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Abstract
Erbium is well-recognized as a key element for optical amplification at the 1550 nm operation band. However, the limited solubility of this material in vitreous matrices sets a critical constraint to the achievable optical gain, which limits its applicability in photonic integrated platforms. One of the solutions to increase the concentration of erbium is to employ a crystalline structure instead of a glass. In this paper, we characterize samples of erbium and erbium-ytterbium oxalate single crystals synthesized using the gel diffusion method. X-ray diffraction spectra and thermogravimetric analyses reveal that the synthesis method indeed generated the expected compound, and the pump-and-probe experiments demonstrate an on-off gain coefficient of ≈ 6.5 dB/mm, making this material a high-potential candidate for the implementation of integrated optical amplifiers.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Integrated photonics has emerged as a cost-efficient technology not only for next-generation high-capacity optical communication systems but also for future signal processing applications [1,2]. In particular, for systems operating at 1550 nm, silicon photonics has attracted increasing attention due to its compatibility with complementary metal oxide semiconductor (CMOS) manufacturing infrastructure and because of the significant refractive index contrast that allows the implementation of compact devices [3]. In spite of the aforementioned advantages, loss management still represents the Achilles heel of photonic chips. Therefore, in recent years, several solutions have been proposed to integrate optical sources and amplifiers with passive optical devices [4,5]. Parametric amplification based on the Kerr effect was proposed in [6]. Unfortunately, the low efficiency of this effect requires high power levels, which generate free carriers that further reduce the overall performance [7]. Heterogeneous integration with III-V semiconductor materials, on the other hand, poses serious challenges, mainly regarding annealing and coupling [8,9]. Alternatively, erbium-doped materials have been proposed to build the core or the cladding of integrated active waveguides [10].
Regarding the use of erbium-doped materials to develop integrated optical sources and amplifiers, [11] and [12] review recent advances. It is worth noting that multiple materials were adopted as matrices, such as silica [13], phosphate [14], and alumina [15]. More recently, erbium-doped lithium niobate thin film has been proposed as a platform for integrated erbium-doped waveguides [16]. For instance, in [17] and [18], a ring laser and a 16-dB net gain amplifier were demonstrated, respectively. These solutions have shown their potential to build integrated light sources and amplifiers but are unsuitable for building complex functionalities at a reasonable cost. To overcome this limitation, an approach that has been broadly adopted is to combine a silicon-based integration platform and erbium-doped glasses. In this sense, in [19], erbium-doped alumina was employed to compensate for the transmission loss in ring resonators, whereas, in [20], erbium-doped tellurite was used as a coating for silicon nitride, achieving a 5-dB amplifier. However, the optical gain of optical glasses is limited by the ionic quenching, which sets a maximum limit to the rare-earth concentration [21]. One of the solutions to increase the erbium concentration level and, consequently, to allow the implementation of compact devices is to employ erbium crystals instead of glasses. In contrast to glasses, where the erbium has to be located in interstitial spaces, the erbium ions in crystals have their positions well-defined. Consequently, erbium concentrations significantly higher than those in glasses can be achieved.
Among the explored erbium crystalline compounds, we can mention the erbium oxide Er2O3, whose photoluminescence spectrum and decay time were characterized in [22]. According to these analyses, the authors expected a gain coefficient of 30 dB/cm. Short after, in [23], a ring resonator was used to estimate a resonant absorption of 364 dB/cm experimentally. Similarly, experiments on erbium-based hybrid slot waveguides demonstrated that by integrating an atomic scale engineered erbium-doped aluminum oxide directly on a silicon nitride slot waveguides, a net material gain coefficient as high as 52.4$\pm$13.8 dB/cm can be achieved, reporting the highest value for a device based on erbium-silicon integration [24]. Erbium silicates have also been studied. For instance, in [25], a gain of 47.7 dB/cm is predicted. Even higher gain coefficients can be achieved by suppressing the up-conversion process by diluting yttrium within the crystalline structure [26]. Thus, in [27], a modal gain of 30 dB/cm in a silicon-based photonic crystal slot waveguide made of ErxY2-xSiO5 (x=0.4) is reported. More recently, erbium chloride silicate has been employed to build the core of a waveguide, attaining a record gain at 1550 nm of 100 dB/cm [28].
