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Abstract
Rare-earth-doped ZBLAN (ZrF4-BaF2-LaF3-AlF3-NaF) fibers have evolved to become promising candidates for efficient UV-visible emission because of their low phonon energy and low optical losses, as well as their well-defined absorption bands. We investigate the efficient emission of UV-visible light in a low-concentration (0.1 mol%) Ho3+-doped ZBLAN fiber excited by a 532 nm CW laser. In addition to the direct populating of the thermalized 5F4+5S2 levels by ground-state absorption, the upconversion processes responsible for UV-visible emission from the higher emitting levels, 3P1+3D3, 3K7+5G4, 5G5, and 5F3, of the Ho3+ ions are examined using excited-state absorption. The dependence of UV-visible fluorescence intensity on launched green pump power is experimentally determined, confirming the one-photon and two-photon characters of the observed processes. We theoretically investigate the excitation power dependence of the population density for nine Ho3+ levels based on a rate equation model. This qualitative model has shown a good agreement with the measured power dependence of UV-visible emission. Moreover, the emission cross-sections for blue, green, red, and deep-red light in the visible region are measured using the Füchtbauer–Ladenburg method and corroborated by McCumber theory, and the corresponding gain coefficients are derived. We propose an alternative approach to achieve efficient UV-visible emission in an Ho3+-doped ZBLAN fiber using a cost-effective, high-brightness 532 nm laser.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fluoride glass has been the workhorse behind fiber lasers since its invention in 1975 [1]. Its wide transparency window and low phonon energy have made it the gain material of choice for fiber lasers that use rare-earth transitions at wavelengths ranging from 0.28 to 4.3 µm [2–8]. Zirconium fluoride glass, commonly known as ZBLAN (ZrF4-BaF2-LaF3-AlF3-NaF), is the most stable heavy-metal fluoride glass reported so far. Owing to their transmission window that extends deep into the infrared and also in the UV-visible ranges, ZBLAN fibers represent an attractive candidate for a wider spectrum of photonic applications including spectroscopy, sensing, and data transmission, when comparing ZBLAN fibers with other types of fibers [9–15]. Typically, fluorescence emission of UV-visible light has been widely studied in rare-earth-doped ZBLAN fibers excited at 200–1200 nm, as summarized in Fig. 1 [16–46]. These results suggested the feasibility of a broad range of robust and reliable ZBLAN fiber lasers operating at wavelengths inaccessible before [2–4]. As nearly all rare-earth-doped ZBLAN fiber lasers are pumped in the 0.44- to 1.2-µm region, they can take advantage of the relatively mature InGaN (0.44–0.45 µm), InGaAlP (0.63–0.69 µm), and InGaAlAs (0.78–1.2 µm) semiconductor laser technology, as well as diode-pumped solid-state laser sources, such as the Nd3+-doped YAG laser (1.0–1.1 µm) and the Yb3+-doped silica fiber laser (1.1–1.2 µm). Thus, the potential for the development of fiber laser sources based on rare-earth-doped ZBLAN fiber is significant.
Fig. 1. Summary of UV-visible emission versus excitation wavelength in rare-earth-doped ZBLAN fibers.
Excitation of the Ho3+ ions in the visible region gives rise to efficient UV-visible emission. For example, red upconversion pumping of Ho3+-doped ZBLAN fibers with krypton and dye lasers has been demonstrated to be able to operate at wavelengths of 360, 485, 550, and 750 nm [17,47]. Unfortunately, these lasers in the context of fiber laser pumping have some disadvantages with regard to their inherent long-term costs and bulky and complex structure. Direct blue pumping of visible Ho3+-doped ZBLAN fiber lasers have attracted great interest due to the availability of inexpensive commercial blue laser diodes (LDs) [18,48]. This growing visible laser technology however suffers from several limitations, such as low operation power and poor reliability, all of which are due to the poor beam quality and the low temperature stability of blue LDs. In the case of a red LD pump, there are also limitation from reduced pumping effectiveness. Therefore good-quality of light is required to excite an Ho3+-doped ZBLAN fiber, which, in turn, requires a good-quality laser pump. Recently, the idea of the red-solid-state laser pumping of Ho3+-doped ZBLAN fiber operating at visible wavelengths has been proposed and also demonstrated [19,49]. The result of a watt-level visible Ho3+-doped ZBLAN fiber laser in the green spectral range benefits from high-power pump light with good beam quality produced by a red-solid-state laser source. However, such red-solid-state lasers are not commercially available and are prohibitively expensive to make.
As the development of commercial Nd3+-doped solid-state lasers and Yb3+-doped silica fiber lasers has made significant progress, high power, cost-effective, and compact green-frequency-doubling laser at 532 nm is now readily available. The inherent high beam quality of 532 nm laser contributes to the high-efficiency coupling of pump light into the ZBLAN fiber. More importantly, the energy of such a 532 nm laser matches well with the energy structures of the Ho3+ ions, so that the green laser can resonate with the thermalized 5F4+5S2 levels [50,51]. However, there has been only one report on the use of a 532 nm green continuous-wave (CW) laser for the excitation of Ho3+ ions in a ZBLAN fiber until now [52]. This previous demonstration of an efficient laser emission at the mid-infrared wavelength of 3.22 µm makes direct pumping into the emitting levels of 5F4+5S2 feasible [52]. Interestingly, benefiting from the low phonon energy of the ZBLAN matrix, an Ho3+-doped ZBLAN fiber permits long metastable state lifetimes, which are pivotal to the upconversion process [53]. The large excited-state absorption (ESA) of the Ho3+ ions enables a sequential two-photon upconversion process, where the resulting emission from the higher emitting levels is shorter in wavelength than that of the pump laser [49]. Therefore, we conducted a study to investigate the possibility of using an Ho3+-doped ZBLAN fiber excited by a 532 nm CW laser for efficient UV-visible emission.
