Erbium-doped Fiber Amplifier Gain Research Articles

Performance enhancement of optical pulse coding phase-sensitive OTDR system with genetic-optimized code

Optical pulse coding (OPC) in phase-sensitive optical time-domain reflectometry (φ-OTDR) traditionally relies on standard coding sequences as probe pulse trains, which usually suffer the problem of distorted probe pulse caused by the gain saturation in erbium-doped fiber amplifier (EDFA). To improve the signal-to-noise ratio (SNR) and mitigate distortion caused by the EDFA gain saturation, a genetic-optimized code (Go-code) based OPC φ-OTDR (GOPC φ-OTDR) scheme is proposed in this paper. The unique Go-code sequence generated by the distributed genetic algorithm (DGA) is explored in the field of φ-OTDR for the first time, and the coding sequence was optimized to adapt to the vibration sensing requirements in φ-OTDR. Theoretical analyses focused on EDFA gain saturation effects and coding gain were conducted. The experiment of GOPC φ-OTDR demonstrated significant improvements compared with Golay φ-OTDR, achieving less distortion in decoding response and approximately 7.48 dB phase demodulation SNR enhancement within a 10-km sensing range. This research marks Go-code's pioneering exploration into φ-OTDR, demonstrating substantial advancements in optimization metrics, and opening avenues for exploring advanced OPC technologies.

Simultaneous realization of high gain and low DMG of four-mode EDFA under bidirectional hybrid-mode pump.

We theoretically and experimentally verify that, the bidirectional hybrid-mode pumping scheme can address the optimization problem of trade-off between high gain and low differential modal gain (DMG) of four-mode erbium-doped fiber amplifier (4M-EDFA), in comparison with traditional both forward and backward hybrid-mode pumping scheme. It is noticed that, when the total pump power is fixed, the bidirectional hybrid-mode pumping scheme can not only achieve higher gain, but also suppress DMG due to different overlap integrals for the forward and backward pumping schemes. The bidirectional hybrid-mode pumped 4M-EDFA is developed with the forward pumping at LP02 mode and the backward pumping at LP21 mode, under a pump power ratio of 30%:70%. Thus, we can achieve an average gain of up to 21.16 dB and a low DMG of 0.43 dB at 1550 nm, and an average gain of up to 20.64 dB with a DMG of less than 1.6 dB over the C-band. In particular, the bidirectional hybrid-mode pumping scheme allows us to tailor the gain characteristics of the few-mode erbium-doped fiber amplifiers (FM-EDFAs), by adjusting the power ratio between forward and backward pumps.

Optimizing elastic optical networks quality of transmission with an empirical optical amplifier gain saturation model

In this paper, we revisit the problem of adjusting transceiver power, amplifier gain, and nodal gain in optical-bypass-enabled networks, taking into account an empirical model of erbium-doped fiber amplifier (EDFA) gain saturation. We assume that network demands have been routed via the shortest possible paths. A heuristic algorithm, which estimates the degradation of the signal-to-noise ratio (SNR) for each demand, is used to assign the modulation level and spectrum slots to the routed demands. Our optimization process aims to maximize the minimum SNR margins of demands, by adjusting EDFA small-signal gain, variable optical attenuator (VOA) attenuation, and transceiver power. Constraints and impairments imposed by the physical-layer include EDFA and VOA gain limits, transceiver power limits, receiver sensitivity, insertion loss of optical switch input ports, EDFA gain saturation, EDFA noise, and fiber non-linear interference. These are modeled using the Gaussian noise model. The proposed optimization problem is formulated as a geometric programming problem and then converted into an equivalent convex problem.Numerical results suggest that in the optimal solution of our optimization, all demands are served with typically low bit error rates (BER) (<10−4). We calculate the operational gains of the EDFA to set the spans to full compensation whenever possible. Pre-amplifiers and line amplifiers do not experience gain saturation due to relatively small input powers, while approximately 10% of boosters undergo more than a 1 dB gain reduction due to high input powers. We observe that overlooking the effect of EDFA gain saturation and physical-layer-imposed constraints such as nodal gain limits or transceiver power limits during network optimization leads to a considerable number of blocked demands due to SNR degradation or high BER (>10−3).

