D iscussion

In holeburning the transition linewidth enters in both the burning and reading process and so from a measured holewidth of 3.7 ± 1 kHz it is concluded that the maximum value of the transition linewidths is 1.9 ± 0.5 kHz. This value is smaller than the 2.5 kHz (1 /(7tT2) obtained from photon echo measurements made on the line centre of the inhomogeneous profile. However, both values are considered to be larger than the homogeneous linewidth. The photon echo measurements at line centre are considered to be broadened by what is termed spectral diffusion. The magnitude of the instantaneous spectral diffusion depends on the probability of the excitation of adjacent ions and in the holeburning measurements the rate is much smaller. For example, if it is assumed that there is no correlation between the frequency of the ions and their separation, then the probability of exciting adjacent ions will be proportional to the width of the spectral region of the inhomogeneous line excited. If we compare the case of burning a hole 5

optically excited state ground state ±1/2

I

Figure 3.10 An example of an optical pumping cycle induced by driving a transition between hyperfine levels in the optically excited state. In an axial site where only AI=0 optical transitions are allowed the rf driving field can be used to gate the holeburning process.

kHz wide, 100% deep with a photon echo measurement using a laser with a linewidth of 1 MHz, 7c/2 pulses of 1 ps a crude estimate tells us that 1 MHz/ 5 kHz = 200 times less ions are excited in the holeburning measurement. It is concluded that the spectral diffusion is not a contributing factor to the holebuming linewidth.

Echo measurements avoiding spectral diffusion by working in the wings of the line suggest that the homogeneous linewidth is at most 625 Hz. However, the magnetic field fluctuations and lifetime contributions to the homogeneous linewith have been estimated to be less than 300 Hz [MacFarlane et al. 1981]. If this was the homogeneous linewidth then the larger amount of the hole linewidth would arise from laser jitter. As the laser linewidth contributes to both the burning and the probing of the hole the laser linewidth must be less than 2 kHz over time scales of the order of 10 ms. If, however, the non­ line centre echo measurement gives the true homogeneous linewidth then the conclusion would be that the laser jitter is smaller and closer to 1 kHz in the time scale of the holebuming.

The holeburning spectra showing double peaks demonstrates another characteristic of the laser; it occasionally makes frequency jumps of up to 5 kHz. As similar jumps are not observed in the error signal used in stabilising the laser it appears that these jumps are associated with the reference cavity.

In all of this section it is implied that the spectral hole serves as a completely stable frequency reference. Clearly, however, there are physical effects that can lead to the shift of the frequency of a hole. The frequency of the transition is sensitive to both the electric (crystal field) and magnetic fields in its environment. The crystal field depends on both the pressure on the crystal and the temperature so we can expect the hole frequency to shift with changes in either of these two parameters. Local changes in the crystal field due to the relaxation of strain field are also possible [Sellars et al. 94]. These may cause a drift in the centre frequency of the hole. Such drifts should be easy to diagnose as the local changes will tend to be random from site to site so their dominant effect on the hole will be to broaden it. Any drift in the hole centre frequency is likely to be seen as a distortion of the hole's symmetry as it broadens.

The sensitivity of the transition frequency to magnetic fields is, for moderate field levels, dominated by the enhanced nuclear magnetic moments associated with the ground and excited states of the Eu3+ ion, which are of the order of a few kHz/G. It is relatively straightforward to stabilise the external magnetic field to the mG level, so that the resulting frequency fluctuations will only be of the order of Hz. As discussed in Section

3.3 the local fluctuation in the magnetic field is likely to be of the order of hundreds of hertz. As with the local variations in the local crystal field, the local fluctuations in the magnetic

field will be random and will tend to broaden the hole rather than resulting in a significant drift in the hole frequency.

Further work is required to determine the long term stability of the hole frequency, which will have significance not only for the use of spectral holes as a frequency reference but also for the optical data storage applications of rare earth doped crystals.

3.8 Conclusion

Ultra-narrow optical holeburning has been demonstrated in Y2 0 3:Eu^+ , a system with very narrow homogeneous linewidths. A hole linewidth of 3.7 ± 0.5 kHz was observed. The claimed homogeneous linewidth is 625 Hz and from this linewidth a holewidth of 1.26 kHz could be anticipated using a laser with no jitter. From the observed linewidth, therefore, the laser linewidth was estimated to be less than 2 kHz on a 10 ms time scale. Thus the holeburning has been used to characterise the laser stability.

Although for these very narrow lines the laser jitter adds to the observed hole linewidth, at higher temperature, where the homogeneous linewidths are larger, the laser jitter makes a negligible contribution Hence, for the higher temperature measurements above 8 K we have shown that there is a strong correspondence between the linewidths determined by holebuming and the data from earlier photon echo measurements.

The generation of a frequency discriminator produced by transmitting FM modulated light through a holeburning medium has been demonstrated. This signal has been used to diagnose various instabilities in the stabilised laser described in Chapter 2 and with the information, the stability was further improved. Frequency drifts over a longer term are still known to be present and to eliminate such drifts a technique of locking to the hole has at least been demonstrated to be feasible.

I conclude that very narrow holeburning has been demonstrated, it has also been shown that holebuming provides a convenient reliable frequency reference technique.