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Abstract
A few-mode erbium-doped waveguide amplifier (FM-EDWA) with a confined Er3+ doped ring structure is proposed to equalize the differential modal gain (DMG). The FM-EDWA amplifying three spatial modes (LP01, LP11a and LP11b) is optimized by genetic algorithm and fabricated using precise lithography overlay alignment technology. We observe gain values of over 14 dB for all modes with DMG of 0.73 dB at 1529 nm pumped only with LP01 for the power of 200 mW. Furthermore, a flat gain of more than 10 dB is demonstrated across 1525-1565 nm, with a sufficiently low DMG of less than 1.3 dB.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The exponential growth of data traffic in recent years has by now practically exhausted all known dilatant means (e.g. wavelength and polarization multiplexing, and higher-order modulation formats) of increasing the capacity limit in single-mode fibers (SMFs) [1,2]. Mode-division multiplexing (MDM) has been seen as a promising route to overcome the expected capacity crunch while minimizing the energy cost per bit sent [3–5]. Optical communication systems based on MDM improve capacity by using the modal orthogonality as an additional degree of multiplexing freedom. Mode-division multiplexing (MDM) is one of the actively studied approaches for providing high-capacity optical links.
The few-mode amplifier is a crucial component to compensate for the transmission loss of the MDM transmission system. Rare-earth-doped few-mode fiber amplifier reveals a number of benefits in terms of outstanding thermo-optical properties, large gain, excellent noise quality and thus has been widely used in MDM systems and implemented in commercial [6–9]. With the rapid development of photonic integration technology, all-optical communication is proceeding in the direction of miniaturization and integration. Multiple and multi-function devices with high-density integration on a chipset [10–12] is the the inevitable course. However, it is hard to effectively compensate for on-chip modal devices due to the inappropriate size of the FM-EDFAs. In contrast, erbium-doped waveguide amplifiers (EDWA) could improve the performance of on-chip system by effectively compensating for the loss [13–15]. At present, some reports relevant to few-mode erbium-doped waveguide amplifier have been published. Zhang Xucheng et al. established the theoretical model of few-mode erbium-ytterbium co-doped optical waveguide amplifier to analyze the three-mode and five-mode group gain characteristics and unprecedented doping configuration with ion-concentration layered doping to equalize modal gain [16]. Sun Xiangyu et al. realized LP01 and LP11 amplification with a maximum gain of 3.46 dB and 3.52 dB, respectively, in LP01-mode waveguide and LP11-mode waveguide based on a highly Er3+-doped phosphate glass [17]. As reported above, simultaneous amplification of multiple modes with low differential modal gain (DMG) in a single waveguide remains a challenge due to mode competitions and crosstalk effects in experiment. In our recent work [18], we successfully demonstrated a three-mode polymer waveguide amplifier supporting LP01, LP11a and LP11b modes. A reconfigurable pump configuration scheme is adopted to balance the modal gain per mode. The waveguide amplifier achieved an average gain of 10.4 dB with a DMG of less than 0.4 dB when pumped with LP01 and LP21b modes. However, due to the necessity of employing multiple pumping sources, this solution is not suitable for on-chip integrated devices in terms of cost and integration.
To solve this problem, the FM-EDWA employing ring-core erbium-doped with low DMG equipped with only one pump is first demonstrated in this paper. Organic polymers with the excellent properties of simple processing for complex structure, ease of integration, and low cost were chosen as the host material [19–21]. The theoretical simulation of this ring-core FM-EDWA was developed to investigate and verify its optical properties. We provide simulation results for a step-index three-mode waveguide, demonstrating the feasibility of DMG control by adjusting the Er ions doping distribution. We fabricated the ring-core erbium-ytterbium co-doped waveguide amplifier. The experimental setup for the modal gain was deployed. And the insertion loss, crosstalk and near-field profiles of LP01, LP11a and LP11b were also characterized. Effective equalization was achieved pumped only with LP01.
