Modeling erbium-doped fiber amplifiers

Erbium-doped fiber amplifiers are modeled using the propagation and rate equations of a homogeneous two-level laser medium. Numerical methods are used to analyze the effects of optical modes and erbium confinement on amplifier performance, and to calculate both the gain and amplified spontaneous emission (ASE) spectra. Fibers with confined erbium doping are completely characterized from easily measured parameters: the ratio of the linear ion density to fluorescence lifetime, and the absorption of gain spectra. Analytical techniques then allow accurate evaluation of gain, saturation, and noise in low-gain amplifiers (G≲20 dB)     

Dynamic gain compensation in saturated erbium-doped fiber amplifiers

Dynamic compensation of low-frequency gain fluctuations in saturated erbium-doped fiber amplifiers is demonstrated. This compensation, based on a simple feedback-loop scheme makes it possible to reduce transient gain fluctuations efficiently across the whole amplifier bandwidth using only a low-power optical feedback signal. Such an, automatic gain control technique could be applied to suppress data packet interference due to traffic bursts in multiple-access networks, as well as in the implementation of long-haul fiber systems using erbium fiber amplifiers.<>     

Analysis of AC gain tilt in erbium-doped fiber amplifiers

We analyze theoretically and experimentally the dependence of AC gain tilt variations on gain variations in homogeneously broadened erbium-doped fiber amplifiers. Theoretically, we find that this dependence can be evaluated from the fiber's absorption spectrum. This is experimentally verified for gain variations induced by a pump-power reduction. For AM CATV, AC gain tilt variations limit how much the gain can vary before composite second order distortions become too large. From this point of view, for an erbium-doped alumino-germanosilicate fiber, an operating wavelength between 1542-1555 nm is more suitable than other ones in the long wavelength range of the EDFA, normally considered for AM CATV.     

AC and DC gain tilt of erbium-doped fiber amplifiers

AC gain tilt and DC gain tilt are defined as the variable gain of an erbium-doped fiber amplifier (EDFA) with input laser wavelength chirp due to modulation, and with different static laser unmodulated wavelengths of no modulation. This paper proposes a novel experimental setup for measuring AC gain tilt. This paper also clarifies experimentally and theoretically the dependency of the AC gain tilt on the input light modulation frequency from near DC to high frequency. The measured AC gain tilt values at high frequency resemble the measured spontaneous gain tilt values for input wavelengths from 1530 to 1580 nm. The influence of the AC gain tilt effect on AM-SCM video transmission systems is evaluated     

Optical gain control of erbium-doped fiber amplifiers with asaturable absorber

Optical gain control (OGC) can be used to lock the inversion of an erbium-doped fiber amplifier (EDFA), assuming that the gain medium is homogeneous. However, EDF's exhibit certain degrees of spectral hole burning. As a result, when the OGC laser power and the spectral-hole depth at the laser wavelength change, the inversion of the EDFA changes accordingly with a fixed OGC cavity loss. In this work, a saturable absorber is placed in the OGC laser cavity to adjust the cavity loss dynamically and compensate the gain tilt caused by the OGC laser spectral hole burning. It is demonstrated that the steady state gain variation of a surviving channel in an optically gain controlled EDFA is improved from 1.3 dB (with a fixed loss) to 0.4 dB (with a saturable absorber in the cavity). The transient response of this gain control scheme is also discussed     

Modeling of noise in erbium-doped fiber amplifiers in the saturatedregime

We have made a theoretical study of the noise figure of erbium-doped fiber amplifiers in the saturated regime. The noise figures of amplifiers subjected to specific gain and gain compression requirements were calculated for various amplifier lengths. The resulting noise figures together with the required pump and input signal powers map out all possible solutions given constraints on gain, compression, pump power, output signal power, and noise figure. In some cases, requirements on the output signal power prohibit any solutions. A way to solve this problem is the introduction of a post-amplifier loss. For this configuration, two possible solutions exist, which collapse into one solution at a certain critical loss, under which there exist no solutions. When the impact of amplified spontaneous emission is neglected in the model, only one solution is obtained, and the critical loss is much smaller than when the amplified spontaneous emission is included in the model. We conclude that amplified spontaneous emission generally has to be taken into account, even when the gain is as low as 10 dB, to accurately predict the noise performance of erbium-doped fiber amplifiers     

Modeling gain dynamics of thulium-doped fiber amplifiers

The transient response of single-(14xx nm) and dual-(14xx + 1550 nm) wavelength-pumped thulium-doped fiber amplifiers is modeled. With an optimally chosen method for numerical integration of rate equations involving several energy levels, we can estimate the transient response and frequency dependent characteristics during add-drop transitions. Results correspond to the experimental data with good accuracy.     

