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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 17 — Aug. 13, 2012
  • pp: 18803–18818
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High-energy, in-band pumped erbium doped fiber amplifiers

Ee-Leong Lim, Shaif-ul Alam, and David J. Richardson  »View Author Affiliations


Optics Express, Vol. 20, Issue 17, pp. 18803-18818 (2012)
http://dx.doi.org/10.1364/OE.20.018803


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Abstract

We have demonstrated and compared high-energy, in-band pumped erbium doped fiber amplifiers operating at 1562.5 nm under both a core pumping scheme (CRS) and a cladding pumping scheme (CLS). The CRS/CLS sources generated smooth, single-peak pulses with maximum pulse energies of ~1.53/1.50 mJ, and corresponding pulse widths of ~176/182 ns respectively, with an M2 of ~1.6 in both cases. However, the conversion efficiency for the CLS was >1.5 times higher than the equivalent CRS variant operating at the same pulse energy due to the lower pump intensity in the CLS that mitigates the detrimental effects of ion concentration quenching. With a longer fiber length in a CLS implementation a pulse energy of ~2.6 mJ is demonstrated with a corresponding M2 of ~4.2. Using numerical simulations we explain that the saturation of pulse energy observed in our experiments is due to saturation of the pump absorption.

© 2012 OSA

1. Introduction

Eye safe, high energy erbium based 1.55 μm pulsed sources are highly desirable for many practical applications such as remote sensing where light scattering from targets gives rise to eye-safety concerns. Furthermore, due to the availability of telecom grade components, the system functionality and cost of 1.55 μm pulsed fiber lasers is expected, in the short term at least, to be more attractive than thulium based 1.90 μm eye-safe pulsed variants.

Recently, in-band pumped (also known as resonantly-pumped or tandem-pumped) erbium doped fiber amplifiers (IP-EDFAs) have attracted considerable interest as a potential approach to address the low-efficiency commonly found in 980 nm pumped EDFAs and 9xx nm pumped Er/Yb co-doped fiber (EYDF) amplifiers. In particular, optical-to-optical conversion efficiencies of ~69% and ~80% have been demonstrated in cladding- and core-pumped implementations respectively [5

5. J. Zhang, V. Fromzel, and M. Dubinskii, “Resonantly cladding-pumped Yb-free Er-doped LMA fiber laser with record high power and efficiency,” Opt. Express 19(6), 5574–5578 (2011). [CrossRef] [PubMed]

, 6

6. E. L. Lim, S. Alam, and D. J. Richardson, “Highly efficient, high power, inband-pumped Erbium/Ytterbium-codoped fiber laser,” CLEO (2011).

]. However, it has been found that the conversion efficiency can be impaired by concentration quenching effects in higher erbium concentration fibers [7

7. E. L. Lim, S. U. Alam, and D. J. Richardson, “Optimizing the pumping configuration for the power scaling of in-band pumped erbium doped fiber amplifiers,” Opt. Express 20(13), 13886–13895 (2012). [CrossRef] [PubMed]

]. The use of a CRS is particularly attractive for pulsed amplifiers since it allows for lower doping concentrations (which helps reduce concentration quenching effects) and also provides for shorter pump absorption lengths - resulting in an inherently shorter device and thus reduced effective nonlinear lengths [8

8. J. C. Jasapara, M. J. Andrejco, A. DeSantolo, A. D. Yablon, Z. Varallyay, J. W. Nicholson, J. M. Fini, D. J. DiGiovanni, C. Headley, E. Monberg, and F. V. DiMarcello, “Diffraction-limited fundamental mode operation of core-pumped very-large-mode-area Er fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 3–11 (2009). [CrossRef]

].

The IP-EDFA is also attractive as a pulse amplifier for high pulse energy extraction applications. In such systems, the maximum extractable energy is typically limited by the maximum stored energy of the active fiber before self-saturation by amplified spontaneous emission (ASE), or spurious lasing set in. The extent of ASE buildup depends on the level of backscattered light due to reflection at the fiber facets as well as Rayleigh back-scattering (RBS). While the fiber facet reflection can be managed by the use of an end-cap, the RBS can only be reduced by using a doped fiber with a lower core numerical aperture (NA) since the fraction of RBS captured back into the guided mode is proportional to NA2 [9

9. N. A. Brilliant, R. J. Beach, A. D. Drobshoff, and S. A. Payne, “Narrow-line ytterbium fiber master-oscillator power amplifier,” J. Opt. Soc. Am. B 19(5), 981–991 (2002). [CrossRef]

]. A typical ytterbium-sensitized EDF has a ~0.22 core NA, due to the phosphorous-doping required for efficient pump energy transfer. In comparison, the IP-EDFA permits the use of pure erbium doped fiber, where an NA as low as ~0.066 has been demonstrated in an index guided fiber [10

10. D. Taverner, D. J. Richardson, L. Dong, J. E. Caplen, K. Williams, and R. V. Penty, “158-µJ pulses from a single-transverse-mode, large-mode-area erbium-doped fiber amplifier,” Opt. Lett. 22(6), 378–380 (1997). [CrossRef] [PubMed]

] or <0.04 in a photonic crystal fiber [11

11. V. Kuhn, D. Kracht, J. Neumann, and P. Wessels, “Er-doped photonic crystal fiber amplifier with 70 W of output power,” Opt. Lett. 36(16), 3030–3032 (2011). [CrossRef] [PubMed]

]. Therefore, the pure-erbium doped fiber can potentially reduce RBS by >14 dB, i.e. (0.22/0.04)2≈30.25, compared to EYDF-based systems. Meanwhile, the absence of ytterbium in pure erbium doped fiber completely eliminates the possibility of ytterbium co-lasing [12

12. Y. Jeong, S. Yoo, C. A. Codemard, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, P. W. Turner, L. Hickey, A. Harker, M. Lovelady, and A. Piper, “Erbium: Ytterbium codoped large-core fiber laser with 297-W continuous-wave output power,” IEEE J. Sel. Top. Quantum Electron. 13(3), 573–579 (2007). [CrossRef]

], which can be difficult to manage, especially in a low repetition rate system. The use of low NA fiber also reduces the number of guided modes and improves the output beam quality for a given core diameter.

In this article, the net cross section and transparency inversion in IP-EDFAs are first discussed. Next, we investigate through experiment the characteristics of high energy, IP-EDFAs operating at 1562.5 nm for both CRS and CLS based, fully-fiberized, master oscillator power amplifier (MOPA) configurations. Finally, a numerical model is used to help identify and understand the mechanism that leads to the saturation of pulse energy observed in our experiments.