An alternative group of high-potential compounds is the lanthanide-oxalates. These materials present distinctive optical features, like a natural quenching-free luminescence effect [29] and a high active ion concentration in the order of 10$^{21}$ ions/cm$^{3}$ in single crystals, which could facilitate high optical gain for potential applications in solid-state devices [30]. Erbium oxalate, Er2(C2O4)3, is particularly interesting for applications operating at 1550 nm. This material was synthesized in 1969 by Steinfink and Brunton [31]. The thermal and spectroscopic characterizations were carried out in [32] and [33], respectively. The optical gain of this material at 1550 nm, however, remains unexplored, and consequently, delving into this feature is necessary.
In the present study, we use the well-known gel-diffusion method to generate macroscopic single crystals with mm-scale dimensions [34–36]. The synthesized crystals are optically characterized, revealing an on-off gain coefficient of 6.5 dB/mm for a pump power of 20 dBm. Experimental results also show that co-doping with ytterbium results in a reduced gain coefficient. The rest of the paper is organized as follows: in Section 2, the material synthesis and its structural analysis are presented. The optical gain at 1550 nm of the fabricated samples is characterized in Section 3, and, finally, in Section 4, the main conclusions of the work are drawn.
2. Structural characterization and experimental setup
2.1 Material synthesis and structural characterization
Samples of erbium oxalate and erbium-ytterbium oxalate were synthesized. In the erbium oxalate samples, 100% of the rare earth atoms are erbium, and therefore, we will refer to them as Er-100. In the erbium-ytterbium oxalate sample, 90% of the rare earth atoms are erbium, and 10% are ytterbium. It is worth noting that in contrast to dopants in glasses, in crystals, stoichiometry fixes the number of rare earth atoms, and, in consequence, we are free to modify only the ratio of the different rare earth atoms. In order to synthesize the erbium and erbium-ytterbium oxalate crystals, we employed analytical-grade erbium and ytterbium oxide powder (Er$_{2}$O$_{3}$, Yb$_{2}$O$_{3}$, Strem Chemicals, 99.999%), ammonium oxalate monohydrate powder ((NH$_{4}$)$_{2}$C$_{2}$O$_{4} \cdot$H$_{2}$O, J. T. Baker, 99.9%), nitric acid (HNO$_{3}$, Sigma Aldrich, 99.999%) and sodium metasilicate (Na$_{2}$SiO$_{3}$, Sigma Aldrich, MW: 122.06 g/mol). Erbium (Er-100) and erbium-ytterbium (Er-90) oxalate crystals were grown by single diffusion gel technique, using hydrosilica gel as the medium of crystal growth. The gel was prepared by dissolving sodium metasilicate in distilled water (SMS, 1:4), after which it was mixed with an aqueous 0.36 M Ammonium Oxalate Solution (AOS) that was previously acidified with nitric acid to obtain a solution with pH=9. The resulting solution was stirred magnetically for a few seconds and then was rapidly transferred into test tubes with an internal diameter of 15 mm and length of 150 mm, keeping them undisturbed for 24 hours for the gel set. Simultaneously, a 0.5 M erbium nitrate or erbium-ytterbium nitrate solution made from oxides and nitric acid was acidified at 50${\%}$ by volume with nitric acid. The solution was poured gently over the set gel, dripping it through the walls of the test tube in order not to break the gel. Rare-earth ions slowly diffused through the narrow pores of the hydrosilica gel and reacted with the oxalate anions leading to the formation of rare-earth oxalate crystals. Optically transparent and pink single crystals of dimensions ranging from 0.5$\times$0.3$\times$0.1 to 3$\times$2$\times$1 mm were grown during a period of two weeks. Well-faceted single crystals were obtained under the following conditions: aqueous sodium metasilicate solution (1:4), gel pH 9, gel concentration (SMS/AOS) 1:20 in weigh, ammonium oxalate solution 0.36 M, erbium nitrate or erbium-ytterbium nitrate solution acidified with nitric acid at 50${\%}$ by volume 0.5 M, reaction temperature 60 $^{\circ }$C. The resulting crystals suspended within the gel column can be seen in Fig. 1(a).
