Abstract

We report a numerical investigation on a trench-assisted few-mode erbium-doped fiber amplifier supporting 6 spatial modes with a very low differential modal gain. The numerical investigation is based on the experimentally measured parameters of extended L-band Er3+ doped fiber. The results show that the differential modal gain of 6 spatial modes covering the spectral range from 1570 to 1616 nm was reduced to as low as 0.28 dB by a mode hybrid core pumped architecture at a 1550 nm pump wavelength. Compared with cladding pumping, our method achieved a gain efficiency increased by 23.1% and a smaller differential modal gain when both average gains reached 20 dB. It is suggested that our investigation shows great potential for decreasing the differential modal gain effectively.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The orthogonality of the modes in the optical fiber allows each mode to transmit information separately, creating a new dimension for optical fiber communication [1]. Compared with single-mode fiber (SMF), few-mode fiber (FMF) has a larger core which leads to a higher nonlinear threshold [2] and it integrates the coherent optical communication technologies, which can increase communication capacity significantly [3]. The long-haul transmissions of mode division multiplexing (MDM) communication system are largely founded on the outstanding characteristics of the few-mode erbium-doped fiber amplifier (FM-EDFA). Compared with the traditional EDFA, the FM-EDFA has another important parameter-differential modal gain (DMG), not just the gain and noise figure, which affects the average and outage capacities of the MDM system [4]. So far, Three main ways have been used to reduce DMG: a. managing the spatial distribution of the erbium concentration, such as double-ring doping [58], multi-ring doping [9], large-scale doping [10,11], and other complex doping profiles [12,13]; b. adjusting the mode field distribution by controlling the refractive index profile, for example, multi-element fiber amplifier [14,15], ring core erbium-doped fiber [12,1618], center depressed core index profile [19] and trench-assisted fiber [17,20]; c. tailoring the pump field intensity distribution, including changing the mode content of pump light [2123] and cladding pumping [20,24]. Apart from the strategies mentioned above, many efforts have been made to minimize the DMG such as a laser-inscribed void introducing extra mode-dependent loss [25], oversizing a core diameter or increasing numerical aperture (NA) to expand the number of modes but only use LPn1 modes [26,27], gradient descent optimization algorithm [28] and genetic algorithm [29] as guidance of doping. These technologies have obtained DMG values of less than 1 dB across the C-band.

Generally speaking, one technique is not enough to reduce DMG, while multiple techniques used in combination are preferred, especially in higher mode count amplifiers. A trench-assisted EDF combination with the cladding-pumped schema was proposed [20] to reduce DMG for C-band, which doesn’t require the complicated fiber manufacturing process. Nevertheless, few studies on L-band have been reported, which are the best choice to address the growing need for increased data network when C-band is exhausted in the future [30]. The gain at L-band is relatively inefficient because it suffers from the excited-state absorption (ESA) after the 1580 nm wavelength [31] and has a much smaller emission cross-section than C-band. Well-chosen C-band wavelengths as auxiliary pumps [32,33] or sole pumps [34,35] were used to enhance the gain of L-band EDFA. References [3638] reported that the utilization of higher power C-band light pumping to extend spectral bandwidth and improve power conversion efficiency (PCE) of L-band EDFAs. For L-band FM-EDFA using cladding pumped-schema, the signal cannot be sufficiently amplified if the fiber length is too short. However, cladding pumping may compromise the optimization effect of DMG because the fiber length used in L-band is usually longer, the pump light intensity will obey the eigenmode mode field distribution rather than uniform distribution at the end of the fiber. Therefore, the cladding pumping is not suitable to reduce DMG for L-band FM-EDFA especially with a low core-cladding ratio.

In this paper, we present a thorough numerical investigation, taking advantage of the mode hybrid core pumped scheme to reduce the DMG of the trench-assisted 6-mode erbium-doped fiber amplifier. The gain efficiency is improved by tightly confining the pump light in the fiber core with a deep refractive index trench and using a C-band pump instead of 1480 nm or 980 nm. Our simulations confirm that the trench and the mode hybrid core pumped scheme play a significant role in DMG optimization and in improving gain efficiency.

2. Fiber design

Figure 1 (a) shows the schematic diagram of our proposed trench-assisted 6-signal-mode EDF with a uniform erbium doping profile. Table 1 shows the definition of the fiber structure parameters where several values are left to specified. At 1600 nm wavelength, for the FM-EDF with $N{A_1} = \textrm{0}\textrm{.12}$, $a = 11\mu m$, a map of allowable 6-signal mode area for the combination of d and $N{A_2}$ is shown in Fig. 1 (b). The white region is the 6-signal-mode working area. The two gray areas from left to right indicate the LP31 mode is far from the cut-off and the LP02 mode is cut-off.

 figure: Fig. 1.

Fig. 1. (a) Refractive index profile of proposed trench-assisted 6-mode EDF (colored region represents the doping region). (b) Map of the allowable 6-signal mode area for the trench width ($d$) and $N{A_2}$ of trench-assisted 6-mode EDF

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Table 1. Fiber Parameters

To demonstrate the confinement degree of the core to energy, the mode-related CF (confinement factor) is introduced [20] as the ratio between the power in the core and that of the whole fiber cross-section for a certain mode. Increasing CF by adding a refractive index trench can bring increased gain efficiency with the augment of the proportion of core power. And the energy of all modes is tightly bounded in the core combined with high-order mode pumping, which can dramatically reduce the DMG. Figure 2(a) illustrates the relationship between the CF and $N{A_2}$ for $d = 4\mu m$. The CF of all modes at 1600 nm increases with the growth of $N{A_2}$ and gradually approaches to 1. When $N{A_2}$ is greater than 0.12, the CF of all modes exceeds 90%. In the case of $d = 4\mu m$ and $N{A_2}\textrm{ = 0}\textrm{.19}$, the normalized intensity of each mode is shown in Fig. 2(b). The correlation between the pump mode and signal mode depends on their overlapping degree. The greater an overlap is, the greater the gain of signal mode is. For convenience, the overlap factor of the pump and signal intensity profile is defined as:

$$\Gamma _{p,i}^{s,j} = \int\limits_0^{2\pi } {\int\limits_{ - a}^a {{I_{s,j}}(r,\varphi )} } {I_{p,i}}(r,\varphi )rdrd\varphi ,$$
where i and $j$ are the mode order of pump and signal, respectively. As listed in Table 2, the relationships of the overlap factor between four mode groups with pump modes including LP01, LP11, LP21, and LP02 are as follows:
$$\begin{array}{l} \Gamma _{p,01}^{s,01} > \Gamma _{p,01}^{s,02} > \Gamma _{p,01}^{s,11} > \Gamma _{p,01}^{s,21}\\ \Gamma _{p,11}^{s,01} \approx \Gamma _{p,11}^{s,11} \approx \Gamma _{p,11}^{s,21} > \Gamma _{p,11}^{s,02}\\ \Gamma _{p,21}^{s,11} \approx \Gamma _{p,21}^{s,21} > \Gamma _{p,21}^{s,01} > \Gamma _{p,21}^{s,02},\\ \Gamma _{p,02}^{s,02} > \Gamma _{p,02}^{s,01} > \Gamma _{p,02}^{s,11} \approx \Gamma _{p,02}^{s,21} \end{array}$$

 figure: Fig. 2.

Fig. 2. (a) The CF as a function of the $N{A_2}$ for each mode at 1600 nm wavelength. (b) Normalized intensity of each mode for 980 nm pump (solid line) and 1600 nm signal (dashed line) in trench-assisted 6-mode EDF along with the fiber radius position.

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Table 2. The normalized overlap factors of the 980 nm pump (columns) and 1600 nm signal (rows) intensity

It is due to the difference in the degree of overlap between the pump mode and the signal mode that we can equalize the DMG by changing the mode content of the pump light.

3. Gain modeling

3.1 Giles model

The evolution of the beam in the erbium-doped fiber can be described by the rate equation [39].

$$\begin{array}{l} \frac{{d{P_k}}}{{dz}} = {u_k}({\sigma _{ek}} - {\sigma _{esa,k}})\int\limits_0^{2\pi } {\int\limits_0^\infty {{i_k}(r,\varphi )} } {n_2}(r,\varphi ,z)rdrd\varphi ({P_k}(z) + mh{v_k}\Delta v)\\ - {u_k}{\sigma _{ak}}\int\limits_0^{2\pi } {\int\limits_0^\infty {{i_k}(r,\varphi )} } {n_1}(r,\varphi ,z)rdrd\varphi {P_k}(z), \end{array}$$
where the ${u_k} ={\pm} 1$ means the direction of propagation and is either forward (1) or backward (-1); $mh{v_k}\Delta v$ is the contribution of the spontaneous emission due to the m degenerate states; ${\sigma _{ek}}$ and ${\sigma _{ak}}$ are the emission and absorption cross-section at wavelength position k; ${\sigma _{esa,k}}$ is the ESA cross-section; ${P_k}$ and ${i_k}$ are the total power and the normalized intensity distribution for beams; ${n_1}(r,\varphi ,z)$ and ${n_2}(r,\varphi ,z)$ are the erbium ions density in the lower level and upper level. The two integrals are respectively the overlap of the optical intensity profile. In addition, the distribution of the ions at the upper and lower levels on the cross-section of the fiber indicates that only the part overlapping with erbium ions will experience attenuation and amplification. For a two-level system, the variations on ion populations of the ground and metastable states with the k beams are shown below:
$$\begin{aligned}\frac{{d{n_2}(r,\varphi ,z)}}{{dz}} &= {n_1}(r,\varphi ,z)\sum\nolimits_k {\frac{{{P_k}(z){i_k}(r,\varphi )({\sigma _{ak}})}}{{h{v_k}}}} \\ & - {n_2}(r,\varphi ,z)\sum\nolimits_k {\frac{{{P_k}(z){i_k}(r,\varphi )({\sigma _{ek}} - {\sigma _{esa,k}})}}{{h{v_k}}} - } \frac{{{n_2}(r,\varphi ,z)}}{\tau },\end{aligned}$$
$${n_t}(r,\varphi ,z) = {n_1}(r,\varphi ,z) + {n_2}(r,\varphi ,z),$$
where the particle conservation for the two-level system is illustrated, and ${n_t}(r,\varphi ,z)$ represents the total erbium ion density.

3.2 Multimode rate equations for Er3+ doped amplifier

When the Er3+ dopant distribution is uniform in the longitudinal direction and the intra-mode coupling in the fiber is ignored, the simultaneous amplification of different signal modes will induce a competitive effect [40] affected by the pump field, signal field and transverse doping distribution. This can make ions redistribute on the upper and lower levels, as illustrated in Fig. 3 (a).

 figure: Fig. 3.

Fig. 3. (a) Three-level diagram of Er3+ in FM-EDF. (b) Schematic diagram of fiber amplifiers.

