Quantitative analysis of optical power budget of bismuth oxide-based erbium-doped fiber

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1 Journal of Luminescence 128 (28) Quantitative analysis of optical power budget of bismuth oxide-based erbium-doped fiber Hideaki Hayashi a,b,, Setsuhisa Tanabe a, Naoki Sugimoto b a Graduate School of Human and Environmental Studies, Kyoto University, Yoshida nihonmatsu-cho, Sakyo-ku, Kyoto , Japan b Research Center, Asahi Glass Co., Ltd., 115 Hazawa-cho, Kanagawa-ku, Yokohama , Japan Received 6 May 27; accepted 9 August 27 Abstract We investigated optical power budget of Bi 2 O 3 -based erbium-doped fiber (BIEDF). Lateral spontaneous emissions and scattering laser powers in the BIEDF were measured quantitatively by using an integrating sphere. Compared with the power of amplified spontaneous emission and signal detected at the output fiber end, it was found that considerable powers were consumed by the laterally emitting lights. As an optically undetected loss limits power conversion efficiency (PCE) of the fiber amplifier, the effect of nonradiative decay from the termination level of pump excited state absorption (pump ESA) was estimated from decay rate analyses of the relevant levels. The nonradiative loss was comparable to amplified signal power in the BIEDF when pumped with a 98-nm LD. Nonradiative decay following cooperative upconversion (CUP) process is also discussed using rate equations analysis. r 27 Elsevier B.V. All rights reserved. PACS codes: e; q; 42.7.Ce Keywords: Erbium-doped fiber; Bismuth oxide; Lateral emissions; Integrating sphere; Excited state absorption; Cooperative upconversion 1. Introduction Optical amplifiers for wavelength division multiplexing (WDM) network system have been developed with exponential increase of information capacity [1]. As a practical amplification medium, erbium-doped fibers (EDFs) have been extensively studied due to their excellent gain operation around 1.5 mm in the loss minimum window of a transmission silica fiber [2]. Silica-based EDFs have been installed in the actual optical network system and practically played a critical role. However, their power conversion efficiency (PCE) is limited to 5 55% when pumped with 98-nm laser diode (LD) at present (i.e. ER- 19 amplifier by Sumitomo Electric Industries, Ltd., or HP98 amplifier by OFS). Although the PCE is one of the most important factors for the amplifier design, it is not Corresponding author. Research Center, Asahi Glass Co., Ltd., 115 Hazawa-cho, Kanagawa-ku, Yokohama , Japan. Tel.: ; fax: address: hideaki-hayasi@agc.co.jp (H. Hayashi). perfectly understood what limits the PCE in the EDFs. Fig. 1 shows the 4f energy level diagram of Er 3+ ion and the transitions that are measured or discussed in this paper. In addition to basic amplification properties or loss origins such as background losses and splice losses, the losses that are related to amplified spontaneous emission () [3,4], excited state absorption (ESA) [5], and cooperative upconversion (CUP) [6] have been examined in detail. However, except for these emissions or loss origins which can be evaluated at the output end of the fiber, considerable optical power budget of the EDFs is not clear. For example, lateral spontaneous emission of 155-nm band has not ever been evaluated quantitatively, although there is a report that the lateral emission spectra have been measured to calculate the cross-section [7]. In order to optimize the PCE and amplifier performance, understanding of overall optical power budget of the EDFs is essential. In this study, we construct a novel evaluation system for measuring lateral emissions from the EDF by using an integrating sphere. We used a Bi 2 O 3 -based EDF (BIEDF) /$ - see front matter r 27 Elsevier B.V. All rights reserved. doi:1.116/j.jlumin