In this work, efficient UV-visible emission in a 532 nm CW laser-pumped Ho3+-doped ZBLAN fiber is demonstrated for the first time. One-photon and two-photon processes were involved in the pumping mechanism and identified using the excitation power dependence of the fluorescence intensity and the population density for certain transitions, arising from 5F4+5S2, 5F5, 5F3, 5G5, 3K7+5G4, and 3P1+3D3, of the Ho3+ ions. Visible fluorescence spectra show the emission cross-sections for typical transitions 5F3→5I8 (blue), 5F5→5I8 (green), 5F4+5S2→5I8 (red), and 5F4+5S2→5I7 (deep-red) evaluated by the Füchtbauer–Ladenburg (F-L) method and compared with predictions from McCumber theory. Knowledge of absorption and emission cross-sections have enabled the determination of gain coefficients at visible wavelengths for various values of excited population. These results lay the groundwork for new designs of UV-visible Ho3+-doped ZBLAN fiber lasers with high-brightness 532 nm laser pumping.
2. Results and discussion
2.1 Absorption spectrum
A visible absorption spectrum of an Ho3+-doped ZBLAN fiber was recorded using an optical spectrum analyzer (OSA, Ocean Optics USB2000+). The Ho3+-doped ZBLAN fiber has a core/cladding diameter of 9/125 µm and a NA of 0.24 (Fiberlabs Inc.). The nominal dopant concentration of the Ho3+ ions provided by the manufacturer is ${N_{Ho}} = 1.8 \times {10^{19}}\; ions \cdot c{m^{ - 3}}$, corresponding to 1000 ppm mol. For our fiber sample, with the sufficiently low ion concentration of 0.1 mol%, the ion-ion energy transfer is negligible. Figure 2 shows a typical absorption spectrum for a 0.1 mol% Ho3+-doped ZBLAN fiber measured at visible wavelengths. Seven absorption bands, located at 415, 449, 466, 472, 484, 535, and 640 nm, are observed. The absorption coefficient (${\alpha _\lambda }$) is determined to be approximately 0.08 $\textrm{c}{\textrm{m}^{\textrm{ - 1}}}$ at λ = 532 nm.
2.2 Fluorescence spectrum and pump mechanism
The levels excited during pumping of the Ho3+-doped ZBLAN fiber at 532 nm were identified using fluorescence measurements. Two segments of the Ho3+-doped ZBLAN fiber were used for efficient UV-visible emission. For a short fiber length of 0.17 m, direct visible emission was measured between 510 nm and 780 nm; in this portion of fiber, minimized reabsorption effects do not appreciably affect the green and red spectral shapes [48]. For a long fiber length of 1.4 m, upconversion UV-visible emission was detected between 340 nm and 500 nm, in which enough gain was produced for the relatively weak upconversion transition. Figure 3 shows the fluorescence spectra measured with the OSA and the assigned transitions and peak wavelengths. All the emission wavelengths in the spectra were recorded at the pump end. This is because of the high pump power at the front end of the fiber, and also because some of the emissions may have been reabsorbed before reaching the end of the fiber.
Figure 3(a) shows that the visible emission bands peaking at 543 nm and 750 nm via direct pumping can be assigned to the transitions 5F4+5S2→5I8 and 5F4+5S2→5I7, respectively, which corresponds to the typical emissions under 450 nm and 640 nm excitation [18,19]. Red emission peaks at 656 nm via direct pumping and is attributed to the transition 5F5→5I8. A shorter-wavelength region of red emission at around 645 nm is observed, attributed to the 5F3→5I7 transition involved in an upconversion process. Figure 3(b) shows several other UV-visible upconversion emissions of the Ho3+ ions. Three typical emissions centered at 357, 408, and 457 nm originate from the upper emitting levels 3P1+3D3 to the lower levels 5I7, 5I6, and 5I5, respectively; while the three typical emissions peaking at around 390, 420, and 486 nm arise from the transitions 3K7+5G4→5I8, 5G5→5I8, and 5F3→5I8, respectively. Moreover, a shorter-wavelength region of blue emission at around 480 nm is observed, arising from the 3K7+5G4→5I7 transition.
