diffraction

Energy transfer can occur between molecules or ions of different types. For example, energy transfer between a first ion and second ion occurs with the de-excitation of first ion from an excited state to the ground state and the simultaneous excitation of second ion from the ground state to an excited state. Note that for energy transfer, the ground states of both ions are involved.

The example diagram below shows an Yb3+ ion and an Er3+ ion. The energy states of each ion are enclosed within green rectangular boxes. The Yb3+ ion and an Er3+ ion can undergo energy transfer when the Yb3+ ion that is initially in the 2F7/2 ground state (0) absorbs light at 980 nm (top left portion of the diagram) and thereby promotes an electron to the 2F5/2 state (1) (shown in the bottom left portion of the diagram). This is depicted in the diagram by placing ‘e-‘ at the level of the 2F5/2 state (1). The Er3+ ion initially has an electron in the 4I15/2 ground state (2). The two ions exchange energy by energy transfer (shown in the bottom right portion of the diagram). The electron on the Yb3+ ion loses energy and transitions to the 2F7/2 ground state (0). Simultaneously, the electron on the Er3+ ion gains an equal amount of energy and transitions to the 4I11/2 excited state (4). The drop in energy for the Yb3+ ion is equal to the increase in energy for the Er3+ ion, thereby conserving energy in the energy transfer transitions.


Energy transfer

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 two states (0) and (1) for Yb3+ ions and four states (2), (3), (4) and (5) for Er3+ ions, the rate equations describing energy transfer would have the following form:

N0  / t = c N1 N2

N1  / t = − c N1 N2

N2  / t = − c N1 N2

N4  / t = c N1 N2
(rate equations)

where c s a cross-relaxation rate for this type of ion, and N0, N1, N2, and N4 are population densities of ions that are in the 2F7/2 ground state (0), the 2F5/2 intermediate excited state (1), the 4I15/2 ground state (2) of Er3+,and the 4I11/2 its intermediate excited state (3), respectively.

Energy transfer with up-conversion can occur between molecules or ions of different types. Energy transfer with upconversion can occur if, for example, both a first ion and a second ion have electrons in excited states of the respective ions. During energy transfer with up-conversion the first ion is de-excited from an excited state to the ground state and the second ion is simultaneously excited from an excited state to a higher excited state. Note that once the second ion is in the higher excited state, it may emit a photon that has a higher energy than photons normally emitted from the lower excited state.

The example diagram below shows an Yb3+ ion and an Er3+ ion. The Yb3+ ion and an Er3+ ion can undergo energy transfer with upconversion after both the Yb3+ ion and the Er3+ ion are initially promoted to their excited states 2F5/2 and 4I11/2 , respectively, by absorbing light at 980 nm (shown in the bottom left portion of the diagram). The two ions exchange energy by energy transfer with upconversion (shown in the bottom right portion of the diagram). The electron on the Yb3+ ion loses energy and transitions to the 2F7/2 ground state (0). Simultaneously, the electron on the Er3+ ion gains energy and transitions to the 4S3/2 excited state (5). The drop in energy for the Yb3+ ion is equal to the increase in energy for the Er3+ ion, thereby conserving energy in the energy transfer with upconversion transitions.

Energy transfer upconversion

If one restricts the model to only two states (0) and (1) for Yb3+ ions and four states (2), (3), (4) and (5) for Er3+ ions, the phenomenological rate equations describing time-resolved dynamics of population densities of ions undergoing energy transfer up-conversion would have the following form:

N0  / t = c N1 N4

N1  / t = − c N1 N4

N4  / t = − c N1 N4

N5  / t = c N1 N4
(rate equations)

where c s a cross-relaxation rate for this type of ion, and N0, N1, N4, and N5 are population densities of ions that are in the states (0), (1), (4) and (5), respectively.



See also: Cross-relaxation, Upconversion.





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