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

Ojambati, Oluwafemi Stephen; Yılmaz, Hasan; Lagendijk, Ad; Mosk, Allard; Vos, Willem L.

doi:10.1088/1367-2630/18/4/043032

Cited by 30 publications

(40 citation statements)

References 63 publications

(135 reference statements)

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“…Remarkably, our finding about the contribution of m = 1 to the total internal energy density agrees very well with the heuristic model in Ref. [45] that wavefront shaping predominately couples light to the fundamental diffusion eigensolution. The contribution of m = 2 is negligible compared to m = 1 since m = 2 has negative energy density in almost half of the sample depth, which cancels out the positive energy density (see Fig.…”

Section: Energy Density Of Shaped Wavessupporting

confidence: 90%

“…In Ref. [45], our team reported the first measurement of the total energy density of light inside a three-dimensional (3D) scattering medium and reported an enhanced total energy density for shaped waves. The results were interpreted with a heuristic model that the total energy density of shaped waves can be described with only the fundamental eigenfunction of the diffusion equation, which agreed well with experimental observation.…”

Section: Introductionmentioning

confidence: 99%

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

Ojambati¹,

Mosk²,

Vellekoop³

et al. 2016

Opt. Express

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Abstract: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.

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Section: Energy Density Of Shaped Wavessupporting

confidence: 90%

Section: Introductionmentioning

confidence: 99%

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

Ojambati¹,

Mosk²,

Vellekoop³

et al. 2016

Opt. Express

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“…The incomplete control dramatically weakens the open channels [23], although a notable enhancement of total transmission has been achieved [20,24]. Furthermore, an enhancement of total energy stored inside a 3D scattering sample is reported [25], but direct probe and control of light intensity distribution inside the scattering medium are still missing.In this Letter, we demonstrate experimentally control of energy density distribution inside a scattering medium.Instead of the open slab geometry, we fabricate a silicon waveguide that contains scatterers and has reflecting sidewalls. The intensity distribution inside the twodimensional waveguide is probed from the third dimension.…”

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confidence: 99%

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confidence: 99%

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

et al. 2016

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We demonstrate experimentally an efficient control of light intensity distribution inside a random scattering system. The adaptive wavefront 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 open or closed channels of the disordered system, we not only vary the total energy stored inside the system by 7.4 times, 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.PACS numbers: 42.25. Bs, 42.25.Dd, It has long been known that in disordered media there are many fascinating counter-intuitive effects resulting from interferences of multiply scattered waves [1,2]. One of them is the creation of transmission eigenchannels which can be broadly classified as open and closed [3,4]. Existence of high-transmission (open) channels allows an optimally prepared coherent input beam transmitting through a lossless diffusive medium with order unity efficiency. Opposite to that, waves injected to lowtransmission (closed) channels can barely penetrate the medium and are mostly reflected instead. In general, the penetration depth and energy density distribution of multiply scattered waves inside a disordered medium are determined by the spatial profiles of the transmission eigenchannels that are excited by the incident light. The distinct spatial profiles of open and closed channels suggest that selective coupling of incident light to these channels enables an effective control of total transmission and energy distribution inside the random medium [5,6]. Since the energy density determines the light-matter interactions inside a scattering system, manipulating its spatial distribution opens the door to tailoring optical excitations as well as linear and nonlinear optical processes such as absorption, emission, amplification, and frequency mixing inside turbid media. The potential applications range from photovoltaics [7,8] In recent years there have been numerous theoretical and experimental studies on transmission eigenchannels [5,[13][14][15][16][17]. While they can be deduced from the measured transmission matrix [18][19][20][21], it is difficult to directly probe their spatial profiles inside three-dimensional (3D) random media. So far, the open and closed channels are observed only with acoustic wave inside a two-dimensional (2D) disordered waveguide [22], but controlling the energy density distribution has not been realized due to lack of an efficient wavefront modulator for acoustic wave or microwave. The advantage for optical wave is the availability of spatial light modulator (SLM) with many degrees of freedom, however, the commonly used samples in the optics experiment have an open slab geometry, making it impossible to control all input modes due to finite numerical aperture of the imaging...

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“…Other ways to overcome inefficient coupling of light into scattering materials have included the use of wavefront shaping (18)(19)(20) to promote coupling into the fundamental diffusion mode (21) or the open/closed eigenchannels (22,23) of the material, thereby controlling energy density (13). An optimum wavefront of the incident light is determined via iterative search algorithms (24,25) or measurement of the transmission/reflection matrix (26) to promote coupling into these modes.…”

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confidence: 99%

Enhanced coupling of light into a turbid medium through microscopic interface engineering

Thompson

Hokr

Kim

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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There are many optical detection and sensing methods used today that provide powerful ways to diagnose, characterize, and study materials. For example, the measurement of spontaneous Raman scattering allows for remote detection and identification of chemicals. Many other optical techniques provide unique solutions to learn about biological, chemical, and even structural systems. However, when these systems exist in a highly scattering or turbid medium, the optical scattering effects reduce the effectiveness of these methods. In this article, we demonstrate a method to engineer the geometry of the optical interface of a turbid medium, thereby drastically enhancing the coupling efficiency of light into the material. This enhanced optical coupling means that light incident on the material will penetrate deeper into (and through) the medium. It also means that light thus injected into the material will have an enhanced interaction time with particles contained within the material. These results show that, by using the multiple scattering of light in a turbid medium, enhanced light-matter interaction can be achieved; this has a direct impact on spectroscopic methods such as Raman scattering and fluorescence detection in highly scattering regimes. Furthermore, the enhanced penetration depth achieved by this method will directly impact optical techniques that have previously been limited by the inability to deposit sufficient amounts of optical energy below or through highly scattering layers.turbid media | enhanced transmittance | optical coupling | optical scattering | spectroscopy O ptical detection and spectroscopy has drastically changed the way we look at and measure the world today. Observation of the interaction of light with matter provides us with a host of tools to promote research, security, safety, and health. These optical tools include the detection of harmful or explosive materials (1-3), the remote detection of chemicals from a distance (4), the optical diagnosis of colloidal suspensions for genomics and drug delivery (5), and even the use of lasers for defense (6). Remote sensing techniques (7) allow us to image/detect structures through the atmosphere or ocean. Optical methods are also an integral part of biomedical research, diagnosis (8), and treatment (9) of many of today's most prevalent illnesses (10). However, the sensitivity and usefulness of any optical method is severely limited by the occurrence of optical scattering. This limitation is further amplified when the density of scatterers is high enough for multiple scattering to occur. In this article, we show that modification of the geometry of the optical interface significantly improves the coupling efficiency of light into a highly scattering medium, thereby reducing the detrimental effects of scattering. This enhanced coupling is evident through the observation of increased spatial diffusion, two orders of magnitude greater transmission, and over an order of magnitude greater interaction time of light within the material. This translates...

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

Cited by 30 publications

References 63 publications

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

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

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

Enhanced coupling of light into a turbid medium through microscopic interface engineering

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