A Comprehensive Study on EDFA Gain Flattening for WDM Transmission using Cascaded Fiber Bragg Gratings

The gain flattening of optical amplifiers plays a crucial role in optical Wavelength Division Multiplexing (WDM) communication systems, ensuring uniform amplification across all channels. This study focuses on investigating the gain flattening characteristics of Erbium-Doped Fiber Amplifiers (EDFAs) using cascaded Fiber Bragg Gratings (FBGs) in the C-band wavelength range. A comparative analysis of various optical amplifiers revealed that EDFA exhibited the highest gain variation, making it an optimal choice for gain flattening. The key parameters to achieve optimal EDFA gain flattening include the wavelengths of the channels, EDFA length, noise figure (NF), and the number of cascaded FBGs. Simulation experiments are conducted using Optisystem software (ver. 14.2) and the obtained results reveal that EDFA gain flatness can be achieved within the wavelength range of 1531 to 1533 nm, utilizing an EDFA length of 6 m and 12 cascaded FBGs. These findings contribute to the advancement of gain flattening techniques in optical WDM systems, enhancing their performance and reliability.

Experimental–Simulation Analysis of a Radiation Tolerant Erbium-Doped Fiber Amplifier for Space Applications

Research on optical amplifiers has highlighted how ionizing radiation negatively impacts the performance of erbium-doped fiber amplifiers (EDFAs), through the degradation of their gain. The amplitudes and kinetics of this degradation are mainly explained by the radiation-induced attenuation (RIA) phenomenon at the pump and signal wavelengths. In this work, the gain degradation of a radiation tolerant EDFA (exploiting a cerium-co-doped active optical fiber) induced by ionizing radiation up to 3 kGy (SiO2), at two dose rates, 0.28 Gy/s and 0.093 Gy/s, is studied through an experimental/simulation approach. Using a home-made simulation code based on the rate and power propagation equations and including the RIA effects, the radiation-dependent performance of EDFAs were estimated. The variations in the spectroscopic parameters caused by irradiation were also characterized, but our results show that they give rise to EDFA gain degradation of about 1%. To overcome the issue of overestimating the RIA during the radiation tests on the sole active rare-earth-doped fiber, a new RIA experimental setup is introduced allowing us to better consider the photobleaching mechanisms related to the pumping at 980 nm. A good agreement between experimental and simulated gain degradation dose dependences was obtained for two different irradiation conditions, thus also validating the simulation code for harsh environments applications.

Building a digital twin of an EDFA for optical networks: a gray-box modeling approach

High-accuracy physical layer models enable intelligent, self-driving optical networks. The dynamic wavelength-dependent gain characteristics of erbium-doped fiber amplifiers (EDFAs) remain a crucial problem in terms of modeling. The gain model directly determines the power spectrum and is therefore important for estimating the optical signal-to-noise ratio as well as the magnitude of fiber nonlinearities. Black-box data-driven models have been widely studied, but they require a large size of data for training and suffer from poor generalizability. In this paper, we derive the gain spectra of EDFAs as a simple univariable linear function; then, based on it, we propose a gray-box EDFA gain modeling scheme. Experimental results show that, for automatic gain control (AGC) and automatic power control (APC) EDFAs, our model built with 8 data samples can achieve better performance than the neural network (NN) based model built with 900 data samples, which means the required data size for modeling can be reduced by at least 2 orders of magnitude. Moreover, in the experiment, the proposed model demonstrates superior generalizability to unseen scenarios since it is based on the underlying physics of EDFAs. With the proposed scheme, building a customized digital twin of each EDFA in optical networks becomes more feasible, which is essential, especially for next-generation multiband network operations.