2. Net cross section and transparency inversion

In this section, we will discuss the net cross-section in IP-EDFAs. The net cross section is defined as [13

13. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-doped fiber amplifiers: fundamentals and technology (Academic Press, 1999).

]:
σnet(λ)=σe(λ)n2σa(λ)n1,
(1)
where n2 and n1 are the normalized ion densities (with respect to the total ions) in the upper and lower energy state respectively while σe(λ) and σa(λ) are the emission and absorption cross section respectively. The net cross-section describes the gain and the absorption properties of fiber amplifiers at a particular inversion level. An IP-EDFA is essentially a quasi-three level laser system involving mainly two energy manifolds, i.e. 4I13/2 as the upper energy level and 4I15/2 as the lower energy level. In a laser system, there is an inversion level at which saturation of pump absorption occurs, i.e. no further pump photons can be absorbed in order to excite additional ions into the upper lasing level. The saturation of pump absorption occurs when the maximum possible population inversion that can be built-up by a given pump wavelength is reached. In the literature this situation is typically known as pump saturation and, in this article, we also refer to it as population inversion saturation. When the saturation of pump absorption and population inversion occurs, the active medium exhibits neither amplification nor absorption and becomes transparent at the pump wavelength, i.e. σnet(λ) = 0. From Eq. (1), the transparency inversion level, ntransparency, at a particular wavelength can be written as:

ntransparency=σa(λ)σa(λ)+σe(λ).
(2)

Based on the cross sectional data given in [13

13. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-doped fiber amplifiers: fundamentals and technology (Academic Press, 1999).

], the net cross sections at five different normalized inversion levels (i.e. values of n2) are shown in Fig. 1
Fig. 1 The net cross-section at five normalized inversion levels. The dashed black lines show the pump (1535 nm) and signal (1562.5 nm) wavelength used in our experiments.
. When all the ions are in the ground state, i.e. n2 = 0.0, the absorption peak is located at 1530 nm. In our experiments we use a pump wavelength of ~1535 nm since this represents the shortest wavelength that our pump fiber laser can operate efficiently at. For a 1535 nm pump wavelength, the maximum inversion is 0.50 due to the transparency condition. At this inversion level, the gain peak is located at 1562.5 nm, which itself has a transparency inversion of 0.36. Hence, the signal wavelength was chosen to be 1562.5 nm for our experiments.

3. Experimental setup

For the CRS, the signal and pump were combined and launched into the final stage Er-LMA fiber via a conventional, single-mode wavelength division multiplexer (WDM). The measured pulse energy after the WDM was 130 μJ. The pump source was a fiber Bragg grating stabilized 1535 nm single mode fiber laser [6

6. E. L. Lim, S. Alam, and D. J. Richardson, “Highly efficient, high power, inband-pumped Erbium/Ytterbium-codoped fiber laser,” CLEO (2011).

]. Due to the large mode field mismatch between the Er-LMA and the SMF-28 fiber used within the WDM, a mode field adaptor (MFA) was used between the WDM output and the Er-LMA fiber. The MFA comprised a short length of intermediate fiber with a 25 μm core diameter and 0.1 NA that was carefully tapered-spliced between the Er-LMA and SMF-28 such that most of the power was coupled into the LP01-mode. Since the Er-LMA was a double-clad fiber, a cladding-mode filter was used to remove any power inadvertently launched into the cladding. Overall, 89% of the available pump and signal powers after the WDM coupler were coupled into the Er-LMA fiber core.

For the CLS, a tapered fiber bundle (TFB) was spliced to the output of the WDM (which was retained in the CLS setup since it served to help eliminate out-of-band ASE). The 1535 nm pump laser was then spliced to one of the pump ports of the TFB to facilitate cladding pumping of the active fiber. We found that the MFA used within the CRS-setup introduced a relatively high insertion loss for pump light launched into the inner cladding, which was likely due to scattering of light at the glass-air interface along the taper. To avoid this loss, the TFB output was spliced to an intermediate passive fiber (4MF) with 24/125 μm core/cladding diameter and a core NA of 0.12 (supporting 4 transverse modes at 1550 nm). This intermediate fiber was then spliced to the active fiber.

4. Experiment

The MOPA setup shown in Fig. 2 can be divided into 3 different stages, i.e. the Q-switched seed laser, the pre-amplifier and the final stage IP-EDFA. The characteristics of the seed laser and the pre-amplifier are briefly described below, followed by a detailed discussion on the respective performance of the CRS and CLS IP-EDFAs.

4.1 Seed laser characteristics

Figure 3(a)
Fig. 3 (a) The seed pulse shape (with the peak power determined by fitting the area under the measured pulse shape to the measured pulse energy). (b) The normalized output spectrum of the Q-switched seed laser.
shows the output pulse from the Q-switched seed fiber laser operated with a 500 ns AOM-rise time so as to avoid the modulated pulse envelope frequently obtained from Q-switched fiber lasers as discussed in Ref [14

14. E. L. Lim, S. U. Alam, and D. J. Richardson, “The multipeak phenomena and nonlinear effects in Q-Switched fiber lasers,” IEEE Photon. Technol. Lett. 23(23), 1763–1765 (2011). [CrossRef]

]. A well-defined single-peak pulse shape with no observable multiple-peak phenomenon was obtained. The measured spectrum (see Fig. 3(b)) exhibits sidebands developed due to the effect of modulational instability and four wave mixing processes within the laser cavity [14

14. E. L. Lim, S. U. Alam, and D. J. Richardson, “The multipeak phenomena and nonlinear effects in Q-Switched fiber lasers,” IEEE Photon. Technol. Lett. 23(23), 1763–1765 (2011). [CrossRef]

]. By adjusting the input pump power, output pulses with the same pulse energy (~17 μJ), optical signal to noise ratio (OSNR) (~32 dB) and pulse width (~116 ns) can be generated at pulse repetition rates between 0.3 and 5.0 kHz.

