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Abstract
In this study, erbium-doped fiber (EDF) and Panda-type polarization maintaining erbium-doped fiber (PM-EDF) were fabricated from the same erbium-doped preform. The intrinsic influence of stress induced by the Panda-type design on the optical properties was investigated. A local structural model of EDF was developed to simulate the introduction of stress by varying the length of non-bridging oxygen (NBO) bonds between erbium ions (Er3+) and the silica network, providing theoretical insights. An increase in bond length (indicative of tensile stress), results in decreased excitation and emission intensities for EDF, and the peaks exhibit redshifts. Conversely, a decrease in bond length (indicative of compressive stress), leads to increased excitation and emission intensities, with the peaks showing blueshifts. Experimentally, PM-EDF demonstrated a lower absorption coefficient compared to EDF, with absorption peaks experiencing redshifts of approximately 2 nm. Furthermore, the emission intensity was diminished, and the emission peak at 1530 nm displayed a redshift of around 3 nm. The fluorescence lifetime was shortened to 9.99 ms. Additionally, the total gain of PM-EDF decreased by approximately 4 dB, and the bandwidth narrowed by roughly 13%. The experimental outcomes largely align with the simulation predictions, further corroborating the significant impact of stress on the optical properties of PM-EDF.
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1. Introduction
Erbium-doped fibers (EDFs), whose emission band at ∼1530 nm aligns with the low-loss window of silica optical fibers, have been extensively studied and applied in the field of optical fiber communication [1,2]. The advancement of light detection and ranging (LIDAR) [3], optical measurement sensing [4], and related fields has led to the increased demands for the performance of EDFs. Polarization control of light in fibers, especially in erbium-doped fiber (EDF) systems, is crucial. The most efficient way to achieve linear polarization in the output beam is by designing the waveguide structure of EDF as a polarization maintaining structure, such as the Panda-type polarization maintaining erbium-doped fiber (PM-EDF) [5,6]. The introduction of Panda-type stress-applying parts (SAPs) not only induces stress at the fiber core, but also potentially impacts the local lattice environment of erbium ions (Er3+). The latter effect can correspondingly lead to alterations in the luminescent properties of Er3+ [7].
The stress influence upon the properties of Er3+ has been investigated in crystal, ceramic and fiber. For example, Valiente et al. examined the impact of high pressure (up to 7.5 GPa) on the photoluminescence properties of Er/Yb co-doped KY(WO4)2 single-crystal thin films [8], and found that the pressure caused a shift in Raman spectrum. Qi et al. investigated the alterations in Raman spectrum and up-conversion photoluminescence spectrum of Er-doped BaBi4Ti4O15 ceramic samples across a pressure range of 0 GPa to 22.4 GPa [9]. The study revealed that the peak in Raman spectra presented a red shift with the increase of the pressure, and that the general trend of the up-conversion photoluminescence was diminished. Runowski et al. explored the high-pressure luminescence characteristics of Er-doped YVO4 materials [10], and observed that an increase in pressure could lead to the enhancement of the crystal field strength, thereby causing the more significant splitting of Stark sublevels. Leto et al. probed the nanoscale stress fields utilizing the wavelength shift of selected spectral bands in Er-doped silica fibers [11], and observed a linear correlation between peak frequency shift and external stress for suitable bands with a relatively high reliability. The aforementioned studies collectively suggest that the luminescent properties of Er3+ undergo alterations when subjected to stress. However, the influence of stress induced by Panda-type SAPs upon the luminescent properties of Er3+ in PM-EDF has been rarely reported.
Hence, in this work, the finite element models, and local structural models of EDF and PM-EDF were developed to investigate the influence of stress induced by the Panda-type design on the luminescence characteristics of Er3+. Subsequently, EDF and PM-EDF were fabricated by modified chemical vapor deposition (MCVD) technology, using the same erbium-doped preform. Experimental comparisons were conducted on their absorption properties, fluorescence properties, excitation and emission characteristics, fluorescence lifetime, and gain characteristics.
