Multiple-scattering-free light scattering spectroscopy with mode selectivity

Seeing through the dynamics of turbid media is often demanded in both science and technology. Dynamic light scattering is one of the most powerful means to study the dynamics of various condensed matter systems, in particular, soft matter systems, in a nondestructive manner. However, its applicability is often limited by multiple scattering of light, which severely distorts the signal. To overcome this problem, cross correlation spectroscopy has been developed. Here, we propose another physical principle by which we can avoid the effects of multiple scattering. We demonstrate that this method allows not only Rayleigh but also Brillouin scattering measurements even in very turbid colloidal suspensions. This method opens a possibility of optically characterizing the dynamics (translational and rotational diffusion, thermal diffusion, and acoustic phonon dynamics) of turbid materials with mode selectivity.

Figure 1

(Color online) (a) Principle of producing a dynamic light-field grating. ${\mathbf{k}}_1$ and ${\mathbf{k}}_2$ are the wave vectors of pump beams $L_1$ and $L_2$, respectively. $L_p$ is the probe beam. $L_p$ is scattered by the material grating produced by the light-field grating induced by the pump beams $L_1$ and $L_2$ [see (b)]. $L_s$ is the scattered light with the wave vector ${\mathit{k}}_2$. $L_l$ is the local light, which is mixed with $L_s$ on a photodiode PD1. We also mix $L_1$ with $L_p$, whose polarization direction is slightly rotated by a polarizer, on a photodiode PD2, to produce a reference signal for a phase-sensitive two-phase lock-in detection. See text on the details. (b) Schematic figure of the excitation of coherent concentration modulation. Propagating modulated light field and the resulting modulation of a colloid concentration are shown.

Figure 2

(Color online) A block diagram of our COLS system. BS stands for beam splitter, PBS1 and PBS2 for polarizing beam splitters, AOM1–3 for acousto-optic modulators, PD1 and PD2 for photodetectors, A1 and A2 for analyzers (polarizing plates), HP1 and HP2 for $\lambda /2$ plates, and PC for a computer. $\parallel$ indicates light with horizontal polarization, while $\perp$ does light with vertical polarization.

Figure 3

(Color online) A block diagram for COBS. The meaning of the symbols is the same as in Fig. 2. The only difference is that we use frequency-tunable lasers for this experiment.

Figure 4

(Color online) Measurements of translational collective diffusion. (a) Typical complex spectra of a PS latex aqueous suspension ($a=54\text{nm}$, $c_0=0.1\text{wt}\mathrm{\%}$, and the cell $\text{thickness}=1\text{mm}$) in a back scattering configuration $\left(\theta =175°\right)$. HWHM was 770 Hz. The frequency resolution bandwidth was set to be 200 Hz. The solid lines are the fitted theoretical curves [see Eq. (2)]. (b) Stokes-Einstein relation of PS suspensions of various particle sizes ($c_0=0.1\text{wt}\mathrm{\%}$ for all). Straight line shows the result of the least square fitting of the relation: $D_c=\left(k_{B}T/6\pi \eta \right)\left(1/a\right)$.

Figure 5

(Color online) Dispersion relations of PS latex aqueous suspensions. The samples are suspensions of PS latex $\left(a=54\text{nm}\right)$. (a) Dispersion relations measured by conventional (photon counting) dynamic light scattering spectroscopy, which deviates from the expected relation (solid line). The concentrations of suspensions are 0.05 (orange circles), 0.2 (blue diamonds), and 1.0 wt% (red triangles), respectively. (b) Dispersion relation measured by CORS for the 1.0 wt% suspension $\left(a=54\text{nm}\right)$. The expected relation ${\tau }^{-1}\propto q^2$ (solid line) holds quite well even under strong multiple scattering. (c) Transmittance of the incident light in PS aqueous suspensions $\left(a=54\text{nm}\right)$. The photographs of samples in optical cells, which are used for light scattering measurements, are also shown for the two concentrations (0.2 and 1 wt%).

Figure 6

(Color online) Complex Brillouin spectra measured for a turbid colloidal suspension ($c_0=0.5\text{wt}\mathrm{\%}$ and $a=54\text{nm}$) at $T=20°\text{C}$. The sample was filled in a cell of 1 mm thickness, and the optical transmission was 12.6%. The scattering angle was $5.75°$ $\left(q=1886{\text{cm}}^{-1}\right)$. The phonon frequency and the HWHM were determined to be 280 and 3.5 MHz, respectively, by fitting the theoretical curves (solid lines). The frequency resolution bandwidth was set to be 2 MHz.