Rare earth-doped integrated glass components: modeling and optimization

Abstract

Abstruct-For the integrated optic erbium-doped phosphate silica amplifier, a comprehensive model is presented which includes high-concentration dissipative ion-ion interactions. Based on actual waveguide parameters, the model is seen to reproduce measured gains closely. A rigorous design optimization is performed, and the influence of variations in the launched pump power, the core cross section, the waveguide length, the erbium concentration, and the background losses are evaluated. Optimal design proposals are given, and the process reproducibility of the proposed optimal design is examined. Requirements for process parameter control in me wafer fabrication are set up.

Monte Carlo simulations of homogeneous upconversion in erbium-doped silica glasses

“…The quadratic model can be shown theoretically, if migration is assumed sufficiently strong (the kinetic limit) [21] and the model has been supported by some experimental results [4], [23]. Other authors have suggested a cubic model [2], [24].…”

“…For erbium-doped fiber amplifiers, a reduction in gain from 18.3 to 6.9 dB due to quenching is described in [1] for an Er concentration of 6.4 10 m . In erbium-doped silica waveguides for integrated optics, Er concentrations as high as 1.0-2.0 10 m (corresponding to 1.3-2.5 wt.% Er may be necessary to simultaneously ensure sufficient gain and compactness of the components [2], [3], and consequently, quenching is a very serious problem with such devices. For example, a reduction in gain from 37 to 13 dB at an Er concentration of 1.15 10 m is reported in [2].…”

“…The spatial distribution of excited Er ions will, therefore, differ from the distribution of all Er ions. 2 Instead, we consider the probability of finding the th Er ion excited at time together with the joint probability of finding the Er ions and both excited at time . When these probabilities are known, the population inversion can be found as (5) and the number of upconversion processes occurring per time and volume unit is given by (6) In the Appendix, it is shown that, under assumptions 3)-5), the time development of the single ion probabilities is governed by the following system of ordinary differential equations: (7) whereas the second-order joint probabilities obey (8) In (7), the single ion probabilities are coupled to the second-order joint probabilities which are then coupled to the third-order joint probabilities through (8).…”

“…1 illustrates how energy-transfer upconversion between two Er ions, initially excited to the manifold, leads to the quenching of the donor ion and thus depopulates which serves as the upper laser level for amplification of light in the 1550-nm wavelength band [2], [4], [10], [11]. The acceptor ion will normally return to the manifold and only in around 0.1% of the cases will relax to the ground level by spontaneous photon emission [4].…”

“…For this purpose, an adequate model for homogeneous upconversion is essential. Furthermore, a model for homogeneous upconversion-together with a model for upconversion in clusters-is a key point in the modeling and design of high-concentration erbium-doped devices [2], [3].…”