Based on the above results we propose the following pumping mechanisms for the appearance of UV-visible emission from the Ho3+ ions in the ZBLAN fiber, as illustrated in Fig. 4. By absorbing an initial 532 nm photon, the thermalized 5F4+5S2 levels are populated from the ground-state level 5I8 and then non-radiatively decay down to the lower level 5F5 and populate the first two excited-state levels 5I6 and 5I7 radiatively. There are two possible intermediate levels i.e., 5I6 and 5I7, for ESA processes because of their longer lifetimes of 3.2 ms and 12.5 ms, respectively [17]. A second absorbed 532 nm photon through ESA processes from the 5I6 and 5I7 levels brings the ion to the levels 3H6 and 5G5, which relax non-radiatively to the levels 3K7+5G4 and 5F3, respectively. However, because of the low phonon character of the ZBLAN matrix, the levels 3K7+5G4, 5G5, and 5F3 also decay radiatively. Therefore, the UV emission at 390 nm and the blue emission at 480 nm originate from the upper levels 3K7+5G4 [see Fig. 3(b)]. This confirms that the ESA process from level 5I6 is active indeed. Compared to the 390 nm emission, the intense 5G5→5I8 emission centered at 420 nm confirms an active ESA process from level 5I7 [see Fig. 3(b)]. Moreover, using the thermalized 5F4+5S2 levels as the intermediate levels because of their long lifetime of 0.30 ms [54], another second absorbed 532 nm photon via an ESA process, i.e., 5F4+5S2→3H5, brings the ion to the levels 3P1+3D3, which are populated rapidly via non-radiative de-excitation.
Fig. 4. Partial energy-level diagram of the Ho3+ ions illustrating the laser excitation and emission transitions. The green dashed line arrows (upward) represent the resonant absorption of one green photon and the sequential absorption of two green photons. The colored solid line arrows (downward) represent the emission transition of the upper emitting levels. The gray dashed line arrows (downward) represent non-radiative relaxation of an excited-state level by multi-phonon emission.
To identify the pumping processes for these UV-visible emissions, their integrated fluorescence intensities were measured as a function of launched pump powers. It has been shown previously that the number of photons that are required to populate the upper emitting levels can be obtained by the relation ${I_f} \propto P_l^n$, where ${I_f}$ is the fluorescence intensity, ${P_l}$ is the launched pump laser power, and n is the number of the pump laser photons required. Figure 5 presents the log-log scale of integrated fluorescence intensity versus launched pump power. A straight line fit results in a slope close to 1 (i.e., $n = 0.94{\; }$ at green wavelengths and $n = 0.95$ at deep-red wavelengths) indicating that the one-photon excitation occurs. The similarity of the values of the slopes is not surprising, since both emissions originate from the same upper levels, 5F4+5S2. A slope value of $n = 0.82$ at red wavelengths also indicates that the one-photon excitation process is present, but the value is smaller below 1. This may be attributed to the 5F3→5I7 emission involved [see Fig. 3(a)]. The n values exceed 1 including 2.00, 1.81, 2.05, 1.46, 2.24, 1.88, and 1.59 for the 357, 390, 408, 420, 457, 480, and 486 nm emission bands, respectively. Therefore, the two-photon excitation mechanism is involved in populating the emitting levels of 3P1+3D3, 3K7+5G4, 5G5, and 5F3. The similar values $n = 2$ for the three emission peaks of 357 ($n = 2.00$), 408 ($n = 2.05$), and 457 ($n = 2.24$) nm provide further evidence that these emissions all originate from the same upper levels. Moreover, the two emissions at 390 nm and 480 nm show the similarity of the n values between 1.81 and 1.88, also illustrating that both emissions share the same upper emitting levels. However, the n values for the 420 nm and 486 nm peaks are only 1.46 and 1.59, respectively. Although the $n = 1.46$ and $n = 1.59$ values suggest that both the 5G5 and 5F3 levels are populated by the two-photon process, the relatively smaller $n = 1.46$ and $n = 1.59$ indicates that the populating procedures for these two levels are different.
Fig. 5. Double-logarithmic representation of the measured UV-visible fluorescence intensity versus launched green pump power.
To perform a kinetic analysis of our proposed model for the UV-visible emission in an Ho3+-doped ZBLAN fiber, the population densities of the above-mentioned levels, 5I8, 5I7, 5I6, 5F5, 5F4+5S2, 5F3, 5G5, 3K7+5G4, and 3P1+3D3, of the Ho3+ ions need to be investigated. According to the energy levels shown in Fig. 4, keeping rapid non-radiative relaxations and model simplicity in mind, only nine levels of the Ho3+ ions are considered; their population densities are marked from ${N_1}$ to ${N_2}$. We performed a calculation of the rate equations for the population densities ${N_i}$ given by Eqs. (1)–(10) using a computer MATLAB program incorporating the Runge–Kutta numerical method [55–57].
Numerically obtained, the evolution of the population for the nine Ho3+ levels as a function of launched green pump power is presented in Figs. 6(a), 6(c), and 6(e). The results illustrate that the population inversion of the typical upper levels including, 5F5, 5F4+5S2, 5F3, 5G5, 3K7+5G4, and 3P1+3D3, can be obtained by excitation from a 532 nm CW laser. These direct and upconversion processes are experimentally identified by the power dependence curves of the emission intensities, as shown in Figs. 6(b), 6(d), and 6(f), which show good agreement with the theoretical predications given by a steady-state rate equation model.
Fig. 6. Calculated dependence of the populations of nine typical levels of 5I8, 5I7, 5I6, 5F4+5S2, 5F5, 5F3, 5G5, 3K7+5G4, and 3P1+3D3 on launched pump power in the Ho3+-doped ZBLAN fiber under 532 nm CW laser excitation.