Open EDFA gain spectrum dataset and its applications in data-driven EDFA gain modeling

Optical networks satisfy high bandwidth and low latency requirements for telecommunication networks and data center interconnection. To improve network resource utilization, machine learning (ML) is used to accurately model optical amplifiers such as erbium-doped fiber amplifiers (EDFAs), which impact end-to-end system performance such as quality of transmission. However, a comprehensive measurement dataset is required for ML to accurately predict an EDFA’s wavelength-dependent gain. We present an open dataset consisting of 202,752 gain spectrum measurements collected from 16 commercial-grade reconfigurable optical add–drop multiplexer (ROADM) booster and pre-amplifier EDFAs under varying gain settings and diverse channel-loading configurations over 2,785 hours in total, with a total dataset size of 3.1 GB. With this EDFA dataset, we implemented component-level deep-neural-network-based EDFA models and use transfer learning (TL) to transfer the EDFA model among 16 ROADM EDFAs, which achieve less than 0.18/0.24 dB mean absolute error for booster/pre-amplifier gain prediction using only 0.5% of the full target training set. We also showed that TL reduces the EDFA data collection requirements on a new gain setting or a different type of EDFA on the same ROADM.

Probabilistic low-margin optical-network design with multiple physical-layer parameter uncertainties

Analytical models for quality of transmission (QoT) estimation require safety design margins to account for uncertain knowledge of input parameters. We propose and evaluate a design procedure that gradually decreases these margins in the presence of multiple physical-layer uncertainties (namely, connector loss, erbium-doped fiber amplifier gain ripple, and fiber type) by leveraging monitoring data to build a probabilistic machine-learning-based QoT regressor. We evaluate the savings from margin reduction in terms of occupied spectrum and number of installed transponders in the C and C+L bands and demonstrate that 4%–12% transponder/spectrum savings can be achieved in realistic network instances by simply leveraging the SNR monitored at receivers and paying off a low increment in the lightpath disruption probability (at most 1%–4%).

300 km ultralong fiber optic DAS system based on optimally designed bidirectional EDFA relays

Optical fiber distributed acoustic sensing (DAS) based on phase-sensitive optical time domain reflectometry (φ-OTDR) is in great demand in many long-distance application fields, such as railway and pipeline safety monitoring. However, the DAS measurement distance is limited by the transmission loss of optical fiber and ultralow backscattering power. In this paper, a DAS system based on multispan relay amplification is proposed, where the bidirectional erbium-doped fiber amplifier (EDFA) is designed as a relay module to amplify both the probe light and the backscattering light. In the theoretical noise model, the parameters of our system are carefully analyzed and optimized for a longer sensing distance, including the extinction ratio (ER), span number, span length, and gain of erbium-doped fiber amplifiers. The numerical simulation shows that a bidirectional EDFA relay DAS system can detect signals over 2500 km, as long as the span number is set to be more than 100. To verify the effectiveness of the scheme, a six-span coherent-detection-based DAS system with an optimal design was established, where the cascaded acoustic-optic modulators (AOMs) were used for a high ER of 104 dB. The results demonstrate that the signal at the far end of 300.2 km can be detected and recovered, achieving a high signal-to-noise ratio of 59.6 dB and a high strain resolution of 51.8pε/Hz at 50 Hz with a 20 m spatial resolution. This is, to the best of our knowledge, a superior DAS sensing distance with such a high strain resolution.

