Modeling Of Erbium-doped Fiber Amplifiers Research Articles

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).

Simulation of the optical erbium doped fiber amplification for performance analysis

Abstract In this contribution, innovations in the simulation of the optical transmission path are presented specifically, the dynamic performance analysis of erbium doped fiber amplifier (EDFA) properties for system applications is focused. Our EDFA simulation model is based on population equations of ions that can describe mutual relations between three states of ions in the EDFA amplifier. The presented numerical approach includes a signal gain and noise contributions to the single input channel amplification using the steady state modelling coming out of a dynamic model. The EDFA model in the steady state can be consequently applied for a purpose of advanced si mulations performed in the complete optical transmission path.

High speed optical switching gain based EDFA model with 30 Gb/s NRZ modulation code in optical systems

Abstract This study presents high speed optical switching gain based Erbium doped fiber amplifier model. By using the proposed model the optical fiber loss can be minimized. The system is stabilized with the power budget of 25.875 mW a long 75 km as a length of optical fiber in this study can be verified. The modulation rate of 10 Gb/s can be upgrade up to reach 30 Gb/s. The suitable power for the optical transmitter is −2.440 dBm and NRZ modulation code is verified. The receiver sensitivity can be upgraded with the minimum bit error rate and max Q factor are 1.806 e−009 and 5.899.

Output Signal Power Analysis in Erbium-Doped Fiber Amplifier with Pump Power and Length Variation Using Various Pumping Techniques

The scope of this paper is to analyze the output signal power with pump power and length variation in cascaded EDFA simulation model performance. This paper describes the simulation model of Erbium-Doped Fiber Amplifier (EDFA) of variable lengths (10 m, 50 m, and 120 m) with dual pumping techniques (dual forward pumping with two 980 nm wavelengths, dual forward and backward pumping with two 980 nm wavelengths) and Tri-pumping techniques. The simulation models consist of input source and pump power coupled by WDM coupler which gives optimized signal power in the above-mentioned simulation model. The simulation model consists of source with multiple wavelengths (1520 nm–1618 nm), pumping source with the wavelength 980 nm, isolator, and filter. The resulting models accurately represent EDFA optimized output signal power. Simulation results show that choosing careful fiber length 120 m and pump power 1 W in dual pumping provided 0.07 W optimized output signal power compared to other pumping techniques.

Analysis of Augmented Gain EDFA Systems using Single and Multi-wavelength Sources

The scope of this paper is to analyze the performance of augmented gain EDFA systems using Single and Multiwavelength Input sources. The Performance of an Optical Communication system can be improved by the use of EDFAs as an Optical Amplifier. Erbium doped fiber amplifier (EDFA) is an important element in DWDM networks. We can achieve a flat gain spectrum by modeling the dynamic characteristics of an EDFA. This paper presents basic EDFA model operating on single (1550nm) and multi (1520-1610) nm wavelength operation with their simulation results. For the present work, we have used EDFA design software tool. It simulates various characteristics such as amplified spontaneous emission, gain, noise figure etc. in efficient manner. The working principle of this software provides accurate simulations and results. It confirms the excellent agreement between simulations and results obtained in real EDFA design. The proposed model consists of an input source, isolator, pump source, erbium fiber and WDM coupler. By changing the design parameters such as Input signal power and Pump Power, the different performance parameters (gain and noise figure) can be optimized. Without changing the values of isolator, erbium fiber length and WDM coupler and keeping the values of Input signal power -30dBm and Pump Power 80mW the obtained optimized gain is 34.45dB for single wavelength source and 32.924 dB for multi wavelength source. General Terms Spectrum, Networks, Multiplexing.

Simple and efficient ANN model proposed for the temperature dependence of EDFA gain based on experimental results

This study deals with the Artificial Neural Network (ANN) model of erbium-doped fiber amplifier (EDFA) gain in C band based on our experimental results at the temperature range of 0–60°C. An ANN with three inputs and one output is considered where the inputs are signal power, wavelength, temperature and the output is EDFA gain. The network parameters are optimized by monitoring mean square error (MSE) at the output. The proposed dynamic model tremendously reduces the computational in the order of milliseconds which computes the EDFA gain at different operating conditions and is in very good agreement with our experimental findings.

A new simple model for EDFA incorporated in the irradiated environment for inter-satellite optical communication

A new simple model for the erbium-doped fiber amplifier (EDFA) incorporated in the irradiated environment for inter-satellite optical communication is proposed. In the model, all factors caused by irradiation are assumed to be equivalent to a unique factor, which is the reduction number of active Er3+. In this case, one can directly predict the output power of the 1550 nm EDFA and avoid its computing by using only the evolution of 1310 nm absorption similar to the models previously elaborated. Two equivalent EDFAs are irradiated with 60Co rays at different doses. The experimental and simulation results show that the model can predict the output-power degradation with an accuracy better than 13% under irradiation of 20 krad. Such an accuracy is good enough for inter-satellite optical communication systems on low Earth orbit (LEO).