2. Theoretical studies
2.1 Finite element models of EDF and PM-EDF
Traditional Panda-type polarization-maintaining fibers (PMFs) have two circular B2O3-doped silica SAPs symmetrically positioned on either side of the fiber core. In the stress region, the thermal expansion coefficient is significantly higher compared to the surrounding silica cladding [12]. Therefore, the optical fiber cools to room temperature, the stress region contracts more than the surrounding silica cladding. This differential contraction leads to stress exertion on the core after solidification and cooling, causing core deformation. This deformation could potentially influence the local crystal lattice environment of Er3+, thus leading to alterations in the optical properties of EDF.
In order to assess the stress distribution on the cores of EDF and PM-EDF, simulations and analyses were conducted utilizing the commercial software COMSOL Multiphysics, which is based on finite-element analysis method (FEM) [13]. The cross-section schematics of EDF and PM-EDF are shown in Fig. 1. The core radius (a) was 4.25 µm, while the cladding radius (W) was 62.50 µm. Meanwhile, the stress region radius (R) was established at 13.00 µm, and the distance from the inner edge of the stress region to the fiber center (L) measured 7.00 µm.
The relationship between the effective refractive index within the optical fiber and wavelength, as well as doping concentration, could be ascertained following the hybrid Sellmeier dispersion equation [14]. At the wavelength of 1550 nm, the fiber core was composed of Er2O3-doped-SiO2, with a refractive index of 1.452. The SAPs composed of B2O3-doped-SiO2 with a refractive index of 1.437, while the cladding was constructed from pure silica with a refractive index of 1.444. The thermal expansion coefficient of doped materials could be obtained using a mixture model according to molar percentage. The expression is presented in Eq. (1) [12].
where α0 and α1 denote the thermal expansion coefficients of the background material and doped material, respectively; and m is the molar percentage of the doped material. Table 1 presents additional material parameters used in the modeling process, which have been sourced from previous studies [15,16].
Table 1. Material parameters used for modeling
The simulation included annealing the preform at 1100°C by integrating the wave optics module with the solid mechanics module. As the optical fiber cooled from its molten state to ambient temperature, thermal stress developed in both the x and y directions within the fiber core. This cooling process also led to variations in the refractive indices along the x and y directions [17,18]:
For comparison, except for the parameter settings in the SAPs, the other parameter settings of the EDF model and PM-EDF model remained consistent. The stress-induced birefringence of the EDF and PM-EDF is illustrated in Fig. 2. The stress-induced birefringence at the EDF core is 2.73 × 10−9, indicating hardly significant birefringence induced by EDF self-stress. The stress-induced birefringence of PM-EDF stress is 1.93 × 10−4, which is attributed to the thermal stress introduced by SAPs. The von Mises stress distribution in the cross-section of the EDF and PM-EDF is shown in Fig. 3. The maximum stress on the EDF core reaches 9.52 × 107 Pa, while the maximum stress on the PM-EDF core reaches 11.06 × 107 Pa. Transverse tensile stress is clearly present in the PM-EDF core, and the introduction of SAPs results in a rise of approximately 1.54 × 107 Pa in stress on the fiber core. This increased tensile stress leads to deformation of the fiber core, thus affecting the local lattice environment of Er3+ within the fiber core and the optical properties of EDF.
2.2 Local structural model of EDF
To delve deeper into the effects of stress introduced by SAPs on the luminescent properties of EDF, a local structural model specifically designed for EDF was hereby developed. Silica optical fiber is commonly comprised of varying numbers of SiO4 tetrahedral units, which assemble into three-membered rings (3MR), 4MR, 5MR, and 6MR [19,20]. The 3MR microstructure model is extensively employed for doping in amorphous silicon matrices [21–24]. Hence, in this study, the 3MR structure was adopted as the base unit of the silica glass network for constructing the local model structural of EDF.
All calculations were conducted using Gaussian 09 program. The structural optimization of the Er-3MR compound was conducted utilizing Becker-type three-parameter Lee-Yang-Parr (B3LYP) hybrid functional method within the framework of density functional theory (DFT) [25,26]. The O, H, and Si elements were modeled using the 6-31 + G** basis set, taking into account computational resources and accuracy considerations. Additionally,11 valence electron RECPs were utilized for the trivalent state of the erbium element [23,27].