Performance improvements by dynamic amplifier reconfigurations for C + L-band optical networks in the presence of stimulated Raman scattering

C+L-band optical networks suffer from transmission impairments including amplified spontaneous emission noise and Kerr-induced and stimulated-Raman-scattering-induced nonlinear interference. The generalized signal-to-noise ratio (GSNR) profiles across different links of the network play a crucial role in determining the overall network traffic load and operating margins, but the GSNR is highly dependent on the signal power profiles along the link and time-varying channel-loading conditions, particularly for future dynamic mesh networks. As the network is dynamically loaded, we monitor the GSNR across the active channels of each link and investigate the benefits of regularly reconfiguring the erbium-doped fiber amplifier (EDFA) gain and tilts to optimize either (1) the mean GSNR minus the GSNR standard deviation (i.e., to achieve a high and flat GSNR across channels) or (2) the minimum GSNR to improve the traffic load and/or GSNR margins. Different lightpath provisioning strategies are studied, and simulation results for COST 239, a German network, and a sample Alibaba production network show that, compared with static EDFA configurations assuming fully loaded conditions, the GSNR margin and hence network robustness with dynamic EDFA reconfigurations can be improved by at least 0.45, 0.57, and 0.72 dB, respectively, with similar or better network blocking probability. Alternatively, the improved GSNR profiles can enable an average network capacity improvement of at least 9%, 8%, and 16%, respectively, in principle when operating at the same GSNR margin at 30% spectral occupancy.

Optimization criteria and design of few-mode Erbium-doped fibers for cladding-pumped amplifiers.

We propose a novel optimization method that combines two design criteria to reduce the differential modal gain (DMG) in few-mode cladding-pumped erbium-doped fiber amplifiers (FM-EDFAs). In addition to the standard criterion that considers the mode intensity and dopant profile overlap, we introduce a second criterion that ensures that all doped regions have the same saturation behavior. With these two criteria, we define a figure-of-merit (FOM) that allows the design of FM-EDFAs with low DMG without high computational cost. We illustrate this method with the design of six-mode erbium-doped fibers (EDFs) for amplification over the C-Band targeting designs that are compatible with standard fabrication processes. The fibers have either a step-index or a staircase refractive index profile (RIP), with two ring-shaped erbium-doped regions in the core. With a staircase RIP, a fiber length of 29 m and 20 W of pump power injected in the cladding, our best design leads to a minimum gain of 22.6 dB while maintaining a DMGmax under 0.18 dB. We further show that the FOM optimization achieves a robust design with low DMG over a wide range of variations in signal power, pump power and fiber length.

Spectral optimization of Stokes channels for multi-wavelength Brillouin fiber lasers

In this paper, through a semi-analytical model, we demonstrate the spectral optimization of Stokes channels for cascaded multi-wavelength Brillouin fiber lasers. Here we develop an improved version of an earlier model, introducing the erbium-doped fiber amplifier gain saturation into the mathematical formalism of the laser, making our model more accurate. Our results reveal that with the proper selection of laser component parameters, it is possible to increase the number of generated Stokes channels significantly and generate them with high flatness. Specifically, 75 and 69 Stokes channels were generated within a 3.7 and 3 dB range, respectively.

On Sparse Gain Flattening in Pump-Constrained Submarine Links

Having in mind the capacity optimization of power-constrained submarine links, by following the work in (Cho <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2020) we first compare the achievable information rate (AIR) of gain-flattened and un-flattened short links (called here blocks) of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}\leq 12$</tex-math></inline-formula> spans with span loss 16.5 dB and with end-span single-stage co-pumped erbium-doped fiber amplifiers (EDFA) when the transmitted wavelength division multiplexed (WDM) channels all have the same transmitted power. All EDFAs have the same pump power and the same physical parameters. In the flattened case, each EDFA is followed by an ideal gain-flattening filter (GFF) that chops off the EDFA gain exceeding the span loss. No GFFs are used in the un-flattended case. We show that, for block length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}&gt;7$</tex-math></inline-formula> , at large-enough input power the AIR of the GFF block exceeds that of the no-GFF block, while for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}\leq 7$</tex-math></inline-formula> at large input power the AIR is about the same. We next build a long submarine link by concatenating many <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}$</tex-math></inline-formula> -span no-GFF blocks, and placing a GFF at the last EDFA of each block in order to flatten the block gain down to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}$</tex-math></inline-formula> -span loss, and calculate the AIR of the resulting sparse-GFF submarine link, accounting also for nonlinear interference. For a 287-span case-study link with span loss 9.5 dB, we show that the best power efficiency is achieved by blocks of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}=6$</tex-math></inline-formula> (i.e., one GFF every 6 spans) when the pump is around 11 mW. When the GFF excess loss is 0.3 dB the top-AIR gain over the standard all-GFF system is 9.5%, a value that decreases to 4% when the excess loss is zero. Considering that modern submarine-grade GFFs have almost zero excess loss, and that the most efficient pump power is likely too low to operate with, we conclude that sparse-GFF links offer little advantage in practice over the current design.