2. Theoretical model and simulation results
The Er3+-Yb3+ co-doped six-level few-mode amplification system was modeled and shown in Fig. 1. The basic principle of the multi-mode signal amplification remains based on stimulated absorption, achieving population inversion between 4I13/2 and 4I15/2 excited states by pump and excited radiation to realize the amplification, similar to single-mode amplification. Nevertheless, the difference lies in the fact that there will be competition among signal modes that are amplified simultaneously. And the overlap of multiple signal modes, pump modes and active media is different, which directly affects mode gain and DMG. To visualize the impact, overlap integral factors are employed. However, due to the increase of signal modes, when different modes are amplified simultaneously, there will be a competitive effect [22], the conventional overlap integral factors are no longer suitable. In order to fully consider the influence of the overlapping distribution of different pumping modes and signal light on the gain of FM-EDWA, we modified the overlapping integral factor as:
As can be seen from the equation mentioned above, the gain of each mode in the FM-EDWA is not only related to the normalized light intensity of the pump mode, but also to the Er3+ distribution in the core. In a uniform doping profile, the difference in intensity overlapping between the guided mode and the pump mode mainly causes the DMG. Taking the example of a three-mode waveguide, the intensity profile of the fundamental mode (LP01) is mainly distributed in the core center, while the spatial distribution of higher-order modes (LP11a, LP11b) is mainly located in the outer layer. The light intensity of the higher-order mode is weaker in the center core and stronger in the outer layer compared to the fundamental mode, which results in a lower gain of the higher-order mode compared to the gain of LP01 in the case of uniform doping. Therefore, it is reasonable to increase the doping concentration of the waveguide outer layer to narrow the gap between the fundamental signal mode and the highest order signal mode in view of their intensity profile distribution. To enable gain equalization of three signal modes and simplify pump configuration, a waveguide structure with layered doping of erbium ions is proposed as shown in Fig. 2(a). Figure 2(b) shows the concentration distribution and refractive index distribution of erbium ion within the waveguide core. The dominant photoresist SU-8 (n = 1.576 at 1529 nm and n = 1.581 at 976 nm) is chosen as the host material for the core. The few-mode square waveguide supporting three signal LP modes (LP01, LP11a, LP11b) is optimized by effective index method (EIM) with an overall size of 5 µm × 5 µm in the core region. The outer layer of the designed erbium ion core structure is highly doped with a thickness of x. NaYF4: Er3+,Yb3+ nanocrystals (NCs) are doped to compound the inner with a lower concentration (N2) and the outer layer with a higher concentration (N1) of the core. Polymethyl methacrylate (PMMA) (with refractive indices of 1.485 at 1529 nm and 1.493 at 976 nm) and SiO2 (with refractive indices of 1.444 at 1529 nm and 1.451 at 976 nm) serve as the upper cladding and the under cladding, respectively.
Fig. 2. (a) Cross-sectional view of the waveguide. (b) the profile of the relative refractive index and erbium ion concentration in the FM-EDWA.
The proposed structure involves simultaneous optimization of several variables, such as doping concentration and radius, taking into account the characteristics of multi-variable simultaneous optimization and global search of genetic algorithm. Genetic algorithm [23] which mimics the principle of biological genetic evolution is adopted for optimization. Combined with the overlap integrals, three parameters x, N1 and N2 are optimized to achieve the gain equalization. The parameter x is limited to less than a/2 ([0, 2.5 µm]), and the concentration of each dopant is no more than 3 × 1026 ions/m3 to prevent quenching of NCs. The maximum iteration number is set to 200. A higher overlap between the signal and pump modes will result in higher modal gain [24]. Therefore, the modified overlap integral factor can be used as an indicator to quantify DMG. The fitness function is defined as the criterion for evaluating optimization results in the optimization process:
where $\overline \Gamma $ is, as in the figure file. The average overlap integral of modes and $\Delta \Gamma $ is the maximum overlap integral difference between modes. Then since the doped structure with higher mode gain and minimum DMG between modes is more easily retained, the optimal erbium-doped distribution can be obtained. The optimal parameters of the erbium-doped structure in the core region are x = 1.305 µm, N1= 3 × 1026 ions/m3 N2 = 1.896 × 1026 ions/m3. We calculated the overlap integral factor per mode before and after adjusting the doping distribution by GA, as shown in Table 1. In the case of LP01 pump, the difference of overlap integral factors between the signal modes LP01,s and LP11,s is as high as 0.12 for the conventional uniformly doped. With the ring-core structure waveguide optimally designed by genetic algorithm, the minimum difference of the overlap integral can be reduced to 0.01 under the condition of maintaining the ideal gain value. This result shows that the few-mode waveguide has an effective impact on gain equalization. To make a contrast with our previous work, we also calculate the equalization when LP21b is pumped. In both structures, the overlap integrals of the LP11,s signal modes are always higher than the fundamental mode, and the difference is not effectively decreased. This is why the LP01p was chosen as the pump mode.