Fig. 1. (a) Photograph of the outcome of the gel-diffusion technique, where well-faceted and optically transparent erbium and erbium-ytterbium oxalate single crystals were grown. The inset shows a magnified image of some synthesized crystals. (b) Rietveld refinement profile of powder XRD data for Er-100 oxalate. Single crystal XRD patterns for Er-100 and Er-90 and crystal structure are shown in the insets. (c) Thermogravimetric analyses (TGA) and Differential Thermogravimetric Analysis (DTG) for erbium oxalates.
Chemical and structural characterization of the synthesized rare-earth oxalates was achieved by thermogravimetric analysis (TGA) and X-ray diffractometry (XRD). TGA analysis was performed on both powder and single crystal Er-Oxalates using a SDT Q600 TA Instruments, Fig. 1(b). The thermal decomposition nature of rare-earth oxalates reveals two mass loss stages with the stable end product as rare-earth oxide. The first stage corresponds to the dehydration of the compounds, while the second is due to the decomposition of the anhydrous rare-earth oxalate. The four non-coordinated water molecules are lost between 40-120 $^{\circ }$C, corresponding to a 13.9% of mass loss. The coordination water, three water molecules, evaporates from the structure between 120-390 $^{\circ }$C, representing a mass loss of 9.3%. Coordination water provides stability to the Ln$^{3+}$ cations acting as a Lewis base and therefore, they are lost at higher temperatures [37]. Finally, the anhydrous Er-Oxalates are found to be unstable and begin to rapidly decompose into rare-earth carbonate and carbon monoxide beyond 400 $^{\circ }$C, getting converted to Ln$_{2}$O$_{3}$ at 800 $^{\circ }$C with the release of carbon dioxide. The mass loss in this last stage corresponds to 27.7%, respectively. This information corroborates the chemical composition of the compounds and supports that the number of water molecules present was 10, as reported in the literature [38].
On the other hand, the crystal structure was analyzed by the Rietveld method, employing X-ray powder and single crystal diffraction data, which were recorded on a Siemens D5000 X-ray Powder Diffraction System with Cu K$\alpha$ radiation ($\lambda$ = 1.5405 $\mathring {A}$). The XRD results, including both the observed and calculated X-ray spectra, alongside their difference and Bragg position, are shown in Fig. 1(c). Both the powder and single crystal XRD data for Er-100 and Er-90 samples match the Rietveld refinement profile (inset Fig. 1(c)) and present a close agreement with the standard data (COD ID: 2202899) reported by Irina V. et al. [38], demonstrating that the generated crystals are indeed the desired materials. Erbium and erbium-ytterbium oxalates crystallize in the P2$_{1}$/c monoclinic system, with lattice parameters listed in Table 1. Each metal atom is coordinated with three bidentate oxalate chelates, and three water molecules complete the coordination sphere (CN=9), inset Fig. 1(c). The polymeric structure in 3D shows that the coordination polyhedron ErO$_{9}$ is a distorted three-capped trigonal prism where the Er-O distances range from 2.35(4) to 2.52(7) $\mathring {A}$ (average 2.40(6) $\mathring {A}$) while the Ln-Ln distances range from 6.32(1) to 10.75(9) $\mathring {A}$ (average 8.83(6) $\mathring {A}$), which reasonably agree with the values reported in [38]. These distances explain the attractive natural quenching-free luminescence exhibited by Ln-oxalates and point out that the Ln-Ln distance in erbium oxalate is longer than that of the critical value estimated of 7.644 $\mathring {A}$ to initiate concentration quenching according to the approach described in [29].