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The complicated integrals in Eq. (3) can be solved by the multilayered method [40], and the discrete model of transverse mode competition [41] in Er3+ doped multimode fiber amplifier after taking into consideration the influence of spontaneous emission can be expressed as follows:

$$\begin{array}{l} \pm \frac{{d{P_{P,i,j}}}}{{dz}} = {\sigma _{ej}}\sum\limits_{k = 1}^M {{N_{2k}}} (z){\Gamma _{i,j,k}}{P_{P,i,j}}(z) - {\sigma _{aj}}\sum\limits_{k = 1}^M {{N_{1k}}} (z){\Gamma _{i,j,k}}{P_{P,i,j}}(z),\\ \frac{{d{P_{S,i,j}}}}{{dz}} = ({\sigma _{ej}} - {\sigma _{esa,j}})\sum\limits_{k = 1}^M {{N_{2k}}} (z){\Gamma _{i,j,k}}{P_{S,i,j}}(z) - {\sigma _{aj}}\sum\limits_{k = 1}^M {{N_{1k}}} (z){\Gamma _{i,j,k}}{P_{S,i,j}}(z),\\ \pm \frac{{d{P_{ASE,i,j}}}}{{dz}} = ({\sigma _{ej}} - {\sigma _{esa,j}})\sum\limits_{k = 1}^M {{N_{2k}}} (z){\Gamma _{i,j,k}}{P_{ASE,i,j}}(z) - {\sigma _{aj}}\sum\limits_{k = 1}^M {{N_{1k}}} (z){\Gamma _{i,j,k}}{P_{ASE,i,j}}(z)\\ + mh{v_j}\Delta v({\sigma _{ej}} - {\sigma _{esa,j}})\sum\limits_{k = 1}^M {{N_{2k}}} (z){\Gamma _{i,j,k}}, \end{array}$$
$${\Gamma _{i,j,k}} = \frac{{\int\limits_0^{2\pi } {\int\limits_{{r_{k - 1}}}^{{r_k}} {{i_{i,j}}(r,\varphi )rdrd\varphi } } }}{{\int\limits_0^{2\pi } {\int\limits_0^\infty {{i_{i,j}}(r,\varphi )rdrd\varphi } } }},$$
$$\frac{{{N_{2k}}(z)}}{{{N_{1k}}(z)}} = \frac{{\sum\limits_i {\sum\limits_j {\frac{{{P_{i,j}}(z){\Gamma _{i,j,k}}{\sigma _{aj}}}}{{h{v_j}}}} } }}{{\sum\limits_i {\sum\limits_j {\frac{{{P_{i,j}}(z){\Gamma _{i,j,k}}({\sigma _{\textrm{e}j}} - {\sigma _{esa,j}})}}{{h{v_j}}}} } + \frac{{{A_k}}}{\tau }}},$$
where ${P_{P,i,j}}$ and ${P_{S,i,j}}$ are the pump and signal powers of mode i and frequency j respectively, and ${P_{ASE,i,j}}$ is the i mode ASE power of the j frequency within $\Delta v$ bandwidth centered on ${v_j}$; ${\pm}$ refers to the direction of transmission, as shown in Fig. 3 (b). M is the number of divided layers. ${N_{2k}}$ and ${N_{1k}}$ are the erbium ion densities of the lower and upper levels at the ${k^{th}}$ layer, and ${A_k} = \pi (r_k^2 - r_{k - 1}^2)(k = 1,2,\ldots ,M)$ is the area of the ${k^{th}}$ layer. The power filling factor ${\Gamma _{i,j,k}}$ is defined as the ratio of the layer k to total power, which can be calculated by COMSOL when the refractive index profile of fiber is atypical. The signal gain and NF are defined as:
$$Gain(dB) = 10\log 10(\frac{{{P_s}(z = L)}}{{{P_s}(z = 0)}}),$$
$$NF(dB) = 10\log 10(\frac{{2{n_{sp}}(G - 1)}}{G} + \frac{1}{G}) = 10\log 10(\frac{{{P_{ASE}}}}{{hv\Delta vG}} + \frac{1}{G}),$$
$${n_{sp}} = {1 / {(1 - \frac{{{\sigma _{ep}}{\sigma _{as}}}}{{{\sigma _{ap}}{\sigma _{es}}}})}},$$
where the noise factor ${n_{sp}}$ at high pump powers is simplified to Eq. (11) [39].

4. Numerical simulation results and discussion

Figure 4 (a) shows the absorption cross-section, emission cross-section and ESA cross-section of a measured extended home-made Er/Al/La/Ge/P co-doped L-band fiber from the 1500 to 1630 nm. The simulation parameters are consistent with those in Table 3 unless otherwise specified below.

 figure: Fig. 4.

Fig. 4. (a) Absorption and emission cross-sections as a function of wavelength from 1500 to 1630 nm for L-band Er3+ doped fiber (green line is ESA cross-section after 1580 nm). (b) Power spectrum evolutions of four mode groups with fiber length with the equal proportion of pump mode components (LP01, LP11, LP21, LP02) and a pump wavelength of 980 nm.

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Table 3. Simulation Parameters

Figure 4 (b) shows the reabsorbing process that the pump light simultaneously excites the C-band multi-mode amplified spontaneous emission (ASE) light, and then works with the generated forward-propagating C-band ASE to provide gain for the L-band signal. References [3638] present thorough simulations and experimental results, taking advantage of the C-band light source in the wavelength range from 1530 nm to 1550 nm to achieve higher gain than conventional laser diode pumps at 1480 nm for L-band EDFAs. Here, three wavelengths are used for L-band amplification, one is located at the absorption peak (1536 nm) while the other two are located to the left (1530 nm) and right (1550 nm) of the absorption peak. First of all, to control the DMG of four mode groups, the optimal fiber length should be determined for different pump wavelengths. The results plotted in Fig. 5 (a)-(d) show that with 980, 1530, 1536 and 1550 nm pump wavelength, the optimum gain lengths are 4.7, 10.8, 11.8, 16.2 m, and the DMG at this fiber length are 1.33, 1.19, 0.95, and 1.06 dB, respectively.

 figure: Fig. 5.

Fig. 5. Variations of gain of different signal mode groups and total gain of all modes with fiber length at (a) 980 nm, (b) 1530 nm, (c) 1536 nm, and 1550 nm pump wavelength.

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4.1 Reducing DMG by regulating pump mode content

Considering that the overlap factors of LP01 pump mode and the four signal mode groups are too different from each other to be controlled, the LP11, LP21 and LP02 modes hybrid pumped architecture is adopted. When the ratio of each pump mode is adjusted from 0 to 1, the calculated maximum DMG values depend on the pump mode contents as illustrated in Fig. 6. Three phenomena can be seen from the results in Fig. 6 (a)-(d): I) Whenever whether 980 nm or C-band wavelength pumping is used, the DMG can be lower than 0.5 dB by adjusting the pump mode contents. II) Compared to other pump wavelengths, the wavelength of 1536 nm acquires a larger region probably covering more than 2/3 of the effective area when DMG is less than 1.5 dB. DMG is less sensitive to changes in pump mode composition with 1530 nm pumping for our trench-assisted 6-mode EDF. III) No matter which pump wavelength is selected, the proportion of LP11 pump mode in the region where the DMG is lower than 0.5 dB is extremely small. As the optimization effect of DMG with LP11 mode pumping is not evident, only LP21 and LP02 pump modes are used for combined pumping. The DMG changing trend curves are plotted in Fig. 7. For all pump wavelengths, DMG is minimized when the ratio of pump power between LP21 and LP02 modes is around 0.7:0.3. Specifically, DMG is as low as 0.40, 0.33, 0.42 and 0.28 dB respectively when pump wavelengths are 980, 1530, 1536, and 1555 nm.

 figure: Fig. 6.

Fig. 6. Calculated maximum DMG values as a function of the ratio of LP01, LP11 and LP21 pump mode power to total power with a pump wavelength of (a) 980 nm, (b) 1530 nm, (c) 1536 nm, and (d) 1550 nm at signal wavelength ranging from 1570 to 1618 nm.

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 figure: Fig. 7.

Fig. 7. Calculated maximum DMG values as a function of the ratio of LP11 and LP21 pump mode power to total power.

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Figure 8 (a)-(d) show gain and NF across the L-band for four pump wavelengths when the DMG is the smallest. The gain obtained by the 980 nm pumping is much lower than that of the C-band pumping. However, the noise performance of the 980 nm pump exhibits the best because the emission cross-section at this wavelength is 0, where the number of Er3+ ions can be fully reversed. Since the emission cross-section at 1550 nm has exceeded the absorption cross-section, the noise performance manifests the worst. The noise factor is closely related to the ratio of the emission cross-section and absorption cross section of pump wavelength expressed as ${{{\sigma _{ep}}} / {{\sigma _{ap}}}}$ at a fixed signal wavelength. The larger the value, the greater the noise factor, as illustrated in Eq. (10) and Eq. (11). The C-band was used because of its ability to enhance the gain of the L-band. It’s important to select the appropriate pump wavelength to balance the gain and noise figure. As shown in Fig. 8, of the use of the pump wavelengths of absorption cross-section greater than emission-section like 1536 nm or 1530 nm, the noise figure <6 dB and the gain >12 dB from the wavelength range of 1570-1616 nm was obtained.

 figure: Fig. 8.

Fig. 8. Spectral variation of gains (solid line) and noise figures (dashed line) at pump wavelength (a) 980 nm, (b) 1530 nm, (c) 1536 nm, and (d) 1550 nm at signal wavelength ranging from 1570 to 1618 nm.

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4.2 Pump power tolerance discussion

Additionally, we studied the DMG and average gain fluctuations caused by pump power changes. Figure 9 shows the effect of pump power on average gains and DMG under different pump wavelengths. The average gain initially increases linearly with the increase of pump power, and then enters the saturation state. With sufficient pumping, it has the potential to achieve higher gain as the pump wavelength increases, while DMG is maintained below 0.6 dB when the pump power varies from 500 to 1300 mW. Particularly, when using a 1530 nm pump, the average gain is nearly 20 dB, and DMG is less than 0.4 dB with a total power of 1 W.

 figure: Fig. 9.

Fig. 9. (a) Effect of pump power on average gains and DMG under different pump wavelengths and pump forms. (b) Gain coefficient versus pump power for cladding pumping and core pumping at a pump wavelength of 1530 nm.

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4.3 Comparison of core pumping and cladding pumping

Finally, we simulated and compared the influences of core pumping and cladding pumping on gain and DMG for our 6-LP EDFA. The fiber that uses cladding pumping adopts a double-clad structure. The inner cladding radius is 43.6 μm [20], and the core-cladding ratio is 6.37%. Compared with core pumping, cladding pumping has the possibility of obtaining higher gains under high power pumping condition (>1.3 W). But the core pumping is more likely to achieve higher gain when the pump power is lower. As shown in Fig. 9 (a), at a pump wavelength of 1530 nm, when the total gain reaches approximately 20 dB, the pump power required for cladding pumping and core pumping is 1.3 W and 1 W, respectively, and DMG is 0.59 dB and 0.39 dB, respectively. The gain efficiency was increased by 23.1%, and DMG was decreased by 0.2 dB through using core pumping. Owing to the existence of the threshold pump power [39], the actual part of the fiber core acting on amplification is not enough to provide gain at low power due to the limitation of the core-cladding ratio on the cladding pumping, and higher gain efficiency can be obtained only at high power. However, more than 95% of the pump energy in our FM-EDF is tied to the core by adding a refractive index trench. The maximum gain coefficient of core pumping is approximately double that of the cladding pumping, as described in Fig. 9 (b).

5. Fabrication discussion

The trench-assisted 6-mode EDF designed in this paper can adopt Er/Al/La/Ge/P co-doped methods to realize L-band amplification, and it can be fabricated based on the MCVD (Modified Chemical Vapor Deposition) technology combined with the liquid-phase doping technology. The low refractive index trench can be formed by deposition of SF6 during the cladding deposition process. The depth and width of the trench are determined by the flow rate of SF6 and the number of claddings deposited, respectively. The Erbium, aluminum and lanthanum ions were doped into the fiber core by liquid phase method while the phosphorus and germanium ions are deposited by vapor phase deposition method. The NA can be adjusted by regulating the flow of P and germanium during the process of the gas phase doping.

