Optimal pump wavelength in the4I15/2-4I13/2 absorption band for efficient Er3+-doped fiberamplifiers

The authors report the measured gain of a highly efficient erbium-doped fiber amplifier pumped at wavelengths between 1.46 and 1.51 μm. The optimal pump wavelength, λ_opt, was determined to be 1.475 μm. At this wavelength, the maximum gain coefficients for signals at 1.531 and 1.544 μm were 2.3 and 2.6 dB/mW, respectively. At λ_opt, high gains ranging from 32 dB at pump power P_p=20 mW up to 40 dB at P _p=80 mW were obtained. These modest pump powers are within the capabilities of currently available 1.48-μm diode lasers. The width about λ_opt for 3-dB gain variation exceeded 27 nm for P_p=10 mW and 40 nm for P_p >20 mW. With this weak dependence on pump wavelength, single-longitudinal-mode lasers do not have a significant advantage over practical Fabry-Perot multimode pump lasers     

Thermal shifts of the spectral lines in the 4F3/2 to 4I11/2 manifold of anNd:YAG Laser

A report is presented of the thermal shifts of eleven of the twelve lines from the ⁴F_3/2 Stark energy levels to the ⁴I_11/2 energy levels in an Nd:YAG laser for a temperature change from 20-200°C. The thermal shift difference between the Stark sublevels R₁, R₂ in ⁴F_3/2 is found to be about -0.6±0.6 cm^-1/100°C. Within experimental uncertainty, all of the lasing lines either moved to longer wavelength or remained unchanged with increasing temperature     

Measurement of the stimulated emission cross section for the 4F3/2-4I13/2transition of Nd3+ in YAlO3 crystal

A method for the simultaneous measurement of the stimulated emission cross section and fluorescence lifetime by studying the relation between laser parameters and the laser relaxation oscillation frequency is discussed. The stimulated emission cross section for the ⁴F_3/2-⁴I_13/2 transition of Nd³⁺ ion in YAP crystal was measured to be (22±1)×10^-20 cm²     

Local fractional population measurement of the upper state 4I13/2 of an erbium-doped fiber amplifier

A method of measuring the local fractional population of the upper state ⁴I_13/2 of an erbium-doped amplifier is investigated. The local fractional population is related theoretically by EDF parameters to the local spontaneous emission (SE) power that leaks laterally from the EDF. The proportional constant between the fractional population and the detected SE power is determined experimentally by measuring saturated spontaneous emission power. The local fractional population of a 19.7 m-long EDF, pumped with a 1.48 μm light and injected with a 1.552 μm signal light, was measured by detecting the local SE power with a Ge photodiode having a diameter of 2 mm. The measured fractional population coincides with the calculated value     

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     

Erbium-doped single- and double-pass Ti:LiNbO3 waveguideamplifiers

Single-pass and double-pass Er-diffused Z- and X-cut Ti:LiNbO₃ waveguide amplifiers, optically pumped at λ _p≈1484 nm, have been investigated. With a 48 mm long Z-cut amplifier device, Er-diffusion doped at 1100°C, 6.7 dB (coupled pump power P_p,c=170 mW) and 14.7 dB (P_p,c=90 mW) net small-signal gain have been achieved with a single-pass and a double-pass configuration, respectively, at the signal wavelength λ_s=1531 nm. A Z-cut sample doped at 1135°C showed a considerably improved behavior. 11.3 dB single-pass net small-signal gain has been obtained (P_p,c=170 mW; sample length 5.7 cm). Theoretical calculations predict gain figures up to 20 dB in single-pass and 40 dB in double-pass Er:Ti:LiNbO₃ amplifiers with increased (realistic) lengths of 10 cm     

Theoretical modeling of optical amplification in Er-doped Ti:LiNbO3 waveguides

An accurate theoretical analysis is presented describing optical amplification in Er-diffused Ti:LiNbO₃ channel waveguides. It follows as far as possible the theory already developed for Er-doped fibers. As optical pumping around λ_p≈1.48 μm is considered, a quasi-two-level model for the Er³⁺ ions is used with wavelength-dependent cross sections. The optical gain in the 1.53 μm<λ<1.64-μm wavelength range is evaluated. The characteristic parameters, as Er concentration profile, cross sections, pump, and signal mode distributions and waveguide (scattering) losses are taken from experiments. Examples of numerically calculated pump-, small-signal-gain-, and ASE-evolutions are presented. The model has been tested by comparing computed and experimentally observed gain characteristics for Xˆ- and Yˆ-cut LiNbO₃; an almost quantitative agreement has been obtained     

