Cumulative waveform distortion in cascaded optical amplifierrepeaters for multigigabit IM/DD systems

An analysis was conducted of a cumulative pattern-dependent waveform distortion in cascaded semiconductor laser and Er³⁺-doped fiber amplifiers. At 2.5 Gb/s, cumulative waveform distortion limits the number of cascaded amplifiers to about 20 for the semiconductor amplifiers. The Er³⁺-doped fiber amplifier is relatively unaffected-over 100 stages can be cascaded. The Er³⁺ amplifier is seen to be the better choice for long-haul multigigabit systems     

Improved gain performance in Yb3+-sensitized Er3+-doped alumina (Al2O3) channel opticalwaveguide amplifiers

Small-signal amplification in short, Yb³⁺-sensitized, Er³⁺-doped alumina (Al₂O₃) channel optical waveguides with high Er³⁺ concentrations is analyzed. Taking into account uniform up conversion, excited state absorption (ESA) from the Er³⁺ metastable level (⁴I_13/2 ), and Yb³⁺→Er³⁺ energy transfer by cross relaxation, the obtainable gain improvements compared to Yb³⁺ -free Er³⁺-doped Al₂O₃ optical waveguides are investigated. The amplifier model is based on propagation and population rate equations and is solved numerically by combining finite elements and the Runge-Kutta algorithm. The analysis predicts that 5-cm long Yb³⁺/Er³⁺ co-doped Al₂O ₃ waveguides show 13-dB net signal gain for 100 mW pump power at λ_p=980 nm     

Er3+-doped fiber amplifier pumped by 0.98 μm laserdiodes

The performance of an Er³⁺-doped fiber amplifier pumped by 0.98 μm InGaAs laser diodes (LDs) is reported. By using a fiber with low Er³⁺ content and optimizing the fiber length, a maximum signal gain of 37.8 dB at 30-mW pump power was realized at a signal wavelength of 1.536 μm. A maximum gain coefficient of 1.9 dB/mW at 14 mW pump power was achieved. It was found that the fiber amplifier pumped by the 0.98-μm LDs is twice as efficient as that pumped by 1.48-μm LDs, from the viewpoint of both required fiber length and the attained gain     

Fundamental limits on Nd3+-doped fiber amplifierperformance at 1.3 μm

To explore the fundamental limits on performance at 1.3 μm, a model for Nd³⁺-doped fiber amplifiers which includes signal saturation and excited state absorption (ESA) at the signal wavelength has been constructed. Ignoring ESA, the difference in pump efficiency between a low-performance and a high-performance glass host is ≈60%, indicating that ESA is the critical parameter distinguishing experimental results reported for different materials. The pump efficiency for a linear Nd³⁺ amplifier is an order of magnitude less than for an Er³⁺ amplifier without ESA and degrades still further with its inclusion. Applications as power amplifiers are more promising, because, in principle, high power conversion efficiencies can be obtained     

Diode-array pumping of Er3+/Yb3+ Co-dopedfiber lasers and amplifiers

Single-mode double-clad Er³⁺/Yb³⁺ co-doped fibers are shown to be suitable for diode array pumping at around 960 nm. A fiber laser with 96-W output power at 1.53 μm and a power amplifier exhibiting a small signal gain of 24 dB and a saturated output power of +17 dBm are reported     

Low noise, all-optical gain controlled Er3+ doped fibreamplifier using asymmetric control laser cavity design

The authors demonstrate an Er³⁺ doped fibre amplifier with all-optical, automatic gain control and with near quantum limited, 1480 nm pumped noise performance. The amplifier gain is controlled by in-band laser action, and two design considerations are established for optimum noise performance: the control laser wavelength should be located in a region of high amplifier gain, and the laser cavity should be constructed to be as asymmetric as possible, ensuring minimum laser power at the signal input end of the amplifier     

Modeling of Yb3+-sensitized Er3+-doped silicawaveguide amplifiers

A model for Yb³⁺-sensitized Er³⁺-doped silica waveguide amplifiers is described and numerically investigated in the small-signal regime. The amplified spontaneous emission in the ytterbium-band and the quenching process between excited erbium ions are included in the model. For pump wavelengths between 860 and 995 nm, the amplified spontaneous emission in the ytterbium-band is found to reduce both the gain and the optimum length of the amplifier significantly. The achievable gain of the Yb³⁺-sensitized amplifier is found to be higher than in an Er³⁺-doped silica waveguide without Yb ³⁺ (18 dB versus 9 dB for a pump power of 100 mW). However, it is important to optimize the Yb-concentration according to the choice of pump wavelength     

Parameters for Quantitative Comparison of Two-, Three-, and Four-Level Laser Media, Operating Wavelengths, and Temperatures