Table 1. The overlap integral of signal modes in FM-EDWA: (a) before and (b) after adjustment of the concentration
3. Experimental setup and results
The polymer FM-EDWA with ring-core erbium-doped was fabricated using precise lithography overlay alignment technology. The diagram of which is shown in Fig. 3(a). NaYF4: 2% Er3+, 20% Yb3+ nanocrystals were synthesized by solvothermal decomposition method. Two parts of 0.005 g nanocrystals were dissolved in toluene to form the solution by ultrasonically agitating for 3 h. The solution was then mixed with SU-8 2005 (Microchem) photoresist at a mass ratio of 1:3.16 and 1:5 for the inner core and outer core active materials of the waveguide, respectively. Conventional semiconductor processes, including spin coating, photolithography, and development were performed to fabricate the inner core of the device. On top of the inner core, the outer layer of high concentration doping material is uniformly coated, followed by high precision plate matching and secondary exposure. The outer core of the device is fabricated through wet etching. Figure 3(b) shows an optical microscope image by 1000-diameters of the cross section with upper cladding. The waveguide core layer measured 5.5 µm × 5.2 µm in size, with a thickness of the outer layer at 1.2 µm. The inner waveguide structure is completely covered, and no solubility was observed between the cladding and the core layer.
Fig. 3. (a) Fabrication processes for polymer optical waveguide amplifiers. (b)The microscope photo of cross section of waveguide.
We established the experimental system to characterize the gain and crosstalk performance of the FM-EDWA. The schematic of the experimental setup is shown in Fig. 4. A 976 nm laser (ASPMPL-976) was used as the pump source, and a tunable laser (Santec TSL-210) with a wavelength ranging from 1510 to 1590 nm was utilized as the signal source. The signal light was divided into three channels by a beam splitter (BS) and then passed through polarization controllers (PCs) and a variable optical attenuator (VOA). The VOA was used to adjust the optical power, ensuring that the optical power per mode input to the FM-EDWA remained consistent. The pump was injected into a WDM couplers (976 nm/1530 nm) and coupled with one of the signal lights. The mode-selective photonics lanterns (MSPLs) [25–27] were served as modal multiplexer and demultiplexer. The optical beam was imported to the corresponding port of input MSPL 1 to degenerate LP01 modes. The other two signal lights were immitted into the LP11a and LP11b ports of the MSPL 1. The signal and pump modes were multiplexed at the output few-mode fiber of the photonic lantern and injected into the waveguide through end-face coupling. The signal and pump light interacted with the gain medium, then were exported and collected by the MSPL 2 for demultiplexing. The mode-demultiplexed output signals were fed into an optical spectrometer (Anritsu-MS9740a) for spectral measurement. Furthermore, to verify the modal purity, we observed the light spot per mode before and after amplification. The near-field modal images of the signal and pump light at the input and output facets of the FM-EDWA were captured directly by a beam analysis camera (Spiricon SP503U) and shown in Fig. 5(a) and (b), respectively. For comparison, the modal profiles per mode of the output facets of the undoped waveguide with the same structure were observed to analyze the impact of the waveguide structure on the optical field, as shown in Fig. 5(c). As can be seen, the photonic lantern excited pure signal modes, and the waveguide structure we fabricated transmitted the signal and pump modes well. When compared to the spots before and after amplification, it was evident that the modal purity and fidelity were well preserved. The poor spatial distribution of amplification patterns could be attributed to mode mixing and the loss of the pump mode during amplification.
Fig. 5. Images of near-field modal profiles for the signal and pump light at the (a) input and (b) output facets of the FM-EDWA. (c) Output facets of the undoped waveguide with the same structure.
We also measured the modal crosstalk between different signal modes in a 0.3 cm long waveguide. Table 2 shows examples of the output spectra for the LP01, LP11a and LP11b mode signals, along with the crosstalk spectra of the different mode signals. As can be seen, in the case of back-to-back connections, the crosstalk caused by two photonics lanterns is less than -16.92 dB. After the amplifier is connected, the crosstalk between the modes slightly increases to less than -12.47 dB. We used the truncation method [28] to measure the insertion loss of 0.3 cm, 0.7 cm, 1.3 cm, 1.7 cm and 2.5 cm at the wavelength of 1529 nm and 1300 nm for the three signal modes. The transmission losses of the three modes are similar, and the loss ranges at 1529 nm and 1300 nm are 4.58 ± 0.2 dB/cm and 3.98 ± 0.2 dB/cm, respectively. By making the difference, the absorption loss of the device is calculated to be about 0.6 dB/cm.