2 334 H. Hayashi et al. / Journal of Luminescence 128 (28) Energy (h1 3 cm -1 ) GSA ESA 98 nm 55 nm-se 155nm- SE for the evaluation due to its potential for high-performance amplifier [8 11]. The lateral emissions such as spontaneous emission, upconversion emission around 55 nm, scattering light of LD, and the scattering light of signal or were measured quantitatively as well as the in-situ data results of the gain properties as a fiber amplifier. A 98-nm LD was used for the pumping of the BIEDF. The variations of the lateral emissions with signal wavelength, signal power, or pump power were investigated. In addition, we estimated the effect of other nonradiative decay processes that follow pump excited state absorption (pump ESA) and the CUP. To investigate the nonradiative decay from the termination level of the pump ESA, the luminescence decay of the 55- nm band was measured. The effect of the CUP is then discussed theoretically using rate equations and optical propagation equations. Finally, we present the optical power budget of the BIEDF. 2. Experimental procedure 2.1. Preparation of BIEDF Signal Er 3+ CUP Amp. Sig. 4 F 7/2 2 H 11/2 4 S 3/2 4 I 15/2 The glass preform containing Bi 2 O 3 and SiO 2 as main constituents was prepared using a conventional melting method. For the fiber core composition,.5 mol% of Er 2 O 3 was added to the glass batch. Single-mode EDF (cladding diameter of 125 mm) with plastic coatings was then fabricated. The core diameter of the BIEDF was 3.9 mm. The refractive index of the core and the numerical aperture (NA) of the fiber at 155 nm were 2.3 and.2, respectively. A BIEDF of 16 cm length was fusion-spliced to high-na silica fibers (i.e. Nufern 98HP) using a commercial fusion-splicer. The insertion loss of the spliced BIEDF at 131 nm was.61 db. By using a cutback method, the propagation loss of the BIEDF at 131 nm was estimated to be.77 db/m. Accordingly, the average NR 4 F 9/2 4 I 9/2 4 I 11/2 4 I 13/2 Fig. 1. The 4f energy diagram of Er 3+ ion and the relevant transitions. A 98-nm LD was used for pumping. GSA, ground state absorption; ESA, excited state absorption; Amp. Sig., amplified signal;, amplified spontaneous emission; 155 nm-se, 155-nm band spontaneous emission; 55 nm-se, 55-nm band spontaneous emission; CUP, cooperative upconversion; NR, nonradiative decay. splice loss per point was estimated to be.24 db. Angled cleaving and splicing were applied to suppress the reflection due to the large difference of refractive indices between the BIEDF and the silica fibers [1]. It was confirmed that pigtailed BIEDFs passed Bellcore (Telcordia) GR-1221 CORE qualification test [12] Lateral emission measurement of BIEDF Experimental setup for evaluating the lateral and fiberpropagating emission powers is shown in Fig. 2. The BIEDF of 16 cm length was coiled with 6 cm diameter and set in an integrating sphere (1 in.: Model LMS-1s, Labsphere Inc.). The input and output ends of high-na silica fibers were connected with instruments through small hole (5 mm diameter) of the integrating sphere. The splice points were set just outside of the sphere. It was then pumped with an LD (FITEL) in the forward direction at the wavelength of 98 nm. The pump power and temperature of the LD were controlled with an LD-driver (Model 525, Newport Corp.) and a temperature-controller (Model 325, Newport Corp.), respectively. A tunable laser (Model TLS21, Santec Corp.) was used for a singlechannel signal source, and then the pump light and the signal light were coupled using a WDM coupler/isolator (WDM/ISO). The spontaneous emissions and scattering lights laterally emitted from the BIEDF were detected with two kinds of fiber multichannel CCDs with Si and InGaAs detectors. Each CCD coupled proprietary spectrometer. The maximum wavelength ranges of the visible spectrometer (Model USB-2, Ocean Optics Inc.) and the nearinfrared spectrometer (Model NIR-512, Ocean Optics Inc.) were 35 1 nm and 9 17 nm, respectively. A premium-grade fiber with 1-mm core (Model QP1-2-VIS/NIR, Ocean Optics Inc.) was used to link the CCD and the output port of the sphere. For the spectral calibration, a standard halogen lamp (Model SCL-6, Labsphere Inc.) was used. The lamp was set at the center of the sphere and driven at 2.6 A with a current-regulated dc stabilized power supply (Model PAN-5A, Kikusui Electronics Corp.). The absolute power of total radiant flux of lateral emissions was then calculated. At the same time, the output spectra of fiber-propagating signal and were detected with an optical spectrum analyzer (OSA; Model MS978A, Anritsu Corp.) with 1-nm resolution. Signal source Pump LD OSA WDM /ISO Integrating sphere BIEDF Device Under Test Splice point CCD/ Spectrometer Fig. 2. Experimental setup for evaluating the lateral and fiber-propagating emission powers of the BIEDF. Basically, the splice points were set outside of the integrating sphere. PC