Several parameters are proposed for describing the statistical thermodynamic component of the exchange of photons between a pump and a laser beam. They are based on the occupation probability of absorbing and emitting, pump and laser levels, and are complementary to the optical cross sections. The ldquooccupation factor,rdquo f ₀ , is appropriate for describing an optical amplifier in the small signal regime. f ₁ is appropriate for describing an amplifier in the large signal regime, e.g., a laser. They serve to facilitate a quantitative comparison of laser gain media, operating temperatures, and choice of pump and laser wavelengths. After a simple scaling, both occupation factors have a numerical value that coincides well, in most cases, with conventional usage of the terms two-, three-, and four-level laser. They can thus serve as an unambiguous, quantitative alternative to the quasi-two-, quasi-three-, and quasi-four-level terminology. The proposed definitions are general enough to apply to many types of gain media, but are particularly useful for comparing systems with discrete levels, pumped with a narrowband source, in near-resonance with the laser wavelength. Several low-quantum-defect combinations of pump and laser wavelengths are analyzed for Er³⁺ , Nd³⁺ , Yb³⁺ , and Ho³⁺ in YAG, as a function of temperature.     

Rayleigh scattering influence on performance of 10 Gb/s opticalreceiver with Er-doped optical fiber preamplifier

The achievement of -30.8 dBm (630 photon/bit) receiver sensitivity at 10 Gb/s, with an Er³⁺-doped optical fiber preamplifier, is discussed. This is an 8.3-dB sensitivity improvement over the avalanche-photodiode/FET receiver. Power penalties caused by a noise increase due to Rayleigh backscattering by the transmission optical fiber have been evaluated. Approximately -30-dB Rayleigh scattering from a 20-km optical fiber resulted in a 3.5-dB power penalty for a 25-dB-gain optical amplifier     

Er3+-Yb3+ and Er3+ doped fiberlasers

Single-mode fiber lasers operating at ~1.57 μm are described. Output powers of >2 mW are reported for laser diode pumped operation. Direct comparison is made between fiber lasers using sensitized erbium (Er³⁺ and Yb³⁺) and erbium on its own. The performance of Er³⁺-Yb³⁺ fiber lasers is analyzed in more detail as a function of fiber length. Both CW and Q-switched operations are studied and the results obtained demonstrate that practical sources at 1.5 μm are available from diode pumped Er³⁺ -Yb³⁺ systems     

Effects of concentration on the performance of erbium-doped fiberamplifiers

The dependence of erbium-doped fiber amplifier (EDFA) performance on the erbium ion concentration is studied experimentally and theoretically. The quantum efficiency of the amplifier is found to he strongly dependent on the erbium ion concentration, the signal wavelength, and the relative propagation direction of the pump and signal beams. This dependence is fully explained by the presence of an upconversion mechanism between ions residing in pairs or larger clusters and suggests that other sources of amplifier performance degradation (back-ground loss, excited state absorption, homogenous upconversion) are negligible. The experimental data show that in the present EDFA designs with over 80% quantum/conversion efficiency, the aluminum co-doped fibers with erbium ion concentration less than 20×10²⁴ m^-3 (900 molar ppm Er³⁺) are most suitable     

Optimum design of Er3+-Yb3+ codoped fibersfor large-signal high-pump-power applications

A comprehensive numerical fiber amplifier model has been used to optimize Er³⁺-Yb³⁺ codoped active fiber for maximum gain and quantum conversion efficiency (QCE) at large signal operation. The optimum cutoff wavelength of the LP₁₁ mode has been found to increase from 800 mm at low pump powers (≈50 mW) to 1400 mn at pump powers higher than 500 mW. While at low pump powers fibers with higher numerical aperture give higher QCE, at high pump levels better large signal performance is achieved with fibers having lower numerical aperture     

The effect of pair-induced energy transfer on the performance ofsilica waveguide amplifiers with high Er3+/Yb3+concentrations

High-concentration Er³⁺/Yb³⁺ co-doped silica waveguide amplifiers are numerically analyzed. With optimized rare-earth concentrations the effect of Er³⁺/Er³⁺ ion-pairs can be neglected and each Er³⁺ ion can be assumed to be paired only to the surrounding Yb³⁺ ions. The rate-equations model includes uniform upconversion mechanisms from ⁴I_13/2 and ⁴I_11/2 erbium levels and an Yb³⁺ to Er³⁺ pair-induced energy transfer process. Numerical results demonstrate the possibility of fabricating short- and high-gain integrated optical amplifiers; it is shown that net gain as high as 3 dB/cm can be obtained     

Er–Yb Waveguide Amplifiers in Novel Silicate Glasses

A set of novel silicate glasses containing ZnO and co-doped with Er³⁺ and Yb³⁺ was designed as substrates for optical waveguide amplifiers. Characterized by exceptionally low up-conversion, minimum Er concentration quenching and high mechanical as well as chemical stability, the reported glasses can compete with phosphate-based materials typically used in the state-of-art active devices. Straight channel waveguides with propagation losses as low as 0.18 dB/cm were fabricated in these substrates using Ag⁺ hArr Na⁺ and K ⁺ hArr Na⁺ thermal ion exchange. Net on-chip gain values of 6.7 dB at 1537 nm were measured and a net fiber to-fiber gain of 5 dB was achieved when pumped at 976 nm. A six-level spatially resolved numerical model of an Er-Yb co-doped active waveguide was developed to analyze and optimize the amplifier performance. Modification of the rare-earth dopant concentration and the channel waveguide geometry was proposed to increase the gain figure and improve the overall amplifier efficiency.     