Table 1. Chemical composition and lattice parameters of erbium and erbium-ytterbium oxalates. Lattice parameters were obtained by Rietveld refinement of the XRD data using a pseudo-Voigt function and the Full-Prof Suite software (version July-2017).
For each material, large dimension crystals were selected to perform the optical gain characterization. In particular, the employed erbium and erbium-ytterbium oxalate samples had thicknesses of 0.59(3) and 0.64(2) mm, respectively, which were measured using a digital gauge with a precision of 0.001 mm.
2.2 Setup for optical gain characterization
In order to characterize the amplification capability of the synthesized erbium and erbium-ytterbium oxalate crystals we adopted a conventional pump-and-probe setup with a pump wavelength of 980 nm and probe (signal) wavelength of 1550 nm, whose setup is depicted in Fig. 2. Both the pump and signal beams were generated using continuous-wave (CW) lasers equipped with pigtail connections. The two beams were then combined using a fiber-based wavelength division multiplexing (WDM), whose output is connected to the input of a U-bench collimator that facilitated the alignment and overlap of the two beams. The crystal under test was mounted on a thin silica slide in the center of the U-bench. Afterward, the pump and signal beams at the output of the U-bench were analyzed using an Anritsu MS9740A optical spectrum analyzer, which allowed the wavelength discrimination between the two beams.
Fig. 2. Block diagram of the pump-and-probe experimental setup used to characterize the on-off gain coefficient of the synthesized erbium and erbium-ytterbium oxalate crystals. WDM: wavelength division multiplexing, OSA: optical spectrum analyzer.
The on-off gain coefficient is a good way to characterize the capability of a material to amplify the signal. As presented in [39], the on-off gain can be calculated as:
Since this gain depends on the thickness of the crystal sample, it is usually normalized by its thickness, $L$, giving as a result the so-called on-off gain coefficient:
One of the key performance analyses to assess the amplification capabilities of the material is the gain versus pump power characteristic. Therefore, alongside with the on-off gain measurement, we need to quantify the intensity of the pump beam. In order to avoid the necessity to remove the sample after each spectrum capture, the output power of the pump laser was measured for different driving currents. After certifying that the relation between the pump power and the driving current was stable for long times, this curve was employed as calibration to estimate the pump power level.
3. Optical gain characterization and result discussion
In Fig. 3 and Fig. 4 we show captured spectra for two synthesized samples employing the experimental setup presented in Section 2. The spectra depicted in Fig. 3 correspond to the output of the erbium oxalate sample considering three different configurations: (i) output spectrum in the absence of pump (pump off), (ii) output spectrum when the sample is illuminated with a low-power pump (pump on with $P_{pump}$ = 18.43 dBm), and (iii) output spectrum with a higher pump power level (pump on with $P_{pump}$ = 20.53 dBm). The pump and probe in the vicinity of 980 and 1550 nm, respectively, can be clearly observed in the whole spectrum presented in Fig. 3(a). However, the power difference in the pump and probe are difficult to discern. For the sake of clarity, in Fig. 3(b) and (c) we present details of the spectrum in the regions of interest, that is 980 and 1550 nm. Looking at Fig. 3(b), it is possible to see the difference between the configuration when pump is off and when it is on. The difference between the traces for different pump levels is less significant but it is still perceptible. In regards to signal amplification, the traces in Fig. 3(c) demonstrate the amplification capability of the synthesized samples. In addition, it can be seen that as we expected, the signal amplification increases as the pump power does. In Fig. 4, we present similar spectra for the erbium-ytterbium oxalate sample. An initial qualitative comparison between the spectra corresponding to the erbium and erbium-ytterbium oxalate shows a significant power difference between the two cases. In principle, this would not necessarily mean a lower gain but a higher transmission loss (this extend will be numerically assessed in the next subsection).
Fig. 3. Captured optical spectra for the erbium oxalate sample in the range (a) 960 to 1600 nm, (b) 960 to 990 nm, and (c) 1546 to 1559 nm. Spectra in absence of pump and with two pump power levels are shown (18.43 and 20.53 dBm).
