Upconversion is a type of energy transfer that can occur between molecules or ions that are chemically identical. Upconversion can occur, for example, if molecules or ions of one type have electrons in excited states. Upconversion occurs with the de-excitation of a molecule or ion from an excited state to the ground state and the simultaneous excitation (via energy transfer) of an identical molecule or ion from an excited state to a higher excited state.
The example diagram below shows two sets of energy states for two identical Er3+ ions (the energy states of each ion are enclosed within green rectangular boxes) and transformations of their states under upconversion. The pair of Er3+ ions can undergo upconversion when both ions are initially in their respective ground states 4I15/2 (state (0)) and absorb light at 980 nm (top left portion of the diagram). Electrons (shown on the diagram as ‘e-‘ are thereby promoted to the 4I11/2 excited state (2) (shown in the bottom left portion of the diagram). This is depicted in the diagram by placing ‘e-‘ at the level of each 4I11/2 excited state (2). The two Er3+ ions exchange energy by upconversion (shown in the bottom right portion of the diagram). The electron on the left Er3+ ion loses energy and transitions to the ground state 4I15/2 (state (0)). Simultaneously the electron on the right Er3+ ion gains energy and transitions to the higher 4S3/2 excited state (3). As the result, it is possible for the ion on the right to emit a photon of higher energy than the original 980 nm photons. The drop in energy for the Er3+ ion on the left is equal to the increase in energy for the Er3+ ion on the right, thereby conserving energy in the upconversion transitions.
Processes of this nature can be modeled by phenomenological rate equations which describe the time-resolved dynamics of population densities of ions being in different energy states. If one restricts the model to only four different states for Er3+ ions, the rate equations describing upconversion would have the following form:
∂N0 / ∂t = c (N2)2
∂N2 / ∂t = − 2 c (N2)2
∂N3 / ∂t = c (N2)2
where c s a cross-relaxation rate for this type of ion, and N0, N2, N3 are population densities of ions that are in the 4I15/2 ground state (0), the 4I11/2 intermediate excited state (2) and the 4S3/2 upper excited state (3), respectively.
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