Analysis of gain dynamics of erbium-doped fiber amplifiers for wavelength-division-multiplexing networks

The gain dynamics in erbium-doped fibers (EDFs) with various numerical apertures (NAs) and cutoff wavelengths used in amplifiers employed in wavelength-division-multiplexing (WDM) networks is investigated by using the time-dependent amplifier model. The calculation shows that the transient response at a time immediately after some channels have been dropped depends on the cutoff wavelength, and the cutoff wavelength for the highest transient response is independent of NA. The calculation also shows that the transient response for a constant cutoff wavelength increases with an increase in NA. Experimental results for the transient response of EDFs with similar NAs and different cutoff wavelengths agree with the calculated results for various input signal powers, input signal power changes, and surviving channel wavelengths when there is no influence of neglection of amplified spontaneous emission and EDF background loss on the calculation.     

Polarization dependent gain in erbium-doped fiber amplifiers:computer model and approximate formulas

A computer model for polarization dependent gain (PDG) in Er-doped fiber amplifiers (EDFA) is presented. The model assumes that each erbium ion possesses an ellipsoidal gain surface and that all ion orientations are equally likely. By dividing the ions into subsets based upon orientation and computing the inversion of each subset in the presence of polarized pump and signal waves, the model predicts the dependence of the PDG induced by this polarization hole-burning (PHB) on the design of the EDFA, the signal degree and state of polarization (SOP), and the pump SOP. For moderate gain amplifiers (made from the same fiber) with the same gain peak wavelength and the same compression level, the magnitude of the PDG is nearly independent of the EDFA gain. Internal and random fiber birefringence are included to model real fibers. In fibers which cause the signal SOP to walk rapidly around the Poincare sphere, the PDG is reduced by a factor of 2/3 when compared with a linear polarization-maintained signal. Scrambled signals and partially-polarized saturating tones are also considered. Simple rules are derived for predicting the PDG of a given EDFA     

Modulation instability in erbium-doped fiber amplifiers

The onset of modulation instability in erbium-doped fiber amplifiers (EDFAs) is studied through a stability analysis of the underlying nonlinear Schrodinger equation. The existence of gain in EDFAs lowers the threshold for modulation instability considerably compared with the case of undoped fibers. Modulation instability generates multiple pulses when a single pulse is amplified. It can also create multiple subpulses in mode-locked fiber lasers, a feature observed experimentally. Numerical simulations show that EDFAs can convert a continuous-wave optical signal into a train of high-repetition rate femtosecond pulses     

Performance of high-concentration erbium-doped fiber amplifiers

The full characteristics for two high-concentration erbium-doped fibers are reported. The comparison of the fibers characteristics indicates that design of fiber geometry can be used to partially compensate for the degradation of the amplifiers performance due to upconversion processes. For high NA fiber the 22-dB small-signal gain, and 3.5-dB noise figure are obtained from a 24-cm length of fiber. We report a photon quantum conversion efficiency of 28%, which corresponds to the highest efficiency obtained in heavily doped fibers     

Transient analysis of erbium-doped fiber amplifiers

The transient response of an erbium-doped fiber amplifier (EDFA) pumped at 1.48 μm, taking into account the gain-saturation effects due to the amplified spontaneous emission (ASE), is studied theoretically and experimentally. The theoretical model is used to predict the gain saturation and recovery times of an EDFA and its effects to the amplification of optical pulses     

Spectral hole burning in erbium-doped fiber amplifiers

A new theoretical/numerical model of the spectral hole burning (SHB) effect in erbium-doped fiber amplifiers (EDFAs) is suggested. A new measurement technique for SHB measurement is developed. Experiments are conducted to identify the particular mechanism of SHB. A computer simulation program is developed using this approach. The shape and depth of the spectral hole are in accordance with the suggested theory.     