4.2 Pre-amplifier characteristics

The output spectrum of the pre-amplifier (green line in Fig. 4(a)
Fig. 4 (a) The normalized output spectrum before WDM (green line), after WDM (blue line) and the transmission response of the WDM (red line). (b) The pre-amplifier pulse shape.
) is nonlinearly broadened compared to the input spectrum (Fig. 3(b)) due to the high pulse peak powers along the 4.55 m long EYDF pre-amplifier. When the output pulses from the EYDF pre-amplifier pass through the WDM the pulse spectrum is further broadened due to nonlinear effects in the WDM pigtail and then partially filtered due to the WDM wavelength response (red line in Fig. 4(a)). The corresponding output spectrum represented by the blue line in Fig. 4(a) shows the effect of both the additional nonlinear effects and the WDM filtering response. The width of the output pulse is also increased relative to the seed laser pulse (Fig. 4(b)) due to the effects of dynamic gain-saturation [16

16. A. E. Siegman, Laser (University Science Books, 1986).

]. Here again, by adjusting the input pump power, output pulses with the same pulse energy (~130 μJ), OSNR (~18 dB) and pulse width (~149 ns) can be generated at repetition rates between 0.3 and 5.0 kHz.

4.3 In-band pumped final amplifier characteristics

In this section, the detailed performances of the CRS and CLS MOPAs are presented and compared.

Pulse energy and residual pump

The pulse energies were measured using a pyroelectric joulemeter (Ophir PE-10SH), which is insensitive to any continuous wave radiation components such as inter-pulse ASE and residual pump. Figure 5(a)
Fig. 5 (a) The pulse energy at different input pump powers at 0.3 kHz in the CRS (blue) and CLS (red) MOPAs. (b) The residual pump power at different pulse energies. Note that the residual pump in the CRS has been scaled up by a factor of 10 so that the residual pump for both pumping schemes can be displayed on the same graph.
shows the pulse energy generated against input pump power at 0.3 kHz for the CLS and CRS. At low input pump powers, the pulse energy from the CRS is initially lower than for the CLS but it increases more rapidly as the input pump power is increased. For example, with 3 W input pump power the output energy is ~0.41 mJ for the CLS, while it is only ~0.1 mJ for the CRS. At ~6.2 W input pump, the pulse energies for the CLS and the CRS are the same. Beyond that, the pulse energy for the CRS exceeds that of the CLS however it exhibits a stronger pulse energy saturation behavior. The origin of this “cross-over” in pulse energy for the CRS and CLS is due to the effect of pair-induced quenching as we will show in Section 5.2. The pulse energies in both cases start to saturate at an input pump power of ~7.0 W. The maximum output pulse energies are ~1.53 mJ and ~1.50 mJ for the CRS and CLS respectively.

Figure 5(b) shows the residual pump power versus pulse energy for the CRS and CLS cases at 0.3 kHz. The residual pump powers for the CRS have been scaled up by a factor of 10 so that the residual pump powers for both the CLS and CRS can be displayed on the same graph. The residual pump for the CRS is insignificant for pulse energies below ~1.2 mJ but increase exponentially at energies above this. For the CLS, the residual pump increases linearly up to a pulse energy of ~1.2 mJ and exponentially thereafter. Hence, the residual pump for the CLS is much higher than the CRS, and the residual pump starts to increase rapidly at a pulse energy of ~1.2 mJ.

Absorbed pump and conversion efficiency

Figure 6(a)
Fig. 6 (a) The pulse energy at different levels of absorbed pump at 0.3 kHz in the CRS (blue) and CLS (red) MOPAs. (b) The conversion efficiency versus pulse energy.
shows the pulse energy generated against absorbed pump for the CLS and CRS at 0.3 kHz. It can be seen that much more pump power has been absorbed by the CRS in order to generate the same pulse energy. For example, the pump power absorbed to generate ~1.4 mJ energy pulses with the CRS (~8.6 W) is ~1.54 times higher than that required for the CLS (~5.6 W). Hence, for the generation of pulses with the same energy the CLS absorbs less pump power than the CRS.

Figure 6(b) shows the conversion efficiency (CE), i.e. the ratio of signal power (pulse energy × repetition rate) to the absorbed pump power, against pulse energy. The CE reaches a maximum for a pulse energy of ~1.2 mJ, which indicates that pulse energy saturation takes place at energies beyond this. This coincides with the exponential increase in residual pump at energies observed beyond ~1.2 mJ (see Fig. 5(b)), and suggests that the pulse energy saturation is primarily caused by saturation of the pump absorption. For the same pulse energy, the lower pump intensity in the CLS case helps to mitigate the detrimental effect of PIQ and results in a correspondingly higher efficiency in the CLS [7

7. E. L. Lim, S. U. Alam, and D. J. Richardson, “Optimizing the pumping configuration for the power scaling of in-band pumped erbium doped fiber amplifiers,” Opt. Express 20(13), 13886–13895 (2012). [CrossRef] [PubMed]

] as we shall show in Section 5. As shown in Fig. 6(b), the CLS is at least 1.5 times more efficient than the CRS in the range of 0.1-1.4 mJ.

Population inversion buildup time and repetition rate

Figure 7(a)
Fig. 7 (a) The pulse energy versus repetition rate for the CLS at a pump power of ~16.1 W. The inset shows the inter-pulse temporal response measured at the fiber output. (b) The output energy (left axis) and residual pump power (right axis) versus repetition rate for 4 different input pump powers for the CRS (cyan: 5.92 W, red: 8.33 W, green: 11.86 W and blue: 14.92 W).
shows the pulse energies for the CLS at different repetition rates at the maximum input pump of 16.1 W. The pulse energy saturates at a repetition rate of 1.0 kHz. The inset shows the temporal response of the system at a repetition rate of 0.3 kHz as measured using a fast photodiode. The two spikes at ~0.0 ms and ~3.3 ms correspond to the arrival of the output signal pulses. The vertical scale of the figure (i.e. 0-1 mV) is chosen such that the response in-between the two output pulses, which is what we are interested in, is clearly shown. The maximum voltage response of the output pulse is much higher than the ~1 mV and has saturated the detection system. The response in-between the output pulses shows the build-up of inter-pulse ASE. The ASE build-up time, i.e. the time required for the ASE to reach steady state, is ~1 ms. The ASE build-up time also corresponds to the population inversion build-up time of the system since the ASE originates directly from the population inversion and accords well with the observed saturation in pulse energy at ~1.0 kHz. The CRS exhibits very similar behavior.

