Doubly doped crystal
Chapter 4 Chapter 4 System issues in two-center holographic recording
4.5 Multiplexing holograms In two-center record-
4.5.1 Dynamics of recording and erasure in two-center record-
mg
When multiple holograms are recorded using two-center recording, each hologram is erased by both sensitizing and recording beams during the recording of subsequent holograms. We performed a series of recording and erasure experiments to assess the dynamics of the processes and to measure the time constants involved. Erasure is performed by the UV light and one of the red beams to get information about the erasure of a hologram while subsequent holograms are recorded. Experimental results for 4 cycles of recording and erasure are depicted in Figure 4.12. The experimental conditions are as described above. The first recording curve looks different than the rest. This is due to the UV pre-exposure of the sample before the experiment. It
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Recording
100
Reading
200 Time (min)
300 400
Figure 4.11: Recording and read-out curve for a plane-wave hologram in a 0.85 mm thick LiNb03:Fe:Mn crystal. The crystal was homogeneously pre-exposed to UV light for at least one hour before the experiment. Then a plane-wave hologram was recorded using two red beams (wavelength 633 nm, intensity of each beam 300 m W /cm2) with simultaneous presence of the UV beam (wavelength 404 nm, intensity 4 mW /cm2). The hologram was then read-out by one of the recording beams.
results in a larger electron concentration in the Fe traps than the steady-state value (which is due to the simultaneous presence of UV and red, not UV only). This yields a faster initial recording. The recording curves can be approximated by mono- exponential formulas as
y'ri = Ao[1 - exp(-tITr)]. ( 4.23) The erasure curves can be approximated by bi-exponential formulas as
y'ri = A exp( -tITe!) + B exp( -tITe2)' (4.24) In these equations, T) is the intensity diffraction efficiency of the hologram, Tr is the recording time constant, and Tel and Te2 are the two erasure time constants. Typical mean-square errors for the recording and erasure fits are 2 x 10-8 and 4 x 10-9, respectively. The bi-exponential behavior of the erasure is due to the fact that the overall space-charge pattern is the sum of the two space-charge patterns in Fe and IVln centers. The space-charge pattern in Fe centers gets erased (and transferred to Mn centers) faster than the portion in Mn centers due to the presence of the strong red light. When the whole space charge pattern settles down in Mn centers, the erasure is performed more slowly as only UV light can excite electrons from these centers to the conduction band for erasure. Figure 4.13 shows the effect of different erasure mechanisms. Three different erasure curves after recording a plane-wave hologram to saturation are depicted in Figure 4.13. These three mechanisms are erasure with UV and one red beam, erasure with UV only, and partial erasure by red light to a steady state and then final erasure by UV only. The curves are normalized to result in the same starting point for all three curves. As Figure 4.13 shows, for erasure with red light, only part of the hologram is erased due to the transfer of electrons from Fe to Mn centers. This partial erasure can not be represented very well by a mono-exponential formula due to the bleaching of Fe centers by red light. The average electron concentration in Fe centers becomes smaller and smaller with time during red illumination resulting in slower erasure with time. After all electrons are transferred to Mn centers, the remaining hologram can be erased with UV light only, and the
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500 1000 1500Time (min)
Figure 4.12: Diffraction efficiency TJ versus time for four cycles of recording and erasure with UV and red light in a LiNb03:Fe:Mn crystal.
erasure can be represented very well by a mono-exponential formula (typical mean square error of 2 x 10-9). The hologram can also be erased from the beginning with UV light only resulting in a bi-exponential erasure. However, the erasure behavior is closer to mono-exponential compared to erasure with UV and red. This is because the excitation rate of the electrons from Fe and Mn centers are closer to each other when there is no red light during the erasure.
During hologram multiplexing, each hologram is erased by the UV and red beams that record the subsequent holograms. Therefore, the erasure is bi-exponential, and the conventional recording schedule [73] can not be used. However, the following observation can lead us to a similar recording schedule. When the holograms are read- out at the end of the recording sequence, the electronic charge remaining in Fe centers is transferred to Mn centers resulting in some partial erasure. The erasure during the read-out is different for different holograms in the sequence. The holograms that are recorded earlier have less charge in Fe centers than those recorded later in
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100 150 200 250
Time (min)
Figure 4.13: Normalized diffraction efficiency 1] versus time for different erasure mech- anisms in two-center holographic recording.
the recording sequence, since the earlier holograms are erased longer than the later ones. Therefore, the later holograms suffer more from partial erasure during read- out. After sufficient read-out, this partial erasure is complete for all holograms and further read-out is non-destructive. If each hologram is the sum of a red-erasable part and a non-red-erasable part, we will have only the non-red-erasable part remaining after sufficient read-out. During the exposure schedule, this part is erased mainly by UV light (with some help from red light) and its erasure is represented by one of the exponentials (the one with larger time constant) in Equation (4.24). Therefore, we can ignore the red-erasable part, represent the effective erasure by a mono-exponential formula, and use the conventional recording schedule [73] to record many holograms. The
M/#
is given byM/#
=;5'Ao
Te2Tr (4.25)
where ;5' represents the partial loss of the hologram due to electron transfer from Fe
to Mn centers. The value of ,BAa can be measured experimentally by recording a grating to saturation and reading it out for a long time with only red light as shown in Figure 4.11. The remaining persistent diffraction efficiency is (,BAa)2.