3 H. Hayashi et al. / Journal of Luminescence 128 (28) First, we measured the spectral power distribution of various emissions. The pump power, the input signal power, and the signal wavelength dependences of the emissions were then investigated Lifetime measurement To analyze the effect of the nonradiative decay from the termination level of the pump ESA, luminescence decay of 55-nm band was measured, and then the quantum efficiency of the Er 3+ : 4 S 3/2 level was calculated from the measured lifetime [13]. Second harmonic of Nd:YVO 4 laser at 532 nm (Model J8-H1-532QW, Spectra-Physics Inc.) was used as a pump source. The pump power was adjusted to 1 W, and the pump light that was modulated into pulses (repetition: 15, Hz, pulse width: 13 ns) was incident on the optically polished Er-doped Bi 2 O 3 -based glass sample ( mm in size). The luminescence of 55-nm band of the glass sample was monochromated (Model 1681B, Spex) and detected with a photomultiplier (Model 1424M, Spex) to which.8 kv of voltage was applied. The signal was collected using a sampling oscilloscope (5 MHz, Model TDS52, Tectronix Corp.), and the lifetime was determined by least-square fitting of the obtained decay curve with exponential functions Calculation of CUP process We can estimate the effect of the CUP process using the rate equations analysis. Fig. 3 shows the 4f energy level diagram of Er 3+ ions and transitions used for the analysis. When a BIEDF is pumped with a 98-nm LD, the time dependence of populations can be expressed as follows [2,14,15]: dn 1 dt Energy (x1 3 cm -1 ) ¼ðA 21 þ R 21 þ W 21 ÞN 2 ðr 13 þ R 12 ÞN 1 þ CN þ R 31 N 3 þ A 41 N 4, N 4 N 3 N 2 N 1 R 34 R 13 R 31 A 41 A 21 R 12 R 21 Er 3+ Amp. Sig. 4 F 7/2 4 I 9/2 ð1þ 2 H 11/2 4 S 3/2 4 F 9/2 4 I 11/2 4 I 13/2 4 I 15/2 Fig. 3. The 4f energy diagram of Er 3+ ion and the transitions used for the rate equations analysis. C W 43 W 32 W 21 dn 2 dt dn 3 dt ¼ ða 21 þ R 21 þ W 21 ÞN 2 þ R 12 N 1 þ W 32 N 3 2CN 2 2, (2) ¼ R 13 N 1 ðw 32 þ R 34 þ R 31 ÞN 3 þ W 43 N 4 þ CN 2 2, (3) dn 4 ¼ ða 41 þ W 43 ÞN 4 þ R 34 N 3, (4) dt where N 1, N 2, N 3, and N 4 represent the population of the 4 I 15/2, 4 I 13/2, 4 I 11/2, and 4 F 7/2 levels, respectively. For simplicity, we neglected the intermediate levels between the 4 I 11/2 and the 4 F 7/2 levels, and assumed that all the photons pumped at the 4 F 7/2 level via the pump ESA transit nonradiatively to the 4 S 3/2 level. Total Er 3+ ion number density for the calculation is given by N=N 1 +N 2 +N 3 +N 4, and set to m 3, which corresponded to.5 mol% of Er 2 O 3. R 21, R 12, R 31, R 13, and R 34 are radiative transition rates between these levels that are calculated from absorption and emission cross-sections (s e s, sa s, se p, sa p, and s ESA, respectively). A 21 and A 41 represent spontaneous emission probabilities that are calculated by the Judd Ofelt analysis. Nonradiative transition probability, W 43, is calculated in the way described in Section W 21 and W 32 can be also estimated from the lifetime measurements of the bulk glasses in the same way as described in Section 2.3. The fiber length and the NA were set to 16 cm and.2, respectively. C represents the CUP coefficient. Here we assumed homogeneous distribution of Er 3+ ions in the glass and homogeneous upconversion process [6,16 18]. Mode field diameters at 98 nm and at 153 nm were set to 4.2 and 6.3 mm, respectively. The signal and pump lightwaves propagating along the fiber in forward direction (I s and I p ) are expressed as the following set of ordinary differential equations [2,14,15]: di s dz ¼ðse s N 2 s a s N 1ÞG s I s a s I s, (5) di p dz ¼ ðsa p N 1 s e p N 3 þ s ESA N 3 ÞG p I p a p I p, (6) where G s and G p are the overlap factors at the signal wavelength and pumping wavelength, respectively. a s and a p are the parameters that represent the intrinsic fiber background loss at the signal and pumping wavelength, respectively. Here we assumed that the a s was identical to a p, and treated them as fitting parameters. We applied the Quimby s assumption that s ESA is equal to 2s a p [19]. Although spontaneous decay was accounted for, the was neglected since the input signal power was sufficiently large ( dbm) and the fiber length was sufficiently short. Splice loss from the BIEDF to high-na silica fiber was set to.24 db/point. Assuming a steady-state condition (the time derivatives to be zero), the set of differential equations was numerically