Interestingly, the efficient 3P1+3D3→5I7 emission at 357 nm, shown in Fig. 3(b), is in contrast to the inefficient four-level laser action scheme with one-photon excitation at 287 nm and two-photon excitation at 488 nm in Ref. [60]. The primary reason for this inefficient four-level scheme is that the terminated level 5I7 is very long-lived, at over 12 ms [17,54]. Therefore, such a level can act as an active ion population reservoir, which prevents it from contributing to the efficient transition. As for 532 nm CW laser pumping, significant inversion is, however, expected for the emitting levels 3P1+3D3 against the terminated level 5I7 with further increasing pump power, as predicted in Figs. 6(a) and 6(e). This suggests effective population build-up is enabled by the ESA process of the 5I7→5G5 transition. Notably, under 532 nm CW laser excitation, efficient 5F4+5S2→5I7 emission at 750 nm is expected for the same ESA process of the 5I7→5G5 transition involved [see Fig. 3(a)]. This is also in contrast to what has been reported for inefficient deep-red laser action with direct pumping at 450 nm [18]. Strong population inversion is typically observed for upconversion pumping involving the lower level of a self-terminating transition, which decreases the terminal level lifetime [53]. Under upconversion pumping at 532 nm, efficient CW laser oscillation of the Ho3+-doped ZBLAN fiber can be realized for self-terminating transitions, including 3P1+3D3→5I7 at 357 nm and 5F4+5S2→5I7 at 750 nm.
2.3 Typical visible absorption and emission cross-sections
The measured fluorescence spectra (see Fig. 3), combined with the calculated values of ${A_{ij}}$ (see Table 4.2 in Ref. [58]), enabled a determination of the effective emission cross-sections in the visible region, including blue, green, red, and deep-red wavelengths, using the F-L method [61], as shown by the colored solid curves of Fig. 7. The maximum values of the emission cross-sections extracted from Figs. 7(a)–7(d) reach $0.55 \times {10^{ - 20}}\; c{m^2}$ at 486 nm, ${\; }0.78 \times {10^{ - 20}}\; c{m^2}$ at 543 nm, ${\; }0.68 \times {10^{ - 20}}\; c{m^2}$ at 656 nm, and $0.90 \times {10^{ - 20}}\; c{m^2}$ at 750 nm, respectively. These values are more than one order of magnitude higher than those of the Ho3+-doped ZBLAN fiber for the mid-infrared wavelength of approximately 3 µm ($0.4 \times {10^{ - 21}}\; c{m^2}$) [62]. The values are also comparable with those of previous reports on Ho3+-doped fluoroaluminate glass fiber at around 2.9 µm ($0.73 \times {10^{ - 20}}\; c{m^2}$) [63] and Ho3+-doped fluoroindate glass fiber at around 3.9 µm ($0.34 \times {10^{ - 20}}\; c{m^2}$) [64].
Fig. 7. Comparison of measured emission cross-sections obtained using the F-L relation (colored solid curves) with those calculated using absorption cross-sections obtained using McCumber theory (colored dotted curves) for typical transitions: (a) 5F3→5I8 (blue), (b) 5F4+5S2→5I8 (green), (c) 5F5→5I8 (red), and (d) 5F4+5S2→5I7 (deep-red). The corresponding absorption cross-sections are indicated by black curves.
As a comparison, the McCumber’s calculations of the emission cross-sections using the measured absorption cross-sections are given as colored dotted curves in Figs. 7(a)–7(c) [65,66]. Both methods yield quantitative estimates and agree well with each other except for the short-wavelength side in Fig. 7(b), which shows a greater separation between the measured and calculated emission cross-sections at green wavelengths. We attribute this to the 532 nm pumping, which is resonant, and thus affects the short-wavelength side of the green emission band. The corresponding absorption cross-sections are presented as black curves in Fig. 7. Considering that the deep-red emission takes place between the two excited-state levels 5F4+5S2 and 5I7, its absorption cross-section can be in turn derived from the emission cross-section using McCumber theory, as shown in Fig. 7(d). The use of McCumber theory to assess the cross-section of a transition not involving the ground level has been proposed in the previous studies [67,68].
In order to further evaluate the visible gain characteristics, the wavelength-dependent net gain $G(\lambda )$ as a function of population inversion for the upper levels 5F3, 5F4+5S2, and 5F5 was analyzed qualitatively using Eq. (11):
where ${\sigma _{emi}}(\lambda )$ and ${\sigma _{abs}}(\lambda )$ are the stimulated emission and the absorption cross-sections for a given transition, respectively, P is the population inversion parameter fractional factor of the excited Ho3+ ions, and ${N_{Ho}}$ is the total concentration of the Ho3+ ions.As shown in Fig. 8, the gain coefficients with various values of P are calculated for the four typical visible wavelengths of interest. The visible gain coefficient increases, and the gain band shifts toward the short wavelength side with increasing P. This is because the typical transitions of the Ho3+ ions, including 5F3→5I8, 5F4+5S2→5I8, 5F5→5I8, and 5F4+5S2→5I7, correspond to the three-level and quasi-three-level schemes. Reabsorption is minimized as the increase of P. The positive gain thresholds are first reached for $P = 0.2$, $0.2$, $0.2$, and $0.4$ at the blue, green, red, and deep-red wavelengths, respectively. As shown in Figs. 8(a) and 8(c), the maximum gain coefficient reaches $0.1{\; }c{m^{ - 1}}$ or more for the 5F3→5I8 and 5F5→5I8 transitions at the blue and red wavelengths, respectively. When P reaches 0.8, the gain coefficient reaches more than $0.02\; c{m^{ - 1}}$ over a wide blue spectral range from 483 to 490 nm. For the green, red, and deep-red wavelengths, the gain coefficient of more than $0.02{\; }c{m^{ - 1}}$ is achieved at the wider spectral ranges of 535–555, 640–663, and 745–760 nm, respectively. This result indicates that the Ho3+-doped ZBLAN fiber is a potential, active laser medium which achieves broadband tunable visible laser output [49].
