S IMULACIÓN INICIAL DEL CONJUNTO CONTROLADO

The curves do not appear to fit well to a model based on the usual inverse exponential saturation, but simply for the sake of comparison, we have calculated the writing time constants assuming the maximum refractive index modulation is achieved in

each case at the maximum diffraction effrciency using the same method as that used in ref [Tao94] assuming that T|sat is a function of the total writing power. This gives a writing time constant of 30.4s for the curve using PCMs and 42.2s for the curve without. The experiment was repeated several times using different spatially separate parts of the same crystal and similar results were obtained. It is possible that this arrangement can be theoretically modelled by coupled wave theory although this has not yet been carried out.

We conclude that the method using two PCMs results in reproducible higher rates of growth of diffraction effrciency Le. shorter writing time constants, resulting in a higher maximum diffraction effrciency. This supports our proposition that increased hght intensity is achieved resulting in faster growth of dififraction effrciency. The higher maximum value may be linked to a better diffraction effrciency uniformity with depth. This recording method was also used to record up to 24 angularly multiplexed holographic gratings which were used in the system described in the next chapter.

3.4.3 B ra g g -o ff diffraction in a LiN bO s:Fe crystals

In volume holography, the angular selectivity is essential for both the storage and retrieval of multiplexed holograms. The selective angle determines the optimum angular separation during recording to achieve a storage capacity as high as possible with minimum cross­ talk. The optimum access configuration must be used during readout that results in the highest dififraction effrciency and signal-to-noise ratio. Both the effects of polarisation and intensity couphng on the angular sensitivity have been demonstrated by S. Tao et al. [Tao93 & 94]. In their efforts they, for the first time, experimentally verified the theories proposed by Heaton et al [Hea84], who concluded that the maximum diffraction effrciencies of photorefractive gratings should happen at reading angles very slightly different from the writing angles. Tao et al. [Tao94] referred to this phenomenon as the “Bragg-shift”. According to Heaton's and Tao's results, a slanted grating will be recorded by two writing beams with unequal beam intensity (beam ratio, q, is not equal to 1) in a photorefractive crystal using a symmetrical geometry. As a result, the maximum diffraction effrciency of grating occurs at a readout angle different from the recording angle. However, there is still a shift in the Bragg angle when the exposure of the recording process exceeds some level even when the grating is formed by two writing beams with equal beam intensities, i.e. q=I. In this section we experimentally investigate these

peculiarities of the angular sensitivity and the diffraction efficiency of single transmission gratings recorded in a photorefractive LiNhOsiFe crystal.

We use an experimental arrangement similar to that used for investigating the phase-conjugate storage with two PCMs as shown in Fig. 3.10. The writing wavelength was 514.5 nm and the reading either 632.8 nm or 514.5 nm operating at a lower power level, which eliminated erasing during readout. We monitor the grating formation process by using a red probe beam from a helium-neon laser (^=632. Snm). The diffraction efficiency of the grating was measured by blocking one of the writing beams.

We first performed a series of measurements of the optimum angular deviation for our sangle and the results are shown in Table 3.1. and Fig. 3.12. In Table 3.1 we have found that The maximum diffraction occurs when the readout angles are 0.006° ( ^ 1 ) , and 0.008° (ç=5), and 0.016° (^ 1 0 ), respectively. There are shghtly greater than those achieved when read out at the writing angle for q=\ and 5.

Table 3.1 Experimental measurements o f the grating formation with respect to different exposures fo r beam ratio, q=lR/Io, equal to 1, 5 and 10. A symmetric recording was used with a writing angle o f 25° between the object beam and reference beam. Exposure (J/cm^) 6.2 12.5 25.2 37.8 63.0 88.2 113.0 151.0 1^0 = 3.3mWj33mW=10 Bragg-shifled angle (“) 0.000 0.004 0.006 0.008 0.014 0.018 0.022 0.022 Itotai=6.6mW ^ B ta g g (%) 5.1 10.1 12.2 11.4 7.9 5.9 4.2 3.6