Fig. 4. Captured optical spectra for the erbium-ytterbium oxalate sample in the range (a) 960 to 1600 nm, (b) 960 to 990 nm, and (c) 1546 to 1559 nm. Spectra in absence of pump and with two pump power levels are shown (18.43 and 20.53 dBm).
In order to characterize the dependency of the on-off gain coefficient as a function of the pump power level, we captured the spectra for pump power levels ranging from 12.77 to 20.56 dBm (14.64 to 20.56 dBm, in the case of erbium-ytterbium oxalate). In Fig. 5(a) we show the measured signal power as a function of the pump power for both the erbium and erbium-ytterbium oxalate samples. The power difference with respect the signal power in the absence of pump power is shadowed. For the erbium oxalate case, the signal power in the absence of pump, $P_\text {signal}^\text { off}$ is $-13.3$ dBm, whereas for the erbium-ytterbium oxalate sample it is $-25.3$ dBm. Comparing the curves for both samples, it is clear that the erbium oxalate sample presents a significantly higher signal power. When we subtract the signal power in the absence of pump and normalize it by the sample thickness (following Eq. (2)), we obtain the data presented in Fig. 5(b). As can be observed, the erbium oxalate sample show a significant higher gain compared to erbium-ytterbium oxalate sample. Indeed, the on-off gain of the former is as high as $\approx$ 6.5 dB/mm for a pump power of 20 dBm. According to the data presented in Fig. 5(b), it seems that the on-off gain of the erbium oxalate sample reach saturation at a pump power level of 19 dBm. However, this statement needs further analysis using even higher pump power, which is not possible with the actually available equipment.
Fig. 5. (a) Signal power in terms of the pump power for the erbium and erbium-ytterbium oxalate crystalline samples. (b) Measured on-off gain for the two characterized samples.
Comparing the two samples, it is clear that erbium oxalate outperforms erbium-ytterbium oxalate in terms of the on-off gain. This can be explained by the larger concentration of erbium in the erbium oxalate sample, which is the element responsible for the inter-band transition that leads to gain in the 1550 nm band. In contrast to what happens in erbium-doped glasses, where the ytterbium plays a critical role as an anti-quenching agent and helps to increase the overall gain coefficient, the separation between erbium atoms in the erbium oxalate is large enough to prevent quenching. Consequently, the presence of ytterbium does not positively contribute to the increase of the on-off gain; instead, it has a detrimental effect.
When we contrast the obtained results with those of other high-gain materials reported in the literature, we should distinguish whether we are comparing the erbium oxalate with doped glasses or other crystalline materials. Doped glasses tend to present lower gain coefficients than crystalline materials due to the limited ion solubility. In order to overcome this constraint, different glass matrices have been proposed. For example, in [39], a 0.4 dB/mm gain coefficient is achieved by employing sodium-zinc phosphates as a glass host, whereas in [18], lithium niobate is doped with erbium ions, achieving a gain coefficient as high as 0.62 dB/mm. Even with these hosts, the achieved gain coefficients are lower than the value we report for the erbium oxalate. Since rare earth elements already have a dedicated position in crystalline materials, the amount of erbium can be significantly increased, and consequently, enhanced gain coefficients are possible. Among the crystalline materials reported, we can mention erbium oxide, whose gain coefficient is expected to be higher than 0.30 dB/mm. Another explored material is erbium silicate. In [25], the authors performed a luminescence analysis and estimated that a gain coefficient of 47.7 dB/mm could be achieved. However, experimentally they could only attain a modal gain of 3 dB/mm [27]. The highest gain coefficient is reported in [28], where a nanowire of erbium chloride silicate is used to demonstrate an unprecedented 10 dB/cm gain. According to the authors, such a high gain is possible due to the high quality of the manufactured nanowire, which is 20 $\mu$m long. It is then not clear whether larger guiding structures can be built keeping such a high gain coefficient. Consequently, even if the reported erbium oxalate does not present the highest reported gain coefficient, it is possible to claim that, to our best knowledge, it is the material with the highest reported gain coefficient in macroscopic erbium crystalline compounds.