Three potential local structural models of EDF were constructed, involving equivalent quantities of O, Si, H, and Er atoms in each structure (Fig. 4). In model (a), Er3+ was embedded into the 3MR structure. In model (b), Er3+ was coordinated to the 3MR structure via an O-Si-O linkage. In model (c), Er3+ was coordinated to the 3MR structure via non-bridging oxygen (NBO). After structural optimization calculation, the ground state structure with the minimum energy was obtained, and the bonding energy (eV) was calculated following Eq. (4) [23]:
where, n, m, and k denote the number of Si, O, and H atoms in the models, respectively. As shown in Table 2, the calculated bonding energies for models (a), (b), (c) are 5.2472, 6.2698, and 6.2890, respectively. Model (c) exhibits the highest bonding energy, indicating its superior stability. Consequently, further analyses were conducted utilizing model (c).Table 2. Bonding energy parameters of different Er-3MR models
Upon determining the optimal structure, the energy levels and excitation-emission characteristics were assessed using the application of time-dependent density functional theory (TD-DFT) [28]. The parameters of the excited state for the local structural model of EDF are presented in Table 3. Eight excited states with wavelength of 1556.0, 954.1, 948.8, 779.7, 761.0, 745.6, 632.9, and 622.9 nm are observed, with corresponding oscillator strengths (f) of 0.0115, 0.0185, 0.0121, 0.0078, 0.0163, 0.0152, 0.0612, and 0.0112, respectively.
Table 3. Excited state parameters of Er-3MR
The determined oscillator strengths, in conjunction with the absorption peak positions, were broadened by Gaussian broadening to obtain the corresponding absorption spectra, as shown in Fig. 5(a). The absorption wavelengths are found to be at 631.6, 756.1, 951.4, and 1556.0 nm, respectively. This trend closely matches the experimentally tested EDF absorption spectra [29,30], although with a margin of error of approximately 20∼30 nm. This very phenomenon may be attributed to the more complex dopant materials and local structure of experimentally prepared fibers. However, theoretical calculations fail to entirely replicate these influential factors. By optimizing the relevant excited states, the emission spectra were obtained, as depicted in Fig. 5(b). The emission wavelength is observed at 1580.2 nm, with corresponding oscillator strengths (f) of 0.0184.
2.3 Local structural model of introducing stress
To explore the Er-3MR model response to stress, compressive and tensile stress were applied to the basis of model (c). According to Hooke's law, an object subjected to stress produced strain. Therefore, the strain produced by the Er-3MR model after stress was simulated by gradually altering the NBO bond length between Er3+ and the 3MR structure, as shown in Fig. 6(a). Compared to the initial value, the NBO bond length ranged from -1% (compressive strain) to +1% (tensile strain), involving increments of 0.2%. Besides, flexible scans were employed to adjust the bond length and optimize the structure, as shown in Fig. 6(b). After altering the bond length, a decrease in bonding energy is observed, indicating that the stability of the Er-3MR structure is compromised under stress conditions compared to its stress-free state.
Fig. 6. (a) NBO bond between Er3+ and 3MR structure; (b) Bonding energy of Er-3MR structure with strain ranging from -1% to +1%.
Figure 7(a) shows the trend of oscillator strength variation for each excited state concerning strain. Oscillator strength reflects the energy magnitude acquired by particles during transitions from the ground state to higher energy levels. Herein, with increasing tensile strain (indicative of ε values increase), the oscillator strengths of different excited states decrease. For instance, when the tensile strain increases from 0 to 1%, the oscillator strength of the excited state S0-S2 at around 950 nm decreases correspondingly from 0.0185 to 0.0182. This suggests that diminishing of the stimulated absorption of Er3+ from 4I15/2 energy level to 4I11/2 energy levels, which leads to a reduction in the number of electrons transitioning to 4I11/2 energy level. Conversely, as compressive strain increases (indicative of ε values decrease), the oscillator strengths of various excited states increase correspondingly. The trend of excitation energy variation for each excited state in relation to strain is shown in Fig. 7(b). The excitation energy denotes the energy level position of the respective excited state. Alterations in excitation energy led to the shifts of excitation energy levels of Er3+. Under tensile strain, the excitation energy decreases, resulting a redshift in the absorption peak. For instance, when the tensile strain increases from 0 to 1%, the excitation energy of the excited state S0-S2 at around 950 nm decreases from 1.2995 to 1.2989, resulting in a redshift of 0.7 nm in the absorption peak. Conversely, under compressive strain, the excitation energy increases, leading to a blueshift in the absorption peak.