Figure 7(b) shows the pulse energy and the residual pump for CRS as a function of repetition rate for 4 different input pumps. When the input pump is set to 5.92 W (cyan lines), there is no saturation of the pulse energy or rapid increase of residual pump across all repetition rates. At an input pump of 14.92 W (blue line), the residual pump is small at 5.0 kHz. When the repetition rate decreases, the pulse energy increases but starts to saturate below 1.25 kHz. Meanwhile, the residual pump also starts to increase rapidly below 1.25 kHz. In fact, saturation of the pulse energy is always accompanied by a rapid increase in residual pump power at different input pump powers as shown in Fig. 7(b). Hence, when the repetition rate decreases, the pulse energy saturation coincides with the rapid increase of residual pump. This phenomenon strongly suggests that the saturation of pulse energy is due to saturation of pump absorption and population inversion.

Our findings also imply that as the repetition rate decreases the input pump can produce inversion in a longer fiber length, i.e. the optimal length of fiber is increased. In fact, although it has been not highlighted previously, the simulation result in Fig. 9 of ref [17

17. Y. Wang and H. Po, “Dynamic characteristics of double-clad fiber amplifiers for high-power pulse amplification,” J. Lightwave Technol. 21(10), 2262–2270 (2003). [CrossRef]

]. also shows that the optimal fiber is increased by ~2.4 times when the repetition rate is reduced from 100 kHz to 10 kHz. Therefore, we conclude that for a given input pump, the optimal length of the fiber amplifier increases as the repetition rate is reduced.

Output spectra, pulse shapes and beam quality

Figure 8(a)
Fig. 8 (a) The normalized CRS output spectra at 3 different repetition rates at maximum input pump power. (b) The CRS pulse shapes at 4 different input pump powers at a repetition rate of 0.3 kHz.
shows the CRS output spectra at 3 repetition rates at maximum input pump power. At high repetition rate (i.e. 5.0 kHz), the ASE build-up occurs at wavelengths longer than the signal wavelength (see the red curve). As the repetition rate decreases, the ASE build-up shifts toward shorter wavelengths (as shown by the green and blue curves). This phenomenon can be explained as follows: given that the input pulse energy into the final amplifier was the same for the different repetition rates, a higher repetition rate results in a lower inversion for a fixed input pump. As shown in Fig. 1, at a lower inversion (for example, normalized inversion level of 0.36), longer wavelengths have a higher gain than shorter wavelengths. Consequently the ASE in the long wavelength region (~1585 nm) builds up at the expense of short wavelength components (~1550 nm). As the repetition rate decreases, a higher inversion is built up in-between the pulses resulting in the observed shift of the gain peak towards the shorter wavelength side. Analogously, at a fixed repetition rate, the ASE gain peak also shifts from longer to shorter wavelengths when the pump power increases. The CLS also exhibits a similar build-up of ASE with respect to the repetition rate and pump power. Hence, when the inversion level is increased, the ASE gain peak shifts from longer to shorter wavelengths.

Figure 8(b) shows the pulse shapes at a repetition rate of 0.3 kHz for the CRS at 4 input pump powers. As the input pump power is increased from 4.86 W to 14.92 W, a higher inversion is built-up in the active fiber. This, in turn, leads to an increase in the output energy (0.68 to 1.53 mJ) and the associated pulse peak power (~3.8 kW to ~8.0 kW). Meanwhile, the pulse appears to arrive earlier whilst its width increases from 167 to 176 ns which again we believe to be due to the dynamic gain saturation effect acting on a Gaussian-like input pulse [16

16. A. E. Siegman, Laser (University Science Books, 1986).

]. The evolution of the pulse shape for the CLS is similar to that for the CRS. For the CLS, at maximum input pump power and 0.3 kHz repetition rate, the measured pulse width is ~182 ns with a peak power of ~7.3 kW. At maximum input pump power, the M2 of the output beam was measured to be ~1.6 in both cases.

In summary, the pulse energies for the CRS and CLS are shown to exhibit a “cross-over” with respect to the input pump power at a repetition rate of 0.3 kHz. Due to significantly lower absorbed pump power for the CLS as compared to the CRS, the CLS is more efficient than the CRS. It has also been shown that as the population inversion increases, due to either increase in pump power or decrease in repetition rate, the saturation of pulse energy always coincides with the rapid increase of residual pump.

4.4 CLS experiment with a longer length of fiber

Figure 9(a)
Fig. 9 (a) The pulse energy against input pump power at a repetition rate of 0.3 kHz with a 19.5 m length of fiber. (b) The residual pump power at different pulse energies. The inset shows the conversion efficiency against pulse energy.
shows the pulse energy against input pump power at a repetition rate of 0.3 kHz. The maximum pulse energy of ~2.6 mJ was measured at ~23.5 W of input pump power. Figure 9(b) shows that the residual pump grows rapidly at a pulse energy of ~2 mJ, which corresponds well with the onset of saturation of the conversion efficiency at ~2 mJ shown in the inset of Fig. 9(b). Hence, the saturation of pulse energy again coincides with a rapid increase in the pump power, which again suggests pump and population inversion saturation. The output pulse has a FWHM of 100 ns and a fitted peak power of ~24 kW. We attribute the shorter pulse width compared to the input pulse width again to gain saturation effects associated with the specific shape of the Q-switched pulse. The M2 of the output beam was measured to be ~4.2. The lower beam quality in this case is due to the longer active fiber length that prevents us from performing active alignment of the cores when splicing between the 4MF and the LMA at the signal wavelength.

During the experiment described in Section 4.3, we also experimentally investigated the effect of splicing conditions on the output pulse energy. Our results showed that by degrading the quality of the launch into the fundamental mode (and hence launching more light in to higher-order modes) increases in pulse energy of up to ~10% can be achieved, albeit with an associated degradation in output beam quality. Consequently we conclude that the ~70% pulse energy increase observed when using a longer fiber is indeed due primarily to the increase in fiber length while the decrease of beam quality playing only a secondary role. Hence, with the increase in fiber length and pump power we have been able to scale the pulse energy from the CLS based approach to ~2.6 mJ.

5. Mechanism for pulse energy saturation due to pump saturation

5.1 The simulation model

Simulation approach

The general approach we used to simulate low repetition rate fiber amplifiers is similar to that used in [20

20. J. Nilsson and B. Jaskorzynska, “Modeling and optimization of low-repetition-rate high-energy pulse amplification in cw-pumped erbium-doped fiber amplifiers,” Opt. Lett. 18(24), 2099–2101 (1993). [CrossRef] [PubMed]

], where the behavior of the fiber amplifier is considered in two separate steps:

Step 1: Excitation step

In this step, the ions in the active fiber are assumed to be excited by the pump power for a sufficiently long duration such that in the absence of signal power a steady state population inversion is reached. Within the inset of Fig. 7(a), it is shown that the population inversion build-up time is ~1 ms. Therefore, this steady state assumption is valid for repetition rates of 1 kHz and below. This steady state behavior can be simulated using the continuous wave EDFA model.