Cascaded Two-Wavelength Lasers and Their Effects on C-Band Amplification Performance for Er3+-Doped Fluoride Fiber

In this paper, we report cascaded two-wavelength 853-nm (⁴ S_3/2rarr⁴I_13/2 transition) and 1533-nm (⁴I_13/2rarr⁴I_15/2 transition) lasing from Er³⁺-doped fluoride fiber pumped at 974 nm. The cavity for cascaded two-wavelength lasing is composed of two fiber ends with 4% Fresnel reflection. Its optical-to-optical efficiency is up to 26.6%. Its effects on C-band fiber amplifiers and green upconversion fiber lasers are discussed. A new way to get high efficiency and low noise C-band amplifier is suggested, i.e., a fluoride-based Er³⁺-doped fiber amplifier including 853-nm lasing cavity. Our simulated results show that such a new amplifier can enhance the signal gain greatly and break the limit of the saturated gain intensity for a normal amplifier     

Experimental and theoretical analysis of efficient erbium-dopedfiber power amplifiers

The efficiency of Er³⁺-doped fiber power amplifiers (EDFAs) pumped at 980 nm was experimentally investigated and quantum conversion efficiencies (QCE) up to 0.89 were achieved. The experiment was accurately simulated by a computer model using only measured input parameters. The model was further used in an analysis of power amplifiers pumped at 980 and 1480 nm that included waveguide optimization and Er³⁺ confinement. The QCE can be enhanced by increasing the numerical aperture (NA) and confining the Er³⁺ ions to the central region of the core. At pump powers typically used for packaged EDFAs (25-100 mW). QCE can be improved by up to 60% by increasing the NA from 0.15 to 0.25, and confined Er³⁺ doping can provide an improvement of up to 20%. However, NA and Er³⁺ confinement have insignificant effects on the noise figure when both the cutoff wavelength and the fiber length are optimized with respect to QCE     

Laser action from Ho3+, Er3+, and Tm3+in YAlO3

Laser action has been observed for the following rare-earth ions in YAlO3:Ho³⁺(sensitized with Er³⁺and Tm³⁺), Er³⁺, and Tm³⁺(sensitized with Er³⁺) at wavelengths of 2.123, 0.851, and 1.861 μm, respectively. Measurements of spectroscopic properties, fluorescence kinetics, and laser performance of these ions in YAlO3are reported.     

Energy recycling versus lifetime quenching in erbium-doped 3-μmfiber lasers

Based on recently published spectroscopic measurements of the relevant energy-transfer parameters, we performed a detailed analysis of the population mechanisms and the characteristics of the output from Er ³⁺-singly-doped and Er³⁺, Pr³⁺-codoped ZBLAN fiber lasers operating at 3 μm, for various Er³⁺ concentrations and pump powers. Whereas both approaches resulted in similar laser performance at Er³⁺ concentrations <4 mol.% and pump powers <10 W absorbed, it is theoretically shown here that the Er³⁺-singly-doped system will be advantageous for higher Er³⁺ concentrations and pump powers. In this case, energy recycling by energy-transfer upconversion from the lower to the upper laser level can increase the slope efficiency to values greater than the Stokes efficiency, as is associated with a number of Er³⁺-doped crystal lasers. Output powers at 3 μm on the order of 10 W are predicted     

Modeling and optimization of short Yb3+-sensitized Er3+-doped fiber amplifiers

Short high-concentration Yb³⁺-sensitized Er³⁺-doped fiber amplifiers are modeled and numerically investigated in the small-signal domain. Concentration quenching is included with a term quadratic in the concentration of excited Er³⁺ . We find that for fibers shorter than 1 m, the small-signal gain can be larger for sensitized fibers than for non-sensitized ones (31 dB gain vs. 22 dB at 5 cm). Without concentration quenching (e.g. for long fibers), Yb³⁺-free amplifiers have a higher small-signal gain. The achievable gain of the sensitized amplifier is independent of the pump laser wavelength, if the Yb-concentration is correspondingly optimized. However, restrictions on allowable Yb-concentrations imply that for a specific pump wavelength, a finite range of amplifiers lengths is suitable     

Signal-induced refractive index changes in erbium-doped fiberamplifiers

This paper reports the measurement and analysis of signal power-induced changes in the refractive index spectrum of an aluminosilicate erbium-doped fiber amplifier (EDFA). For a constant 980 nm pump power of 11 mW, a 1553 nm signal power of 4.6 mW caused a peak-to-trough change in refractive index of (3.8±0.4)×10 ^-8 across the EDFA gain spectrum. A Kramers-Kronig transform of the signal-induced change in absorption coefficient agreed well with the measured change in refractive index. This result conflicts with the behavior of the system predicted by a homogeneously broadened two-level model and suggests limitations in the representation of the Er³⁺ :glass system by a discrete set of homogeneously broadened transitions