Novel fiber sensor arrays using erbium-doped fiber amplifiers

We examine the signal-to-noise ratio (SNR) performance of a novel type of time domain multiplexed sensor arrays in which low gain (1-10 dB) fiber amplifiers are incorporated to compensate for splitting losses between sensors. The system noise figure for passive and amplified sensor arrays is presented, along with expressions to optimize the array parameters for high SNRs. We show that practical amplified sensor arrays exhibit low system noise figures that allow much larger arrays (hundreds of sensors) than passive arrays     

Inherent enhancement of gain flatness and achievement of broad gainbandwidth in erbium-doped silica fiber amplifiers

We report new methods to inherently increase the flatness and bandwidth of erbium-doped silica fiber amplifiers from three perspectives: fiber design, pump-signal WDM coupler optimization, and amplifier structure. First, to achieve inherent control of the gain spectrum, a new type of composite fiber structure with an Er-doped core and a Sm-doped cladding ring is proposed and experimentally demonstrated. Interaction of the optical field with the Sm-doped cladding to produce evanescent wave filtering is modeled, which provides an in-line control of gain fluctuation in the erbium-doped flier amplifier (EDFA) C band, 1530-1560 nm. Second, the effect of the spectral characteristics of WDM couplers over the L band of an EDFA is explored. A fused taper fiber coupler for a 1480-nm pump is optimized for signals in the wavelength range of 1570-1610 nm by measuring the small-signal gain, gain tilt, and noise figure in an L-band EDFA. Finally, a new all-fiber structure for a wide-band EDFA, where the L and C bands were coupled serially, is demonstrated with optimized pump-signal couplers. Further optimization of the new composite fiber structure and the transient effects in the serially coupled EDFAs are also discussed     

Detailed design analysis of erbium-doped fiber amplifiers

When pumping the erbium-doped fiber amplifier at 0.98 and 1.48 mu m, the optimum cutoff wavelength for step profiles with arbitrary numerical aperture is shown to be 0.80 and 0.90 mu m, respectively. The use of a confined erbium profile can improve the gain coefficient up to 45%. The index raising co-dopant is shown to be very significant for the gain coefficient when pumping at 0.98 mu m.<>     

Noise figure of erbium-doped fiber amplifiers in saturatedoperation

We have developed a simple electrical noise figure measurement technique for the characterization of optical amplifiers. By subtracting the results of noise measurements at identical detected power levels made with and without the amplifier present, we are able to achieve an accuracy of ±0.3 dB in measured noise figure. Using this technique we obtain an excellent agreement between electrically and optically measured noise figures for two 98O-nm-pumped, copropagating erbium-doped fiber amplifiers (EDFA's) operating in saturation     

Design optimization for efficient erbium-doped fiber amplifiers

The gain and pumping efficiency of aluminosilicate erbium-doped fiber amplifiers (EDFAs) are analyzed as a function of guiding parameters and Er-doping profile for two pump wavelengths of λ _p=980 nm and λ_p=1.47 μm. Three designs of fiber-amplifier waveguides are considered: one with the same mode size as standard 1.5-μm communication fibers (type 1); one with the same mode size as standard 1.5-μm dispersion-shifted fibers (type 2); and one with mode size smaller than those of communication fibers (type 3). For the 1.47-μm pump, fundamental LP₀₁ mode excitation is assumed, while for the λ_p=980-nm pump, concurrent excitation of LP₁₁ modes is considered. It is shown that excitation of higher-order pump modes at 980 nm does not significantly affect the amplifier gain performance. The effect of concentrating the Er³⁺ doping near the center of the fiber core is shown to increase the amplifier gain coefficients by a factor of 1.5 to 2     

Efficient erbium-doped fiber amplifiers incorporating an opticalisolator

A composite-EDFA configuration which incorporates an optical isolator has been investigated theoretically and experimentally. The isolator prevents the build-up of the backward-ASE and results in an amplifier with high gain and near-quantum-limited noise figure (NF). The optimum position of the isolator has been calculated as a function of the pump power so that minimum NF and maximum gain are achieved simultaneously. It is shown that under practical pump powers, the optimized composite EDFA exhibits a gain improvement of about 5 dB and a NF reduction in excess of 1.5 dB when compared with an optimized conventional EDFA. It is also shown that with further optimization the composite EDFA can be employed in a practical fiber link as a pre-amplifier without the use of an input isolator. Finally, a high-gain composite EDFA has been experimentally demonstrated which exhibits a gain of 51 dB (54 dB) and NF of 3.1 dB for only 435 mW (93 mW) of pump power