6. Conclusion

We report a numerical investigation on trench-assisted few-mode erbium-doped fiber amplifier supporting 6 spatial modes with experimentally measured parameters of extended L-band Er3+ doped fiber. Based on mode hybrid core pumped architecture, the DMG reaches its minimum when the power ratio of the LP21 mode and the LP02 mode is about 0.7:0.3, regardless of which pump wavelength was selected. The fluctuation of DMG caused by the change of pump power was also studied which was always maintained at a low value under the optimal pump mode contents. For four signal mode groups at a pump wavelength of 1550 nm, we achieved a gain greater than 12 dB with a DMG of 0.28 dB across the range of 1570-1616 nm. It is suggested that our investigation shows great potential for decreasing the DMG effectively. Compared with cladding pumping, our method achieved a gain efficiency increase of 23.1% and a smaller DMG when both average gains reached 20 dB. The amplifier performance can be further improved with different C-band wavelengths hybrid pumping.

Funding

National Key Research and Development Program of China (2017YFB1104400).

Disclosures

The authors declare no conflicts of interest.

Data availability

No data were generated or analyzed in the presented research.

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21. N. Bai, E. Ip, Y. Luo, G. D. Peng, T. Wang, and G. Li, “Experimental study on multimode fiber amplifier using modal reconfigurable pump,” Opt. InfoBase Conf. Pap. (2012). [CrossRef]  

22. M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, N. Hanzawa, and F. Yamamoto, “L-band 2-LP mode EDFA with low modal dependent gain,” Conf. Opt. Fiber Commun. Tech. Dig. Ser. 2015–June, 5–7 (2015).

23. G. Lopez-Galmiche, Z. Sanjabi Eznaveh, J. E. Antonio-Lopez, A. M. Velazquez Benitez, J. Rodriguez Asomoza, J. J. Sanchez Mondragon, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, C. M. Okonkwo, and R. Amezcua Correa, “Few-mode erbium-doped fiber amplifier with photonic lantern for pump spatial mode control,” Opt. Lett. 41(11), 2588–2591 (2016). [CrossRef]  

24. Y. Jung, E. L. Lim, Q. Kang, T. C. May-Smith, N. H. L. Wong, R. Standish, F. Poletti, J. K. Sahu, S. U. Alam, and D. J. Richardson, “Cladding pumped few-mode EDFA for mode division multiplexed transmission,” Opt. Express 22(23), 29008–29013 (2014). [CrossRef]  

25. Y. Yamashita, T. Matsui, M. Wada, S. Aozasa, T. Sakamoto, and K. Nakajima, “Differential modal gain reduction using a void inscribed in a two-mode-erbium doped fiber,” Opt. InfoBase Conf. Pap. Part F174-, 5–7 (2020).

26. Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

27. N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

28. G. Le Cocq, Y. Quiquempois, and L. Bigot, “Optimization Algorithm Applied to the Design of Few-Mode Erbium Doped Fiber Amplifier for Modal and Spectral Gain Equalization,” J. Lightwave Technol. 33(1), 100–108 (2015). [CrossRef]  

29. Q. Kang, E.-L. Lim, F. P. Y. Jung, C. Baskiotis, S. Alam, and D. J. Richardson, “Minimizing differential modal gain in cladding-pumped EDFAs supporting four and six mode groups,” Opt. Express 22(18), 21499–21507 (2014). [CrossRef]  

30. B. J. Puttnam, R. S. Luís, W. Klaus, J. Sakaguchi, J. D. Mendinueta, and Y. Awaji, “2.15 Pb/s Transmission Using a 22 Core Homogeneous Single- Mode Multi-Core Fiber and Wideband Optical Comb,” Eur. Conf. Opt. Commun.22–24 (2015).

31. M. Bolshtyansky, I. Mandelbaum, and F. Pan, “Signal excited-state absorption in the L-band EDFA: Simulation and measurements,” J. Lightwave Technol. 23(9), 2796–2799 (2005). [CrossRef]  

32. M. A. Mahdi, F. R. Mahamd Adikan, P. Poopalan, S. Selvakennedy, W. Y. Chan, and H. Ahmad, “Long-wavelength EDFA gain enhancement through 1550 nm band signal injection,” Opt. Commun. 176(1-3), 125–129 (2000). [CrossRef]  

33. S. Hwang and K. Cho, “Gain tilt control of L-band erbium-doped fiber amplifier by using a 1550-nm band light injection,” IEEE Photonics Technol. Lett. 13(10), 1070–1072 (2001). [CrossRef]  

34. A. Altuncu and A. Başgümüş, “Gain enhancement in L-band loop EDFA through C-band signal injection,” IEEE Photonics Technol. Lett. 17(7), 1402–1404 (2005). [CrossRef]  

35. Y. Zhang, X. Liu, J. Peng, X. Feng, and W. Zhang, “Wavelength and power dependence of injected C-band laser on pump conversion efficiency of L-band EDFA,” IEEE Photonics Technol. Lett. 14(3), 290–292 (2002). [CrossRef]  

36. C. Lei, H. Feng, Y. Messaddeq, and S. LaRochelle, “Investigation of C-band pumping for extended L-band EDFAs,” J. Opt. Soc. Am. B 37(8), 2345–2352 (2020). [CrossRef]  

37. C. Lei, H. Feng, L. Wang, Y. Messaddeq, and S. Larochelle, “An extended L-band EDFA using C-band pump wavelength,” Opt. InfoBase Conf. Pap. Part F174-OFC 2020(c), 6–8 (2020).

38. C. Lei, H. Feng, Y. Messaddeq, and S. Larochelle, “Investigation of Bi-Directionally, Dual-Wavelength Pumped Extended L-Band EDFAs,” IEEE Photonics Technol. Lett. 32(18), 1227–1230 (2020). [CrossRef]  

39. C. R. Giles and E. Desurvire, “Modeling Erbium-Doped Fiber Amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991). [CrossRef]  

40. M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers,” Opt. Express 15(6), 3236–3246 (2007). [CrossRef]  

41. N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” IEEE Photonic Soc. 24th Annu. Meet., 589–590 (2011).

References

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  1. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
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  2. R. J. Essiambre and A. Mecozzi, “Capacity limits in single-mode fiber and scaling for spatial multiplexing,” Opt. InfoBase Conf. Pap. (2012).
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  3. G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
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  4. K.-P. Ho and J. M. Kahn, “Mode-dependent loss and gain: statistics and effect on mode-division multiplexing,” Opt. Express 19(17), 16612–16635 (2011).
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  5. Q. Kang, E. Lim, Y. Jung, J. K. Sahu, F. Poletti, C. Baskiotis, S. Alam, and D. J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP 01 pump configuration,” Opt. Express 20(19), 20835–20843 (2012).
    [Crossref]
  6. Q. Kang, E. L. Lim, Y. Jung, J. K. Sahu, F. Poletti, S. Alam, and D. J. Richardson, “Modal Gain Control in a Multimode Erbium Doped Fiber Amplifier Incorporating Ring Doping,” Eur. Conf. Opt. Commun.5–7 (2012).
  7. Q. Kang, E. Lim, Y. Jung, F. Poletti, S. Alam, and D. J. Richardson, “Design of Four-Mode Erbium Doped Fiber Amplifier with Low Differential Modal Gain for Modal Division Multiplexed Transmissions,” Opt. Fiber Commun. Conf. 20130–2 (2013).
  8. C Jin, B Ung, Y Messaddeq, and S LaRochelle, “Tailored modal gain in a multi-mode erbium-doped fiber amplifier based on engineered ring doping profiles,” Proc. SPIE 8915, 89150A (2013).
    [Crossref]
  9. Z. Zhang, Q. Mo, C. Guo, N. Zhao, C. Du, and X. Li, “Gain Equalized Four Mode Groups Erbium Doped Fiber Amplifier with LP 01 Pump,” Opt. InfoBase Conf. Pap. Part F138-ACPC 2019(i), 24–26 (2016).
  10. A. Gaur and V. Rastogi, “Design and Analysis of Annulus Core Few Mode EDFA for Modal Gain Equalization,” IEEE Photonics Technol. Lett. 28(10), 1057–1060 (2016).
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  11. Y. Wakayama, K. Igarashi, D. Soma, H. Taga, and T. Tsuritani, “Novel 6-mode fibre amplifier with large erbium-doped area for differential modal gain minimization,” Eur. Conf. Opt. Commun.94–96 (2016).
  12. M. Yamada, D. Nobuhira, S. Miyagawa, O. Koyama, and H. Ono, “Doping concentration distribution in 2-signal LP-mode ring-core erbium-doped fiber,” Appl. Opt. 56(36), 10040–10045 (2017).
    [Crossref]
  13. Z. Zhang, C. Guo, L. Cui, Y. Zhang, C. Du, and X. Li, “All-fiber few-mode erbium-doped fiber amplifier supporting six spatial modes,” Chin. Opt. Lett. 17(10), 100604 (2019).
    [Crossref]
  14. G. Le Cocq, Y. Quiquempois, A. Le Rouge, H. El Hamzaoui, K. Delplace, and L. Bigot, “Few mode Er3+-doped fiber with micro-structured core for mode division multiplexing in the C-band,” Opt. Express 21(25), 31646–31659 (2013).
    [Crossref]
  15. S. Jain, Y. Jung, S. U. Alam, J. K. Sahu, and D. J. Richardson, “Few-mode multi-element fiber amplifier for mode division multiplexing,” Opt. Express 22(23), 29031–29036 (2014).
    [Crossref]
  16. A. Gaur, G. Kumar, and V. Rastogi, “Dual-core few mode EDFA for amplification of 20 modes,” Opt. Quantum Electron. 50(2), 66 (2018).
    [Crossref]
  17. Ankita Gaur and Vipul Rastogi, “Modal gain equalization of 18 modes using a single-trench ring-core EDFA,” J. Opt. Soc. Am. B 35(9), 2211–2216 (2018).
    [Crossref]
  18. Y. Amma, T. Hosokawa, H. Ono, S. Member, K. Ichii, K. Takenaga, S. Matsuo, M. Yamada, and S. Member, “Ring-Core Multicore Few-Mode Erbium-Doped Fiber Amplifier,” IEEE Photonics Technol. Lett. 29(24), 2163–2166 (2017).
    [Crossref]
  19. M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, and K. Nakajima, “Differential Modal Gain Reduction of L-band 5-Mode EDFA Using EDF with Center Depressed Core Index,” J. Lightwave Technol. 35(4), 762–767 (2017).
    [Crossref]
  20. Z. Zhang, C. Guo, L. Cui, Q. Mo, N. Zhao, C. Du, X. Li, and G. Li, “21 Spatial Mode Erbium-Doped Fiber Amplifier for Mode Division Multiplexing Transmission,” Opt. Lett. 43(7), 1550–1553 (2018).
    [Crossref]
  21. N. Bai, E. Ip, Y. Luo, G. D. Peng, T. Wang, and G. Li, “Experimental study on multimode fiber amplifier using modal reconfigurable pump,” Opt. InfoBase Conf. Pap. (2012).
    [Crossref]
  22. M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, N. Hanzawa, and F. Yamamoto, “L-band 2-LP mode EDFA with low modal dependent gain,” Conf. Opt. Fiber Commun. Tech. Dig. Ser. 2015–June, 5–7 (2015).
  23. G. Lopez-Galmiche, Z. Sanjabi Eznaveh, J. E. Antonio-Lopez, A. M. Velazquez Benitez, J. Rodriguez Asomoza, J. J. Sanchez Mondragon, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, C. M. Okonkwo, and R. Amezcua Correa, “Few-mode erbium-doped fiber amplifier with photonic lantern for pump spatial mode control,” Opt. Lett. 41(11), 2588–2591 (2016).
    [Crossref]
  24. Y. Jung, E. L. Lim, Q. Kang, T. C. May-Smith, N. H. L. Wong, R. Standish, F. Poletti, J. K. Sahu, S. U. Alam, and D. J. Richardson, “Cladding pumped few-mode EDFA for mode division multiplexed transmission,” Opt. Express 22(23), 29008–29013 (2014).
    [Crossref]
  25. Y. Yamashita, T. Matsui, M. Wada, S. Aozasa, T. Sakamoto, and K. Nakajima, “Differential modal gain reduction using a void inscribed in a two-mode-erbium doped fiber,” Opt. InfoBase Conf. Pap. Part F174-, 5–7 (2020).
  26. Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).
  27. N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).
  28. G. Le Cocq, Y. Quiquempois, and L. Bigot, “Optimization Algorithm Applied to the Design of Few-Mode Erbium Doped Fiber Amplifier for Modal and Spectral Gain Equalization,” J. Lightwave Technol. 33(1), 100–108 (2015).
    [Crossref]
  29. Q. Kang, E.-L. Lim, F. P. Y. Jung, C. Baskiotis, S. Alam, and D. J. Richardson, “Minimizing differential modal gain in cladding-pumped EDFAs supporting four and six mode groups,” Opt. Express 22(18), 21499–21507 (2014).
    [Crossref]
  30. B. J. Puttnam, R. S. Luís, W. Klaus, J. Sakaguchi, J. D. Mendinueta, and Y. Awaji, “2.15 Pb/s Transmission Using a 22 Core Homogeneous Single- Mode Multi-Core Fiber and Wideband Optical Comb,” Eur. Conf. Opt. Commun.22–24 (2015).
  31. M. Bolshtyansky, I. Mandelbaum, and F. Pan, “Signal excited-state absorption in the L-band EDFA: Simulation and measurements,” J. Lightwave Technol. 23(9), 2796–2799 (2005).
    [Crossref]
  32. M. A. Mahdi, F. R. Mahamd Adikan, P. Poopalan, S. Selvakennedy, W. Y. Chan, and H. Ahmad, “Long-wavelength EDFA gain enhancement through 1550 nm band signal injection,” Opt. Commun. 176(1-3), 125–129 (2000).
    [Crossref]
  33. S. Hwang and K. Cho, “Gain tilt control of L-band erbium-doped fiber amplifier by using a 1550-nm band light injection,” IEEE Photonics Technol. Lett. 13(10), 1070–1072 (2001).
    [Crossref]
  34. A. Altuncu and A. Başgümüş, “Gain enhancement in L-band loop EDFA through C-band signal injection,” IEEE Photonics Technol. Lett. 17(7), 1402–1404 (2005).
    [Crossref]
  35. Y. Zhang, X. Liu, J. Peng, X. Feng, and W. Zhang, “Wavelength and power dependence of injected C-band laser on pump conversion efficiency of L-band EDFA,” IEEE Photonics Technol. Lett. 14(3), 290–292 (2002).
    [Crossref]
  36. C. Lei, H. Feng, Y. Messaddeq, and S. LaRochelle, “Investigation of C-band pumping for extended L-band EDFAs,” J. Opt. Soc. Am. B 37(8), 2345–2352 (2020).
    [Crossref]
  37. C. Lei, H. Feng, L. Wang, Y. Messaddeq, and S. Larochelle, “An extended L-band EDFA using C-band pump wavelength,” Opt. InfoBase Conf. Pap. Part F174-OFC 2020(c), 6–8 (2020).
  38. C. Lei, H. Feng, Y. Messaddeq, and S. Larochelle, “Investigation of Bi-Directionally, Dual-Wavelength Pumped Extended L-Band EDFAs,” IEEE Photonics Technol. Lett. 32(18), 1227–1230 (2020).
    [Crossref]
  39. C. R. Giles and E. Desurvire, “Modeling Erbium-Doped Fiber Amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
    [Crossref]
  40. M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers,” Opt. Express 15(6), 3236–3246 (2007).
    [Crossref]
  41. N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” IEEE Photonic Soc. 24th Annu. Meet., 589–590 (2011).

