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Fig. 1 presents a schematic of the proposed DMG equalization scheme. Various guided modes with the same launch power were transmitted over the FMF, and all the guided modes experienced nearly the same attenuation. However, when the FM-EDFA was used to compensate for the transmission attenuation, a DMG occurred, which is defined as the maximum gain difference between the guided modes at a specific wavelength, as shown in Eq. 1
$$ DMG\left( \lambda \right) = \mathop {\max }\limits_{m \ne n} \left| {G\left( {m,\lambda } \right) - G\left( {n,\lambda } \right)} \right| $$ (1) where G is the gain value at the specific guide mode, λ is the operational wavelength, and m and n are the indices of the guided mode. Two metrics were defined to evaluate the performance of the DMG equalizer: DMGmax and DMGave.
The DMGmax indicates the maximum DMG and DMGave is the average DMG in Eq. 1. Subsequently, to minimize the DMG, an in-line DMG equalizer with different mode attenuations (DMA) is cascaded after the FM-EDFA, and the DMA is defined as follows:
$$ DMA\left( \lambda \right) = {A_{L{P_{01}}}}\left( \lambda \right) - {A_{HOM}}\left( \lambda \right) $$ (2) where $A_{LP_{01}} $ is the attenuation of the LP01 mode and AHOM is the attenuation of the high-order modes (HOMs). By modifying the RI of the FMF core via femtosecond laser micromachining, a higher attenuation is applied to the LP01 mode while minimizing its impact on the HOMs. Finally, the higher gain of the LP01 mode can be effectively reduced by cascading the fabricated DMG equalizer, consequently achieving the DMG equalization of the FM-EDFA.
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Fig. 2a presents a schematic diagram of the proposed DMG equalizer. The femtosecond laser was focused on the core of the FMF to generate RI modulation. The modified RI region induced by the femtosecond laser was then modeled as a cuboid, whose width W, height H, length L, and RI modulation depth ∆n can be flexibly manipulated by adjusting the femtosecond laser micromachining parameters, as shown in Fig. 2b, c. A simulation based on the beam propagation method was implemented to theoretically investigate the performance of the DMG, as shown in Fig. 2d. Various guided modes are expected owing to leakage of the fiber cladding, consequently suffering different attenuations. The LP01 mode, whose profile is mainly concentrated at the center, experiences a larger attenuation than that of the HOMs. As shown in Fig. 2d, different attenuations of the LP01, LP11, and LP21 modes were achieved by modeling a DMG equalizer in the FMF core. Because the degenerate modes are continuously and randomly coupled along the FMF, only the attenuation of the mode-group is considered. Therefore, by optimizing the DMG equalizer parameters, the variable-mode-dependent attenuation among the various mode-group can be obtained. Finally, an all-fiber DMG equalizer with a variable range was anticipated.
Fig. 2 Schematic of the proposed DMG equalizer based on femtosecond laser micromachining. a. Schematic of the top-view of the modified RI region. b. Side view of the modified RI region. c. Modified RI profile following femtosecond laser micromachining. d. Simulation of the mode field and attenuation variations when different modes pass through the tailored RI region; the white dotted area indicates the modified RI region.
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To verify the feasibility and advantages of the proposed DMG equalization strategy, a simple-structured and cost-effective 3-LP mode group EDFA with uniform Erbium doping and fundamental mode core-pumping was numerically investigated to introduce a larger DMG and identify the relationship between the DMG and pumping parameters, including the pumping power and EDF length, as shown in Fig. 3a.
Fig. 3 DMG arising in 3-LP mode-group FM-EDFA. a DMG under different pumping powers and lengths at 1550 nm. b DMG over the C-band under the conditions of a 4.5 m EDF and 600 mW fundamental mode pump.
As shown in Fig. 3a, when the pumping power and EDF length were varied from 200 to 600 mW and 1 to 7 m, respectively, the DMG between the 3-LP mode-group fluctuated from 4.8 dB to 16.2 dB. Subsequently, an FM-EDFA configuration with a 4.5 m EDF and 600 mW fundamental mode pump power was selected to verify the DMG equalization process, where the DMGmax and DMGave over the C-band were 10 dB and 8.95 dB, respectively, as shown in Fig. 3b.
