Control of Energy Density inside a Disordered Medium by Coupling to Open or Closed Channels

We demonstrate experimentally the efficient control of light intensity distribution inside a random scattering system. The adaptive wave front shaping technique is applied to a silicon waveguide containing scattering nanostructures, and the on-chip coupling scheme enables access to all input spatial modes. By selectively coupling the incident light to the open or closed channels of the disordered system, we not only vary the total energy stored inside the system by a factor of 7.4, but also change the energy density distribution from an exponential decay to a linear decay and to a profile peaked near the center. This work provides an on-chip platform for controlling light-matter interactions in turbid media.

Figure 1

On-chip disordered waveguide with a tapered lead. (a) Top-view scanning electron micrograph (SEM) of a fabricated silicon waveguide. A ridge waveguide (lead) is tapered from the width $W_1=330\mu \mathrm{m}$ at the edge of the wafer to the width $W=15\mu \mathrm{m}$, in order to increase the degree of control of the light that is injected to the disordered waveguide. (b) Magnified SEM of the disordered region of the waveguide that consists of a random array of air holes ($\text{diameter}=90\mathrm{nm}$). (c) Magnified SEM showing the air holes distributed randomly within the waveguide with a filling fraction of 6%. (d) The sidewalls of the waveguide are made of a triangular lattice of air holes ($\text{diameter}=360\mathrm{nm}$) with a lattice constant of 505 nm, which supports a full photonic band gap at the wavelength $\lambda =1.51\mu \mathrm{m}$.

Figure 2

Wave front shaping experiment to control the intensity distribution inside a disordered waveguide. (a) A schematic of the experimental setup. Laser (HP 8168F) output at $\lambda =1510\mathrm{nm}$ is collimated (by lens $L_1$), expanded (by $L_2$, $L_3$), and linearly polarized (by a polarized beam splitter PBS) before being modulated by a phase-only SLM (Hamamatsu X10468). Two lenses ($L_4$, $L_5$) are used to project the SLM plane to the pupil plane of an objective $O_1$ ($100\times$, $\mathrm{NA}=0.7$), and the edge of the wafer is placed at the focal plane. The SLM imposes phase modulation only in one direction in order to generate a line at the front end of the coupling waveguide. A sample phase pattern on the SLM is shown. The light scattered out of the sample plane is collected by another objective $O_2$ ($100\times$, $\mathrm{NA}=0.7$) and imaged to an InGaAs camera (Xenics XEVA 1.7-320) by a tube lens ($L_6$). $M_1$ and $M_2$ are mirrors and BS is a beam splitter. (b) An optical image of the illumination line ($330\times 1.1\mu \mathrm{m}$) on the waveguide facet. The input intensity is modulated along the line. (c) An image of the spatial distribution of the light intensity inside the disordered waveguide for a random input wave front. The spatial resolution is about $1.1\mu \mathrm{m}$. The ratio $S$ of the integrated intensities over the two rectangles at the back and front side of the waveguide is used as feedback for optimizing the input wave front.

Figure 3

Experimental control of the intensity distribution inside the disordered waveguide. (a)–(c) Two-dimensional intensity distribution $I(y,z)$ inside the disordered waveguide shown in Fig. 1 for (a) random input fields, (b) optimized input for maximum light penetration (maximizing $S$), and (c) optimized input for minimum light penetration (minimizing $S$). (d)–(f) The cross-section-averaged intensity $I(z)$ obtained from $I(y,z)$ in (a)–(c). The dashed lines are experimental data and the solid lines are simulation results.

Figure 4

Numerical simulation of the wave front shaping experiment. (a),(c) Weight $w(\tau )$ of each transmission eigenchannel in the input field obtained by maximizing (a) or minimizing (c) the light penetration into the disordered waveguide with the cost function $S$ (black solid line). For comparison, $w(\tau )$ for the random input field (blue solid line) and for the input field of the maximum (a) or minimum (c) transmission eigenchannel after removal of amplitude modulation (red dotted line) are also shown. (b),(d) Cross-section-averaged intensity distribution $I(z)$ for the maximized (b) or minimized (d) $S$ (black solid line), as well as the maximum (b) or minimum (d) transmission channel with (green dash-dotted line) and without amplitude modulation (red dotted line).