2020 (2)

C. Lei, H. Feng, Y. Messaddeq, and S. LaRochelle, “Investigation of C-band pumping for extended L-band EDFAs,” J. Opt. Soc. Am. B 37(8), 2345–2352 (2020).
[Crossref]

C. Lei, H. Feng, Y. Messaddeq, and S. Larochelle, “Investigation of Bi-Directionally, Dual-Wavelength Pumped Extended L-Band EDFAs,” IEEE Photonics Technol. Lett. 32(18), 1227–1230 (2020).
[Crossref]

2019 (1)

2018 (3)

2017 (3)

2016 (2)

2015 (1)

2014 (4)

2013 (3)

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

C Jin, B Ung, Y Messaddeq, and S LaRochelle, “Tailored modal gain in a multi-mode erbium-doped fiber amplifier based on engineered ring doping profiles,” Proc. SPIE 8915, 89150A (2013).
[Crossref]

G. Le Cocq, Y. Quiquempois, A. Le Rouge, H. El Hamzaoui, K. Delplace, and L. Bigot, “Few mode Er3+-doped fiber with micro-structured core for mode division multiplexing in the C-band,” Opt. Express 21(25), 31646–31659 (2013).
[Crossref]

2012 (1)

2011 (1)

2007 (1)

2005 (2)

M. Bolshtyansky, I. Mandelbaum, and F. Pan, “Signal excited-state absorption in the L-band EDFA: Simulation and measurements,” J. Lightwave Technol. 23(9), 2796–2799 (2005).
[Crossref]

A. Altuncu and A. Başgümüş, “Gain enhancement in L-band loop EDFA through C-band signal injection,” IEEE Photonics Technol. Lett. 17(7), 1402–1404 (2005).
[Crossref]

2002 (1)

Y. Zhang, X. Liu, J. Peng, X. Feng, and W. Zhang, “Wavelength and power dependence of injected C-band laser on pump conversion efficiency of L-band EDFA,” IEEE Photonics Technol. Lett. 14(3), 290–292 (2002).
[Crossref]

2001 (1)

S. Hwang and K. Cho, “Gain tilt control of L-band erbium-doped fiber amplifier by using a 1550-nm band light injection,” IEEE Photonics Technol. Lett. 13(10), 1070–1072 (2001).
[Crossref]

2000 (1)

M. A. Mahdi, F. R. Mahamd Adikan, P. Poopalan, S. Selvakennedy, W. Y. Chan, and H. Ahmad, “Long-wavelength EDFA gain enhancement through 1550 nm band signal injection,” Opt. Commun. 176(1-3), 125–129 (2000).
[Crossref]

1991 (1)

C. R. Giles and E. Desurvire, “Modeling Erbium-Doped Fiber Amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
[Crossref]

Ahmad, H.

M. A. Mahdi, F. R. Mahamd Adikan, P. Poopalan, S. Selvakennedy, W. Y. Chan, and H. Ahmad, “Long-wavelength EDFA gain enhancement through 1550 nm band signal injection,” Opt. Commun. 176(1-3), 125–129 (2000).
[Crossref]

Alam, S.

Q. Kang, E.-L. Lim, F. P. Y. Jung, C. Baskiotis, S. Alam, and D. J. Richardson, “Minimizing differential modal gain in cladding-pumped EDFAs supporting four and six mode groups,” Opt. Express 22(18), 21499–21507 (2014).
[Crossref]

Q. Kang, E. Lim, Y. Jung, J. K. Sahu, F. Poletti, C. Baskiotis, S. Alam, and D. J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP 01 pump configuration,” Opt. Express 20(19), 20835–20843 (2012).
[Crossref]

Q. Kang, E. L. Lim, Y. Jung, J. K. Sahu, F. Poletti, S. Alam, and D. J. Richardson, “Modal Gain Control in a Multimode Erbium Doped Fiber Amplifier Incorporating Ring Doping,” Eur. Conf. Opt. Commun.5–7 (2012).

Q. Kang, E. Lim, Y. Jung, F. Poletti, S. Alam, and D. J. Richardson, “Design of Four-Mode Erbium Doped Fiber Amplifier with Low Differential Modal Gain for Modal Division Multiplexed Transmissions,” Opt. Fiber Commun. Conf. 20130–2 (2013).

Alam, S. U.

Altuncu, A.

A. Altuncu and A. Başgümüş, “Gain enhancement in L-band loop EDFA through C-band signal injection,” IEEE Photonics Technol. Lett. 17(7), 1402–1404 (2005).
[Crossref]

Alvarado Zacarias, J. C.

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

Amezcua Correa, A.

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

Amezcua Correa, R.

G. Lopez-Galmiche, Z. Sanjabi Eznaveh, J. E. Antonio-Lopez, A. M. Velazquez Benitez, J. Rodriguez Asomoza, J. J. Sanchez Mondragon, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, C. M. Okonkwo, and R. Amezcua Correa, “Few-mode erbium-doped fiber amplifier with photonic lantern for pump spatial mode control,” Opt. Lett. 41(11), 2588–2591 (2016).
[Crossref]

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

Amezcua-Correa, R.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Amma, Y.

Y. Amma, T. Hosokawa, H. Ono, S. Member, K. Ichii, K. Takenaga, S. Matsuo, M. Yamada, and S. Member, “Ring-Core Multicore Few-Mode Erbium-Doped Fiber Amplifier,” IEEE Photonics Technol. Lett. 29(24), 2163–2166 (2017).
[Crossref]

Antonio Lopez, J. E.

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

Antonio-Lopez, J. E.

Aozasa, S.

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, and K. Nakajima, “Differential Modal Gain Reduction of L-band 5-Mode EDFA Using EDF with Center Depressed Core Index,” J. Lightwave Technol. 35(4), 762–767 (2017).
[Crossref]

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, N. Hanzawa, and F. Yamamoto, “L-band 2-LP mode EDFA with low modal dependent gain,” Conf. Opt. Fiber Commun. Tech. Dig. Ser. 2015–June, 5–7 (2015).

Y. Yamashita, T. Matsui, M. Wada, S. Aozasa, T. Sakamoto, and K. Nakajima, “Differential modal gain reduction using a void inscribed in a two-mode-erbium doped fiber,” Opt. InfoBase Conf. Pap. Part F174-, 5–7 (2020).

Awaji, Y.

B. J. Puttnam, R. S. Luís, W. Klaus, J. Sakaguchi, J. D. Mendinueta, and Y. Awaji, “2.15 Pb/s Transmission Using a 22 Core Homogeneous Single- Mode Multi-Core Fiber and Wideband Optical Comb,” Eur. Conf. Opt. Commun.22–24 (2015).

Bai, N.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

N. Bai, E. Ip, Y. Luo, G. D. Peng, T. Wang, and G. Li, “Experimental study on multimode fiber amplifier using modal reconfigurable pump,” Opt. InfoBase Conf. Pap. (2012).
[Crossref]

N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” IEEE Photonic Soc. 24th Annu. Meet., 589–590 (2011).