The on-off gain is an important metric to assess the potential of the material as a gain medium. However, it is also important to consider the transmission loss in order to calculate the net optical gain. Therefore, we characterize the transmission loss of the synthesized erbium oxalate crystal by measuring the power with and without the sample under test. These experiments showed a transmission loss at the pump and signal wavelengths of 3.91 dB and 2.87 dB, respectively (as expected, the loss at the pump wavelength is higher than the loss at the signal wavelength). Therefore, the erbium oxalate sample presents a positive net optical gain only for pump power levels above 19 dBm. However, there are two points that deserve attention. On the one hand, the characterized optical transmission loss accounts not only for absorption loss but also the reflection losses in the two facets of the erbium oxalate crystal. On the other hand, the beam within the collimator has a nominal diameter of 0.4 mm, which is significantly broader than in the great majority of integrated photonic applications. Consequently, it is expected that in practical scenarios, net gain will be achieved with significantly lower pump power levels.
Another desirable feature of materials for optical gain media is their stability over time. Even if we have not performed dedicated experiments to assess this characteristic, we measured the same samples with an interval of four months, and the obtained gain coefficients remained unaltered. This indicates that the synthesized samples are stable, at least on the month-scale.
4. Conclusions
Erbium is widely acknowledged for its pivotal role in optical amplification, particularly within the 1550 nm operational band. However, its commendable optical properties are tempered by limited solubility in vitreous matrices, posing a critical constraint on achievable optical gain and restricting its utility in photonic integrated platforms. A potential strategy to overcome this solubility hurdle and enhance erbium concentration involves adopting crystalline structure instead of a glass one. This shift holds promise for unlocking new possibilities and improving the performance of erbium-based optical amplifiers.
This paper characterizes samples of erbium and erbium-ytterbium oxalate single crystals synthesized using the gel diffusion method. Analyzing X-ray diffraction spectra confirms the successful generation of the intended compound, providing insights into fundamental material properties and its potential for optical amplification. In addition, pump-and-probe experiments reveal an on-off gain coefficient of approximately 6.5 dB/mm. This underscores the material’s inherent capacity for efficient light amplification, positioning it as a standout candidate for integrated optical amplifiers.
In conclusion, this study contributes to our understanding of erbium’s behavior in different material structures and emphasizes the potential benefits of crystalline configurations. The findings open avenues for enhanced performance in integrated optical amplifiers and innovative applications in photonics, without compromising clarity.
Funding
UNAM Posdoctoral Program (POSDOC); UAM-Azcapotzalco 276 Department of Electronics; Universidad Autónoma Metropolitana (CB-2016/285600); Sao Paulo Research Foundation (15/24517-8); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, grant number 313378/2021-5); PAPIIT-DGAPA-Universidad Nacional Autónoma de México (IN104322).
Acknowledgments
The authors thank the National Council of Humanities, Sciences and Technologies (CONAHCYT-México) and the UAM-Azcapotzalco Electronics Department for the support provided in carrying out this project. R. E. López-Romero also thanks UNAM Postdoctoral Program (POSDOC) for the scholarship received during his posdoctoral stay. The authors also thank M. C. Ana K. Bobadilla-Valencia for help in DRX data collection.
Disclosures
The authors declare no conflicts of interest.
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.
References
1. E. Pelucchi, G. Fagas, I. Aharonovich, et al., “The potential and global outlook of integrated photonics for quantum technologies,” Nat. Rev. Phys. 4(3), 194–208 (2021). [CrossRef]
2. D. Marpaung, J. Yao, and J. Capmany, “Integrated microwave photonics,” Nat. Photonics 13(2), 80–90 (2019). [CrossRef]
3. S. Y. Siew, B. Li, F. Gao, et al., “Review of silicon photonics technology and platform development,” J. Lightwave Technol. 39(13), 4374–4389 (2021). [CrossRef]
4. W. Shi, C. Zou, Y. Cao, et al., “The progress and trend of heterogeneous integration silicon/III-V semiconductor optical amplifiers,” in Photonics, vol. 10 (MDPI, 2023), p. 161.