4 336 H. Hayashi et al. / Journal of Luminescence 128 (28) Table 1 Parameters used for numerical calculations Parameter Symbol Value Unit Spontaneous emission rate A s 1 A s 1 Nonradiative decay rate W s 1 W 32 33, s 1 W 43 37, s 1 Signal emission cross-section at s e s m nm Signal absorption cross-section at s a s m nm Pump emission cross-section at 98 nm s e p m 2 Pump absorption cross-section at s a p m 2 98 nm Overlap factor at 98 nm G s.82 Overlap factor at 153 nm G p.52 Er 3+ ion density N m 3 Cooperative upconversion coefficient C Fitting m 3 /s parameter Background loss a Fitting parameter integrated using the fourth-order Runge Kutta method with an initial condition at the input end of the fiber (z ¼ m). The parameters used for numerical calculations are shown in Table 1. Input signal and launched pump powers were set to 1 mw ( dbm) and 1 mw, respectively. By using these calculations, we obtained the relationship between the output signal power and the CUP coefficient. 3. Results 3.1. Spectral power distribution First, we show absolute power spectrum of lateral emissions and output emissions from the fiber end (Fig. 4). The ordinate represents spectral power distribution of radiant flux. The upconversion emission around 52 nm ( 2 H 11/2-4 I 15/2 ) and 55 nm ( 4 S 3/2-4 I 15/2 ), the scattering light of LD around 98 nm, the spontaneous emission of 155-nm band, and the were detected with two kinds of multichannel CCDs that were connected with the integrating sphere. We can also see weak emission around 66 nm that is related to the pump ESA process. The spectral shapes of the upconversion emission and the 155- nm band spontaneous emission were approximately identical to those in bulk glass. When 1 mw of pump power and dbm of signal power at 153 nm were used as input, the optical powers of the upconversion emission, the LD scattering, and the 155-nm band spontaneous emission were.2,.2, and 3.1 mw, respectively. Here the splice points were set outside of the integrating sphere. In the case that the splice points were set inside of the sphere, the scattering of the pump LD was increased to 4.3 mw, and 1.8 mw of the scattering light of the amplified signal was detected by the CCD. The optical powers of amplified Spectral power distribution (μw/nm) nm -SE 98nm -Scat Wavelength (nm) signal at 153 nm and band that detected were by the OSA were 11.9 and.2 mw, respectively Signal wavelength dependence Amp.Sig. 155nm -SE Fig. 4. Absolute intensity spectra of various lateral emissions and amplified signal from the BIEDF. Launched pump and input signal power were 1 mw and dbm, respectively. The splice points of the BIEDF were set outside of the integrating sphere. 55 nm-se, 55-nm band spontaneous emission; 98 nm-scat., scattering light of the LD at 98 nm; 155 nm-se, 155-nm band spontaneous emission; Amp. Sig., amplified signal at 153 nm;, amplified spontaneous emission. Optical power (μw) Amp.Sig. 55nm-SE 98nm-Scat. 155nm-SE Wavelength (nm) Fig. 5. Signal wavelength dependence of optical powers of various emissions in the BIEDF. Launched pump and input signal power were 1 mw and dbm, respectively. The splice points of the BIEDF were set outside of the integrating sphere. 55 nm-se, 55-nm band spontaneous emission; 98 nm-scat., scattering light of the LD at 98 nm; 155 nm-se, 155-nm band spontaneous emission; Amp. Sig., amplified signal;, amplified spontaneous emission. Fig. 5 shows the signal wavelength dependences of the optical powers of the lateral emissions and the fiberpropagating emissions. The launched power of the pump LD at 98 nm was fixed to 1 mw. Input signal power was set to dbm. The right axis in the figure shows the gain of the output signal (square plots, unit: db). In the wavelength range from 153 to 156 nm which corresponds to C-band, 1-1 Signal gain (db)