Basgümüs, A.

A. Altuncu and A. Başgümüş, “Gain enhancement in L-band loop EDFA through C-band signal injection,” IEEE Photonics Technol. Lett. 17(7), 1402–1404 (2005).
[Crossref]

Baskiotis, C.

Bigot, L.

Bolshtyansky, M.

Cang, J.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Chan, W. Y.

M. A. Mahdi, F. R. Mahamd Adikan, P. Poopalan, S. Selvakennedy, W. Y. Chan, and H. Ahmad, “Long-wavelength EDFA gain enhancement through 1550 nm band signal injection,” Opt. Commun. 176(1-3), 125–129 (2000).
[Crossref]

Chang, S. H.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Chen, H.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

Cho, K.

S. Hwang and K. Cho, “Gain tilt control of L-band erbium-doped fiber amplifier by using a 1550-nm band light injection,” IEEE Photonics Technol. Lett. 13(10), 1070–1072 (2001).
[Crossref]

Cui, L.

Delplace, K.

Desurvire, E.

C. R. Giles and E. Desurvire, “Modeling Erbium-Doped Fiber Amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
[Crossref]

Du, C.

El Hamzaoui, H.

Ercan, B.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Essiambre, R. J.

R. J. Essiambre and A. Mecozzi, “Capacity limits in single-mode fiber and scaling for spatial multiplexing,” Opt. InfoBase Conf. Pap. (2012).
[Crossref]

Eznaveh, Z. S.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Feng, H.

C. Lei, H. Feng, Y. Messaddeq, and S. LaRochelle, “Investigation of C-band pumping for extended L-band EDFAs,” J. Opt. Soc. Am. B 37(8), 2345–2352 (2020).
[Crossref]

C. Lei, H. Feng, Y. Messaddeq, and S. Larochelle, “Investigation of Bi-Directionally, Dual-Wavelength Pumped Extended L-Band EDFAs,” IEEE Photonics Technol. Lett. 32(18), 1227–1230 (2020).
[Crossref]

C. Lei, H. Feng, L. Wang, Y. Messaddeq, and S. Larochelle, “An extended L-band EDFA using C-band pump wavelength,” Opt. InfoBase Conf. Pap. Part F174-OFC 2020(c), 6–8 (2020).

Feng, X.

Y. Zhang, X. Liu, J. Peng, X. Feng, and W. Zhang, “Wavelength and power dependence of injected C-band laser on pump conversion efficiency of L-band EDFA,” IEEE Photonics Technol. Lett. 14(3), 290–292 (2002).
[Crossref]

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Fontaine, N. K.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

Gaur, A.

A. Gaur, G. Kumar, and V. Rastogi, “Dual-core few mode EDFA for amplification of 20 modes,” Opt. Quantum Electron. 50(2), 66 (2018).
[Crossref]

A. Gaur and V. Rastogi, “Design and Analysis of Annulus Core Few Mode EDFA for Modal Gain Equalization,” IEEE Photonics Technol. Lett. 28(10), 1057–1060 (2016).
[Crossref]

Gaur, Ankita

Giles, C. R.

C. R. Giles and E. Desurvire, “Modeling Erbium-Doped Fiber Amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
[Crossref]

Gong, M.

Gonnet, C.

G. Lopez-Galmiche, Z. Sanjabi Eznaveh, J. E. Antonio-Lopez, A. M. Velazquez Benitez, J. Rodriguez Asomoza, J. J. Sanchez Mondragon, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, C. M. Okonkwo, and R. Amezcua Correa, “Few-mode erbium-doped fiber amplifier with photonic lantern for pump spatial mode control,” Opt. Lett. 41(11), 2588–2591 (2016).
[Crossref]

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Guo, C.

Hanzawa, N.

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, N. Hanzawa, and F. Yamamoto, “L-band 2-LP mode EDFA with low modal dependent gain,” Conf. Opt. Fiber Commun. Tech. Dig. Ser. 2015–June, 5–7 (2015).

Ho, K.-P.

Hosokawa, T.

Y. Amma, T. Hosokawa, H. Ono, S. Member, K. Ichii, K. Takenaga, S. Matsuo, M. Yamada, and S. Member, “Ring-Core Multicore Few-Mode Erbium-Doped Fiber Amplifier,” IEEE Photonics Technol. Lett. 29(24), 2163–2166 (2017).
[Crossref]

Huang, B.

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Hwang, S.

S. Hwang and K. Cho, “Gain tilt control of L-band erbium-doped fiber amplifier by using a 1550-nm band light injection,” IEEE Photonics Technol. Lett. 13(10), 1070–1072 (2001).
[Crossref]

Ichii, K.

Y. Amma, T. Hosokawa, H. Ono, S. Member, K. Ichii, K. Takenaga, S. Matsuo, M. Yamada, and S. Member, “Ring-Core Multicore Few-Mode Erbium-Doped Fiber Amplifier,” IEEE Photonics Technol. Lett. 29(24), 2163–2166 (2017).
[Crossref]

Igarashi, K.

Y. Wakayama, K. Igarashi, D. Soma, H. Taga, and T. Tsuritani, “Novel 6-mode fibre amplifier with large erbium-doped area for differential modal gain minimization,” Eur. Conf. Opt. Commun.94–96 (2016).

Ip, E.

N. Bai, E. Ip, Y. Luo, G. D. Peng, T. Wang, and G. Li, “Experimental study on multimode fiber amplifier using modal reconfigurable pump,” Opt. InfoBase Conf. Pap. (2012).
[Crossref]

N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” IEEE Photonic Soc. 24th Annu. Meet., 589–590 (2011).

Jain, S.

Jin, C

C Jin, B Ung, Y Messaddeq, and S LaRochelle, “Tailored modal gain in a multi-mode erbium-doped fiber amplifier based on engineered ring doping profiles,” Proc. SPIE 8915, 89150A (2013).
[Crossref]

Jung, F. P. Y.

Jung, Y.

Kahn, J. M.

Kang, Q.

Klaus, W.

B. J. Puttnam, R. S. Luís, W. Klaus, J. Sakaguchi, J. D. Mendinueta, and Y. Awaji, “2.15 Pb/s Transmission Using a 22 Core Homogeneous Single- Mode Multi-Core Fiber and Wideband Optical Comb,” Eur. Conf. Opt. Commun.22–24 (2015).

Koyama, O.

Kumar, G.

A. Gaur, G. Kumar, and V. Rastogi, “Dual-core few mode EDFA for amplification of 20 modes,” Opt. Quantum Electron. 50(2), 66 (2018).
[Crossref]

LaRochelle, S

C Jin, B Ung, Y Messaddeq, and S LaRochelle, “Tailored modal gain in a multi-mode erbium-doped fiber amplifier based on engineered ring doping profiles,” Proc. SPIE 8915, 89150A (2013).
[Crossref]

LaRochelle, S.

C. Lei, H. Feng, Y. Messaddeq, and S. LaRochelle, “Investigation of C-band pumping for extended L-band EDFAs,” J. Opt. Soc. Am. B 37(8), 2345–2352 (2020).
[Crossref]

C. Lei, H. Feng, Y. Messaddeq, and S. Larochelle, “Investigation of Bi-Directionally, Dual-Wavelength Pumped Extended L-Band EDFAs,” IEEE Photonics Technol. Lett. 32(18), 1227–1230 (2020).
[Crossref]

C. Lei, H. Feng, L. Wang, Y. Messaddeq, and S. Larochelle, “An extended L-band EDFA using C-band pump wavelength,” Opt. InfoBase Conf. Pap. Part F174-OFC 2020(c), 6–8 (2020).

Le Cocq, G.

Le Rouge, A.

Lei, C.

C. Lei, H. Feng, Y. Messaddeq, and S. Larochelle, “Investigation of Bi-Directionally, Dual-Wavelength Pumped Extended L-Band EDFAs,” IEEE Photonics Technol. Lett. 32(18), 1227–1230 (2020).
[Crossref]

C. Lei, H. Feng, Y. Messaddeq, and S. LaRochelle, “Investigation of C-band pumping for extended L-band EDFAs,” J. Opt. Soc. Am. B 37(8), 2345–2352 (2020).
[Crossref]

C. Lei, H. Feng, L. Wang, Y. Messaddeq, and S. Larochelle, “An extended L-band EDFA using C-band pump wavelength,” Opt. InfoBase Conf. Pap. Part F174-OFC 2020(c), 6–8 (2020).

Li, C.

Li, G.

Z. Zhang, C. Guo, L. Cui, Q. Mo, N. Zhao, C. Du, X. Li, and G. Li, “21 Spatial Mode Erbium-Doped Fiber Amplifier for Mode Division Multiplexing Transmission,” Opt. Lett. 43(7), 1550–1553 (2018).
[Crossref]

G. Lopez-Galmiche, Z. Sanjabi Eznaveh, J. E. Antonio-Lopez, A. M. Velazquez Benitez, J. Rodriguez Asomoza, J. J. Sanchez Mondragon, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, C. M. Okonkwo, and R. Amezcua Correa, “Few-mode erbium-doped fiber amplifier with photonic lantern for pump spatial mode control,” Opt. Lett. 41(11), 2588–2591 (2016).
[Crossref]

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

N. Bai, E. Ip, Y. Luo, G. D. Peng, T. Wang, and G. Li, “Experimental study on multimode fiber amplifier using modal reconfigurable pump,” Opt. InfoBase Conf. Pap. (2012).
[Crossref]

N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” IEEE Photonic Soc. 24th Annu. Meet., 589–590 (2011).

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

Li, X.

Liao, S.

Lim, E.

Q. Kang, E. Lim, Y. Jung, J. K. Sahu, F. Poletti, C. Baskiotis, S. Alam, and D. J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP 01 pump configuration,” Opt. Express 20(19), 20835–20843 (2012).
[Crossref]

Q. Kang, E. Lim, Y. Jung, F. Poletti, S. Alam, and D. J. Richardson, “Design of Four-Mode Erbium Doped Fiber Amplifier with Low Differential Modal Gain for Modal Division Multiplexed Transmissions,” Opt. Fiber Commun. Conf. 20130–2 (2013).

Lim, E. L.

Y. Jung, E. L. Lim, Q. Kang, T. C. May-Smith, N. H. L. Wong, R. Standish, F. Poletti, J. K. Sahu, S. U. Alam, and D. J. Richardson, “Cladding pumped few-mode EDFA for mode division multiplexed transmission,” Opt. Express 22(23), 29008–29013 (2014).
[Crossref]

Q. Kang, E. L. Lim, Y. Jung, J. K. Sahu, F. Poletti, S. Alam, and D. J. Richardson, “Modal Gain Control in a Multimode Erbium Doped Fiber Amplifier Incorporating Ring Doping,” Eur. Conf. Opt. Commun.5–7 (2012).

Lim, E.-L.

Liu, X.

Y. Zhang, X. Liu, J. Peng, X. Feng, and W. Zhang, “Wavelength and power dependence of injected C-band laser on pump conversion efficiency of L-band EDFA,” IEEE Photonics Technol. Lett. 14(3), 290–292 (2002).
[Crossref]

Lopez, J. E. A.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Lopez-Galmiche, G.

Luís, R. S.

B. J. Puttnam, R. S. Luís, W. Klaus, J. Sakaguchi, J. D. Mendinueta, and Y. Awaji, “2.15 Pb/s Transmission Using a 22 Core Homogeneous Single- Mode Multi-Core Fiber and Wideband Optical Comb,” Eur. Conf. Opt. Commun.22–24 (2015).