Fig. 8. Calculated gain coefficients versus visible wavelengths for various values of population inversion parameter P.
The maximum gain coefficient reaches $0.15\; c{m^{ - 1}}$ for the 5F4+5S2→5I8 transition in Fig. 8(b), and a nearly identical value is observed for the 5F4+5S2→5I7 transition in Fig. 8(d). Such a result indicates that the direct pumping process is combined with the upconversion pumping process when 532 nm laser excitation is employed in the Ho3+-doped ZBLAN fiber. As mentioned above, the deep-red emission is strengthened by the ESA process of the 5I7→5G5 transition because the long-lived 5I7 metastable level acts as a good population reservoir, allowing a high density of excited ions to be created. Therefore, the ESA is necessary to depopulate the lower level 5I7, which is typically a self-terminating transition. Therefore, a highly efficient deep-red CW laser output could be realized using 532 nm laser pumping of Ho3+-doped ZBLAN fiber.
3. Conclusion
In summary, we demonstrate the efficient emission of UV-visible light from an Ho3+-doped ZBLAN fiber under 532 nm CW laser excitation. Direct visible emission and upconversion UV-visible emission are observed over a spectral range of 340–780 nm. The proposed pumping mechanisms are identified experimentally using the dependence of UV-visible fluorescence intensity on launched green pump power and explained by a steady-state rate equation model. The responsible upconversion processes are investigated and shown to be ESA processes involving the intermediate levels of 5F4+5S2, 5I6, and 5I7. Typical visible-emission cross-sections calculated from visible fluorescence spectra measurements are given for the blue, green, red, and deep-red wavelengths, and are compared with predictions obtained from McCumber theory; the corresponding gain coefficients are obtained. We anticipate that our work will expand the applicability of the Ho3+-doped ZBLAN fiber and open a new avenue for the development of UV-visible fiber laser sources pumped at 532 nm.
Funding
National Natural Science Foundation of China (62005229); Xiamen Young Innovation Fund Project (3502Z20206030); Fundamental Research Funds for the Central Universities (20720210085).
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. M. Poulain, M. Poulain, and J. Lucas, “Verres fluores au tetrafluorure de zirconium proprieties optiques d’un verre dope au Nd3+,” Mater. Res. Bull. 10(4), 243–246 (1975). [CrossRef]
2. R. M. El-Agmy, “Upconversion CW laser at 284 nm in a Nd: YAG-pumped double-cladding thulium-doped ZBLAN fiber laser,” Laser Phys. 18(6), 803–806 (2008). [CrossRef]
3. D. S. Funk, J. W. Carlson, and J. G. Eden, “Room-temperature fluorozirconate glass fiber laser in the violet (412 nm),” Opt. Lett. 20(13), 1474–1476 (1995). [CrossRef]
4. J. Y. Allain, M. Monerie, and H. Poignant, “Tunable CW lasing around 610, 635, 695, 715, 885 and 910 nm in praseodymium-doped fluorozirconate fibre,” Electron. Lett. 27(2), 189–191 (1991). [CrossRef]
5. X. S. Zhu, J. Zong, K. Wiersma, R. A. Norwood, N. S. Prasad, M. D. Obland, A. Chavez-Pirson, and N. Peyghambarian, “Watt-level short-length holmium-doped ZBLAN fiber lasers at 1.2 µm,” Opt. Lett. 39(6), 1533–1536 (2014). [CrossRef]
6. M. Pollnau, C. Ghisler, W. Lüthy, H. P. Weber, J. Schneider, and U. B. Unrau, “Three-transition cascade erbium laser at 1.7 (µm, 2.7 µm, and 1.6 µm,” Opt. Lett. 22(9), 612–614 (1997). [CrossRef]
7. J. Schneider, C. Carbonnier, and U. B. Unrau, “Characterization of a Ho3+-doped fluoride fiber laser with a 3.9-(m emission wavelength,” Appl. Opt. 36(33), 8595–8600 (1997). [CrossRef]
8. M. R. Majewski, R. I. Wooward, J.-Y. Carreé, S. Poulain, M. Poulain, and S. D. Jackson, “Emission beyond 4((m and mid-infrared lasing in a dysprosium-doped indium fluoride (InF3) fiber,” Opt. Lett. 43(8), 1926–1929 (2018). [CrossRef]