Fig. 7. Variation trend for each excited state with strains from -1% to +1% of: (a) oscillator strength; (b) excitation energy.
The study also illustrated the intrinsic influence of stress on spectroscopic characteristics by depicting absorption and emission spectra under zero strain, ± 0.6% strain, and ±1% strain conditions, as shown in Fig. 8. Under tensile strain, the intensities of absorption peaks around 950 nm weaken, leading to a decrease in the oscillator strength of the emission peak from 0.0184 to 0.0177. Conversely, when subjected to compressive strain, an increase in the absorption peak intensity is observed, leading to an increase in the oscillator strength of the emission peak from 0.0184 to 0.0192. Additionally, the shift in wavelength of the absorption peak and emission peak with strain was presented, as indicated by the insets in Fig. 8(a) and Fig. 8(b), respectively, indicating a certain linear correlation between peak shift and stress. Under a tensile strain of +1%, the absorption peak exhibits a redshift at 950 nm of about 0.7 nm, and the emission peak exhibits a redshift at 1580 nm of approximately 3.0 nm.
Fig. 8. Spectral response to strain in EDF (a) Absorption spectra variations (the inset shows the shift in wavelength of the absorption peak with strain); (b) Emission spectra variations (the inset shows the shift in wavelength of the emission peak with strain).
Based on the calculated excited states levels and their corresponding oscillator strengths, the simplified energy level diagrams for zero strain and ±1% strain were established. The details are presented in Fig. 9, where excitation energy is plotted on the left axis, corresponding to excitation wavelength, while excitation intensity is indicated by oscillator strengths. Ground state absorption (GSA) is denoted by black arrow lines, non-radiative transition (NRT) by dashed lines with green arrows, and potential radiative transition (RT) by blue arrow lines, and solid blue lines show energy levels emitted by the local structure. The green circles represent the number of electrons. In simulation, the introduction of stress leads to a change in the length of the NBO bond between Er3+ and the silica network structure, which alters the oscillator strengths and excitation energies of each excited state of Er3+, affecting the GSA, NRT and RT in Er3+ energy levels. This explains the alterations in both the absorption and emission properties of EDF. Furthermore, the introduction of stress also impacts the emission bandwidth. Under conditions of zero strain, the emission bandwidth is approximately 24 nm, which measured approximately 18 nm under a tensile strain of +1% and approximately 33 nm under a compressive strain of -1%. This will affect the amplification characteristics and gain performance of EDF.
3. Experiments and discussions
3.1 Materials and preparation
To enhance the investigation of intrinsic influence of the stress upon the optical properties of Panda-type EDF, MCVD technology was used to fabricate erbium-doped preform. Then, EDF and PM-EDF were prepared using the same erbium-doped preform, and the elemental composition of EDF and PM-EDF was analyzed using an electron probe microanalyzer (Olympus Bx43, Japan) with point scanning. The dimensions and elemental composition of the fiber samples utilized were consolidated and presented in Table 4. Since they were prepared using the same core preforms, the fiber cores of EDF and PM-EDF shared identical elemental compositions, differing only slightly in element content.
Table 4. Dimensions and elemental concentrations of the fiber sample
Refractive index differences (RIDs) of the fibers were determined utilizing an optical fiber analyzer (S14, Photon Kinetics Inc., USA), as shown in Fig. 10. The RIDs between the core and cladding of the samples are 1.15% and 1.09%, respectively, while that between the B2O3-doped-silica SAPs and the cladding of PM-EDF is measured at 0.80%.