Luo, Y.

N. Bai, E. Ip, Y. Luo, G. D. Peng, T. Wang, and G. Li, “Experimental study on multimode fiber amplifier using modal reconfigurable pump,” Opt. InfoBase Conf. Pap. (2012).
[Crossref]

Mahamd Adikan, F. R.

M. A. Mahdi, F. R. Mahamd Adikan, P. Poopalan, S. Selvakennedy, W. Y. Chan, and H. Ahmad, “Long-wavelength EDFA gain enhancement through 1550 nm band signal injection,” Opt. Commun. 176(1-3), 125–129 (2000).
[Crossref]

Mahdi, M. A.

M. A. Mahdi, F. R. Mahamd Adikan, P. Poopalan, S. Selvakennedy, W. Y. Chan, and H. Ahmad, “Long-wavelength EDFA gain enhancement through 1550 nm band signal injection,” Opt. Commun. 176(1-3), 125–129 (2000).
[Crossref]

Mandelbaum, I.

Matsui, T.

Y. Yamashita, T. Matsui, M. Wada, S. Aozasa, T. Sakamoto, and K. Nakajima, “Differential modal gain reduction using a void inscribed in a two-mode-erbium doped fiber,” Opt. InfoBase Conf. Pap. Part F174-, 5–7 (2020).

Matsuo, S.

Y. Amma, T. Hosokawa, H. Ono, S. Member, K. Ichii, K. Takenaga, S. Matsuo, M. Yamada, and S. Member, “Ring-Core Multicore Few-Mode Erbium-Doped Fiber Amplifier,” IEEE Photonics Technol. Lett. 29(24), 2163–2166 (2017).
[Crossref]

May-Smith, T. C.

Mecozzi, A.

R. J. Essiambre and A. Mecozzi, “Capacity limits in single-mode fiber and scaling for spatial multiplexing,” Opt. InfoBase Conf. Pap. (2012).
[Crossref]

Member, S.

Y. Amma, T. Hosokawa, H. Ono, S. Member, K. Ichii, K. Takenaga, S. Matsuo, M. Yamada, and S. Member, “Ring-Core Multicore Few-Mode Erbium-Doped Fiber Amplifier,” IEEE Photonics Technol. Lett. 29(24), 2163–2166 (2017).
[Crossref]

Y. Amma, T. Hosokawa, H. Ono, S. Member, K. Ichii, K. Takenaga, S. Matsuo, M. Yamada, and S. Member, “Ring-Core Multicore Few-Mode Erbium-Doped Fiber Amplifier,” IEEE Photonics Technol. Lett. 29(24), 2163–2166 (2017).
[Crossref]

Mendinueta, J. D.

B. J. Puttnam, R. S. Luís, W. Klaus, J. Sakaguchi, J. D. Mendinueta, and Y. Awaji, “2.15 Pb/s Transmission Using a 22 Core Homogeneous Single- Mode Multi-Core Fiber and Wideband Optical Comb,” Eur. Conf. Opt. Commun.22–24 (2015).

Messaddeq, Y

C Jin, B Ung, Y Messaddeq, and S LaRochelle, “Tailored modal gain in a multi-mode erbium-doped fiber amplifier based on engineered ring doping profiles,” Proc. SPIE 8915, 89150A (2013).
[Crossref]

Messaddeq, Y.

C. Lei, H. Feng, Y. Messaddeq, and S. LaRochelle, “Investigation of C-band pumping for extended L-band EDFAs,” J. Opt. Soc. Am. B 37(8), 2345–2352 (2020).
[Crossref]

C. Lei, H. Feng, Y. Messaddeq, and S. Larochelle, “Investigation of Bi-Directionally, Dual-Wavelength Pumped Extended L-Band EDFAs,” IEEE Photonics Technol. Lett. 32(18), 1227–1230 (2020).
[Crossref]

C. Lei, H. Feng, L. Wang, Y. Messaddeq, and S. Larochelle, “An extended L-band EDFA using C-band pump wavelength,” Opt. InfoBase Conf. Pap. Part F174-OFC 2020(c), 6–8 (2020).

Miyagawa, S.

Mo, Q.

Z. Zhang, C. Guo, L. Cui, Q. Mo, N. Zhao, C. Du, X. Li, and G. Li, “21 Spatial Mode Erbium-Doped Fiber Amplifier for Mode Division Multiplexing Transmission,” Opt. Lett. 43(7), 1550–1553 (2018).
[Crossref]

Z. Zhang, Q. Mo, C. Guo, N. Zhao, C. Du, and X. Li, “Gain Equalized Four Mode Groups Erbium Doped Fiber Amplifier with LP 01 Pump,” Opt. InfoBase Conf. Pap. Part F138-ACPC 2019(i), 24–26 (2016).

Mori, T.

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, and K. Nakajima, “Differential Modal Gain Reduction of L-band 5-Mode EDFA Using EDF with Center Depressed Core Index,” J. Lightwave Technol. 35(4), 762–767 (2017).
[Crossref]

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, N. Hanzawa, and F. Yamamoto, “L-band 2-LP mode EDFA with low modal dependent gain,” Conf. Opt. Fiber Commun. Tech. Dig. Ser. 2015–June, 5–7 (2015).

Nakajima, K.

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, and K. Nakajima, “Differential Modal Gain Reduction of L-band 5-Mode EDFA Using EDF with Center Depressed Core Index,” J. Lightwave Technol. 35(4), 762–767 (2017).
[Crossref]

Y. Yamashita, T. Matsui, M. Wada, S. Aozasa, T. Sakamoto, and K. Nakajima, “Differential modal gain reduction using a void inscribed in a two-mode-erbium doped fiber,” Opt. InfoBase Conf. Pap. Part F174-, 5–7 (2020).

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Nobuhira, D.

Okonkwo, C. M.

Ono, H.

Y. Amma, T. Hosokawa, H. Ono, S. Member, K. Ichii, K. Takenaga, S. Matsuo, M. Yamada, and S. Member, “Ring-Core Multicore Few-Mode Erbium-Doped Fiber Amplifier,” IEEE Photonics Technol. Lett. 29(24), 2163–2166 (2017).
[Crossref]

M. Yamada, D. Nobuhira, S. Miyagawa, O. Koyama, and H. Ono, “Doping concentration distribution in 2-signal LP-mode ring-core erbium-doped fiber,” Appl. Opt. 56(36), 10040–10045 (2017).
[Crossref]

Pan, F.

Peng, G. D.

N. Bai, E. Ip, Y. Luo, G. D. Peng, T. Wang, and G. Li, “Experimental study on multimode fiber amplifier using modal reconfigurable pump,” Opt. InfoBase Conf. Pap. (2012).
[Crossref]

Peng, J.

Y. Zhang, X. Liu, J. Peng, X. Feng, and W. Zhang, “Wavelength and power dependence of injected C-band laser on pump conversion efficiency of L-band EDFA,” IEEE Photonics Technol. Lett. 14(3), 290–292 (2002).
[Crossref]

Poletti, F.

Y. Jung, E. L. Lim, Q. Kang, T. C. May-Smith, N. H. L. Wong, R. Standish, F. Poletti, J. K. Sahu, S. U. Alam, and D. J. Richardson, “Cladding pumped few-mode EDFA for mode division multiplexed transmission,” Opt. Express 22(23), 29008–29013 (2014).
[Crossref]

Q. Kang, E. Lim, Y. Jung, J. K. Sahu, F. Poletti, C. Baskiotis, S. Alam, and D. J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP 01 pump configuration,” Opt. Express 20(19), 20835–20843 (2012).
[Crossref]

Q. Kang, E. L. Lim, Y. Jung, J. K. Sahu, F. Poletti, S. Alam, and D. J. Richardson, “Modal Gain Control in a Multimode Erbium Doped Fiber Amplifier Incorporating Ring Doping,” Eur. Conf. Opt. Commun.5–7 (2012).

Q. Kang, E. Lim, Y. Jung, F. Poletti, S. Alam, and D. J. Richardson, “Design of Four-Mode Erbium Doped Fiber Amplifier with Low Differential Modal Gain for Modal Division Multiplexed Transmissions,” Opt. Fiber Commun. Conf. 20130–2 (2013).

Poopalan, P.

M. A. Mahdi, F. R. Mahamd Adikan, P. Poopalan, S. Selvakennedy, W. Y. Chan, and H. Ahmad, “Long-wavelength EDFA gain enhancement through 1550 nm band signal injection,” Opt. Commun. 176(1-3), 125–129 (2000).
[Crossref]

Puttnam, B. J.

B. J. Puttnam, R. S. Luís, W. Klaus, J. Sakaguchi, J. D. Mendinueta, and Y. Awaji, “2.15 Pb/s Transmission Using a 22 Core Homogeneous Single- Mode Multi-Core Fiber and Wideband Optical Comb,” Eur. Conf. Opt. Commun.22–24 (2015).

Quiquempois, Y.

Rastogi, V.

A. Gaur, G. Kumar, and V. Rastogi, “Dual-core few mode EDFA for amplification of 20 modes,” Opt. Quantum Electron. 50(2), 66 (2018).
[Crossref]

A. Gaur and V. Rastogi, “Design and Analysis of Annulus Core Few Mode EDFA for Modal Gain Equalization,” IEEE Photonics Technol. Lett. 28(10), 1057–1060 (2016).
[Crossref]

Rastogi, Vipul

Richardson, D. J.

S. Jain, Y. Jung, S. U. Alam, J. K. Sahu, and D. J. Richardson, “Few-mode multi-element fiber amplifier for mode division multiplexing,” Opt. Express 22(23), 29031–29036 (2014).
[Crossref]

Y. Jung, E. L. Lim, Q. Kang, T. C. May-Smith, N. H. L. Wong, R. Standish, F. Poletti, J. K. Sahu, S. U. Alam, and D. J. Richardson, “Cladding pumped few-mode EDFA for mode division multiplexed transmission,” Opt. Express 22(23), 29008–29013 (2014).
[Crossref]

Q. Kang, E.-L. Lim, F. P. Y. Jung, C. Baskiotis, S. Alam, and D. J. Richardson, “Minimizing differential modal gain in cladding-pumped EDFAs supporting four and six mode groups,” Opt. Express 22(18), 21499–21507 (2014).
[Crossref]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Q. Kang, E. Lim, Y. Jung, J. K. Sahu, F. Poletti, C. Baskiotis, S. Alam, and D. J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP 01 pump configuration,” Opt. Express 20(19), 20835–20843 (2012).
[Crossref]

Q. Kang, E. Lim, Y. Jung, F. Poletti, S. Alam, and D. J. Richardson, “Design of Four-Mode Erbium Doped Fiber Amplifier with Low Differential Modal Gain for Modal Division Multiplexed Transmissions,” Opt. Fiber Commun. Conf. 20130–2 (2013).

Q. Kang, E. L. Lim, Y. Jung, J. K. Sahu, F. Poletti, S. Alam, and D. J. Richardson, “Modal Gain Control in a Multimode Erbium Doped Fiber Amplifier Incorporating Ring Doping,” Eur. Conf. Opt. Commun.5–7 (2012).

Rodriguez Asomoza, J.

Ryf, R.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

Sahu, J. K.

Sakaguchi, J.

B. J. Puttnam, R. S. Luís, W. Klaus, J. Sakaguchi, J. D. Mendinueta, and Y. Awaji, “2.15 Pb/s Transmission Using a 22 Core Homogeneous Single- Mode Multi-Core Fiber and Wideband Optical Comb,” Eur. Conf. Opt. Commun.22–24 (2015).

