Gain Saturation Model 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).

Modulational instability of a resonantly polariton condensate in discrete lattices

We study modulational instability of a resonantly polariton condensate in a discrete lattice. Employing a discrete gain-saturation model, we derive the dispersion relation for the modulational instability by means of the linear-stability analysis. Effects of the pumping strength, the nonlinearity, the strength of the detuning, and the coupling strength on the modulation instability are investigated. It is found that the interplay between these parameters will dramatically change the modulational instability condition. We believe that the predicted results in this work can be useful for future possible experiment of exciton-polariton condensate in lattices.

Enhanced gain saturation model of non‐linear semiconductor optical amplifiers

This study proposes an enhanced gain saturation model of non-linear semiconductor optical amplifiers (SOAs) by incorporating material-dependent gain compression factor. The rate equations are utilised with the extra gain compression term for Indium-Gallium-Arsenide material-based SOA to account for the steep relaxation oscillations behaviour of non-linear SOAs. The proposed gain saturation model is verified with experimental results that showed very good agreements with a mean square error of 0.094.

Ultrafast optical switching using parity–time symmetric Bragg gratings

This paper reports on time-domain modeling of an optical switch based on the parity–time (PT) symmetric Bragg grating. The switching response is triggered by suddenly switching on the gain in the Bragg grating to create a PT-symmetric Bragg grating. Transient and dynamic behaviors of the PT Bragg gratings are analyzed using the time-domain numerical transmission line modeling method including a simple gain saturation model. The on/off ratio and the switching time of the PT Bragg grating optical switch are analyzed in terms of the level of gain introduced in the system and the operating frequency. The paper also discusses the effect the gain saturation has on the operation of the PT-symmetric Bragg gratings.

Time dependent model of gain saturation in microchannel plates and channel electron multipliers

Abstract We present and discuss a time dependent solution of the transmission line model of a channel electron multiplier, introduced in a previous paper and already solved in steady-state conditions. The model is applicable to all the situations in which the multiplier input current is sufficiently large so that the statistical variations of the gain for each electron can be ignored and it does not apply to photon counting detectors. By introducing the appropriate boundary conditions the time dependent non-linear equations of the model are reduced to an integral equation in implicit form, whose solution can be calculated numerically by a perturbative approach. In this way the multiplying current signal i(z,t) and the voltage V(z,t) are found as functions of the position z along the channel, and of the time t during the pulse itself, for any arbitrary shape of the input current waveform. The important case of the amplification of input current pulses with a short duration compared to the multiplier recovery time is investigated in detail, showing that the non-linear behavior can be entirely described by a general function of a conveniently defined saturation parameter and that this function is characteristic of any uniform channel multiplier. The model is then used to investigate the recovery of the multiplier after a saturating pulse, and it is found that the gain recovery from weak or moderate saturation levels is exponential to a very good approximation, but with a time constant different from the characteristic time constant RC of the multiplier. Finally the case of pulses of arbitrary shape and duration is considered and examples are given of the amplification of step pulses and of a regular sequence of identical pulses. A remarkable feature of the model is that the solution can be calculated from the time shape of the output pulse, rather than from the input. This makes possible to implement methods for pulse restoration, i.e. for recovering the original input pulse shape from a measured saturated output.

Saturated signal-to-noise ratio of up-stream WRC-FPLD transmitter injection-locked by down-stream data-erased ASE carrier

By controlling the extinction ratio (ER) and overshooting level of the down-stream amplified spontaneous emission (ASE) with a gain-saturation semiconductor optical amplifier (SOA), the down-stream data-erased ASE carrier is re-encoded in an injection-locked weak-resonant-cavity Fabry-Perot laser diode (WRC-FPLD) up-stream transmitter to implement all-ASE based bi-directional WDM-PON system. The effect of ER on the up-stream transmission performance of the down-stream data-erased ASE injection-locked WRC-FPLD is elucidated via the gain-saturation model. It is observed that the communication criterion with a bit-error-rate of <10⁻⁹ at 2.488 Gbit/s can be met only when ER is reduced to <3 dB and overshooting level <-5 dB. The up-stream WRC-FPLD re-encoded ASE data-stream could improve its signal-to-noise ratio (SNR) to 6.4 dB by minimizing the ER and overshooting level of the down-stream data-erased ASE to 2.4 dB and -7.8 dB, respectively, with the gain-saturated SOA. The SNR can also be improved with higher power injecting into the up-stream transmitter until saturation occurs and the optimal window of the ASE injection power is between -7 and -3 dBm.