5 H. Hayashi et al. / Journal of Luminescence 128 (28) we can see that the signal gains more than 1 db were obtained with the BIEDF of only 16 cm length. The optical power of the 155-nm band spontaneous emission was larger than that of the in the entire C-band region. As for the, the spontaneous emission of 155-nm band, and the scattering light of the 98-nm LD, the optical powers of their emissions showed negative correlations with that of the amplified signal at measured wavelengths. The correlation of the was the strongest in these emissions. On the other hand, the optical power of the upconversion emission around 55 nm showed weak positive correlation. Optical power (µw) Amp.Sig. 55nm-SE 98nm-Scat. 155nm-SE 3.3. Signal power dependence The signal power dependences of the optical powers of various emissions are shown in Fig. 6. The launched pump power was set to 1 mw, and input signal wavelength was fixed at 153 nm. The, the spontaneous emission of 155-nm band, and the scattering light of the 98-nm LD decreased with the increase of the input signal power. Even in the small signal region, the lateral emission power was larger than the at the same 155-nm band. On the other hand, the upconversion emission around 55 nm increased with the input signal power. The lateral 155-nm spontaneous emission was larger than the amplified signal when the input signal power was smaller than 2 dbm Excitation power (mw) Fig. 7. Pump power dependence of optical powers of various emissions in the BIEDF. Input signal power was dbm. The splice points of the BIEDF were set outside of the integrating sphere. 55 nm-se, 55-nm band spontaneous emission; 98 nm-scat., scattering light of the LD at 98 nm; 155 nm-se, 155-nm band spontaneous emission; Amp. Sig., amplified signal;, amplified spontaneous emission. Excitation: 532 nm Monitering: 55 nm 3.4. Pump power dependence Fig. 7 shows the pump power dependence of the optical powers of various emissions. All the emission species increased with the pump power, and the dependence of the upconversion emission around 55 nm was nearly 2. The Intensity (arb. unit) τ f =2.7 μs Time (s) [x1-5 ] Optical power (μw) Amp.Sig. 55nm-SE 98nm-Scat. 155nm-SE Fig. 8. Luminescence decay curve of the Er 3+ : 4 S 3/2 level in the Bi 2 O 3 - based glass. Circle plots represent measured data, and solid line represents single exponential fitting of these data. lateral 155-nm spontaneous emission power was larger than the amplified signal when the pump power was smaller than 6 mw. The pump power dependence of the 155 nm emission was small and almost saturated under the pump power of larger than 6 mw Input signal power (dbm) 3.5. Fluorescence lifetime Fig. 6. Input signal power dependence of optical powers of various emissions in the BIEDF. Launched pump power was 1 mw. The splice points of the BIEDF were set outside of the integrating sphere. 55 nm-se, 55-nm band spontaneous emission; 98 nm-scat., scattering light of the LD at 98 nm; 155 nm-se, 155-nm band spontaneous emission; Amp. Sig., amplified signal;, amplified spontaneous emission. Measured luminescence decay curve of 55-nm band ( 4 S 3/2-4 I 15/2 ) is shown in Fig. 8. Sharp peak that can be observed near zero of the decay time must be the scattering of pump LD, because the monitoring wavelength is relatively close to the pumping one. After excluding the

6 338 H. Hayashi et al. / Journal of Luminescence 128 (28) LD scattering, the lifetime of the 4 S 3/2 level was determined to be 2.7 ms by using single exponential function. 4. Discussion 4.1. Lateral emissions from BIEDF When the splice points were set outside of the integrating sphere, the sum of emission powers detected by the OSA and the CCDs were 12.1 and 3.5 mw, respectively. On the other hand, when the splice points were set inside of the sphere, the optical powers of the LD and signal scattering lights increased. The differences should represent the scatterings at the splice points. In this case, the LD and signal scattering lights at the splice points result in 4.1 and 1.8 mw, respectively. The pump power dependence of the upconversion emission in Fig. 7 obeyed quadratic law. This means that the emission occurs as a result of the pump ESA or the CUP, each of which is due to a two-photon process. The optical powers of the upconversion emission showed the positive correlations with that of the amplified signal at measured input signal wavelengths (see Fig. 5). In other words, the upconversion emission power was large at the wavelength at which the output signal power was large. This suggests that the upconversion emission is promoted by the signal photons. In addition to the