Sakamoto, T.

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, and K. Nakajima, “Differential Modal Gain Reduction of L-band 5-Mode EDFA Using EDF with Center Depressed Core Index,” J. Lightwave Technol. 35(4), 762–767 (2017).
[Crossref]

Y. Yamashita, T. Matsui, M. Wada, S. Aozasa, T. Sakamoto, and K. Nakajima, “Differential modal gain reduction using a void inscribed in a two-mode-erbium doped fiber,” Opt. InfoBase Conf. Pap. Part F174-, 5–7 (2020).

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, N. Hanzawa, and F. Yamamoto, “L-band 2-LP mode EDFA with low modal dependent gain,” Conf. Opt. Fiber Commun. Tech. Dig. Ser. 2015–June, 5–7 (2015).

Sanchez Mondragon, J. J.

Sanjabi Eznaveh, Z.

G. Lopez-Galmiche, Z. Sanjabi Eznaveh, J. E. Antonio-Lopez, A. M. Velazquez Benitez, J. Rodriguez Asomoza, J. J. Sanchez Mondragon, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, C. M. Okonkwo, and R. Amezcua Correa, “Few-mode erbium-doped fiber amplifier with photonic lantern for pump spatial mode control,” Opt. Lett. 41(11), 2588–2591 (2016).
[Crossref]

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

Schulzgen, A.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Schülzgen, A.

G. Lopez-Galmiche, Z. Sanjabi Eznaveh, J. E. Antonio-Lopez, A. M. Velazquez Benitez, J. Rodriguez Asomoza, J. J. Sanchez Mondragon, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, C. M. Okonkwo, and R. Amezcua Correa, “Few-mode erbium-doped fiber amplifier with photonic lantern for pump spatial mode control,” Opt. Lett. 41(11), 2588–2591 (2016).
[Crossref]

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

Selvakennedy, S.

M. A. Mahdi, F. R. Mahamd Adikan, P. Poopalan, S. Selvakennedy, W. Y. Chan, and H. Ahmad, “Long-wavelength EDFA gain enhancement through 1550 nm band signal injection,” Opt. Commun. 176(1-3), 125–129 (2000).
[Crossref]

Sillard, P.

G. Lopez-Galmiche, Z. Sanjabi Eznaveh, J. E. Antonio-Lopez, A. M. Velazquez Benitez, J. Rodriguez Asomoza, J. J. Sanchez Mondragon, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, C. M. Okonkwo, and R. Amezcua Correa, “Few-mode erbium-doped fiber amplifier with photonic lantern for pump spatial mode control,” Opt. Lett. 41(11), 2588–2591 (2016).
[Crossref]

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Soma, D.

Y. Wakayama, K. Igarashi, D. Soma, H. Taga, and T. Tsuritani, “Novel 6-mode fibre amplifier with large erbium-doped area for differential modal gain minimization,” Eur. Conf. Opt. Commun.94–96 (2016).

Standish, R.

Taga, H.

Y. Wakayama, K. Igarashi, D. Soma, H. Taga, and T. Tsuritani, “Novel 6-mode fibre amplifier with large erbium-doped area for differential modal gain minimization,” Eur. Conf. Opt. Commun.94–96 (2016).

Takenaga, K.

Y. Amma, T. Hosokawa, H. Ono, S. Member, K. Ichii, K. Takenaga, S. Matsuo, M. Yamada, and S. Member, “Ring-Core Multicore Few-Mode Erbium-Doped Fiber Amplifier,” IEEE Photonics Technol. Lett. 29(24), 2163–2166 (2017).
[Crossref]

Tsuritani, T.

Y. Wakayama, K. Igarashi, D. Soma, H. Taga, and T. Tsuritani, “Novel 6-mode fibre amplifier with large erbium-doped area for differential modal gain minimization,” Eur. Conf. Opt. Commun.94–96 (2016).

Ung, B

C Jin, B Ung, Y Messaddeq, and S LaRochelle, “Tailored modal gain in a multi-mode erbium-doped fiber amplifier based on engineered ring doping profiles,” Proc. SPIE 8915, 89150A (2013).
[Crossref]

Velaquez-Benitez, A.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Velazquez Benitez, A. M.

Wada, M.

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, and K. Nakajima, “Differential Modal Gain Reduction of L-band 5-Mode EDFA Using EDF with Center Depressed Core Index,” J. Lightwave Technol. 35(4), 762–767 (2017).
[Crossref]

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, N. Hanzawa, and F. Yamamoto, “L-band 2-LP mode EDFA with low modal dependent gain,” Conf. Opt. Fiber Commun. Tech. Dig. Ser. 2015–June, 5–7 (2015).

Y. Yamashita, T. Matsui, M. Wada, S. Aozasa, T. Sakamoto, and K. Nakajima, “Differential modal gain reduction using a void inscribed in a two-mode-erbium doped fiber,” Opt. InfoBase Conf. Pap. Part F174-, 5–7 (2020).

Wakayama, Y.

Y. Wakayama, K. Igarashi, D. Soma, H. Taga, and T. Tsuritani, “Novel 6-mode fibre amplifier with large erbium-doped area for differential modal gain minimization,” Eur. Conf. Opt. Commun.94–96 (2016).

Wang, L.

C. Lei, H. Feng, L. Wang, Y. Messaddeq, and S. Larochelle, “An extended L-band EDFA using C-band pump wavelength,” Opt. InfoBase Conf. Pap. Part F174-OFC 2020(c), 6–8 (2020).

Wang, T.

N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” IEEE Photonic Soc. 24th Annu. Meet., 589–590 (2011).

N. Bai, E. Ip, Y. Luo, G. D. Peng, T. Wang, and G. Li, “Experimental study on multimode fiber amplifier using modal reconfigurable pump,” Opt. InfoBase Conf. Pap. (2012).
[Crossref]

Wong, N. H. L.

Xia, C.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Yamada, M.

M. Yamada, D. Nobuhira, S. Miyagawa, O. Koyama, and H. Ono, “Doping concentration distribution in 2-signal LP-mode ring-core erbium-doped fiber,” Appl. Opt. 56(36), 10040–10045 (2017).
[Crossref]

Y. Amma, T. Hosokawa, H. Ono, S. Member, K. Ichii, K. Takenaga, S. Matsuo, M. Yamada, and S. Member, “Ring-Core Multicore Few-Mode Erbium-Doped Fiber Amplifier,” IEEE Photonics Technol. Lett. 29(24), 2163–2166 (2017).
[Crossref]

Yamamoto, F.

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, N. Hanzawa, and F. Yamamoto, “L-band 2-LP mode EDFA with low modal dependent gain,” Conf. Opt. Fiber Commun. Tech. Dig. Ser. 2015–June, 5–7 (2015).

Yamamoto, T.

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, and K. Nakajima, “Differential Modal Gain Reduction of L-band 5-Mode EDFA Using EDF with Center Depressed Core Index,” J. Lightwave Technol. 35(4), 762–767 (2017).
[Crossref]

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, N. Hanzawa, and F. Yamamoto, “L-band 2-LP mode EDFA with low modal dependent gain,” Conf. Opt. Fiber Commun. Tech. Dig. Ser. 2015–June, 5–7 (2015).

Yamashita, Y.

Y. Yamashita, T. Matsui, M. Wada, S. Aozasa, T. Sakamoto, and K. Nakajima, “Differential modal gain reduction using a void inscribed in a two-mode-erbium doped fiber,” Opt. InfoBase Conf. Pap. Part F174-, 5–7 (2020).

Yan, P.

Yuan, Y.

Zaharias, J. C. A.

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

Zhang, H.

Zhang, W.

Y. Zhang, X. Liu, J. Peng, X. Feng, and W. Zhang, “Wavelength and power dependence of injected C-band laser on pump conversion efficiency of L-band EDFA,” IEEE Photonics Technol. Lett. 14(3), 290–292 (2002).
[Crossref]

Zhang, Y.

Z. Zhang, C. Guo, L. Cui, Y. Zhang, C. Du, and X. Li, “All-fiber few-mode erbium-doped fiber amplifier supporting six spatial modes,” Chin. Opt. Lett. 17(10), 100604 (2019).
[Crossref]

Y. Zhang, X. Liu, J. Peng, X. Feng, and W. Zhang, “Wavelength and power dependence of injected C-band laser on pump conversion efficiency of L-band EDFA,” IEEE Photonics Technol. Lett. 14(3), 290–292 (2002).
[Crossref]

Zhang, Z.

Zhao, N.

Z. Zhang, C. Guo, L. Cui, Q. Mo, N. Zhao, C. Du, X. Li, and G. Li, “21 Spatial Mode Erbium-Doped Fiber Amplifier for Mode Division Multiplexing Transmission,” Opt. Lett. 43(7), 1550–1553 (2018).
[Crossref]

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Z. Zhang, Q. Mo, C. Guo, N. Zhao, C. Du, and X. Li, “Gain Equalized Four Mode Groups Erbium Doped Fiber Amplifier with LP 01 Pump,” Opt. InfoBase Conf. Pap. Part F138-ACPC 2019(i), 24–26 (2016).

Adv. Opt. Photonics (1)

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Appl. Opt. (1)

Chin. Opt. Lett. (1)

IEEE Photonics Technol. Lett. (6)

Y. Amma, T. Hosokawa, H. Ono, S. Member, K. Ichii, K. Takenaga, S. Matsuo, M. Yamada, and S. Member, “Ring-Core Multicore Few-Mode Erbium-Doped Fiber Amplifier,” IEEE Photonics Technol. Lett. 29(24), 2163–2166 (2017).
[Crossref]

A. Gaur and V. Rastogi, “Design and Analysis of Annulus Core Few Mode EDFA for Modal Gain Equalization,” IEEE Photonics Technol. Lett. 28(10), 1057–1060 (2016).
[Crossref]

S. Hwang and K. Cho, “Gain tilt control of L-band erbium-doped fiber amplifier by using a 1550-nm band light injection,” IEEE Photonics Technol. Lett. 13(10), 1070–1072 (2001).
[Crossref]

A. Altuncu and A. Başgümüş, “Gain enhancement in L-band loop EDFA through C-band signal injection,” IEEE Photonics Technol. Lett. 17(7), 1402–1404 (2005).
[Crossref]

Y. Zhang, X. Liu, J. Peng, X. Feng, and W. Zhang, “Wavelength and power dependence of injected C-band laser on pump conversion efficiency of L-band EDFA,” IEEE Photonics Technol. Lett. 14(3), 290–292 (2002).
[Crossref]

C. Lei, H. Feng, Y. Messaddeq, and S. Larochelle, “Investigation of Bi-Directionally, Dual-Wavelength Pumped Extended L-Band EDFAs,” IEEE Photonics Technol. Lett. 32(18), 1227–1230 (2020).
[Crossref]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Opt. Commun. (1)

M. A. Mahdi, F. R. Mahamd Adikan, P. Poopalan, S. Selvakennedy, W. Y. Chan, and H. Ahmad, “Long-wavelength EDFA gain enhancement through 1550 nm band signal injection,” Opt. Commun. 176(1-3), 125–129 (2000).
[Crossref]

Opt. Express (7)

Q. Kang, E.-L. Lim, F. P. Y. Jung, C. Baskiotis, S. Alam, and D. J. Richardson, “Minimizing differential modal gain in cladding-pumped EDFAs supporting four and six mode groups,” Opt. Express 22(18), 21499–21507 (2014).
[Crossref]