5. S. Liu and A. Khope, “Latest advances in high-performance light sources and optical amplifiers on silicon,” J. Semicond. 42(4), 041307 (2021). [CrossRef]
6. M. A. Foster, A. C. Turner, J. E. Sharping, et al., “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006). [CrossRef]
7. A. Gil-Molina, I. Aldaya, J. L. Pita, et al., “Optical free-carrier generation in silicon nano-waveguides at 1550 nm,” Appl. Phys. Lett. 112(25), 1 (2018). [CrossRef]
8. D. Liang and J. E. Bowers, “Recent progress in heterogeneous III-V-on-silicon photonic integration,” Light: Advanced Manufacturing 2, 59–83 (2021).
9. W. Xie, C. Xiang, L. Chang, et al., “Silicon-integrated nonlinear III-V photonics,” Photonics Res. 10(2), 535–541 (2022). [CrossRef]
10. Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light: Sci. Appl. 4(11), e358 (2015). [CrossRef]
11. J. D. Bradley and M. Pollnau, “Erbium-doped integrated waveguide amplifiers and lasers,” Laser Photonics Rev. 5(3), 368–403 (2011). [CrossRef]
12. Z. Chen, G. Dong, G. Barillaro, et al., “Emerging and perspectives in microlasers based on rare-earth ions activated micro-/nanomaterials,” Prog. Mater. Sci. 121, 100814 (2021). [CrossRef]
13. W. J. Miniscalco, “Erbium-doped glasses for fiber amplifiers at 1500 nm,” J. Lightwave Technol. 9(2), 234–250 (1991). [CrossRef]
14. Y. Yan, A. Faber, H. de Waal, et al., “Erbium-doped phosphate glass waveguide on silicon with 4.1 db/cm gain at 1.535 μm,” Appl. Phys. Lett. 71(20), 2922–2924 (1997). [CrossRef]
15. G. Van den Hoven, R. Koper, A. Polman, et al., “Net optical gain at 1.53 μm in Er-doped Al2O3 waveguides on silicon,” Appl. Phys. Lett. 68(14), 1886–1888 (1996). [CrossRef]
16. J. Zhou, Y. Liang, Z. Liu, et al., “On-chip integrated waveguide amplifiers on erbium-doped thin-film lithium niobate on insulator,” Laser Photonics Rev. 15(8), 2100030 (2021). [CrossRef]
17. T. Li, K. Wu, M. Cai, et al., “A single-frequency single-resonator laser on erbium-doped lithium niobate on insulator,” APL Photonics 6(10), 101301 (2021). [CrossRef]
18. M. Cai, K. Wu, J. Xiang, et al., “Erbium-doped lithium niobate thin film waveguide amplifier with 16 dB internal net gain,” IEEE J. Sel. Top. Quantum Electron. 28(3), 1–8 (2022). [CrossRef]
19. P. Jarschel and N. Frateschi, “Resonant amplification via Er-doped clad Si photonic molecules: Towards compact low-loss/high-Q Si photonic devices,” Solid-State Electron. 155, 144–149 (2019). [CrossRef]
20. H. C. Frankis, H. M. Mbonde, D. B. Bonneville, et al., “Erbium-doped TeO2-coated Si3N4 waveguide amplifiers with 5 dB net gain,” Photonics Res. 8(2), 127–134 (2020). [CrossRef]
21. T. Georges, E. Delevaque, M. Monerie, et al., “Pair induced quenching in erbium doped silicate fibers,” in Optical Amplifiers and Their Applications (Optica Publishing Group, 1992), p. WE4.
