Dynamic optical storage means that a storage process as shown in Fig.1 is passed. Via phase correct back coupling by means of nonlinear optical phase conjugation the information stored in a photorefractive crystal is periodically read out, transmitted into a second crystal acting as an auxiliary memory and from this transmitted back into the first crystal. This way the stored information is refreshed.

Figure 1: Dynamic optical storage.

A series of storage cycles should be simulated mathematically in order to get the time development of the refractive index modulation Dn(t) in the crystals in dependence on various parameters (intensities, cycle times, material parameters).

The course of the storage cycles is shown schematically in Fig.2. When X₁ is read the hologram in this crystal described by Dn(X₁) is erased.

Figure 2: Storage cycles.

The output intensity of X₁ (=S') decreases. At the same time, the hologram in X₂ is build up, Dn(X₂) increases. When crystal X₂ is read all processes proceed in opposite direction.

If a hologram in a photorefractive crystal is read by illuminating the crystal by a wave with spatial and temporal constant intensity the refractive index modulation Dn decreases and with that the output intensity. The results of measurements are shown in Fig.3 left side. Functions of the form

(1)

fit good to the intensity decrease.

Figure 3: Intensity made available by reading a hologram (left) and build-up of Dn with constant intensity (right).

The right side of Fig.3 shows the build-up of the refractive index modulation Dn(t) with a temporal constant intensity I. The graphs can be described by

(2)

with

and .

This equation is only valid for a constant intensity, but the intensity that is available to write a hologram develops according Fig.3 left side.

The time of the process is divided in finite parts, and during every part the intensity is set to a constant value as symbolically shown in Fig.4. The real development is approximated by a step like development. By it, equation (2) is independently valid within every time period.

Fig.5 shows the principle of the following calculations. The build-up of Dn is calculated within time period one (0 ®t₁). Then the calculation is continued with the next intensity value in time period two (t₁®t₂), and it is started with the Dn that is already reached at t₁, and so on. In Fig.5, this is equivalent to jumping from one graph to the next.

Figure 4: Approximated step like intensity development

Using fine time steps we get the result shown in Fig.6. It is the goal to reach a Dn as high as possible in order to preserve the information that is to store. Therefore, we stop the write process when Dn(t) reaches its maximum.

Figure 5: Approximated step like intensity development

In the following the hologram that is now written in the crystal X₂ is read out and will be re-written into crystal X₁. Dn(t) for X₁ is calculated just as for X₂.

Figure 6: Build-up process. Left: Dn(t), parameter a₃ of eqn.(1) varied. Right: function Dn(t) and its derivation.

Now, one refresh cycle has been passed through. If we go on, we get Dn(k), where k is the cycle number. If it is possible to reach a steady and non-zero Dn(k) for high k, we succeed in storing the information, at least theoretically.

Fig.7 presents the result of a simulation. The refractive index modulation Dn is shown as a function of the cycle number k. The solid line shows the result for Dn if the hologram is only read out from one crystal without refresh.

Dn decreases in both cases, but it is obvious that the information is much longer preserved if using the refresh. This is mainly important after a higher number of cycles (inserted picture in Fig.7). Without refresh the information (the hologram) is almost fully erased after a time of 15 cycles, but with refresh a considerable value of Dn is preserved longer.

Figure 7: Result of a simulation.

A large number of parameters (e.g. the values a_n in eqns.(1) and (2) ) can be varied in order to optimize the process and reach a storage for any length of time. But the expenditure of calculation is high.

However, a mathematical simulation method describing a dynamic storage process is shown.

Acknowledgment

This research has been partially supported by the Deutsche Forschungsgemeinschaft (DFG) within the Innovationskolleg "Optische Informationstechnik" (INK 1/A1) at the Friedrich-Schiller-Universität Jena.