Form factor in persistent hole burning in multiple scattering optical media

This paper presents detailed experiments on persistent hole burning in photoreactive and multiple scattering media. The dependence of the hole shape and width on the sample thickness, transport mean free path, and absorption length was measured. The experimental results show good agreement with a previously reported theoretical calculation on the basis of a diffusion approximation [Phys. Rev. E 70, 046606 (2004)].

Figure 1

Solid lines are experimental results for the persistent hole as a function of angular shift $\theta$ between the writing and reading beams. The sample thickness is $L=\left(\mathrm{a}\right)$ 1.0, (b) 0.4, and (c) $0.2\mathrm{mm}$. The transport mean free path and the absorption length are $l^{*}=60\mu \mathrm{m}$ and $l_a=28800\mu \mathrm{m}$, respectively. Dashed lines are theoretical curves calculated on the basis of Eq. (1), where a Gaussian shaped function is convoluted as the experimental angular resolution.

Figure 2

Solid lines are experimental results for the persistent hole as a function of angular shift $\theta$. The transport mean free path and the absorption length are (a) $l^{*}=11\mu \mathrm{m}$, $l_a=28800\mu \mathrm{m}$, (b) $l^{*}=17\mu \mathrm{m}$, $l_a=28800\mu \mathrm{m}$, and (c) $l^{*}=60\mu \mathrm{m}$, $l_a=580\mu \mathrm{m}$. The sample thickness is $L=1.0\mathrm{mm}$ in all samples. Dashed lines are theoretical curves calculated on the basis of Eq. (1), where the experimental angular resolution is convoluted. Note that the horizontal scale is reduced; therefore the hole width is broad, compared with Fig. 1.

Figure 3

(a) Calculated hole shapes for different sample thickness. From top to bottom, $L=0.2$, 0.4, 0.6, 0.8, and $1.0\mathrm{mm}$, where $l^{*}=60\mu \mathrm{m}$ and $l_a=28800\mu \mathrm{m}$. (b) Hole width as a function of the inverse of the sample thickness. The solid line is the calculated curve for $l_a=28800\mu \mathrm{m}$, while the three dashed curves are $l_a=4000$ and $8000\mu \mathrm{m}$ and infinity, respectively. The transport mean free path is $l^{*}=60\mu \mathrm{m}$. The solid symbols are experimental results shown in Fig. 1. The solid square is for the standard sample. The open circles correspond to the simulation shown in Fig. 3a.

Figure 4

(a) Hole width as a function of the inverse of the diffusive absorption length. The solid line is the calculated curve for $l^{*}=60\mu \mathrm{m}$. The dashed curves are, from top to bottom, $l^{*}=45$, 50, and $80\mu \mathrm{m}$, respectively. The sample thickness is $L=1.0\mathrm{mm}$. The solid circles are experimental results including the data shown in Fig. 2c. The solid square is for the standard sample. (b) Hole width as a function of the inverse of the transport mean free path. The solid line is calculated curve for $l_a=28800\mu \mathrm{m}$. The dashed curves are, from top to bottom, $l_a=20000$ and $60000\mu \mathrm{m}$ and infinity, respectively. $L=1.0\mathrm{mm}$. The solid square is for the standard sample. The solid circles are experimental results including the data shown in Figs. 2a, 2b.