pump ESA, signal ESA using the signal photons can also occur. The initial level of upconversion emission, 4 S 3/2, can be promoted by the signal photons through ESA. It can be said from the above correlation that the effect of the input or output signal wavelength on the signal ESA process is smaller than that of the output signal power. As shown in Fig. 6, the upconversion emission showed the positive correlation with increasing the input signal power. The result also suggests the existence of the signal ESA process using the input and amplified signal photons, because the output signal power of a fiber amplifier increases with the input signal power. On the other hand, the lateral emissions other than the upconversion emission showed the negative correlations with the amplified signal (see Fig. 5). This indicates that more powers are consumed for the output signal power in the C-band by lowering the lateral powers in vain, which is desirable as a fiber amplifier Other origins of loss Other than the lateral emissions described above, various nonradiative decay processes can be considered: deactivation by hydroxyl group in glass, nonradiative decay which is related to the pump ESA, the decay which is related to the CUP, and the multiphonon relaxation from the 4 I 11/2 level. Among these origins, the effect of hydroxyl groups was neglected here because this BIEDF was sufficiently dehydrated during the fabricating process [14] Pump ESA process First, we discuss decay from the 4 S 3/2 level as a result of the pump ESA process. For simplicity, we assumed that all the photons that were excited to the 4 F 7/2 levels relax nonradiatively to the 4 S 3/2 level. This assumption will be valid because the energy gap between the 4 F 7/2 and the 4 S 3/2 is narrow (75 cm 1 ) [2]. The quantum efficiency of an emission, Z, is generally written as follows: Z ¼ A t f ¼ A A þ W, (7) where A is the spontaneous emission probability, W is the nonradiative transition probability, and t f is the fluorescence lifetime. We calculated the A coefficient from the Judd Ofelt analysis (31 s 1 ) [21 23]. Accordingly, the quantum efficiency was estimated to be.8%. The nonradiative energy loss from the 4 S 3/2 level to the 4 I 11/2 level (unit: W), P NR ( 4 S 3/2-4 I 11/2 ), can be then expressed as follows: P NR ð 4 S 3=2! 4 I 11=2 Þ¼ P Rð 4 S 3=2! 4 I 15=2 Þ Z DEð4 S 3=2! 4 I 11=2 Þ DEð 4 S 3=2! 4 I 15=2 Þ, ð8þ where P R ( 4 S 3/2-4 I 15/2 ) is the upconversion emission power, DE is the energy gap between two 4f levels. The nonradiative energy loss from the 4 I 11/2 level to the 4 I 13/2 level, P NR ( 4 I 11/2-4 I 13/2 ), can be considered separately. P NR ð 4 I 11=2! 4 I 13=2 Þ¼½P L fp R ð 4 S 3=2! 4 I 15=2 Þ þ P NR ð 4 S 3=2! 4 I 11=2 Þg P R ð 4 I 11=2! 4 I 15=2 ÞŠ DEð4 I 11=2! 4 I 13=2 Þ DEð 4 I 11=2! 4. ð9þ I 15=2 Þ Here P L is the launched pump power and P R ( 4 I 11/2-4 I 15/2 ) is the optical power of 1-nm emission band. By using these expressions described above, P NR ( 4 S 3/2-4 I 11/2 ) and P NR ( 4 I 11/2-4 I 13/2 ) were calculated to be 13 and 31 mw, respectively. Although the visible upconversion luminescence power was only.2 mw, we have to count the nonradiative decay from the 4 S 3/2 level due to low Z Cooperative upconversion process Next, we estimate the effect of the CUP using the rate equations analysis as described in Section 2.4. Fig. 9 shows the variation of calculated output signal with the CUP coefficients. The difference between the output power at a given CUP coefficient and the output at zero of the coefficient (value at y-intercept) represents energy loss via the CUP process. The calculations were performed for three values of a. For any a, the output power decreased exponentially with the increase of the CUP coefficient. Snoeks et al. reported that the value of the CUP coefficient was m 3 /s in a soda lime silicate glass

