Time development of a persistent hole burning in multiple-scattering media

We investigated the time development of persistent hole burning in photoreactive and multiple-scattering media. In this hole burning, a writing laser beam recodes the volume speckle pattern inside the medium through the photoreactive process, and then the luminescence intensity excited by a reading beam is measured as a function of the frequency or wave vector difference between the writing and reading beams. The time development reflects the statistics of the intensity fluctuations in the speckle inside the medium. One of the striking results is that the maximum hole depth is $\sim 0.26$. We distinguish three types of samples according to the geometric configurations and the photoreactive processes and discuss the hole shape, hole width, and the depth during time development. Hole burning experiments were also performed using a spiropyran derivative photochromic dye. The experimental results showed good agreement with the theory.

Figure 1

Calculated curves for the luminescence intensity as a function of (a) $\Delta kL$ and (b) $\Delta \omega {\tau }_{\mathit{\text{life}}}$, where ${\tau }_{\mathit{\text{life}}}=L^2∕D$, in the type II sample. Solid and dotted lines are for the transmission and the reflection geometries, respectively. From the top to the bottom, $\kappa I_{W_0}=0.1$, 0.5, 2, 5, 50, 200, respectively.

Figure 2

Absorption spectra of SP-1 in PMMA. Solid line is the initial colored state after uv irradiation. Dashed line is the colorless state after ${\mathrm{Ar}}^{+}$ laser irradiation. Inset shows the structural formula of SP1.

Figure 3

Solid and open circles and open squares are luminescence spectra of SP1 in PMMA after laser irradiation of $8\mathrm{s}$, $30\mathrm{s}$, and $53\mathrm{s}$, respectively.

Figure 4

Schematic illustration of the experimental setup for the hole burning in the reflection geometry. M is the mirror, BS is the beam splitter, L is the lens, F1 and F2 are the filters, and PM is the photomultiplier tube.

Figure 5

Experimental results for the time development of the hole burning in the type I sample. (a) Solid and open circles are luminescence intensities at the hole center $\tilde{H}(\Delta k=0)$ and at the background level $\tilde{H}(\Delta k=\infty )$, respectively, as a function of the writing time. The dashed and solid lines are calculated curves on the basis of Eqs. (16, 17). (b) The solid circles are the hole depths. The inset in (a) is a schematic illustration of the type I sample. The gray region represents the photochromic film.

Figure 6

The normalized holes as a function of $\Delta kL$. (a) is for the type I sample. Solid and dashed lines are $T_W=5\mathrm{s}$ and $T_W=240\mathrm{s}$, respectively. (b) is for the type III sample. Solid and dashed lines are $T_W=30\mathrm{s}$ and $T_W=7500\mathrm{s}$, respectively.

Figure 7

The normalized holes width ${\Gamma }_{\Delta k}$ as a function of the normalized writing time. Solid squares and open and solid circles are type I, type II, and type III samples, respectively. The writing time is normalized by the time required for the background level to decrease to $1∕e$ of the initial value for each sample. The dotted line represents ${\Gamma }_{\Delta k}=\mathrm{const}$ for the type I sample, the dashed line is the calculation from Eq. (18) for the type II sample, and the solid line is a guide for eyes for the type III sample.

Figure 8

(a) The luminescence intensity as a function of $\Delta kL$ in the type II sample in the reflection geometry. From the top to the bottom, $T_W=0$, 10, 20, 40, 80, 160, 320, 600, $1260\mathrm{s}$, respectively. (b) The luminescence intensity as a function of $\Delta kL$ in the type III sample in the reflection geometry. From the top to the bottom, $T_W=0$, 30, 330, 1350, 3900, $7500\mathrm{s}$, respectively.

Figure 9

Experimental results for the time development of the hole burning in the type II sample in the reflection geometry. (a) Solid and open circles represent $\tilde{H}(\Delta k=0)$ and $\tilde{H}(\Delta k=\infty )$, respectively. The dashed and solid lines are calculated curves on the basis of Eqs. (24) and (23). (b) The solid circles represent the hole depth. The inset in (a) shows a schematic illustration of the type II sample.

Figure 10

Experimental results for the time development of the hole burning in the type III sample in the reflection geometry. (a) Solid circles and open circles represent $\tilde{H}(\Delta k=0)$ and $\tilde{H}(\Delta k=\infty )$, respectively. The solid and dashed lines are guides for the eyes. The inset in (a) is a schematic illustration of the type III sample. (b) The solid circles represent the hole depth.