Step 2: Pulse amplification step

When the steady state inversion is reached, the pulse amplification is modeled by passing a signal pulse through the fiber amplifier. The amplification of the signal input pulse is simulated by solving the spatio-temporal rate equation using the finite difference method [17

17. Y. Wang and H. Po, “Dynamic characteristics of double-clad fiber amplifiers for high-power pulse amplification,” J. Lightwave Technol. 21(10), 2262–2270 (2003). [CrossRef]

]. The grid spacing used in the time domain was 50 ps and Courant number is 0.9.

Pair-induced quenching

An EDF is a fiber in which erbium ions are incorporated in the glass matrix of the fiber core. The typical average distance between the ions in an EDF is on the nm-scale. For example, based on the cross-section data in [13

13. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-doped fiber amplifiers: fundamentals and technology (Academic Press, 1999).

] the concentration of the EDF used in our experimental was estimated as N = 3.23 × 1025 /m3, which corresponds to an average ion-ion distance (r) of ~3.14 nm, i.e. r = (1/N)1/3. However, in practice, the ion distribution is not fully random and many ions reside close to each other which can lead to concentration quenching. Several models to describe the concentration quenching in erbium doped fiber are to be found in the literature [13

13. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-doped fiber amplifiers: fundamentals and technology (Academic Press, 1999).

, 21

21. E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5(1), 73–75 (1993). [CrossRef]

24

24. S. Sergeyev, S. Popov, D. Khoptyar, A. T. Friberg, and D. Flavin, “Statistical model of migration-assisted upconversion in a high-concentration erbium-doped fiber amplifier,” J. Opt. Soc. Am. B 23(8), 1540–1543 (2006). [CrossRef]

]. In this work, the concentration quenching is modeled using the pair-induced quenching (PIQ) mechanism, which has successfully been used previously to characterize and describe the performance of high concentration EDFAs [13

13. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-doped fiber amplifiers: fundamentals and technology (Academic Press, 1999).

, 21

21. E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5(1), 73–75 (1993). [CrossRef]

, 22

22. P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” J. Lightwave Technol. 15(1), 112–120 (1997). [CrossRef]

]. In this model, the PIQ is an ion-ion interaction process that involves two strongly coupled erbium ions that are in physically close proximity, i.e. when the distance between the ions is on the order of the erbium ion diameter of about 0.2 nm [22

22. P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” J. Lightwave Technol. 15(1), 112–120 (1997). [CrossRef]

]. In this situation, the non-radiative energy transfer between them is so fast that only one ion of the ion-cluster can remain in the excited state. To model this effect the fraction of paired ions in the total ion population is defined as2k. With this, the ion density in the upper energy state in the rate equation can be written as [13

13. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-doped fiber amplifiers: fundamentals and technology (Academic Press, 1999).

, 21

21. E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5(1), 73–75 (1993). [CrossRef]

, 22

22. P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” J. Lightwave Technol. 15(1), 112–120 (1997). [CrossRef]

]:
N2=R12Nt(12k)A+R12+R21+R122kNtA+2R12+R21,
(3)
where N2 and Nt are the population densities of the upper lasing level (4I13/2) and the total population density respectively. R12, R21 and A are the absorption, stimulated emission and spontaneous emission rates respectively. With Eq. (3) and the power evolution equations, the steady state behaviour of the amplifier in the presence of PIQ can be simulated, which corresponds to step 1 of the simulation.

Simulation parameters

When simulating the case of the CLS, the overlap factor at the pump wavelength is reduced by a factor given by the ratio between core to the inner cladding area [25

25. A. Hardy and R. Oron, “Signal amplification in strongly pumped fiber amplifiers,” IEEE J. Quantum Electron. 33(3), 307–313 (1997). [CrossRef]

]. Furthermore, we have also taken into account the attenuation experienced by the cladding guided pump light due to the low-index coating, which we measured to be ~0.15 dB/m at 1535 nm using the corresponding passive version of this fiber (Liekki Passive-40/140 DC). This relatively high loss value results from the strong material absorption of the low-index polymer used as the low-index outer cladding for these fibers at 1535 nm which are designed to guide pump light at far shorter wavelengths.

Limitations

Our modeling makes a number of assumptions and has a number of limitations that it is important to recognize and that will at some level limit its accuracy.

Secondly, the residual pump (see for example Fig. 12(b)) is simulated using step 1 described above, which is based on the steady state assumption in the absence of signal power, i.e. the input pulse is taking no part in the redistribution of the stored energy. However, in practice, the presence of signal power will inevitably affect the inversion level through the process of stimulated emission, which leads to a higher pump absorption and lower residual pump compared to the simulation.

The two limitations discussed above show that our simulation model is likely to overestimate the pulse energy and residual pump power. Nevertheless we still consider it of value and believe that is still able to explain the various effects we have observed and in particular how pump saturation leads to the pulse energy saturation observed in our experiment.

5.2 Explanation for pulse energy saturation due to pump saturation

In this section, we describe the pulse energy saturation mechanism and how concentration quenching leads to the “cross-over” behavior of the output energies between the CRS and CLS.

Inversion level and spatial evolution of pulse energy

From step 1 of the simulation model, the population inversion along the active fiber at different condition can be simulated. Figure 11(a)
Fig. 11 (a) The normalized inversion at an input pump power of 3W (dashed line), 4W (dotted line) and 16 W (solid line) for the CRS (blue) and CLS (red) respectively in the presence of PIQ (i.e. k = 4.1%). (b) The spatial evolution of the pulse energy at input pump power of 3 W (dashed line), 4 W (dotted line) and 16 W (solid line) for the CRS (blue) and CLS (red) respectively in the presence of PIQ (i.e. k = 4.1%).
shows the population inversion for input pump power of 3 W (dashed line), 4 W (dotted line) and 16 W (solid line) for the CLS (red) and CRS (blue) respectively in the presence of PIQ (k = 4.1%). In case of CRS, a significant portion of the input pump power is lost through the PIQ process. Hence, a 3 W input pump is not sufficient to invert the last 1 m section of active fiber. In contrast, for the CLS at 3 W input pump power a more uniform inversion is achieved along the active fiber since PIQ is less detrimental due to the lower pump intensity. When the input pump approaches 4 W, the inversion level of CRS near the end of the active fiber starts to develop. Meanwhile, the overall inversion profile of the CLS increases slightly since the inversion along the fiber length is already close to the transparency inversion of ~0.5. Thus, most of the input pump cannot be absorbed but passes straight through the active fiber. As the pump power is increased even further, only a small fraction of the remaining ions are inverted because the population inversion approaches close to its maximum value (i.e. the saturation of the pump and population inversion has occurred). At 16 W input pump (solid line), the inversion is almost uniform along the entire length of fiber in both cases.