9. I. Cozmuta, S. Cozic, M. Poulain, S. Poulain, and J. R. L. Martini, “Breaking the silica ceiling: ZBLAN based opportunities for photonics applications,” Proc. SPIE 11276, 112760R (2020). [CrossRef]
10. R. Singh, S. Kumar, F.-Z. Liu, C. Shuang, B. Y. Zhang, R. Jha, and B. K. Kaushik, “Etched multicore fiber sensor using copper oxide and gold nanoparticles decorated graphene oxide structure for cancer cells detection,” Biosens. Bioelectron. 168, 112557 (2020). [CrossRef]
11. B. K. Kaushik, L. Singh, R. Singh, G. Zhu, B. Y. Zhang, Q. L. Wang, and S. Kumar, “Detection of collagen-IV using highly reflective metal nanoparticles—Immobilized photosensitive optical fiber-based MZI structure,” IEEE Trans. Nanobiosci. 19(3), 477–484 (2020). [CrossRef]
12. S. Kumar, R. Singh, Q. Yang, S. Cheng, B. Zhang, and B. K. Kaushik, “Highly sensitive, selective and portable sensor probe using germanium-doped photosensitive optical fiber for ascorbic acid detection,” IEEE Sens. J. 21(1), 1 (2020). [CrossRef]
13. G. Zhu, Y. Wang, Z. Wang, R. Singh, C. Marques, Q. Wu, B. K. Kaushik, R. Jha, B. Y. Zhang, and S. Kumar, “Localized plasmon-based multicore fiber biosensor for acetylcholine detection,” IEEE Trans. Instrum. Meas. 71, 1–9 (2022). [CrossRef]
14. A. G. Leal-Junior, A. Frizera, C. Marques, M. R. A. Sánchez, W. M. dos Santos, A. A. G. Siqueira, M. V. Segatto, and M. J. Pontes, “Polymer optical fiber for angle and torque measurements of a series elastic actuator’s spring,” J. Lightwave Technol. 36(9), 1698–1705 (2018). [CrossRef]
15. A. G. Leal-Junior, C. A. R. Diaz, L. M. Avellar, M. J. Pontes, C. Marques, and A. Frizera, “Polymer optical fiber sensors in healthcare applications: a comprehensive review,” Sensors 19(14), 3156 (2019). [CrossRef]
16. M. Malinowski, M. Kaczkan, M. Klimczak, and R. Piramidowicz, “Ultraviolet emission excitation in RE3+ activated fluoride fibers,” Opt. Mater. 31(3), 484–489 (2009). [CrossRef]
17. M. Kowalska, G. Klocek, R. Piramidowicz, and M. Malinowski, “Ultra-violet emission in Ho:ZBLAN fiber,” J. Alloys Compd. 380(1-2), 156–158 (2004). [CrossRef]
18. W. S. Li, J. J. Wu, X. F. Guan, Z. Y. Zhou, H. Y. Xu, Z. Q. Luo, and Z. P. Cai, “Efficient continuous-wave and short-pulse Ho3+-doped fluorozirconate glass all-fiber lasers operating in the visible spectral range,” Nanoscale 10(11), 5272–5279 (2018). [CrossRef]
19. M. N. Chen, W. S. Li, S. H. Ji, X. J. Lin, X. Zhan, H. Y. Xu, and Z. P. Cai, “Study on fluorescence characteristics of the Ho3+:ZBLAN fiber under ∼640 nm excitation,” Opt. Mater. 97, 109351 (2019). [CrossRef]
20. C. Koepke, K. Wisniewski, D. Piatkowski, and M. Malinowski, “Competition between two types of anti-Stokes emission in Ho3+-activated ZBLAN glass,” J. Phys.: Condens. Matter 21(3), 035113 (2009). [CrossRef]
21. Y. Forester, B. R. Redyand, and S. K. Nash-Stevenson, “Energy upconversion and spectroscopic studies of holmium-doped ZBLAN fibers,” Proc. SPIE 3542, 18–25 (1998). [CrossRef]
22. G. K. Liu, Y. H. Chen, and J. V. Beitz, “Photon avalanche up-conversion in Ho3+ doped fluoride glasses,” J. Lumin. 81(1), 7–12 (1999). [CrossRef]
23. A. Wnuk, M. Kaczkan, Z. Frukacz, I. Pracka, G. Chadeyron, M.-F. Joubert, and M. Malinowskia, “Infra-red to visible up-conversion in holmium-doped materials,” J. Alloys Compd. 341(1-2), 353–357 (2002). [CrossRef]
24. P. Stremplewski, C. Koepke, and D. Piatkowski, “Verification of upconversion in ZBLAN:Ho3+ glass under photon-avalanche-type excitation at 980 nm,” Appl. Phys. B 107(1), 171–176 (2012). [CrossRef]
25. X. Zhu, J. Zong, R. A. Norwood, A. Chavez-Person, N. Peyghambarian, and N. Prasad, “Holmium-doped ZBLAN fiber lasers at 1.2 µm,” Proc. SPIE 8237, 823727 (2012). [CrossRef]
26. R. Piramidowicz, A. Bok, M. Klimczak, and M. Malinowski, “UV emission properties of thulium-doped fluorozirconate glasses,” J. Lumin. 129(12), 1874–1877 (2009). [CrossRef]
27. W. Y. Tian and B. R. Reddy, “Ultraviolet upconversion in thulium-doped fluorozirconate fiber observed under two-color excitation,” Opt. Lett. 26(20), 1580–1582 (2001). [CrossRef]
