Oluwafemi Stephen Ojambati

Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium

We demonstrate experimentally that optical wavefront shaping selectively couples light into the fundamental diffusion mode of a scattering medium. The total energy density inside a scattering medium of zinc oxide (ZnO) nanoparticles was probed by measuring the emitted fluorescent power of spheres that were randomly positioned inside the medium. The fluorescent power of an optimized incident wavefront is observed to be enhanced compared to a non-optimized incident wavefront. The observed enhancement increases with sample thickness. Based on diffusion theory, we derive a model wherein the distribution of energy density of wavefront-shaped light is described by the fundamental diffusion mode. The agreement between our model and the data is striking, not in the least since there are no adjustable parameters. Enhanced total energy density is crucial to increase the efficiency of white LEDs, solar cells, and of random lasers, as well as to realize controlled illumination in biomedical optics.We demonstrate experimentally that optical wavefront shaping increases light coupling into the fundamental diffusion mode of a scattering medium. The total energy density inside a scattering medium of zinc oxide nanoparticles was probed by exciting fluorescent spheres that were randomly positioned in the medium and collecting the fluorescent power. We optimized the incident wavefront to obtain a bright focus at the back surface of the sample and found that the concomitant fluorescent power is enhanced compared to a non-optimized incident wavefront. The observed enhancement increases with sample thickness. Based on diffusion theory, we derive a model wherein the distribution of the energy density of wavefront-shaped light is dominated by the fundamental diffusion mode. Our model agrees remarkably well with our experiments, notably since the model has no freely adjustable parameters.

Controlling the intensity of light in large areas at the interfaces of a scattering medium

The recent advent of wave-shaping methods has demonstrated the focusing of light through and inside even the most strongly scattering materials. Typically in wavefront shaping, light is focused in an area with the size of one speckle spot. It has been shown that the intensity is not only increased in the target speckle spot, but also in an area outside the optimized speckle spot. Consequently, the total transmission is enhanced, even though only the intensity in a single speckle spot is controlled. Here, we experimentally study how the intensity enhancement on both interfaces of a scattering medium depends on the optimization area on the transmission side. We observe that as the optimization radius increases, the enhancement of the total transmitted intensity increases. We find a concomitant decrease of the total reflected intensity, which implies an energy redistribution between transmission and reflection channels. In addition, we find qualitative evidence of a long-range reflection-transmission correlation. Our result is useful for efficient light harvesting in solar cells, multichannel quantum secure communications, imaging, and complex beam delivery through a scattering medium.

Three-dimensional spatially resolved optical energy density enhanced by wavefront shaping

While a three-dimensional (3D) scattering medium is from the outset opaque, such a medium sustains intriguing transport channels with near-unity transmission that are pursued for fundamental reasons and for applications in solid-state lighting, random lasers, solar cells, and biomedical optics. Here, we study the 3D spatially resolved distribution of the energy density of light in a 3D scattering medium upon the excitation of highly transmitting channels. The coupling into these channels is excited by spatially shaping the incident optical wavefronts to a focus on the back surface. To probe the local energy density, we excite isolated fluorescent nanospheres distributed inside the medium. From the spatial fluorescent intensity pattern we obtain the position of each nanosphere, while the total fluorescent intensity gauges the energy density. Our 3D spatially resolved measurements reveal that the differential fluorescent enhancement changes with depth, up to 26× at the back surface of the medium, and the enhancement reveals a strong peak versus transverse position. We successfully interpret our results with a newly developed 3D model without adjustable parameters that considers the time-reversed diffusion starting from a point source at the back surface.

Interplay of bloch waves and scattered waves in real photonic crystals

Light propagates inside an ideal and infinite photonic crystal when the Bloch condition is satisfied and any allowed light wave is decomposed in a basis of propagating Bloch waves [1]. In real photonic crystals, light propagation is modified due to unavoidable fabrication-induced structural imperfections in size, positions, and permittivity of the building blocks, as well as the finite size of the crystal. The unavoidable deviations from perfect periodicity result in scattering [2, 3]. Here, we seek to understand the nature of waves inside a real photonic crystal since inevitable disorder plays a significant role in wave propagation.

Looking inside a 3D scattering medium to observe the 3D spatially-resolved optical energy density that is enhanced by wavefront shaping

It is well known that a thick scattering medium (e.g. a slab of paint) is opaque since incident waves are thoroughly scrambled [1, 2]. In the diffusive transport regime, the scattered light has an (ensemble-averaged) energy density that linearly increases with depth from the front surface to about one mean free path 1, and then decreases linearly with depth to the back surface. Two main questions arise: (A) Can one increase (or decrease) the energy density? (B) What is the new position-dependence? Answers to these questions are crucial for light-matter interactions with applications to white LEDs, random lasers, solar cells, and biomedical optics.

Coupling of light into the fundamental diffusion mode of a scattering medium(Conference Presentation)

Diffusion equation describes the energy density inside a scattering medium such as biological tissues and paint [1]. The solution of the diffusion equation is a sum over a complete set of eigensolutions that shows a characteristic linear decrease with depth in the medium. It is of particular interest if one could launch energy in the fundamental eigensolution, as this opens the opportunity to achieve a much greater internal energy density. For applications in optics, an enhanced energy density is vital for solid-state lighting, light harvesting in solar cells, low-threshold random lasers, and biomedical optics. Here we demonstrate the first ever selective coupling of optical energy into a diffusion eigensolution of a scattering medium of zinc oxide (ZnO) paint. To this end, we exploit wavefront shaping to selectively couple energy into the fundamental diffusion mode, employing fluorescence of nanoparticles randomly positioned inside the medium as a probe of the energy density. We observe an enhanced fluorescence in case of optimized incident wavefronts, and the enhancement increases with sample thickness, a typical mesoscopic control parameter. We interpret successfully our result by invoking the fundamental eigensolution of the diffusion equation, and we obtain excellent agreement with our observations, even in absence of adjustable parameters [2]. References [1] R. Pierrat, P. Ambichl, S. Gigan, A. Haber, R. Carminati, and R. Rotter, Proc. Natl. Acad. Sci. U.S.A. 111, 17765 (2014). [2] O. S. Ojambati, H. Yilmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, arXiv:1505.08103.

Mapping the energy density of shaped waves in scattering media onto a complete set of diffusion modes

We study the energy density of shaped waves inside a quasi-1D disordered waveguide. We find that the spatial energy density of optimally shaped waves, when expanded in the complete set of eigenfunctions of the diffusion equation, is well described by considering only a few of the lowest eigenfunctions. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtain the energy density of transmission eigenchannels inside the sample by numerical simulation of the scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results of our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.We show that the spatial distribution of the energy density of optimally shaped waves inside a scattering medium can be described by considering only a few of the lowest eigenfunctions of the diffusion equation. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtained the energy density inside a quasi-1D disordered waveguide by numerical calculation of the joined scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density obtained, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results from our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.