From step 2 of the simulation model, the spatial evolution of the pulse energy along the active fiber can be simulated using the population inversion profile obtained from step 1. The input pulse is a Guassian pulse of width 149 ns (FWHM) and energy of 130 μJ, equivalent to the experimental pulse width and pulse energy at the output of the pre-amplifier in Section 4.2. Figure 11(b) shows the spatial evolution for input pump power levels of 3 W (dashed line), 4W (dotted line) and 16 W (solid line) for both the CRS (blue) and the CLS (red) cases and assuming k = 4.1%. At an input pump power level of 3 W the pulse energy for the CRS grows much faster in the front section of the fiber because the higher pump intensity results in a higher local gain. However, the higher pump intensity also induces a stronger detrimental effect due to PIQ, which in effect reduces the effective pump power available. Consequently, the pump power is not sufficient to invert the rear section of the fiber (blue dashed line in Fig. 11(a)) and so the initially amplified pulse is reabsorbed by the active fiber. On the other hand, the inversion is fairly uniform for the CLS (red dashed line in Fig. 11(a)) since the PIQ is less severe due to the lower CLS pump intensity. Therefore, the pulse is amplified along the full length of active fiber and generates more output energy than the CRS. At an input pump level of 4 W the CRS pulse energy still undergoes reabsorption while the CLS pulse energy grows monotonically along the active fiber. At the output of the fiber, the output pulse from the CRS is already slightly higher in energy than for the CLS. Beyond 4 W of input pump power, the output energies in both cases start to saturate as a result of the saturation of population inversion. At an input pump power level of 16 W the output energy from the CRS (2.43 mJ) is slightly higher than that of the CLS (2.24 mJ).

Output energy and residual pump

Figure 12(a)
Fig. 12 (a) The pulse energy at different input pump power levels in the presence (k = 4.1%) and absence (k = 0.0%) of paired ions. (b) The residual pump power at different output pulse energies. Note that the residual pump power for the CRS with PIQ has been scaled up by a factor of 10 so that the residual pump power can be displayed on the same plot for all cases.
shows the output pulse energy calculated with step 1 and step 2 of the simulation model at different conditions (including the case where paired ions are absent, i.e k = 0.0%). In the absence of paired ions, the absorbed pump energy contributes only to the creation of a population inversion. When the transparency inversion (~0.5 for 1535 nm pump) is reached additional pump power can no longer be absorbed. Under this condition, the active fiber becomes transparent at the pump wavelength and any excess pump power will pass straight through the active fiber, i.e. pump saturation has occurred. This, in turn, leads to the saturation of pulse energy. Furthermore, the pulse energy for the CRS builds-up more rapidly than for the CLS due to the higher pump absorption in the CRS. Hence, the pulse energy for the CRS is always higher than that of the CLS for a given input pump. In the presence of paired ions, the absorbed pump energy not only contributes to the creation of population inversion, but also suffers additional losses due to PIQ. As a result, the pulse energy for the CRS is lower than that of the CLS when the input pump power is below ~3.8 W. Consequently, the pulse energies for the CRS and the CLS exhibit a “cross-over” at ~3.8 W due to the effects of PIQ.

The residual pump power at different output pulse energies can be obtained from step 1 described in Section 5.1. Figure 12(b) shows the residual pump for various output energies and pumping conditions. Note that the residual pump for the CRS, with the effects of PIQ included, have been scaled up by a factor of 10 so that the residual pump powers for all cases can be displayed on the same graph. In the absence of PIQ, the maximum residual pump for the CLS (~12.3 W) is lower than the CRS (~14.7 W) due to the coating attenuation experienced by the cladding guided pump light. If the coating attenuation is not considered, the maximum residual pumps become identical (~14.7 W) for both the CRS and CLS cases. In the presence of PIQ, there is neglible residual pump for up to ~2.0 mJ of pulse energy in the case of the CRS. After that, the pulse energy starts to saturate and the residual pump power increases exponentially up to ~1.2 W at ~2.42 mJ of pulse energy. In the case of the CLS, the residual pump power increases linearly with pulse energy up to ~2.0 mJ, beyond which it increases exponentially with further increases in input pump power. Previously (see the discussion relating to Fig. 12(a)), we have shown that the pulse energy is limited by pump saturation. Therefore, the exponential increase of residual pump is the signature of the pulse energy saturation caused by pump saturation.

Discussion

Comparing Fig. 5 and Fig. 12, both experiment and simulation exhibit the pulse energy “cross-over” behavior and the CRS generates higher pulse energy at the maximum input pump power level. Furthermore, just as in the experiment, the simulated residual pump in the CRS is much lower than that for the CLS when the effects of PIQ are taken into account. Finally, the residual pump increases exponentially as the pulse energy saturates in both experiment and simulation. Therefore, despite the relative simplicity and limitations of our model, the characteristic behaviors of the experiments have been reproduced successfully. Accordingly, we believe that the simulations can be relied upon to understand and to explain our main experimental observations and in particular our description of the mechanism by which saturation of the pump absorption and hence the population inversion leads to pulse energy saturation. Finally, we would like to note that this pulse energy saturation mechanism can also occur in other types of in-band pumped pulsed fiber amplifiers, such as the ~975 nm pumped ytterbium doped fiber amplifiers and is particularly prone to occur when the gain fiber is pumped at a wavelength that exhibits low transparency inversion.

6. Conclusion

We have demonstrated and compared high energy, low repetition rate, nanosecond pulse fully-fiberized MOPAs based on in-band pumped erbium doped fiber amplifiers pumped either using a core-pumping scheme, or a cladding-pumping scheme, and constructed using exactly the same piece of active fiber. The maximum output energies obtained were ~1.53 mJ and ~1.50 mJ for the core-pumping scheme and cladding-pumping scheme respectively. The cladding-pumped MOPA scheme is >1.5 times more efficient in term of conversion efficiency than the equivalent core-pumping scheme variant due to the lower pump intensity in the cladding-pumping scheme which helps to mitigate the detrimental effects of pair-induced quenching. The M2 of the output beam was measured to be ~1.6 in both cases. With a longer length of fiber operated in a cladding-pumped configuration we have achieved an output pulse energy of ~2.6 mJ with an M2 of ~4.2.