Iread=13.5 ^iW TiBragg-ahiAed ( 5.1 12.0 14.2 16.8 13.4 15.0 10.3 8.3

<i = h l I o

= 5.5mWjlhnW= 5

Bragg-shifled angle O

0.004 0.01 0.012 0.014 0.018 0.020 0.022 0.020

Itotai=6.6mW riB rag g ( / o ) 0.5 1.0 2.2 1.7 1.5 1.1 0.7 1.1

Iiead=4.5 (XW r|B ra ^ -8 h ifie d ( 0.7 2.8 11.9 12.2 7.4 4.6 3.0 2.0 <1=IrIIo = 6.0mWf0.6mW= 1 Bragg-shifled angle O 0.006 0.010 0.012 0.016 0.020 0.020 0.024 0.020 Itotai=6.6mW 'HBragg ( / o ) 1.6 2.8 1.3 3.4 4.4 5.0 4.1 6.3 Iread~3.2 riBragg-shified ( 2.5 6.6 4.4 32.0 31.3 28.1 14.1 10.9 90

Fig. 3.12 S-D Plots showing the experimental results fo r angular shift and diffraction efficiency o f the resultant grating with respect to exposure f o r beam ratio, q(lR/Io), equal to 10. A symmetric recording was used with a writing angle o f

D i f f r a c t i o n E f f i c i e n c y ( % ) 11 30-40 ■ 20-30 10-20 □ 0-10 0.008 0.016 , 0.024 «-2 0.032 A n g u l a r D e v i a t i o n f r o m R e c o r d i n g A n g l e (d c g .) 1 1 3 6 3 2 Exposure (J/cm2)

Fig. 3 .1 3 s h o w s the 3-dim ensional p lot o f the dif&action efficien cy w ith resp ect to angular d eviation from recording angle and ex p osu re o f recording for q - 10 case, w e have found that the read ou t angle for the m axim um efficien cy (3 2% ) is B ra gg slfrfted w ith 0 .0 0 8 ° w h en to ta l ex p osu re is 3 7 .8 J/cm^.

C om pare our results w ith th o se obtained from T ao et. al. [T ao 93 & 9 4 ] and H eaton [H ea84], it can clearly b e seen from our experim ental m easurem ents o f se le c tiv e angle for LiNbO s that is u su a lly shifted into a typical an gle depending on n o t on ly intensity ratio

b etw een tw o w ritin g b eam s but the total exposure during the recordm g. T h ese results su g gest that to obtain the optim um readout perform ance from gratings w ritten by tw o beam s in LiNbO g crystal, readout beam s m ust b e angularly shifted w ith a desirable angle.

3.5 Conclusions

In conclusion, we have proposed a contact optical photorefractive holographic correlator enç)loying a 2-f correlation system. This conq)act scheme is suitable for incorporation into an optical photorefractive resonator with the spatio-angular multiplexing (SAM) [Tao93] scheme for recording holograms to inq)lement a high order feedback neural network (HOFNET) [Sel90 & 91] system. Based on the merits of the HOFNET the 2f systems physical length can be shortened to half as much as in the conventional 4f correlation system and losses can be avoided.

We have increased the dif&action efficiency of volume holograms stored in a photorefractive crystal by making use of two self-pui^ped phase conjugate mirrors (SPPCMs) as part of the recording technique. One of the SPPCMs was induced to widen the angular range over which phase conjugation of beams could take place which again has not been done before. We recorded 21 angularly multiplexed holograms. When a single grating was stored the highest efficiency of 32% was obtained using a diode pumped frequency doubled YAG. To our knowledge this is the highest efficiency reported to date for volume holograms in this material.

We discovered that the Bragg-shift depends on the total exposure during the recording and not just on the beam ratio. The Bragg-shift effect was discovered several years earher at UCL by Tao et aL [Tao93] when she found that higher efficiency replay of volume gratings formed in photorefractive crystals was possible by altering the replay angle very shghtly from that used for recording in the case when the two recording beams had had different intensities. In some case we found that an increase in efficiency from 3.4% to 32.8% was possible by choosing the correct angle.