Joint Power and Gain Allocation in MDM-WDM Optical Communication Networks Based on Enhanced Gaussian Noise Model

Achieving reliable communication over different wavelength channels and modes is one of the main goals of Mode Division Multiplexing-Wavelength Division Multiplexing (MDM-WDM) transmission. The reliability can be described by the minimum Signal to Noise Ratio (SNR) margin which depends on launch power, the gain of Few-Mode Erbium-Doped Fiber Amplifiers (FM-EDFA), and the nonlinear impairments of Few-Mode Fiber (FMF). In this paper, we develop the Enhanced Gaussian Noise (EGN) nonlinear model for FMF, which can be used in both weak and strong coupling regimes. We validate the model by comparing simulation results with those obtained through the Split-Step Fourier Method. Based on our proposed EGN model, we address the problem of joint optimized power and gain allocation based on minimum SNR margin maximization when accounting for practical FM-EDFA constraints such as saturation power and maximum gain. The problem is solved using a convex optimization approach and considering different scenarios such as the best equal power, optimized power, and joint optimized power and gain. Results demonstrate that the minimum SNR margin improvement for the joint optimized power and gain allocation compared to the best equal power allocation is <inline-formula> <tex-math notation="LaTeX">$1.4~dB$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$1.7~dB$ </tex-math></inline-formula> for MDM-single channel and single-mode fiber-WDM systems, respectively.

Modeling EDFA Gain: Approaches and Challenges

With the rapid development of virtual/augmented reality and cloud services, the capacity demand for optical communication systems is ever-increasing. To further increase system capacity, current researches focus on efficient and reliable system management, in which the transmission performance should be accurately estimated. The wavelength-dependent gain effects of erbium-doped fiber amplifiers (EDFAs) have a great impact on transmission performance, and therefore a precise EDFA gain model is required. In this paper, we firstly summarize the underlying principles and structures of EDFA, and introduce the gain performance and challenges in modeling. Then, we review the EDFA gain modeling methods. We categorize these researches into analytical modeling methods and machine learning (ML)-based modeling methods, and discuss their feasibilities and performances. In addition, we discuss the remaining problems for applying the models in a system and the possible directions for future investigations.

Nonlinearity Effect on Multiwavelength fiber laser based on Sagnac loop mirror interferometer

This paper demonstrates a multiwavelength fiber laser (MWFL) with erbiumdoped fiber amplifier (EDFA) as gain medium and Sagnac loop mirror interferometer as filter. Stable and flat lasing spectrum was achieved when highly nonlinear fiber (HNLF) was inserted into the laser cavity. The number of lasing lines and extinction ratio (ER) was directly influenced by EDFA gain where at maximum setting, 14 lasing lines with ER of 19 dB were generated. The stable and flat spectrum achieved spanned about 1.6 nm. This is due to the induced intensity dependent loss mechanism in the cavity by adjusting the half-wave plate of the polarization controller in combination with the HNLF. The MWFL output showed peak power variation of about 2.1 dB within 100 minutes of observation time.