A simulation model has been used to understand how saturation of pump absorption and population inversion lead both to output pulse energy saturation and the rapid increase in residual pump observed in our experiment. The model also shows that for the generation of pulses of the same output pulse energy the effects of pair-induced quenching increases the absorbed pump requirements of the core-pumping scheme compared to cladding-pumping scheme. This, in turn, leads to the pulse energy cross-over observed in our experiments. It is shown that, as the inversion level increases in an in-band pumped pulsed fiber amplifier, either due to an increase in pump power or a decrease in pulse repetition rate, pump saturation can cause saturation of the output pulse energy.

References and links

1.

E. Lallier and D. Papillon-Ruggeri, “High energy pulsed eye-safe fiber amplifier,” CLEO EUROPE (2011).

2.

S. Desmoulins and F. Di Teodoro, “High-gain Er-doped fiber amplifier generating eye-safe MW peak-power, mJ-energy pulses,” Opt. Express 16(4), 2431–2437 (2008). [CrossRef] [PubMed]

3.

V. N. Philippov, J. K. Sahu, C. A. Codemard, W. A. Clarkson, J.-N. Jang, J. Nilsson, and G. N. Pearson, “All-fiber 1.15-mJ pulsed eye-safe optical source,” Proc. SPIE 5335, 1–7 (2004). [CrossRef]

4.

Y. Wang and C.-Q. Xu, “Actively Q-switched fiber lasers: Switching dynamics and nonlinear processes,” Prog. Quantum Electron. 31(3-5), 131–216 (2007). [CrossRef]

5.

J. Zhang, V. Fromzel, and M. Dubinskii, “Resonantly cladding-pumped Yb-free Er-doped LMA fiber laser with record high power and efficiency,” Opt. Express 19(6), 5574–5578 (2011). [CrossRef] [PubMed]

6.

E. L. Lim, S. Alam, and D. J. Richardson, “Highly efficient, high power, inband-pumped Erbium/Ytterbium-codoped fiber laser,” CLEO (2011).

7.

E. L. Lim, S. U. Alam, and D. J. Richardson, “Optimizing the pumping configuration for the power scaling of in-band pumped erbium doped fiber amplifiers,” Opt. Express 20(13), 13886–13895 (2012). [CrossRef] [PubMed]

8.

J. C. Jasapara, M. J. Andrejco, A. DeSantolo, A. D. Yablon, Z. Varallyay, J. W. Nicholson, J. M. Fini, D. J. DiGiovanni, C. Headley, E. Monberg, and F. V. DiMarcello, “Diffraction-limited fundamental mode operation of core-pumped very-large-mode-area Er fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 3–11 (2009). [CrossRef]

9.

N. A. Brilliant, R. J. Beach, A. D. Drobshoff, and S. A. Payne, “Narrow-line ytterbium fiber master-oscillator power amplifier,” J. Opt. Soc. Am. B 19(5), 981–991 (2002). [CrossRef]

10.

D. Taverner, D. J. Richardson, L. Dong, J. E. Caplen, K. Williams, and R. V. Penty, “158-µJ pulses from a single-transverse-mode, large-mode-area erbium-doped fiber amplifier,” Opt. Lett. 22(6), 378–380 (1997). [CrossRef] [PubMed]

11.

V. Kuhn, D. Kracht, J. Neumann, and P. Wessels, “Er-doped photonic crystal fiber amplifier with 70 W of output power,” Opt. Lett. 36(16), 3030–3032 (2011). [CrossRef] [PubMed]

12.

Y. Jeong, S. Yoo, C. A. Codemard, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, P. W. Turner, L. Hickey, A. Harker, M. Lovelady, and A. Piper, “Erbium: Ytterbium codoped large-core fiber laser with 297-W continuous-wave output power,” IEEE J. Sel. Top. Quantum Electron. 13(3), 573–579 (2007). [CrossRef]

13.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-doped fiber amplifiers: fundamentals and technology (Academic Press, 1999).

14.

E. L. Lim, S. U. Alam, and D. J. Richardson, “The multipeak phenomena and nonlinear effects in Q-Switched fiber lasers,” IEEE Photon. Technol. Lett. 23(23), 1763–1765 (2011). [CrossRef]

15.

M. N. Zervas, A. Marshall, and J. Kim, “Effective absorption in cladding-pumped fibers,” Proc. SPIE 7914, 79141T (2011). [CrossRef]

16.

A. E. Siegman, Laser (University Science Books, 1986).

17.

Y. Wang and H. Po, “Dynamic characteristics of double-clad fiber amplifiers for high-power pulse amplification,” J. Lightwave Technol. 21(10), 2262–2270 (2003). [CrossRef]

18.

C. C. Ranaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, “Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs,” IEEE J. Quantum Electron. 37(2), 199–206 (2001). [CrossRef]

19.

G. Canat, J. C. Mollier, J. P. Bouzinac, G. M. Williams, B. Cole, L. Goldberg, Y. Jaouen, and G. Kulcsar, “Dynamics of high-power erbium-ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 22(11), 2308 (2005). [CrossRef]

20.

J. Nilsson and B. Jaskorzynska, “Modeling and optimization of low-repetition-rate high-energy pulse amplification in cw-pumped erbium-doped fiber amplifiers,” Opt. Lett. 18(24), 2099–2101 (1993). [CrossRef] [PubMed]

21.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5(1), 73–75 (1993). [CrossRef]

22.

P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” J. Lightwave Technol. 15(1), 112–120 (1997). [CrossRef]

23.

S. Sergeyev, S. Popov, and A. T. Friberg, “Influence of the short-range coordination order of erbium ions on excitation migration and upconversion in multicomponent glasses,” Opt. Lett. 30(11), 1258–1260 (2005). [CrossRef] [PubMed]

24.

S. Sergeyev, S. Popov, D. Khoptyar, A. T. Friberg, and D. Flavin, “Statistical model of migration-assisted upconversion in a high-concentration erbium-doped fiber amplifier,” J. Opt. Soc. Am. B 23(8), 1540–1543 (2006). [CrossRef]

25.

