Coherent HSE

This phenomena occurs in 3-D holograms by illuminating with a reference beam $I_R$ (usually at the same angle of incidence, i.e., at Bragg conditions). Thus, the reference beam is scattered (diffracted) by the holographic grating, the hologram generates a scattered subject beam, $I_S$, which causes interference and further recording with two beams takes place. The coherent HSE depends on the initial diffraction efficiency, the dynamic range of the holographic recording (i.e., the maximum values of the light induced optical constant changes $\Delta n$, $\Delta k$) and the wavelength of recording and readout. The HSE is much stronger for phase holograms than for amplitude holograms. Schwartz observed a strong HSE for small initial diffraction efficiencies $\eta_0 = 10^{-5}\%$ in As$_2$S$_3$ films. The maximum self-enhancement coefficient, $\xi$, for phase holograms (recording at $\lambda_1 = 514.5$ nm; readout at $\lambda_2 = 632.8$ nm) is about 1000 times larger than in LiNbO$_3$. This is clearly demonstrated on figure 10 by Teteris [18].

Figure 10: Self-enhancement of recorded hologram [18]

Such effective self-enhancement in As$_2$S$_3$ films leads to the strong change in the polarisability under illumination and the corresponding large dynamic range for phase recording. The change of the refractive index, $\Delta n$, in As$_2$S$_3$ films is approximately $\Delta n \approx 0.1$, in LiNbO$_3$ crystals is $\Delta n = 3\times10^{-3}$. This large difference in the change in the light induced refractive index explains the difference in the magnitude of the self-enhancement [2,19].

Figure 11: Hologram self-enhancement (HSE) principles [2], (a) recording with two beams; (b1) coherent HSE; (b2) non-coherent HSE with scattered light; (b3) dark reactions enhancement

By recording and readout at the same wavelength ( $\lambda_1 = \lambda_2$) the HSE is smaller [19]. For $\lambda_1 = \lambda_2 = 514.5$ nm, the maximum HSE factor is $\xi \leq 10$. The HSE decreases at higher exposures, when the initial $\eta_0$ is close to $\eta_{\mathrm{max}}$. This means that the recording process is saturated and no further recording is possible. The HSE also depends on the holographic grating period. The maximum value of $\xi$ corresponds to holographic gratings with a period of 1-2 $\mu$m. Thus, the holographic self-enhancement is typical for 3-D holograms and is absent in 2-D holograms ($\xi$ approaches to zero in films with a small thickness or for large holographic grating periods) [2].