Experimental Measurement of Absorption Coefficients for Effective Erbium-Doping Concentration to Optimize Few-Mode Erbium-Doped Fiber Amplifiers with Low Differential Mode Gain

According to the analytical expression for modal gain of few-mode erbium-doped fiber amplifiers (FM-EDFAs), we propose a method of measuring the absorption loss coefficients of few-mode signals in few-mode erbium-doped fibers (FM-EDFs) by extrapolating the mode–gain curve dependent on the average population inversion. The absorption loss coefficient of an FM-EDF was measured in our experimental platform and used to estimate the effective erbium-ion doping concentration. The feasibility of the extrapolation method was verified by simulation and comparison with the transmission method. Furthermore, the FM-EDFAs with high modal gain and low differential mode gain (DMG) could be optimized by adjusting the FM-EDF’s length and pump power. The analysis process presented here is very useful for the efficient design of FM-EDFAs from a practical point of view.

EDFA gain flattening optimization with long period fiber gratings in WDM system

Abstract This paper highlights a proposed optimized gain flatness technique for nonuniform gain spectrum of the erbium-doped fiber amplifier (EDFA) by introduction of long period fiber gratings (LPFG). In this analysis, EDFA gain spectrum has been evaluated between 1525 and 1600 nm with −20 dBm input signal power. Attenuation peaks of LPFG are optimized with a grating period of 240 µm and grating length of 30000 µm in the wavelength range of 1.1–1.8 μm, to compensate the peak gain of EDFA. Results have shown that EDFA peak gain of 35.94 dB is achieved at 1532.89 nm wavelength. This 35.94 dB peak gain is flattened up to 2.65 dB using long period fiber gratings. Also, less than ±0.3 dB gain flatness is achieved between 1528 and 1560 nm wavelength. The proposed less complex technique can be used to modify the grating parameters during fabrication in order to produce the loss peak at desired wavelength, which is efficient to flatten EDFA gain peak.

Machine-learning-based EDFA gain estimation [Invited

Optical transmission systems with high spectral efficiency require accurate quality of transmission estimation for optical channel provisioning. However, the wavelength-dependent gain effects of erbium-doped fiber amplifiers (EDFAs) complicate precise optical channel power prediction and low-margin operation. In this work, we examine supervised machine learning methods using multiple artificial neural networks (ANNs) to build models for gain spectra prediction of optical transmission line EDFAs under different operating conditions. Channel-loading configurations and channel input power spectra are used as an a posteriori knowledge data feature for model training. In a hybrid learning approach, estimated gain spectra calculated by an analytical model are added as an a priori input data feature to further improve the EDFA ANN model performance in terms of prediction accuracy, training time, and quantity of training data. Using these methods, the root mean square error and maximum absolute error of the predicted channel output power can be as low as 0.144 dB and 1.6 dB, respectively.

FBG performance enhancement for sensing and EDFA gain flattening applications

The importance of fiber Bragg gratings (FBGs) is rapidly increasing due to their wide variety of applications. We present herein a full analytical study related to a simple optimization of the performance of FBGs for sensing applications and erbium-doped fiber amplifier (EDFA) gain flattening. In sensing applications, such as strain and temperature change detection, the most important issues are the sensitivity of the sensing process and the maximum value that can be sensed before saturation. Here, we optimized the FBG parameters to obtain the best sensing performance. EDFA gain flattening is performed using one long-period fiber grating and one uniform tilted fiber Bragg grating to compensate the narrow and wide peaks in the EDFA gain variation with input signal wavelength for an Al/P-silica EDFA, respectively. Two different input signal powers are used, applying our flattening technique in each case. The best peak-to-peak value reached is 0.87 dB, corresponding to a flattening efficiency of 81.17%. The validity of this flattening technique is also evaluated through an intensive comparison with other types of EDFAs, where the flattening efficiency is illustrated and compared in each case. We thus optimize FBG performance in a new and simple way for application in sensing and gain flattening applications.