28. J. F. Li, X. L. Wang, H. G. Yang, and Z. K. Jiang, “Ultraviolet upconversion emission from ZBLAN glass doped with Tm3+ ions,” Physcia B 392(1-2), 251–254 (2007). [CrossRef]
29. M. Juárez-Hernández and E. B. Mejía, “Spectral analysis of short-wavelength emission by up-conversion in a Tm3+:ZBLAN dual-diode-pumped optical fiber,” Chin. Opt. Lett. 18(7), 071901 (2020). [CrossRef]
30. J. F. Li, X. L. Wang, and Z. K. Jiang, “Multiphoton upconversion process in Tm3+ doped ZBLAN glass by CW laser irradiation,” Opt. Commun. 282(21), 4249–4251 (2009). [CrossRef]
31. R. M. El-Agmy, N. M. Al-Hosiny, S. Abdallah, and M. S. Abdel-Aal, “Generation of short wavelength in up-conversion of Tm3+ doped fluoride glass and its application in fiber lasers,” J. Mod. Phys. 05(03), 123–127 (2014). [CrossRef]
32. E. B. Mejía, “Ultraviolet emission in Tm3+-doped fluoride fiber pumped with two infrared wavelengths,” J. Appl. Phys. 100(11), 113110 (2006). [CrossRef]
33. A. T. Stanley, E. A. Harris, T. M. Searle, and J. M. Parker, “Upconversion in neodymium doped fluoride glasses,” J. Non-Cryst. Solids 161, 235–240 (1993). [CrossRef]
34. M. Klimczak and R. Piramidowicz, “UV-violet emission properties of 2F(2)5/2 energy level of Nd3+ ions in ZBLAN glass,” Appl. Phys. B 106(4), 1019–1025 (2012). [CrossRef]
35. M. Klimczak, M. Malinowski, and R. Piramidowicz, “Orange and IR to violet up-conversion processes in Nd:ZBLAN glasses,” Opt. Mater. 31(12), 1811–1814 (2009). [CrossRef]
36. C. L. Pope, B. R. Reddy, and S. K. Nash-Stevenson, “Efficient violet upconversion signal from a fluoride fiber doped with erbium,” Opt. Lett. 22(5), 295–297 (1997). [CrossRef]
37. M. Tsuda, K. Soga, H. Inoue, S. Inoue, and A. Makishima, “Upconversion mechanism in Er3+-doped fluorozirconate glasses under 800 nm excitation,” J. Appl. Phys. 85(1), 29–37 (1999). [CrossRef]
38. T. Yamashita and Y. Ohishi, “Optical amplification and laser oscillation characteristics of Tb3+-doped fluoride glass fiber,” Opt. Mater. Express 5(8), 1689 (2015). [CrossRef]
39. U. Weichmann, J. Baier, J. Bengoechea, and H. Moench, “GaN-diode pumped Pr3+:ZBLAN-lasers for the visible wavelength range,” in CLEO/Europe and IQEC 2007 Conference Digest, (Optical Society of America, 2007), paper CJ5_1.
40. K. Chodavarapu, C. R. Puluru, and B. R. Redy, “Ultraviolet emission from praseodymium doped fibers,” Proc. SPIE 5912, 59120B (2005). [CrossRef]
41. C. L. Pope, B. R. Redy, and S. K. Nash-Stevenson, “Blue and violet energy upconversion emission from a ZBLAN fiber doped with praseodymium and ytterbium under dye laser excitation,” Proc. SPIE 3793, 104–147 (1999).
42. H. Okamoto, K. Kasuga, I. Hara, and Y. Kubota, “Visible-NIR tunable Pr3+-doped fiber laser pumped by a GaN laser diode,” Opt. Express 17(22), 20227–20232 (2009). [CrossRef]
43. J. Limpert, H. Zellmer, P. Riedel, G. Maze, and A. Tünnermann, “Laser oscillation in yellow and blue spectral range in Dy3+:ZBLAN,” Electron. Lett. 36(16), 1386–1387 (2000). [CrossRef]
44. M. Z. Amin, S. D. Jackson, and M. R. Majewski, “Experimental and theoretical analysis of Dy3+-doped fiber lasers for efficient yellow emission,” Appl. Opt. 60(16), 4613–4621 (2021). [CrossRef]
45. J. H. Zou, T. R. Li, Y. B. Dou, J. Li, N. Chen, Y. K. Bu, and Z. Q. Luo, “Direct generation of watt-level yellow Dy3+-doped fiber laser,” Photonics Res. 9(4), 446–451 (2021). [CrossRef]
46. R. Piramidowicz, M. Klimczak, and M. Malinowski, “Short-wavelength emission analysis in Dy:ZBLAN glasses,” Opt. Mater. 30(5), 707–710 (2008). [CrossRef]
47. J. Y. Allain, M. Monerie, and H. Poignant, “Room-temperature cw tunable green upconversion holmium fibre laser,” Electron. Lett. 26(4), 261–263 (1990). [CrossRef]
48. W. S. Li, S. H. Zahng, S. H. Ji, B. Xiao, Q. C. Feng, H. Y. Xu, and Z. P. Cai, “High-efficiency broadband tunable green laser operation of direct diode-pumped holmium-doped fiber,” Opt. Express 29(10), 15564–15575 (2021). [CrossRef]