Table 2. The crosstalk of signal modes in MSPL1-MSPL2 and FM-EDWA
Finally, we measured the relative gain characteristics for different signal powers (0 dBm, -5 dBm and -10 dBm) under various pump power at the signal wavelength of 1529 nm, as shown in Fig. 6(a)-(c). The relative gain is defined as $G = 10\lg ({{{P_{on}}} / {{P_{off}}}})$, where Pon and Poff are the output powers of the signal light with and without the excitation of the pump light, respectively. When excited by the pump, the FM-EDWA with a length of 0.3 cm produced bright green up-conversion fluorescence, as shown in the illustration of Fig. 4. As can be seen from the results, the gain of each signal mode increases and tends to saturation with the increase of pump power. Moreover, all guided modes experienced gain increase with a decrease in input signal powers. The maximum measured gain reached 14.91 dB for an input signal power of -10 dBm and a pump power of 200 mW. The minimum DMG of the three modes was 0.73 dB, indicating that the gain of each mode can be well equalized by the concentration layered structure of the waveguide. For comparison, we also measured the gain characteristics with LP21b pumped, as shown in Fig. 6(d)-(f). It was found that the trend of mode gain with signal power and pump power was consistent with the previous changes; however, the gain changes of the LP01 mode signal along with the LP21b pumping power change are significantly lower than those of LP11a and LP11b. The DMG of the three signal modes was up to 5 dB. The main reason is that LP11 mode coincides better with doping at the LP21b,p pump launch condition than the LP01,p. This verifies that the structure we proposed and optimal parameters are effective for modal gain equalization.
Fig. 6. Mode dependent gain pumped by the LP01 mode as a function for a signal power of (a) -10 dBm, (b) -5 dBm and (c) 0 dBm. Mode dependent gain pumped by the LP21b mode as a function for a signal power of (d) -10 dBm, (e) -5 dBm and (f) 0 dBm.
The bandwidth of FM-EDWA is characterized as shown in Fig. 7. We plot the signal gain as a function of signal wavelength for an input signal power of -10 dBm per mode, when the pump spatial mode is LP01 of 200 mW. The modal gain was measured as the wavelength of the input signal varied from 1525 nm to 1565 nm in steps of 5 nm. Within this bandwidth, three signal modes could be effectively amplified with a gain of more than 10 dB. All signal modes peak at 1529 nm with gains of 14.91 dB, 14.35 dB and 14.18 dB respectively, which are determined by the emission peak of the NaYF4: Er3+, Yb3+ nanocrystals. The average gain of the mode was 11.5 dB, and the DMG was controlled within 1.3 dB. Overall, the results indicate that the ring-core FM-EDWA can achieve balanced amplification across the broadband range. The development of this device promotes the development of mode division multiplexing technology for on-chip and short-range communications.
Fig. 7. Modal gain of the FM-EDWA for various wavelength. For input signal power of -10 dBm and LP01 pump power of 200 mW.
4. Conclusion
We described in detail the design of an FM-EDWA supporting 3-LP signal modes with the ring-core doping profile to minimize DMG. The overlap integral parameter was theoretically evaluated, and the genetic algorithm was applied to optimize the thickness and concentration of the inner and outer core layer. The Er3+ distribution achieved the best overlap for pump and signal modes, keeping the DMG as low as possible. We successfully fabricated the ring-core FM-EDWA using precise lithography overlay alignment technology. Experimental results demonstrate that LP01, LP11a and LP11b achieve modal gains exceeding 14 dB at 1529 nm, with a DMG of 0.73 dB using LP01 pump of 200 mW. In the 1525-1565 nm range, there is a flat gain exceeding 10 dB and a low DMG of less than 1.3 dB. The ring-core structure we designed allows precise control of DMG in the FM-EDWA, significantly simplifying the pumping configuration based on LP01-only. The FM-EDWA could be a useful amplifier for constructing an MDM transmission system/network in the future.
Funding
National Key Research and Development Program of China (2021YFB2800502).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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