3.2 Absorption and luminescence properties
The absorption spectra of two fiber samples were determined through the cut-back method using a white source (Yokogawa AQ6315A, Japan), as shown in Fig. 11. Four absorption peaks of EDF are detected at approximately 650, 794, 975, and 1529 nm, involving associated absorption coefficients of 111.0, 22.7, 56.1, and 135.4 dB/m, respectively. These peaks correspond to the transitions from 4I15/2 ground state to 4F9/2, 4I9/2, 4I11/2, and 4I13/2 excited states of Er3+, respectively [29]. Meanwhile, the absorption spectrum of PM-EDF is similar to that of EDF, involving absorption coefficients of 99.6, 22.2, 54.3, and 126.8 dB/m at 652, 797, 977, and 1532 nm, respectively, which are 11.4, 0.5, 1.8, and 8.6 dB/m lower than absorption coefficients of EDF, respectively. Changes in absorption peak at 980 nm and 1530 nm are illustrated in Fig. 11(b) and Fig. 11 (c). The peak redshifts at 980 nm and 1530 nm measure approximately 2 nm and 3 nm, respectively.
Fig. 11. Comparative absorption spectra and peak shifts for EDF and PM-EDF with (a) Absorption spectra of EDF and PM-EDF; (b) Shifts of absorption peak at 980 nm; (c) Shifts of absorption peak at 1530 nm.
Additionally, absorption and emission cross-sections were calculated following McCumber equation [31]. The results are depicted in Fig. 12. The absorption cross-section of EDF is approximately 7.7 × 10−25 m2, whereas that of PM-EDF is approximately 7.4 × 10−25 m2, indicating a lower value compared to EDF. Similar outcomes were observed regarding emission cross-sections. The emission cross-sections of EDF and PM-EDF are approximately 7.7 × 10−25 m2 and 7.4 × 10−25 m2, respectively, and affect the absorption and emission efficiency of active fibers at the same time, also imposing a significant impact on the fluorescence intensity of EDF as well as the gain and gain bandwidth of erbium doped fiber amplifier (EDFA). Specifically, the absorption cross-section determines the efficiency of the pump light energy being absorbed by Er3+ ions. A decrease in the absorption cross-section leads to fewer Er3+ ions being excited to higher energy levels. The emission cross-section determines the efficiency of Er3+ ions in releasing energy upon returning to the ground state, which is directly related to the amplification efficiency of signal light. A reduction in the emission cross-section decreases the emission efficiency of Er3+ ions at the 4I13/2 energy level, leading to a reduction in gain of the EDFA.
Fig. 12. Spectral analysis of EDF with theoretical calculations for (a) Absorption cross-sections; (b) Emission cross-sections.
The photoluminescence (PL), PL excitation (PLE), and PL decay data were obtained using a fluorescence spectrometer (FLS-980, Edinburgh Instruments, UK). Fifty 5cm-coated EDF and PM-EDF samples were measured. The emission spectra of both EDF and PM-EDF, excited at 980 nm, correspond to the electronic transition of Er3+ from 4I11/2 energy levels to 4I15/2 energy levels, as shown in Fig. 13(a). EDF possesses strong emission intensity, consistent with the calculated emission cross-section result. Meanwhile, the emission spectrum exhibits a redshift in peak wavelength, with emission wavelengths of 1530 nm for EDF and 1533 nm for PM-EDF, respectively. In addition, after excitation at 980 nm, the fluorescence decay curves of EDF and PM-EDF were obtained at 4I13/2 level, as shown in Fig. 13(b). The fluorescence lifetime of PM-EDF is 9.99 ms, slightly shorter than the fluorescence lifetime of EDF of 10.20 ms. This reduction may be attributed to the internal stress introduced by SAPs. The variation in fluorescence lifetime caused by stress have also been reported in previous studies [32–34].
Fig. 13. Spectral analysis and lifetime measurements for EDF and PM-EDF (a)Excitation and emission spectra (b) Decay curves.
When both EDF and PM-EDF with identical core compositions were fabricated from the same erbium-doped preform, a decrease in peak intensity, and a redshift in peak wavelength were observed in the absorption, excitation, and emission spectra. It was thus hereby speculated that these findings were related to the introduction of SAPs in PM-EDF, which could be explained by previous theoretical analyses. The introduction of panda-type stress regions in PM-EDF caused tensile stress on the fiber core, resulting in an increase in the NBO bond length within the local structure model of EDF. This extension led to a reduction in the energy transition from the ground state 4I15/2 to the excited state 4I11/2, weakening the stimulated absorption intensity of Er3+, consequently diminishing the intensity of stimulated emission, and decreasing fluorescence lifetime. Simultaneously, the extension of bond length triggered changes in excitation energy, causing redshifts in energy levels, and thus resulting in shifts in the absorption and emission peak wavelength.