49. S. H. Ji, S. Q. Liu, X. J. Lin, Y. Y. Song, B. Xiao, Q. C. Feng, W. S. Li, H. Y. Xu, and Z. P. Cai, “Watt-level visible continuous-wave upconversion fiber lasers toward the “green gap” wavelengths of 535−553 nm,” ACS Photonics 8(8), 2311–2319 (2021). [CrossRef]
50. F. Qin, Y. D. Zheng, Y. Yu, Z. M. Cheng, P. S. Tayebi, W. W. Cao, and Z. G. Zhang, “Ultraviolet and violet upconversion luminescence in Ho3+-doped Y2O3 ceramic induced by 532-nm CW laser,” J. Alloys Compd. 509(4), 1115–1118 (2011). [CrossRef]
51. F. Qin, H. Zhao, M. Y. Lv, L. P. Li, Y. Zhou, Z. J. Wang, Y. D. Zheng, Z. G. Zhang, and W. W. Cao, “Precise determination on the upconversion processes of the ultraviolet upconversion fluorescence of Ho3+-doped Y2O3 ceramic by excitation of a 532-nm continuous-wave laser,” Opt. Lett. 42(12), 2279–2282 (2017). [CrossRef]
52. C. Carbonnier, H. Többen, and U. B. Unrau, “Room temperature CW fibre laser at 3.22 µm,” Electron. Lett. 34(9), 893–894 (1998). [CrossRef]
53. R. Scheps, “Upconversion laser process,” Prog. Quant. Electron. 20(4), 271–358 (1996). [CrossRef]
54. L. Wetenkamp, G. F. West, and H. Többen, “Optical properties of rare earth-doped ZBLAN glasses,” J. Non-Crystal. Solid. 140, 35–40 (1992). [CrossRef]
55. E. Hairer, C. Lubich, and M. Roche, The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods (Springer-Verlag, Berlin, 1989).
56. P. Laperle, R. Vallée, and A. Chandonnet, “Thulium-doped ZBLAN fiber laser,” Proc. SPIE 3611, 228–239 (1999). [CrossRef]
57. X. D. Hu, T. G. Ning, L. Pei, Q. Y. Chen, and J. Li, “Excellent initial guess functions for simple shooting method in Yb3+-doped fiber lasers,” Opt. Fiber Technol. 20(4), 358–364 (2014). [CrossRef]
58. D. S. Funk, “Optical processes and laser dynamics in holmium and neodymium upconversion-pumped visible and ultraviolet fluorozirconate fiber lasers,” Ph.D. dissertation. Univ. of Illinois, Urbaba, 1999.
59. D. Piatkowski, K. Wisniewski, M. Rozanski, C. Koepke, M. Kaczkan, M. Klimczak, R. Piramidowicz, and M. Malinowski, “Excited state abslroption spectroscopy of ZBLAN:Ho3+ glass—experiment and simulation,” J. Phys.: Condens. Matter 20(15), 155201 (2008). [CrossRef]
60. M. Klimczak, M. Cieślik, M. Kaczkan, P. Witoński, and R. Piramidowicz, “UV-violet optical transitions and excitation schemes in Ho3+:ZBLAN fibers,” Proc. SPIE 6937, 693718 (2007). [CrossRef]
61. W. B. Fowler and D. L. Dexter, “Relation between absorption and emission probabilities in luminescent centers in ionic solids,” Phys. Rev. 128(5), 2154–2165 (1962). [CrossRef]
62. J. F. Li, H. Y. Luo, Y. Liu, L. Zhang, and S. D. Jackson, “Modeling and optimization of cascades erbium and holmium doped fluoride fiber lasers,” IEEE J. Select. Topics Quantum Electron. 20(5), 29–35 (2014). [CrossRef]
63. S. J. Jia, Z. X. Jia, C. F. Yao, S. B. Wang, H. W. Jiang, L. Zhang, Y. Feng, G. S. Qin, Y. Ohishi, and W. P. Qin, “Ho3+ doped fluoroaluminate glass fibers for 2.9 µm lasing,” Laser Phys. 28(1), 015802 (2018). [CrossRef]
64. F. Maes, V. Fortin, S. Poulain, M. Poulain, J.-Y. Carrée, M. Bernier, and R. Vallée, “Room-temperature fiber laser at 3.92 µm,” Optica 5(7), 761–764 (2018). [CrossRef]
65. D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136(4A), A954–A957 (1964). [CrossRef]
66. R. M. Martin and R. S. Quimby, “Experimental evidence of the validity of the McCumber theory relating emission and absorption for rare-earth glasses,” J. Opt. Soc. Am. B 23(9), 1770–1775 (2006). [CrossRef]
67. R. S. Quimby and B. Zheng, “New excited-state absorption measurement technique and application to Pr3+ doped fluorozirconate glass,” Appl. Phys. Lett. 60(9), 1055–1057 (1992). [CrossRef]
68. J.-F. Bisson, M. Iyoda, Y. Yasumatsu, M. Endo, and T. Masuda, “Effect of the thermally excited lower laser level in a neodymium-doped fiber,” J. Opt. Soc. Am. B 36(3), 736–745 (2019). [CrossRef]