The DMA of a 3-LP mode group DMG equalizer based on femtosecond laser micromachining to induce RI tailoring was numerically investigated. As shown in Fig. 4a, when the L and ∆n values vary from 0 to 400 μm and from 0 to −0.05, respectively, the DMA changes from 0 to 27.8 dB, which is sufficient to cover the entire DMG range of the 3-LP mode-group EDFA. Subsequently, the capability of the DMG equalization was numerically evaluated, as shown in Fig. 4b.
Fig. 4 DMA introduced by the femtosecond laser micromachining-enabled RI tailoring. a DMA of the 3-LP mode-group DMG equalizer under different lengths and ∆n values at 1550 nm. b Gain profile when a DMG equalizer with a length of 120 μm and ∆n of −0.02 was cascaded after the FM-EDFA.
Before DMG equalization, a 4.5 m EDF was core-pumped with a 600 mW, 980 nm laser in the fundamental mode, and the DMGmax and DMGave over the C-band were 10 dB and 8.95 dB, respectively. When a DMG equalizer with a length of 120 μm and ∆n of -0.02 was cascaded after the designated FM-EDFA, the DMGmax decreased from 10 dB to 1.52 dB, and the average DMGave over the C-band decreased from 8.95 dB to 0.78 dB.
Differential mode-gain equalization via femtosecond laser micromachining-induced refractive index tailoring
- Light: Advanced Manufacturing 5, Article number: (2024)
- Received: 25 August 2023
- Revised: 27 February 2024
- Accepted: 05 March 2024 Published online: 30 April 2024
doi: https://doi.org/10.37188/lam.2024.014
Abstract: The mode-division multiplexing technique combined with a few-mode erbium-doped fiber amplifier (FM-EDFA) demonstrates significant potential for solving the capacity limitation of standard single-mode fiber (SSMF) transmission systems. However, the differential mode gain (DMG) arising in the FM-EDFA fundamentally limits its transmission capacity and length. Herein, an innovative DMG equalization strategy using femtosecond laser micromachining to adjust the refractive index (RI) is presented. Variable mode-dependent attenuations can be achieved according to the DMG profile of the FM-EDFA, enabling DMG equalization. To validate the proposed strategy, DMG equalization of the commonly used FM-EDFA configuration was investigated. Simulation results revealed that by optimizing both the length and RI modulation depth of the femtosecond laser-tailoring area, the maximum DMG (DMGmax) among the 3 linear-polarized (LP) mode-group was mitigated from 10 dB to 1.52 dB, whereas the average DMG (DMGave) over the C-band was reduced from 8.95 dB to 0.78 dB. Finally, a 2-LP mode-group DMG equalizer was experimentally demonstrated, resulting in a reduction of the DMGmax from 2.09 dB to 0.46 dB, and a reduction of DMGave over the C band from 1.64 dB to 0.26 dB, with only a 1.8 dB insertion loss. Moreover, a maximum range of variable DMG equalization was achieved with 5.4 dB, satisfying the requirements of the most commonly used 2-LP mode-group amplification scenarios.
Research Summary
Femtosecond laser micromachining: contributing to few-mode fiber mode channel power equalization
Mode division multiplexing technology exponentially expands the capacity of communication systems by using multiple mutually orthogonal spatial modes within a few-mode fiber as an independent transmission channel. However, due to the different transverse electric field distributions of each mode, there is a huge difference in loss and gain between different modes, which increases the complexity of the received signal processing. Song-nian Fu from China’s Guangdong University of Technology and colleagues now report a differential mode gain equalization through a refractive index tailoring through femtosecond laser micromachining. The team demonstrated that controlled refractive index modulation generated by femtosecond laser within a few-mode fiber can be used to regulate the loss of individual modes flexibly.
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