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     

Acoustically tunable wavelength filter with gain

The first integrated optical amplifying acoustically tunable wavelength filter in Er-doped LiNbO₃ is reported. At the signal wavelength of λ_s=1531 nm a maximum gain of 4.8 dB has been obtained with a coupled pump power of 160 mW (λ_p =1484 nm). Lossless signal transmittance has been achieved with a pump power as low as 13.5 mW for λ_s>1561 nm     

High-nonlinearity fiber optical parametric amplifier with periodicdispersion compensation

Theory shows that the maximum gain and bandwidth of one-pump fiber optical parametric amplifiers made from high-nonlinearity fiber, operated with a pump wavelength λ_p far from the fiber zero-dispersion wavelength λ₀ can greatly be improved by periodic dispersion compensation. We have performed experiments and obtained good agreement with theory: for λ_p=1542 and λ₀=1591 nm, we have increased the bandwidth from 7 to 28 nm, and the maximum gain from 15 to 20 dB, by splicing three pieces of standard fiber at regular intervals in a 40-m long nonlinear fiber     

Evaluation of absorption and emission cross sections of Er-dopedLiNbO3 for application to integrated optic amplifiers

The polarization-dependent absorption and emission spectra of the ⁴I_13/2-⁴I_15/2 transition (λ~1.5 μm) in single crystal bulk Er:LiNbO₃ have been measured. Low-temperature (10 K) measurements of the Stark split energy levels of these two manifolds indicate at least two Er³⁺ sites. McCumber theory is applied to determine the Er:LiNbO₃ absorption and emission cross sections. These values are used to calculate the gain characteristics of Er:LiNbO₃ channel waveguides. Calculations indicate that a gain of 10 dB is achievable in a waveguide of several centimeters using ~20-mW pump power     

Determination of homogeneous linewidth by spectral gainhole-burning in an erbium-doped fiber amplifier with GeO2:SiO2 core

Spectral gain hole-burning was observed at low temperatures in an erbium-doped fiber amplifier with GeO₂:SiO₂ core. At the peak wavelength λ=1.535 μm, homogeneous linewidths determined from the observed hole widths have a power-law dependence on temperature. At room temperature, the extrapolated homogeneous linewidth is 4 nm and the inhomogeneous linewidth is 8 nm     

Ti:Er:LiNbO3 waveguide laser of optimized efficiency

The development of a Fabry-Perot-type Ti,Er:LiNbO₃ waveguide laser of optimized CW output power up to 63 mW (λ_s =1561 nm) at a pump power level of 210 mW (λ_p=1480 nm) and a slope efficiency of up to 37% is reported. The theoretical model for the waveguide laser is presented and applied to determine the optimum resonator configuration using waveguide parameters obtained from a detailed characterization of the laser sample. With pulsed pumping, waveguide laser pulses of up to 6.2 W peak power were observed. Apart from residual relaxation oscillations, the laser emission proved to be shot-noise limited     

Quasi-cyclic codes over Z4 and some new binarycodes

Previously, (linear) codes over Z₄ and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z ₄-QC codes and obtain new binary codes using the usual Gray map. Among the new codes, the lift of the famous Golay code to Z₄ produces a new binary code, a (92, 2²⁴, 28)-code, which is the best among all binary codes (linear or nonlinear). Moreover, we characterize cyclic codes corresponding to free modules in terms of their generator polynomials     

Fluorescence and superfluorescence line narrowing and tunability ofNd3+ doped fibers

