\alpha }_{mat}}$, ${{\beta }_{water}}$, ${{Q}_{mat}}$, ${{Q}_{water}}$ are summarized in Table 1 at various wavebands.
Table 1. Theoretically calculated material and water absorption coefficient and corresponding quality factors of on-chip microsphere lasers at various wavebands.
Water absorption is much lower at 970 nm and 1040 nm than it at 1460 nm and 1550 nm. By comparing ${{Q}_{mat}}$ and ${{Q}_{water}}$ in Table 1 with the intrinsic quality factors of on-chip microsphere lasers in Fig. 3, we find that rare-earth absorption limits the quality factors of microspheres at 970 nm, while both rare-earth and water absorption dominant quality factor at 1460 nm and 1550 nm. Besides, ${{Q}_{water}}$ at 1460 nm, where the water absorption is the maximum among these wavebands, with $\delta$=0.2 nm is slightly higher than the intrinsic quality factor in Fig. 3, while it is slightly smaller with $\delta$=0.3 nm. Thus, the –OHs in the sol-gel silica do not have a significant influence on the quality factors of the on-chip microspheres at these wavebands.
Fig. 5(a) also reveals that the erbium laser emissions are relatively weaker than those of ytterbium, although the on-chip microspheres possess the same ytterbium and erbium ion doping concentrations, which indicates that the energy transfer between Yb$^{3+}$ and Er$^{3+}$ is low. This phenomenon also has been seen in fiber-based resonators [31]. The 1040 nm laser pumped at 980 nm is weaker than it at 970 nm, which is similar with microtoroids lasers [32]. However, the microresonator still prefers ytterbium lasing. Many reasons may attribute to the weaker signal. (1) The absorption cross section of ytterbium ions is larger than erbium ions at 980 nm. Thus, ytterbium ions absorb more pump power. (2) The theoretical water absorption quality factor at 1550 nm is lower than it at 1040 nm (see Table 1). (3) The 1040 nm lasing modes are closer to the 980 nm pump modes than 1550 nm. The overlap factor between the pump and lasing modes may be lower for 1550 nm and the phasing matching may not be perfect at 1550 nm [50,51]. (4) Another loss that may determine the quality factors at 1550 nm is radiation leakage, since the diameter of the resonator is around 20 µm [20]. The loss is lower for the shorter wavelength (1040 nm) [52].
7. Conclusion
In this study, we demonstrate Yb$^{3+}$-doped and Er$^{3+}$/Yb$^{3+}$-codoped on-chip microsphere lasers fabricated by sol-gel synthesis. Single-mode and multi-mode laser emissions are observed at 1040 nm in both Yb$^{3+}$-doped and Er$^{3+}$/Yb$^{3+}$-codoped chip-based microspheres under a pump of 980 nm. Thresholds as low as 5.2 µW and 0.6 µW were observed for 1040 nm laser, respectively. Single-mode and two-mode lasing at 1550 nm were also separately achieved using pumps at 980 nm and 1460 nm, respectively, in the Er$^{3+}$/Yb$^{3+}$-codoped on-chip microspheres. The Er$^{3+}$ in the Er$^{3+}$/Yb$^{3+}$-codoped microspheres can be excited alone using a 1460 nm pump for 1550 nm laser. Quality factor limitations induced by different loss mechanisms are investigated. Compared with the fiber-based microsphere lasers, the on-chip microsphere lasers can easily achieve emissions with smaller diameters.
Funding
National Natural Science Foundation of China (61727801); National Key Research and Development Program of China (2017YFA0303700); The Key Research and Development Program of Guangdong Province (2018B030325002); Beijing Innovation Center for Future Chip; Tsinghua University Initiative Scientific Research Program; China Postdoctoral Science Foundation (2019M660605).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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