3.3 Amplification performance
To further analyze the optical performance of EDF and PM-EDF, their optical amplification was measured using a conventional forward-pumping system [29]. A 980 nm fiber laser device (LD) with an output power of 1200 mW served as the pump source. Optical signals with a power of -20 dBm were generated using a tunable laser source (TLS-710, Santec, Japan) with a linewidth of 100 kHz and a wavelength range of 1480-1640 nm. An isolator (ISO) was utilized to protect both the pump and the TLS, and a wavelength division multiplexer (WDM) combined and separated the pump wavelength and signal wavelength. Additionally, an optical spectrum analyzer (OSA) was employed to detect and calibrate the amplified signal light.
The fluorescence properties of EDF and PM-EDF were initially measured. Both EDF and PM-EDF with a length of 1 m presented good fluorescence properties in the E-band. The fluorescence intensity of 1500-1600 nm for EDF and PM-EDF is shown in Fig. 14(a). As shown in the figure, the fluorescence intensity of PM-EDF is lower than that of EDF, with a reduction of 4 dB in fluorescence intensity at 1530 nm, and the fluorescence peak shows a redshift of 1.2 nm, which is consistent with the conclusions of emission spectrum and fluorescence lifetime tests. Additionally, the full width at half maximum (FWHM) of the emission spectrum in PM-EDF has also decreased. Furthermore, the gain characteristics of EDF and PM-EDF were compared, as shown in Fig. 14(b). The gain bandwidths of EDF and PM-EDF exceeding 20 dB are 51 and 45 nm, respectively. In comparison to EDF, PM-EDF algorithm demonstrated a decrease in gain of around 4 dB overall, accompanied by a bandwidth reduction of approximately 13%. Comparing the fluorescence properties, gain, and gain bandwidth of EDF and PM-EDF, these observations further underscore the reduced excitation and emission efficiency of Er3+ in PM-EDF. This reduction decreases the number of electrons excited to higher energy levels, and diminishes the emission efficiency of Er3+ ions at the 4I13/2 energy level, leading to a decrease in the overall gain of the EDFA. Therefore, during the design and fabrication process of PM-EDF, it is necessary to maintain the required polarization property while optimizing the structure and dimensions of the stress region to reduce the influence of induced stress on the fiber core.
Fig. 14. Luminescence and gain spectra of EDF and PM-EDF (a) Luminescence spectra; (b) Gain spectra.
4. Conclusion
In this study, EDF and PM-EDF were fabricated by MCVD technology, based on the same erbium-doped preform. Finite element models and local structural models for EDF and PM-EDF were constructed. Simulations indicated that the introduction of Stress Applying Parts (SAPs) resulted in an increase in tensile stress of 1.54 × 107 Pa on the PM-EDF core. This stress led to microstructural alterations, including an elongation of the NBO bond length, which in turn caused a decrease in both the excitation and emission intensities of EDF, as well as a redshift in the absorption and emission peaks. Experimentally, PM-EDF, with an identical core composition to EDF, displayed a decreased absorption coefficient and redshifted absorption peaks by approximately 2 nm. The fluorescence intensity was also reduced, with the fluorescence peak at 1530 nm undergoing a redshift of about 1.2 nm. The fluorescence lifetime of PM-EDF shortened to 9.99 ms. These findings are consistent with the theoretical simulation results of tensile stress-affected EDF. Moreover, the total gain of PM-EDF was reduced by about 4 dB, and its bandwidth was decreased by around 13%. This analysis and verification of the stress's intrinsic influence on the optical properties and amplification performance of Panda-type erbium-doped fibers offer valuable insights for the development of high-performance PM-EDFs.
Funding
National Natural Science Foundation of China (61935002); 111 Project (D20031).
Acknowledgments
We appreciate the High Performance Computing Center of Shanghai University for the use of computer resources, and Shanghai Engineering Research Center of Intelligent Computing System. (No. 19DZ2252600)
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.
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