Static Gain Saturation Model of Quantum-Dot Semiconductor Optical Amplifiers

We theoretically investigate the gain saturation behavior of a quantum-dot (QD) semiconductor optical amplifier (SOA), focusing on spectral hole burning (SHB) and total carrier density depletion (TCDD). In the static gain model for a QD-SOA, SHB is modeled by the quantum-mechanical density matrix theory and TCDD is described by the shift of the global quasi-Fermi level. We calculate the gain saturation spectra of a QD-SOA at various injection current densities and qualitatively explain how high-speed cross-gain saturation responses can be affected by injection current density. From the quantum-mechanical description for SHB, we show that the optical power for 3-dB gain saturation due to SHB is proportional to the square of the homogeneous linewidth and the functionality of a QD-SOA can be changed by controlling device parameters such as doping density and barrier potential to adjust the homogeneous linewidth.

Controllable delay of ultrashort pulses in a quantum dot optical amplifier

Optical and electrical tuning of the propagation time of 170 fs pulses in a quantum dot semiconductor amplifier at room temperature is demonstrated. Both pulse slowdown and advancement is possible and we achieve fractional delays (delay divided with pulse duration) of up to 40%. The results are explained by a simple gain saturation model.

Detailed model and investigation of gain saturation and carrier spatial hole burning for a semiconductor optical amplifier with gain clamping by a vertical laser field

A detailed model for semiconductor linear optical amplifiers (LOAs) with gain clamping by a vertical laser field is presented, which accounts the carrier and photon density distribution in the longitudinal direction as well as the facet reflectivity. The photon iterative method is used in the simulation with output amplified spontaneous emission spectrum in the wide band as iterative variables. The gain saturation behaviors and the noise figure are numerically simulated, and the variation of longitudinal carrier density with the input power is presented which is associated with the on-off state of the vertical lasers. The results show that the LOA can have a gain spectrum clamped in a wide wavelength range and have almost the same value of noise figure as that of conventional semiconductor optical amplifiers (SOAs). Numerical results also show that an LOA can have a noise figure about 2 dB less than that of the SOA gain clamped by a distributed Bragg reflector laser.

Performance analyses of flowing chemical oxygen-iodine laser.

A modified simplified rate-equation model that utilizes the Voigt profile function and another gain saturation model deduced from the kinetic equations are presented for performance analyses of a flowing chemical oxygen-iodine laser. Both models are adapted to both the condition of homogeneous broadening and that of inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant. Effects of temperature and iodine density on the output power and on variations of output power, optical intensity, and saturation intensity with flow distance are presented as well. There are differences between results of two models, but both qualitatively agree with known results.

Effects of the Spectral Line Broadened Model on the Performance ofa Flowing Chemical Oxygen-Iodine Laser

A new gain saturation model of chemical oxygen-iodine lasers(COILs) is deduced from the conservation equations of the population numberof upper and lower lasing levels. The present model is compared withboth the Voigt profile function model and its low-pressure limit model.The differences between the Voigt profile function model orits low-pressure limit model and the model presented here are pointed out, suchas the length of power extraction, the optimal range of the thresholdgain. These differences are useful for the optimization of COILadjustable parameters.

Analytical, steady-state model of gain saturation in channel electron multipliers

By using the transmission line modeling (TLM) technique we derive a simple model describing the saturation of the gain in channel electron multipliers and show that it generalizes and extends a previous steady-state model due to Shikhaliev. Then by introducing a physically consistent rational approximation of the non-linear gain equation we derive an exact, steady-state, analytical solution in which, contrary to other authors, empirical assumptions about the functional dependence of the internal voltage are not required. The model is then used to simulate a multianode microchannel plate (MCP) photomultiplier, showing that the computed gain in saturated conditions is qualitatively in agreement with published experimental data. Finally, we discuss the general validity of our model, we suggest possible measurements and comment existing data relevant for its validation.

Influence of gain saturation and carrier dynamic models on the modulation response of quantum well lasers

The main problem for creation of optical communication systems is how quickly the light intensity can be changed under radiation from a laser diode. The modulation capability of lasers with separate confinement heterostructure depends strongly on carrier transport and gain saturation phenomena. Nonlinear gain saturation model in connection with dynamic behavior at high-frequency modulation is discussed and peculiarities of application of a new dynamic model with partial differential equation for the carrier transport in SCH region are shown.