A. Hardy and R. Oron, “Signal amplification in strongly pumped fiber amplifiers,” IEEE J. Quantum Electron. 33(3), 307–313 (1997). [CrossRef]

OCIS Codes
(060.2410) Fiber optics and optical communications : Fibers, erbium
(140.3510) Lasers and laser optics : Lasers, fiber
(140.4480) Lasers and laser optics : Optical amplifiers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: June 7, 2012
Revised Manuscript: July 25, 2012
Manuscript Accepted: July 27, 2012
Published: August 1, 2012

Citation
Ee-Leong Lim, Shaif-ul Alam, and David J. Richardson, "High-energy, in-band pumped erbium doped fiber amplifiers," Opt. Express 20, 18803-18818 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-17-18803


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References

  1. E. Lallier and D. Papillon-Ruggeri, “High energy pulsed eye-safe fiber amplifier,” CLEO EUROPE (2011).
  2. S. Desmoulins and F. Di Teodoro, “High-gain Er-doped fiber amplifier generating eye-safe MW peak-power, mJ-energy pulses,” Opt. Express16(4), 2431–2437 (2008). [CrossRef] [PubMed]
  3. V. N. Philippov, J. K. Sahu, C. A. Codemard, W. A. Clarkson, J.-N. Jang, J. Nilsson, and G. N. Pearson, “All-fiber 1.15-mJ pulsed eye-safe optical source,” Proc. SPIE5335, 1–7 (2004). [CrossRef]
  4. Y. Wang and C.-Q. Xu, “Actively Q-switched fiber lasers: Switching dynamics and nonlinear processes,” Prog. Quantum Electron.31(3-5), 131–216 (2007). [CrossRef]
  5. J. Zhang, V. Fromzel, and M. Dubinskii, “Resonantly cladding-pumped Yb-free Er-doped LMA fiber laser with record high power and efficiency,” Opt. Express19(6), 5574–5578 (2011). [CrossRef] [PubMed]
  6. E. L. Lim, S. Alam, and D. J. Richardson, “Highly efficient, high power, inband-pumped Erbium/Ytterbium-codoped fiber laser,” CLEO (2011).
  7. E. L. Lim, S. U. Alam, and D. J. Richardson, “Optimizing the pumping configuration for the power scaling of in-band pumped erbium doped fiber amplifiers,” Opt. Express20(13), 13886–13895 (2012). [CrossRef] [PubMed]
  8. J. C. Jasapara, M. J. Andrejco, A. DeSantolo, A. D. Yablon, Z. Varallyay, J. W. Nicholson, J. M. Fini, D. J. DiGiovanni, C. Headley, E. Monberg, and F. V. DiMarcello, “Diffraction-limited fundamental mode operation of core-pumped very-large-mode-area Er fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron.15(1), 3–11 (2009). [CrossRef]
  9. N. A. Brilliant, R. J. Beach, A. D. Drobshoff, and S. A. Payne, “Narrow-line ytterbium fiber master-oscillator power amplifier,” J. Opt. Soc. Am. B19(5), 981–991 (2002). [CrossRef]
  10. D. Taverner, D. J. Richardson, L. Dong, J. E. Caplen, K. Williams, and R. V. Penty, “158-µJ pulses from a single-transverse-mode, large-mode-area erbium-doped fiber amplifier,” Opt. Lett.22(6), 378–380 (1997). [CrossRef] [PubMed]
  11. V. Kuhn, D. Kracht, J. Neumann, and P. Wessels, “Er-doped photonic crystal fiber amplifier with 70 W of output power,” Opt. Lett.36(16), 3030–3032 (2011). [CrossRef] [PubMed]
  12. Y. Jeong, S. Yoo, C. A. Codemard, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, P. W. Turner, L. Hickey, A. Harker, M. Lovelady, and A. Piper, “Erbium: Ytterbium codoped large-core fiber laser with 297-W continuous-wave output power,” IEEE J. Sel. Top. Quantum Electron.13(3), 573–579 (2007). [CrossRef]
  13. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-doped fiber amplifiers: fundamentals and technology (Academic Press, 1999).
  14. E. L. Lim, S. U. Alam, and D. J. Richardson, “The multipeak phenomena and nonlinear effects in Q-Switched fiber lasers,” IEEE Photon. Technol. Lett.23(23), 1763–1765 (2011). [CrossRef]
  15. M. N. Zervas, A. Marshall, and J. Kim, “Effective absorption in cladding-pumped fibers,” Proc. SPIE7914, 79141T (2011). [CrossRef]
  16. A. E. Siegman, Laser (University Science Books, 1986).
  17. Y. Wang and H. Po, “Dynamic characteristics of double-clad fiber amplifiers for high-power pulse amplification,” J. Lightwave Technol.21(10), 2262–2270 (2003). [CrossRef]
  18. C. C. Ranaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, “Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs,” IEEE J. Quantum Electron.37(2), 199–206 (2001). [CrossRef]
  19. G. Canat, J. C. Mollier, J. P. Bouzinac, G. M. Williams, B. Cole, L. Goldberg, Y. Jaouen, and G. Kulcsar, “Dynamics of high-power erbium-ytterbium fiber amplifiers,” J. Opt. Soc. Am. B22(11), 2308 (2005). [CrossRef]
  20. J. Nilsson and B. Jaskorzynska, “Modeling and optimization of low-repetition-rate high-energy pulse amplification in cw-pumped erbium-doped fiber amplifiers,” Opt. Lett.18(24), 2099–2101 (1993). [CrossRef] [PubMed]
  21. E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett.5(1), 73–75 (1993). [CrossRef]
  22. P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” J. Lightwave Technol.15(1), 112–120 (1997). [CrossRef]
  23. S. Sergeyev, S. Popov, and A. T. Friberg, “Influence of the short-range coordination order of erbium ions on excitation migration and upconversion in multicomponent glasses,” Opt. Lett.30(11), 1258–1260 (2005). [CrossRef] [PubMed]
  24. S. Sergeyev, S. Popov, D. Khoptyar, A. T. Friberg, and D. Flavin, “Statistical model of migration-assisted upconversion in a high-concentration erbium-doped fiber amplifier,” J. Opt. Soc. Am. B23(8), 1540–1543 (2006). [CrossRef]
  25. A. Hardy and R. Oron, “Signal amplification in strongly pumped fiber amplifiers,” IEEE J. Quantum Electron.33(3), 307–313 (1997). [CrossRef]

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