The inhomogeneous behavior of the 1.06 μm-neodymium transitions in doped optical fibers have been investigated, using the fluorescence line narrowing technique, pumping on the ⁴F_3/2 and ⁴F_5/2 sublevels at 4 K. Each observed transition has been identified. As the pump wavelength varies, the shift of the main fluorescence line is 40 nm, with the two pumping levels. We have studied the spectral behavior of the superfluorescence as a function of the pump wavelength, the temperature, and the absorbed power. The spectral evolution depends on λ_p with 19 nm-tuning range at low temperature. At 300 K, the quasihomogeneous behavior of the transition decreases the tunability to 14 nm. Based on these results, we present a simple technique permitting precise prediction of gain and spectral line shapes of superfluorescent Nd-doped fiber sources     

DC I-V characteristics of field emitter triodes

A simple model that is applicable to Spindt-type emitter triodes is presented. Experimentally, it has been observed that the gate current at zero collector voltage follows the same Fowler-Nordheim law as the collector current at high collector voltage, and that for low emission current densities, the sum of gate and collector currents is constant for any collector voltage and is given by the Fowler-Nordheim current I_FN. Based on these observations, a simple model has been developed to calculate the I-V characteristics of a triode. By measuring the Fowler-Nordheim emission, emission area and field enhancement can be obtained assuming a value for the barrier height. Incorporating the gate current, the collector current can be calculated from I_c=I_FN-I_g as a function of collector voltage. The model's accuracy is best at low current density. At higher emission currents, deviations occur at low collector voltages because the constancy of gate and collector currents is violated     

Dependence of Ti-diffused Er:LiNbO3 laser efficiency onwaveguide fabrication parameters and pump wavelength

The mode size, effective pump area, and coupling efficiency as function of initial Ti-stripe width W, diffusion temperature T, and initial Ti-stripe thickness H in c-cut Ti-diffused Er:LiNbO₃ waveguide laser have been studied theoretically, taking into account optical pumping λ_p=1.477 μm and 0.98 μm. The main features of the mode sizes in terms of these diffusion parameters were collected and, as compared with the experimental results, a qualitative agreement has been achieved. The effective pump areas exhibit both significant initial Ti-stripe width and diffusion temperature dependence, especially for W>9 μm and T>1050°C, whereas the initial Ti-stripe thickness can hardly give influence when pumping with λ_p=0.98 μm radiation. On the other hand, coupling efficiency is approximately unchanged with values 0.76-0.78 for λ_p=1.477 μm and 0.8-0.85 for λ _p=0.98 μm, indicating that there are no optimized values of these parameters to increase slope efficiency through coupling efficiency. Moreover, the 0.98 μm pumping reveal lower threshold and higher coupling efficiency than 1.477-μm pumping. Finally, the appropriate waveguide fabrication parameters were proposed for the fabrication of a more efficient laser     

Binary images of cyclic codes over Z4

We determine all linear cyclic codes over Z₄ of odd length whose Gray images are linear codes (or, equivalently, whose Nechaev-Gray (1989) image are linear cyclic codes or are linear cyclic codes)     

Quarter-micrometer gate ion-implanted GaAs MESFET's with an f1 of 126 GHz

The fabrication and characterization of a 0.25-μm-gate, ion-implanted GaAs MESFET with a maximum current-gain cutoff frequency f_t of 126 GHz is reported. Extrapolation of current gains from bias-dependent S-parameters at 70-100% of I _dss yields f₁'s of 108-126 GHz. It is projected that an f₁ of 320 GHz is achievable with 0.1-μm-gate GaAs MESFETs. This demonstration of f₁'s over 100 GHz with practical 0.25-μm gate length substantially advances the high-frequency operation limits of short-gate GaAs MESFETs     

Modeling of nonhyperbolic sine I-Vcharacteristics in poly-Si resistors

Poly-Si resistors with an unimplanted channel region (and with n-type source/drain regions) can exhibit a nonhyperbolic sine (non-sinh) I-V characteristic at low V_DS and an activation energy which is not simply decreasing monotonically with increasing V_DS. These phenomena are not explained by conventional poly-Si resistor models. To describe these characteristics, a self-consistent model which includes the effects of a reverse-biased diode at the drain end is presented. Numerical simulation results show excellent agreement with experiment in regard to the shape of the I -V characteristic and of the effective activation energy as a function of V_DS