Finite-element modeling of silica waveguide amplifiers with high erbium concentration

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

“…Energy-transfer processes other than the two described above can occur between two interacting Er ions, e.g., cross relaxation between a donor in the manifold and an acceptor in the manifold resulting in two Er ions in the manifold (the reverse process of upconversion) [3]. However, all these processes involve Er ions initially excited to other energy levels than the manifolds and .…”

“…By inserting (13) into (6), a general expression for the number of upconversion processes occurring per time and volume unit in the kinetic limit is reached: (14) From (14), it is seen that in the kinetic limit upconversion depends quadratically on the population inversion for any ion distribution and any radial dependance of the upconversion probability . If furthermore we use the assumption of dipole-dipole interaction, (14) can be rewritten as (15) By finally averaging (15) over the assumed random ion distribution, we find the expression (16) which corresponds 3 to the expression for the kinetic limit in the classical quenching theory [21]. The applicability of the classical quenching theory in the kinetic limit is expectable, since the strong migration erases the special features of selfquenching.…”

“…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].…”

“…However, this classical quenching theory deals with donors and acceptors of distinct sorts and is-as will be demonstrated-not adequate for the treatment of self-quenching in Er systems. 1 In the literature on high-concentration Er -doped devices, homogeneous upconversion is often assumed to depend quadratically on the population of the level, i.e., the number of upconversion processes occurring per time and volume unit is written where is the population concentration of the manifold, and is an upconversion coefficient [3], [4], [6], [7], [18], [22]. The equivalent average quenching rate experienced by an Er ion in the manifold is .…”

“…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].…”