Computer-aided analysis of distortions in SCM systems with EDFAs including chirping effect

In this paper, we have applied an equivalent electrical circuit model of erbium-doped fiber amplifier (EDFA) including chirping effect to analyze the distortions in subcarrier multiplexing (SCM) systems. The model is simple and convenient for analyzing the distortions and performance of lightwave transmission systems using EDFAs, through the aid of a SPICE circuit simulator. The performance evaluation is shown of a 42-channel SCM EDFA system, including the composite second-order distortions (CSO), the allowable modulation index, and the limit on the number of channels.

The amplified model of erbium-doped fiber amplifier (EDFA) with cross-phase modulation (XPM)

Based on the rate equations and the power propagation equations, the amplified model is obtained which considers the cross-phase modulation (XPM)-induced intensity fluctuation between pump power and signal power in erbium-doped fiber amplifier (EDFA). Simulation results show: a higher nonlinear coefficient and a stronger pump power cause a stronger XPM in EDFA. Before the optimal length of EDF, the intensity caused by XPM increases with the increasing length, but after the optimal length, the XPM presents saturation. A bigger nonlinear coefficient γ corresponds to a smaller optimal length and gain, and makes gain saturation more easy. XPM effect will decrease EDFA’s amplified efficiency.

An Efficient Simulation Model of the Erbium-Doped Fiber for the Study of Multiwavelength Optical Networks

The first part of this paper reviews the spectrally resolved erbium-doped fiber model by Saleh, Jopson et al. (1990, IEEE Photon Technol. Lett.2, 714; 1991, Fiber Laser Sources and Amplifiers III, Vol. 1851, pp. 114–119, SPIE). This model is adequate for fast simulation of erbium-doped fiber amplifiers pumped at 980 or 1480 nm which are not self-saturated by amplified spontaneous emission noise. The second part of this paper reviews the wavelength-domain representation of optical signals and network components at the optical transport layer of multiwavelength optical networks. This representation stems from the spectrally resolved model of erbium-doped fiber amplifiers. Optical signals are represented by their carrier wavelength and average power exclusively and not by their temporal waveform, as is customary in simulation of analog and digital communication systems. In addition, network components are fully characterized by their loss or gain as a function of wavelength. The wavelength-domain representation is adequate for efficient steady-state and transient power-budget computations; i.e., it can be used to evaluate the optical signal, amplified spontaneous emission noise, and linear optical crosstalk average powers at all points in a multiwavelength optical network. To illustrate the capabilities of the spectrally resolved erbium-doped fiber model by Saleh, Jopson et al. and the wavelength-domain representation, transient power fluctuations caused by the dynamic interaction of saturated erbium-doped fiber amplifiers and servo-controlled attenuators in a bidirectional ring composed of four wavelength add–drop multiplexers are studied. The mechanisms responsible for this oscillatory behavior are identified and remedies are proposed.

Effects of nonlinear dispersion in EDFA's on optical communication systems

The signal-induced change of the refractive index in an erbium-doped fiber amplifier (EDFA) causes a phase modulation imposed on a signal when passing the EDFA. In this paper, we apply our extended EDFA model on an optical communication system. The model includes this phase modulation, by including the nonlinear dispersion in an EDFA, and the spontaneous emission noise. The influence of these effects on an optical communication system is examined by means of Q-factor and eye diagram. We assume an intensity modulated-direct detection (IM-DD) system operating at 193 THz (1552.5 nm) with a bit rate of 10 Gb/s in the anomalous dispersion regime and a total fiber length of 500 km. The fibers are assumed to be dispersion shifted ones, EDFAs are used to compensate for the fiber loss. By numerical simulation we obtain results for the influence of the phase modulation (nonlinear dispersion) due to the signal induced change of the refractive index in an EDFA and the spontaneous emission noise at different input peak powers. Neglecting the signal-induced change of the refractive index strongly underestimates the Q-factor in the anomalous dispersion regime. Therefore it should be included for reliable system simulations. This can be done with the numerical model presented here.

A model of erbium-doped fiber amplifier gain dynamics

A spatial-mode model of erbium-doped fiber amplifier (EDFA) gain dynamics is presented. The model includes radial distribution of dopant and modal intensity in the optical fiber. The boundary conditions needed for the dynamic model are calculated through a numerical solution of a basic rate equation of a two-level laser system in steady state. The relaxation method is used in the iterative calculation of the propagating equations in order to resolve the forward and backward traveling amplified spontaneous emission. The partial differential equations describing the EDFA dynamic performance are calculated through the finite difference resolution method.