Y. Jung, E. L. Lim, Q. Kang, T. C. May-Smith, N. H. L. Wong, R. Standish, F. Poletti, J. K. Sahu, S. U. Alam, and D. J. Richardson, “Cladding pumped few-mode EDFA for mode division multiplexed transmission,” Opt. Express 22(23), 29008–29013 (2014).
[Crossref]

K.-P. Ho and J. M. Kahn, “Mode-dependent loss and gain: statistics and effect on mode-division multiplexing,” Opt. Express 19(17), 16612–16635 (2011).
[Crossref]

Q. Kang, E. Lim, Y. Jung, J. K. Sahu, F. Poletti, C. Baskiotis, S. Alam, and D. J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP 01 pump configuration,” Opt. Express 20(19), 20835–20843 (2012).
[Crossref]

G. Le Cocq, Y. Quiquempois, A. Le Rouge, H. El Hamzaoui, K. Delplace, and L. Bigot, “Few mode Er3+-doped fiber with micro-structured core for mode division multiplexing in the C-band,” Opt. Express 21(25), 31646–31659 (2013).
[Crossref]

S. Jain, Y. Jung, S. U. Alam, J. K. Sahu, and D. J. Richardson, “Few-mode multi-element fiber amplifier for mode division multiplexing,” Opt. Express 22(23), 29031–29036 (2014).
[Crossref]

M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers,” Opt. Express 15(6), 3236–3246 (2007).
[Crossref]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

A. Gaur, G. Kumar, and V. Rastogi, “Dual-core few mode EDFA for amplification of 20 modes,” Opt. Quantum Electron. 50(2), 66 (2018).
[Crossref]

Proc. SPIE (1)

C Jin, B Ung, Y Messaddeq, and S LaRochelle, “Tailored modal gain in a multi-mode erbium-doped fiber amplifier based on engineered ring doping profiles,” Proc. SPIE 8915, 89150A (2013).
[Crossref]

Other (13)

Z. Zhang, Q. Mo, C. Guo, N. Zhao, C. Du, and X. Li, “Gain Equalized Four Mode Groups Erbium Doped Fiber Amplifier with LP 01 Pump,” Opt. InfoBase Conf. Pap. Part F138-ACPC 2019(i), 24–26 (2016).

R. J. Essiambre and A. Mecozzi, “Capacity limits in single-mode fiber and scaling for spatial multiplexing,” Opt. InfoBase Conf. Pap. (2012).
[Crossref]

Q. Kang, E. L. Lim, Y. Jung, J. K. Sahu, F. Poletti, S. Alam, and D. J. Richardson, “Modal Gain Control in a Multimode Erbium Doped Fiber Amplifier Incorporating Ring Doping,” Eur. Conf. Opt. Commun.5–7 (2012).

Q. Kang, E. Lim, Y. Jung, F. Poletti, S. Alam, and D. J. Richardson, “Design of Four-Mode Erbium Doped Fiber Amplifier with Low Differential Modal Gain for Modal Division Multiplexed Transmissions,” Opt. Fiber Commun. Conf. 20130–2 (2013).

N. Bai, E. Ip, Y. Luo, G. D. Peng, T. Wang, and G. Li, “Experimental study on multimode fiber amplifier using modal reconfigurable pump,” Opt. InfoBase Conf. Pap. (2012).
[Crossref]

M. Wada, T. Sakamoto, S. Aozasa, T. Mori, T. Yamamoto, N. Hanzawa, and F. Yamamoto, “L-band 2-LP mode EDFA with low modal dependent gain,” Conf. Opt. Fiber Commun. Tech. Dig. Ser. 2015–June, 5–7 (2015).

Y. Wakayama, K. Igarashi, D. Soma, H. Taga, and T. Tsuritani, “Novel 6-mode fibre amplifier with large erbium-doped area for differential modal gain minimization,” Eur. Conf. Opt. Commun.94–96 (2016).

Y. Yamashita, T. Matsui, M. Wada, S. Aozasa, T. Sakamoto, and K. Nakajima, “Differential modal gain reduction using a void inscribed in a two-mode-erbium doped fiber,” Opt. InfoBase Conf. Pap. Part F174-, 5–7 (2020).

Z. Sanjabi Eznaveh, N. K. Fontaine, H. Chen, J. E. Antonio Lopez, J. C. Alvarado Zacarias, B. Huang, A. Amezcua Correa, C. Gonnet, P. Sillard, G. Li, A. Schülzgen, R. Ryf, and R. Amezcua Correa, “Ultra-Low DMG multimode EDFA,” 2017 Opt. Fiber Commun. Conf. Exhib. OFC 2017 - Proc. 4–6 (2017).

N. K. Fontaine, B. Huang, Z. S. Eznaveh, H. Chen, J. Cang, B. Ercan, A. Velaquez-Benitez, S. H. Chang, R. Ryf, A. Schulzgen, J. C. A. Zaharias, P. Sillard, C. Gonnet, J. E. A. Lopez, and R. Amezcua-Correa, “Multi-mode optical fiber amplifier supporting over 10 spatial modes,” 2016 Opt. Fiber Commun. Conf. Exhib.10–12 (2016).

B. J. Puttnam, R. S. Luís, W. Klaus, J. Sakaguchi, J. D. Mendinueta, and Y. Awaji, “2.15 Pb/s Transmission Using a 22 Core Homogeneous Single- Mode Multi-Core Fiber and Wideband Optical Comb,” Eur. Conf. Opt. Commun.22–24 (2015).

C. Lei, H. Feng, L. Wang, Y. Messaddeq, and S. Larochelle, “An extended L-band EDFA using C-band pump wavelength,” Opt. InfoBase Conf. Pap. Part F174-OFC 2020(c), 6–8 (2020).

N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” IEEE Photonic Soc. 24th Annu. Meet., 589–590 (2011).

Data availability

No data were generated or analyzed in the presented research.

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Figures (9)

Fig. 1.
Fig. 1. (a) Refractive index profile of proposed trench-assisted 6-mode EDF (colored region represents the doping region). (b) Map of the allowable 6-signal mode area for the trench width ( $d$ ) and $N{A_2}$ of trench-assisted 6-mode EDF
Fig. 2.
Fig. 2. (a) The CF as a function of the $N{A_2}$ for each mode at 1600 nm wavelength. (b) Normalized intensity of each mode for 980 nm pump (solid line) and 1600 nm signal (dashed line) in trench-assisted 6-mode EDF along with the fiber radius position.
Fig. 3.
Fig. 3. (a) Three-level diagram of Er3+ in FM-EDF. (b) Schematic diagram of fiber amplifiers.
Fig. 4.
Fig. 4. (a) Absorption and emission cross-sections as a function of wavelength from 1500 to 1630 nm for L-band Er3+ doped fiber (green line is ESA cross-section after 1580 nm). (b) Power spectrum evolutions of four mode groups with fiber length with the equal proportion of pump mode components (LP01, LP11, LP21, LP02) and a pump wavelength of 980 nm.
Fig. 5.
Fig. 5. Variations of gain of different signal mode groups and total gain of all modes with fiber length at (a) 980 nm, (b) 1530 nm, (c) 1536 nm, and 1550 nm pump wavelength.
Fig. 6.
Fig. 6. Calculated maximum DMG values as a function of the ratio of LP01, LP11 and LP21 pump mode power to total power with a pump wavelength of (a) 980 nm, (b) 1530 nm, (c) 1536 nm, and (d) 1550 nm at signal wavelength ranging from 1570 to 1618 nm.
Fig. 7.
Fig. 7. Calculated maximum DMG values as a function of the ratio of LP11 and LP21 pump mode power to total power.
Fig. 8.
Fig. 8. Spectral variation of gains (solid line) and noise figures (dashed line) at pump wavelength (a) 980 nm, (b) 1530 nm, (c) 1536 nm, and (d) 1550 nm at signal wavelength ranging from 1570 to 1618 nm.
Fig. 9.
Fig. 9. (a) Effect of pump power on average gains and DMG under different pump wavelengths and pump forms. (b) Gain coefficient versus pump power for cladding pumping and core pumping at a pump wavelength of 1530 nm.

Tables (3)

Tables Icon

Table 1. Fiber Parameters

Tables Icon

Table 2. The normalized overlap factors of the 980 nm pump (columns) and 1600 nm signal (rows) intensity

Tables Icon

Table 3. Simulation Parameters

Equations (11)

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Γ p , i s , j = 0 2 π a a I s , j ( r , φ ) I p , i ( r , φ ) r d r d φ ,
Γ p , 01 s , 01 > Γ p , 01 s , 02 > Γ p , 01 s , 11 > Γ p , 01 s , 21 Γ p , 11 s , 01 Γ p , 11 s , 11 Γ p , 11 s , 21 > Γ p , 11 s , 02 Γ p , 21 s , 11 Γ p , 21 s , 21 > Γ p , 21 s , 01 > Γ p , 21 s , 02 , Γ p , 02 s , 02 > Γ p , 02 s , 01 > Γ p , 02 s , 11 Γ p , 02 s , 21
d P k d z = u k ( σ e k σ e s a , k ) 0 2 π 0 i k ( r , φ ) n 2 ( r , φ , z ) r d r d φ ( P k ( z ) + m h v k Δ v ) u k σ a k 0 2 π 0 i k ( r , φ ) n 1 ( r , φ , z ) r d r d φ P k ( z ) ,
d n 2 ( r , φ , z ) d z = n 1 ( r , φ , z ) k P k ( z ) i k ( r , φ ) ( σ a k ) h v k n 2 ( r , φ , z ) k P k ( z ) i k ( r , φ ) ( σ e k σ e s a , k ) h v k n 2 ( r , φ , z ) τ ,
n t ( r , φ , z ) = n 1 ( r , φ , z ) + n 2 ( r , φ , z ) ,
± d P P , i , j d z = σ e j k = 1 M N 2 k ( z ) Γ i , j , k P P , i , j ( z ) σ a j k = 1 M N 1 k ( z ) Γ i , j , k P P , i , j ( z ) , d P S , i , j d z = ( σ e j σ e s a , j ) k = 1 M N 2 k ( z ) Γ i , j , k P S , i , j ( z ) σ a j k = 1 M N 1 k ( z ) Γ i , j , k P S , i , j ( z ) , ± d P A S E , i , j d z = ( σ e j σ e s a , j ) k = 1 M N 2 k ( z ) Γ i , j , k P A S E , i , j ( z ) σ a j k = 1 M N 1 k ( z ) Γ i , j , k P A S E , i , j ( z ) + m h v j Δ v ( σ e j σ e s a , j ) k = 1 M N 2 k ( z ) Γ i , j , k ,
Γ i , j , k = 0 2 π r k 1 r k i i , j ( r , φ ) r d r d φ 0 2 π 0 i i , j ( r , φ ) r d r d φ ,
N 2 k ( z ) N 1 k ( z ) = i j P i , j ( z ) Γ i , j , k σ a j h v j i j P i , j ( z ) Γ i , j , k ( σ e j σ e s a , j ) h v j + A k τ ,
G a i n ( d B ) = 10 log 10 ( P s ( z = L ) P s ( z = 0 ) ) ,
N F ( d B ) = 10 log 10 ( 2 n s p ( G 1 ) G + 1 G ) = 10 log 10 ( P A S E h v Δ v G + 1 G ) ,
n s p = 1 / ( 1 σ e p σ a s σ a p σ e s ) ,