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     

Modeling of gain in erbium-doped fiber amplifiers

An analytic method is described for fully characterizing the gain of an erbium-doped fiber amplifier (EDFA) that is based on easily measured monochromatic absorption data. The analytic expressions presented, which involve the solution of one transcendental equation, can predict signal gains and pump absorptions in an amplifier containing an arbitrary number of pumps and signals from arbitrary directions. The gain of an amplifier was measured over a range of more than 20 dB in both pump and signal powers. The measured theoretical results agreed to within 0.5 dB. Although the results described apply explicitly to EDFAs pumped in the 1480-nm region, they are also applicable to EDFAs pumped in the 980-nm region. The method is valid whenever the gain saturation by amplified spontaneous-emission noise can be neglected, which is typically the case for amplifiers with less than about 20 dB of gain     

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 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.     

Gain tilt of erbium-doped fiber amplifiers due to signal-inducedinversion locking

A theoretical analysis describing an interpretation of the fundamental processes, responsible for the second-order distortion of AM signals in erbium-doped fiber amplifiers (EDFAs) is presented. It is shown that the locked-inversion gain tilt rather than the widely used continuous wave gain tilt is responsible for the distortion. The theoretical analysis is confirmed by experiments showing that the two types of gain tilt may differ by factors of up to 60. In particular, it is demonstrated that the locked-inversion gain-tilt may be significant even at the CW gain peak. Experimental results indicate that the relevant gain tilt can be reduced to acceptable levels by proper design of the EDFA     

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 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)     

Analysis of distributed erbium-doped fiber amplifiers with fiber background loss

An accurate model for erbium-doped fiber amplifiers with fiber background loss applicable to the unsaturated gain regime is presented. Exact analytical solutions are derived for the output pump power, gain, and amplified spontaneous noise as a function of input pump power in the cases of unidirectional or bidirectional pumping. An exact relation is also derived between the pump threshold and the pump required for fiber transparency. Such expressions are particularly useful to model distributed fiber amplifiers and to determine the optimal fiber parameters corresponding to a given pumping scheme. As an example, the analytical solutions are used to study the pump power requirement for distributed fiber amplifiers unidirectionally pumped at 1.48 mu m, and to determine an optimum Er/sup 3+/ absorption coefficient.<>     

S-band erbium-doped fiber amplifiers with a multistage configuration /sub e/sign, characterization, and gain tilt compensation

We report an S-band erbium-doped fiber amplifier (EDFA) with a multistage configuration in terms of its design, gain, and noise characteristics for various pump powers and input signal powers, the temperature dependence of the gain spectra, and gain tilt compensation for changes in input signal power and temperature change. We show that there is a tradeoff between low noise and efficiency in the S-band EDFA and describe the development of an S-band EDFA with a flattened gain of more than 21 dB and a noise figure of less than 6.7 dB. We also show that there is a change in the gain spectra with changes in the pump power and input signal power that is different from that observed in C- and L-band EDFAs, and that our EDFA has a temperature-insensitive wavelength. Furthermore, we develop a gain tilt compensated S-band EDFA that can cope with changes in input signal power and temperature.     

Analysis of polarization-dependent gain in fiber amplifiers

Polarization-dependent gain (PDG) in fiber amplifiers is studied theoretically. A mathematical model is developed by treating the dopant ions in glass host as partially anisotropic oscillators, and both the signal and the pump effects are taken into account. It is illustrated that PDG includes two components. One arises from polarization-selective excitation of the dopant ions by the pump; the other originates from polarization-selective deexcitation of the lasing ions by the saturating signal, known as polarization hole burning (PHB). PDG depends strongly on the operating state of the amplifiers such as the level of gain compression, the anisotropy of the dopant ions, and the relative polarization orientations of the signal and the pump. In a small-signal regime, PDG is induced only by the pump while in large-signal condition it is the sum of the two components. The good agreement between the theoretical calculations and the reported results confirms the validity of the model     

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