A simple model of gain saturation in high gain single pass free electron lasers

The saturation dynamics of a high gain single passage FEL is reproduced by means of an analytical model based on Bloch-type equations, similar to those governing the physics of conventional lasers. The main results of the paper is the proof that the evolution from small to strong signal regime can be described in terms of the logistic function, whose validity is extended to the oscillator regime.

Analysis of emission and gain saturation in gain-switched semiconductor lasers

We calculate the switch-on dynamics of a single-mode bulk GaAs laser diode including carrier kinetics with Boltzmann collision integrals for carrier–carrier and LO–phonon-carrier scattering. The dependencies of the dynamics on the electrical pump amplitude and on the laser frequency are determined. The shortest light pulse with 12.8 ps (FWHM) is obtained for a laser mode in the gain maximum and a pump rate of 15.5 times the threshold value. The resulting differential gain, transparency density, and gain saturation coefficient are calculated as functions of the pump rate and the mode detuning. The gain saturation during the laser switch-on is enhanced at the trailing edge of the light pulse. This is well described by an extended dynamical gain saturation model that includes correction in terms of the light intensity and its first time derivative. The coefficients of this dynamical gain saturation model are determined by a comparison of the detailed carrier kinetics in a laser with the corresponding rate equations.

Simple analytical model of gain saturation in microchannel plate devices

We derive, discuss, and test against experimental data an analytical model of the gain saturation in microchannel plate (MCP) devices. By introducing a simple recharging circuit for each dynode, we extend the well-known, unsaturated gain model of Eberhardt to a microchannel operating in condition of gain saturation and show that the amplification of a current pulse and the voltage drop along the channel can be described by a pair of coupled differential equations. Solutions of these equations are given in various conditions, including an approximate solution, valid in the case of weak saturation and a general solution in implicit form. The behavior of a microchannel operating in current mode is studied by finding the transient and steady-state solutions obtained with an input step current wave form. Exact solutions are given for the charge gain of pulses with a short duration, compared to the dynode recharging time, and for the gain recovery of a microchannel after the amplification of a short pulse. The single channel saturation model is then extended to multistage MCP assemblies by taking into account the statistical distribution of the photoelectrons at the input and the spread of the multiplied electron cloud in the interplate gaps. The expressions found in this way are used for the best fit of experimental data from a Z-stack MCP photomultiplier operated in single and double pulse mode. Satisfactory agreement between the model and experimental data is obtained in the case of single pulse measurements, finding a reduced chi squared χ2=4.67. Less satisfactory agreement is found for double pulse data, giving χ2=7.46 and a clear indication that the model may be significantly improved by taking into account the charge redistribution among the dynodes during the recharging process, neglected in the present formulation.

Parametric dependence of stochastic frequency variations in the gain switching of a single-mode laser diode

The authors have studied the fluctuations in the range of frequency excursions of the optical field from a single-mode laser diode that has been switched-on by a stepwise increase, in the current from a bias level which is below threshold. Both the maximum and the minimum frequencies reached in the transient for each gain-switching event are linear functions of the turn-on time. The statistics of the range of frequency variation for different turn-on events are then easily obtained from the statistics of the turn-on time. The slopes of these functions depend linearly on the injection current of the single-mode laser diode. In addition, they depend not only on the saturation intensity of the single-mode laser diode, but also on the particular form of gain saturation. As a consequence, experimental measurements could be used, in principle, to determine which model of gain saturation best describes the operation of a given single-mode laser diode.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Model of Gain Saturation in A Two-mirror Laser

Abstract An approximate method of analysis of nonlinear operation of Fabry-Perot lasers including longitudinal electric field dependence and the spatial hole burning effect is presented. The method is based on a semiclassical approach and provides an approximate expression relating the normalized small signal gain to the normalized output power and laser parameters. The influence of the spatial hole burning effect on the laser characteristics is investigated. It is shown that this effect determines the value of the optimal coupling strength, as well as causing changes in the laser characteristics.

Gain saturation in free-electron lasers

Abstract We propose a model of gain saturation in a free-electron laser, drawing a parallel with the dynamics of saturation in a conventional laser. The results achieved are then extended phenomenologically to bunched-beam operations and the results has been compared to that measured in the experiments at Los Alamos.

Gain saturation in bunched free-electron lasers.

We propose a model of gain saturation in free-electron lasers operating with a bunched electron beam. A simple method to evaluate the steady-state intensity as a function of the optical cavity length is given and the result is in close agreement with the intensity measured in the Los Alamos free-electron-laser experiment [B. E. Newnam et al., Nucl. Instrum. Methods A 237, 187 (1985)].