7 H. Hayashi et al. / Journal of Luminescence 128 (28) Output power (mw) Soda lime silicate CUP coefficient (m 3 /s) [x1-23 ] that was doped with m 3 of Er 3+ ions [18]. When we assume that the CUP coefficient of the BIEDF ( m 3 of Er 3+ ion number density) is same as that of the soda lime silicate, the curve of a ¼ 4 seems reasonable. In this case, the effect of the CUP process results in approximately 1 mw. If we decrease the Er concentration in glass, the CUP will be reduced because the CUP coefficient is a function of the Er 3+ ion density [24] Energy budget of BIEDF α = α = 4 α = 8 Fig. 9. Variation of signal output power with the CUP coefficient in the BIEDF doped with m 3 of Er 3+ ions. Plots represent calculation data, and solid lines are exponential fitting of these data. Dashed line represents literature value for a soda lime silicate glass doped with m 3 of Er 3+ ions (C ¼ m 3 /s) [18]. Table 2 Energy budget of the BIEDF when pumped with 1 mw of launched power Emission species and source of loss Value (mw) Amplified signal 12 Insertion loss (splice loss+background loss) nm LD scattering (at splice point) nm LD scattering (w/o splice point).2 Signal scattering (at splice point) 1.8 Amplified spontaneous emission nm band spontaneous emission nm band upconversion emission.2 Nonradiative decay from the 4 S 3/2 to the 4 I 11/2 13 Nonradiative decay from the 4 I 11/2 to the 4 I 13/2 31 Nonradiative decay following CUP Approximately 1 Unidentified Approximately 11 Launched pump power: 1 mw; input signal power: 1 mw. The optical power budget of the BIEDF that has been clarified in this paper is shown in Table 2. Here the launched pump power and the input signal power were 1 and 1 mw ( dbm), respectively. The insertion loss of.61 db corresponds to 13.1 mw. The output signal power at 153 nm and the sum of lateral emissions and scattering powers were 11.9 and 9.4 mw, respectively. It can be said that considerable powers were consumed by the lateral emissions and scatterings in the BIEDF. Taking into account the output signal, the, the lateral emissions, and the insertion loss, 65% of total power (65 mw) was not detected either by the CCDs or the OSA. The power of the nonradiative decay from the termination level of the pump ESA to the 4 I 11/2 level was estimated to be 13 mw and that from the 4 I 11/2 level to the 4 I 13/2 level was 31 mw. Approximately 1 mw can be attributed to the nonradiative decay following the CUP. We can say that nonradiative decays above also affect the decrease of the PCE in the BIEDF. Even counting all sources of loss described above, however, we could not identify approximately 11% of total launched power. A possible reason is that we underestimate nonradiative losses at present. For precise estimation of the pump ESA effect, high measurement accuracy of very weak upconversion luminescence is necessary. For the CUP effect, we will have to consider the clustering of the Er 3+ ions and resulting pair-induced quenching [16,25,26]. 5. Conclusions We have analyzed optical power budget of Bi 2 O 3 -based erbium-doped fiber (BIEDF). Lateral spontaneous emissions and scattering laser powers in the BIEDF were evaluated quantitatively by using an integrating sphere. Comparing with amplified signal, it was clarified that considerable power was consumed by the laterally emitting lights (9% for the launched pump power). While the LD scattering, the signal scattering, and the 155-nm band emission powers decreased with increasing input signal power, the lateral 55-nm emission power increased with increasing the input signal power. In the same way, among the lateral emissions, only the 55-nm band showed positive correlation with that of the output signal at measured wavelengths in the C-band. These results suggested that the upconversion emission is promoted by the signal ESA. As a result of decay rate analysis, it was revealed that the nonradiative power loss related to the pump excited state absorption (pump ESA) was comparable with the output signal power (13% for the pump power) because the quantum efficiency of the initial level of the upconversion emission is only.8%. In addition, as a result of rate equations analysis, it was suggested that the effect of nonradiative decay following the cooperative upconversion (CUP) is not negligible when Er 3+ ion density is in the order of 1 26 m 3 (approximately 1% for the pump power). The analyses performed in this paper can be applicable for not only a BIEDF but also commercial silica-based EDFs whose power conversion efficiency (PCE) is usually limited to 5 55% and other rare-earth-doped amplifiers or lasers. The measurement system using an integrating sphere is also useful to analyze the lateral emission from

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