Efficient multiwavelength dynamic model for erbium-doped fiber amplifier

An efficient full spectrum (1480-1600 nm) large-signal transient dynamic model of an erbium-doped fiber amplifier (EDFA) is developed. A technique to speed up the simulation by a factor of 1000 using artificial delay lines based on the transmission-line model (TLM) is presented. Simulations and experimental results show the delay line method is not detrimental to the accuracy of the model. The efficiency of this model means it is ideal for simulating the dynamics of large wavelength division multiplexed (WDM) networks if included in a network simulator.

Analysis of channel addition/removal response in all-optical gain-controlled cascade of erbium-doped fiber amplifiers

Application of the all-optical gain-controlled (AOGC) erbium-doped fiber amplifier (EDFA) for protection surviving channels in a multiwavelength network in which several EDFAs are cascaded is studied. The effects of addition and/or dropping of wavelength channels in a network comprising six concatenated EDFAs have been analyzed by numerical simulation. Only the first EDFA in the cascade is gain clamped using a ring laser configuration. A large-signal EDFA model which incorporates time variation numerical effects and the downstream propagation of signal and pump and downstream and upstream propagation of amplified spontaneous emission (ASE) has been used. In particular, the effects of relaxation oscillations from the gain-controlled EDFA on the surviving channel protection are investigated. It is shown that power excursions caused in an eight-channel wavelength division multiplexed (WDM) network by the loss/addition of 6 channels will be lower than 1 dB and free of relaxation oscillations if the gain-controlled EDFA is strongly inverted and the average normalized population density of the metastable level does not drop below 0.74.

An Explicit Analytical Solution for the Transcendental Equation Describing Saturated Erbium-Doped Fiber Amplifiers

Analytical modeling of erbium-doped fiber amplifiers (EDFA) in all operating regimes (i.e., small-signal, signal-saturated, self-saturated, uni- or bidirectionally pumped) requires solving a transcendental equation derived by Saleh et al. in 1990. In this paper, we describe an approximate, although accurate, explicit analytical solution for such a transcendental equation. The use of this explicit solution alleviates computational time constraints and should therefore permit extensive multidimensional or parametric studies of EDFAs. It could be advantageously applied to the study of multiwavelength amplified network systems, with new potentials for interactive computer-assisted design.

Analytic modeling of erbium-doped fiber amplifiers on the basis of intensity-dependent overlapping factors

Rate equations based on intensity-dependent overlapping factors are integrated to obtain analytic solutions for pump, signal, and amplified spontaneous emission (ASE), even when the coupled signal varies with time. The equations can be applied without the imposition of any restraints on the values of the pump, signal, and ASE powers, the excited-state-absorption cross section, the erbium-density distribution, or other parameters that characterize the fiber. The methods used to calculate pump, signal, and ASE powers are discussed. Experimental techniques to characterize the doped fiber that were based on these analytic expressions are introduced.

Theoretical and experimental investigations on erbium-doped fiber amplifiers

Abstract A comprehensive model of erbium-doped fiber amplifiers (EDFA) is proposed in this paper, taking exited-state absorption (ESA), amplified spontaneous emission (ASE), background absorption, mode field, and Erbium ion radial distribution into account. Computer programs capable of handling forward, backward, and different wavelength bidirectional pumping are developed. Among other things, it is found that under typical conditions, Gaussian field approximations may cause considerable errors. The optimum V-value for small signal gain is much smaller than that for minimum Gaussian or Desurvire spot size; ASE propagating opposite to the pimp beam can be several times higher than at propagating along the pump beam, resulting in a faster-than-linear decrease of the pump power at its beginning portion. Experimental results of domestic-made erbium-doped fibers pumped by 980 nm and 1480 nm laser diodes are also given.

ERBIUM-DOPED FIBER AMPLIFIERS: BASIC PHYSICS AND THEORETICAL MODELING

An extensive outline of the basic physics and modeling of erbium-doped fiber amplifiers is presented. In the first part, the spectroscopic features and properties of the erbium-doped glass laser system are described. In the second part, various theoretical models based on this description are detailed with insights on the approximations made and their corresponding accuracy. Such models are shown to be useful for optimizing the design and device characteristics of Er-fiber amplifiers.

Theoretical modeling of erbium-doped fiber amplifiers with excited-state absorption

Numerical solution of a general rate-equation model of an erbium-doped fiber amplifier highlights several important features of the device. A difference in strong-signal gain between copropagating and counterpropagating signal pump schemes in the presence of pump excited-state absorption is predicted, and this is confirmed by experimen. The detriment in the noise figure previously associated with counterpropagating schemes for only small-signal conditions is shown to be similar for strong signals, corresponding to a power-amplifier operating regime. In addition, a correction to the noise figure is given for the limit of a low-gain amplifier.