22. S. Saini, K. Chen, X. Duan, et al., “Er2O3 for high-gain waveguide amplifiers,” J. Electron. Mater. 33(7), 809–814 (2004). [CrossRef]
23. C. Michael, H. Yuen, V. Sabnis, et al., “Growth, processing, and optical properties of epitaxial Er2O3 on silicon,” Opt. Express 16(24), 19649–19666 (2008). [CrossRef]
24. J. Rönn, W. Zhang, A. Autere, et al., “Ultra-high on-chip optical gain in erbium-based hybrid slot waveguides,” Nat. Commun. 10(1), 432 (2019). [CrossRef]
25. H. Isshiki and T. Kimura, “Toward small size waveguide amplifiers based on erbium silicate for silicon photonics,” IEICE Trans. Electron. E91-C(2), 138–144 (2008). [CrossRef]
26. H. Isshiki, Y. Tanaka, K. Iwatani, et al., “Highly oriented ErxY2−xSiO5 crystalline thin films fabricated by pulsed laser deposition,” in 7th IEEE International Conference on Group IV Photonics, (IEEE, 2010), pp. 311–313.
27. H. Isshiki, F. Jing, T. Sato, et al., “Rare earth silicates as gain media for silicon photonics,” Photonics Res. 2(3), A45–A55 (2014). [CrossRef]
28. H. Sun, L. Yin, Z. Liu, et al., “Giant optical gain in a single-crystal erbium chloride silicate nanowire,” Nat. Photonics 11(9), 589–593 (2017). [CrossRef]
29. D. Alexander, K. Thomas, M. Joy, et al., “Structural and spectroscopic investigations on the quenching free luminescence of europium oxalate nanocrystals,” Acta Crystallogr. Sect. C: Struct. Chem. 75(5), 589–597 (2019). [CrossRef]
30. R. Reisfeld and C. K. Jorgensen, Lasers and Excited States of Rare Earths, vol. 1 (Springer Science & Business Media, 2012).
31. H. Steinfink and G. D. Brunton, “Crystal structure of erbium oxalate trihydrate,” Inorg. Chem. 9(9), 2112–2115 (1970). [CrossRef]
32. W. Que and C. Kam, “Effects of erbium oxalate content and temperature on green up-conversion luminescence of erbium oxalate nanoparticles/titania/ormosil composite thin films,” Opt. Commun. 206(1-3), 211–216 (2002). [CrossRef]
33. R. Pragash, N. Unnikrishnan, and C. Sudarsanakumar, “Spectroscopic properties of Pr3+-doped erbium oxalate crystals,” Pramana 77(6), 1119–1126 (2011). [CrossRef]
34. D. Alexander, K. Thomas, S. Sisira, et al., “Photoluminescence properties of fully concentrated terbium oxalate: a novel efficient green emitting phosphor,” Mater. Lett. 189, 160–163 (2017). [CrossRef]
35. G. Vimal, K. P. Mani, G. Jose, et al., “Growth and characterization of Sm3+ doped cerium oxalate single crystals,” J. Mater. Res. Technol. 5(3), 268–274 (2016). [CrossRef]
36. M. V. John and M. Ittyachen, “Studies on Ce2(C2O4)3 · nH2O crystals grown in hydro-silica gel,” Bull. Mater. Sci. 21(5), 387–391 (1998). [CrossRef]
37. J. Gaffney and N. Marley, General Chemistry for Engineers (Elsevier, 2017).
38. I. V. Kalinina, A. L. Guschin, D. G. Samsonenko, et al., “Hexaaquatrioxalatodierbium (III) tetrahydrate:[{Er (H2O)3}2(C2O4)3]· 4H2O,” Acta Crystallogr. Sect. E: Struct. Reports Online 59(9), m784–m786 (2003). [CrossRef]
39. F. L. F. Rivera, D. Y. M. Velázquez, I. Aldaya, et al., “Characterization of the optical gain in erbium-ytterbium-doped zinc and sodium-zinc phosphate glasses,” Opt. Mater. Express 12(11), 4491–4498 (2022). [CrossRef]
