M. A. Rebolledo

Erbium-doped silica fiber modeling with overlapping factors

A simple model describing the evolution of pump, signal, and amplified spontaneous emission powers in an erbium-doped silica fiber is presented. The model is based on overlapping factors, depending on pump- and signal-coupled powers, which are systematically studied. Accurate results for gain and amplified spontaneous emission are obtained when this model is used. Experiments to measure the characteristic parameters of the fiber appearing in the model are described. Two main advantages of this model are found: computation time is considerably reduced and fiber characterization does not make it necessary to measure the parameters of the fiber as a function of radial or azimuthal coordinates.

In situ measurement of absorption and emission cross sections in Er/sup 3+/-doped waveguides for transitions involving thermalized states

An application to transitions involving thermalized states of a procedure based on the McCumber theory to determine emission and absorption cross sections in waveguides from transversal fluorescence spectra is presented. The procedure is tested in Er-doped Ti:LiNbO/sub 3/ waveguides to provide accurate cross-section values for the recently attractive 550-nm band. We also study the excited-state absorption transition around 860 nm and present, to our knowledge, the first published cross-section values for this transition.

Determination of emission and absorption cross sections of in waveguides from transversal fluorescence spectra

A procedure for the determination of emission and absorption cross sections in integrated waveguides from transversal fluorescence spectra is presented. It is based on an approximate treatment of McCumbers theory, which was demonstrated to provide accurate values for -doped silica fibres. Results on the transition of in waveguides pumped by a 980 nm laser diode are shown and compared to results from attenuation measurements. Advantages over other procedures for waveguide characterization (less dependence on experimental inaccuracies, all measurements are made on the waveguide, consideration of codoping influence and no pump interference around ) are discussed in detail.

Modeling, characterization, and experimental/numerical comparison of signal and fluorescence amplification in Ti,Er:LiNbO/sub 3/ waveguides

A complete model for signal and fluorescence amplification in Ti,Er:LiNbO/sub 3/ waveguides under 1480 and 980 nm excitation, which includes transitions involving high energy levels, is presented. Most of the waveguide parameters that the model requires have been determined or checked in situ. In order to numerically solve the proposed model, the overlapping factors method has been adapted to these waveguides and improved, obtaining a large computing time reduction with sufficiently accurate results. Finally, results from signal gain and ASE spectral measurements and numerical simulations have been compared. The remarkable agreement confirms both the model assumptions and the used characterization techniques. Moreover, the unusually short computing time which is consumed makes the model suitable for design and optimization processes.

In situ assessment and minimization of nonlinear propagation effects for femtosecond-laser waveguide writing in dielectrics

The effect of nonlinear propagation on the shape of the focal volume has been assessed by in situ plasma emission imaging during the subsurface processing of a commercial phosphate glass. The sample was processed with an elliptically shaped femtosecond-laser beam at 1 kHz repetition rate and scanned transversely with respect to the writing beam axis. As a consequence, optimal conditions for minimizing undesirable nonlinear propagation effects during the production of optical waveguides by direct laser writing have been determined. Under these conditions, it is possible to induce structural transformations and still preserve the focal volume shape associated with the linear propagation regime. While at low pulse energy a single scan laser-written structure does not support a guided mode, the use of multiple scans with minimized nonlinear propagation effects enables the production of optical waveguides. The latter show a significantly improved performance in terms of the refractive index change and propagation losses when compared to single scan waveguides.

Analytic modeling of erbium-doped fiber amplifiers on the basis of intensity-dependent overlapping factors

Rate equations based on intensity-dependent overlapping factors are integrated to obtain analytic solutions for pump, signal, and amplified spontaneous emission (ASE), even when the coupled signal varies with time. The equations can be applied without the imposition of any restraints on the values of the pump, signal, and ASE powers, the excited-state-absorption cross section, the erbium-density distribution, or other parameters that characterize the fiber. The methods used to calculate pump, signal, and ASE powers are discussed. Experimental techniques to characterize the doped fiber that were based on these analytic expressions are introduced.

Modeling of integrated erbium-doped waveguide amplifiers with overlapping factors methods

An analysis of the applicability of overlapping factors methods to the modeling of integrated erbium-doped waveguide amplifiers is presented. These methods offer as main advantage a considerable seduction in computation time without a decrease in their effective accuracy. We propose an extension of previous overlapping factors methods in order to model highly erbium-doped waveguide amplifiers. New sets of parameters related to the relevant upconversion and cross-relaxation mechanisms are introduced. Some numerical examples illustrate both working-conditions dependent and independent overlapping factors main dependences, which are fully explained. Finally, the accuracies of the results obtainable by both methods are examined and interpreted and the reduction in computation time is considered.

Full characterization of packaged Er-Yb-codoped phosphate glass waveguides

We present a procedure for the characterization of packaged Er-Yb-codoped phosphate glass waveguides. The procedure is based on precise measurements of the output optical powers when the waveguide is diode-laser pumped at 980 nm. The dependence of these optical powers on the input pump power is then fitted to the results from a numerical model that describes in detail the propagation of the optical powers inside the waveguide. The best fit is obtained for the following parameters: the signal wavelength scattering losses are /spl alpha/(1534)=8.3/spl times/10/sup -2/ dB/cm, the Yb/sup 3+/ absorption and emission cross sections (/spl ap/980 nm) are 5.4/spl times/10/sup -25/ m/sup 2/ and 7.0/spl times/10/sup -25/ m/sup 2/, the Er/sup 3+/ absorption and emission cross sections (/spl ap/980 nm) are 1.6/spl times/10/sup -25/ m/sup 2/ and 1.2/spl times/10/sup -25/ m/sup 2/, the Yb/sup 3+/--Er/sup 3+/ energy-transfer coefficient is 1.8/spl times/10/sup -23/ m/sup 3//s and the cooperative-upconversion coefficient is 8/spl times/10/sup -25/ m/sup 3//s. An approximate method is introduced that allows the determination of the absorption and emission cross section distributions for the erbium /sup 4/I/sub 13/2//spl hArr//sup 4/I/sub 15/2/ transition from the amplified spontaneous emission power spectrum.

Velocity resolution in laser Doppler velocimetry experiments by measuring the Fourier transform of the time-interval probability

Abstract In this paper the resolving power of the Fourier transform of the time-interval probability technique is studied when it is used in a laser Doppler velocimetry experiment to measure a non-steady fluid velocity. It is concluded that for small values of the scattered intensity, differences of velocities as little as 2% can be resolved with a small error.

Erbium-doped fiber characterization by fluorescence dynamics measurement

A technique for erbium-doped fiber characterization is presented. Its foundation lies in the study of the transversal and copropagating fluorescence time evolution when pumping is switched on and off. A model that describes these phenomena is developed, and experimental results, in good agreement with the model, are shown. The stimulated emission cross sections and an effective erbium-density distribution are determined from the measurements.