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Optical physics

Eigenchannels of a scattering medium

Complex media such as random nanostructures and biological tissues induce multiple wave scattering, which interrupts the propagation of waves and attenuates energy transmission. Even for a highly disordered medium, however, it is possible in principle to enhance the delivery of energy to the far side of the medium. Similar to the resonator modes in linear optical cavities, specific modes called eigenchannels exist in a disordered medium and have extraordinarily high transmission. In our study, we experimentally identify the transmission eigenchannels of any given scattering medium by measuring the transmission matrix, and experimentally coupled light to individual eigenchannels by using wavefront shaping. In our early studies, we showed that an eigenchannel transports 3.99 times more energy than uncontrolled waves. This study will open up new avenues for enhancing light energy delivery to biological tissues for medical purposes and for controlling the lasing threshold in random lasers.

Internal field distribution of transmission eigenchannels. We performed finite-difference time-domain method to visualize the field distribution of eigenchannels within the scattering media. From the left, propagation of plane waves, eigenchannels with unity transmittance, and eigenchannels with zero transmittance.

Experimental demonstration of reflection eigenchannels. (a), (b) and (c): Intensity maps of experimentally shaped incident waves for the first eigenchannel, 1280th eigenchannel and normally incident plane wave, respectively. They correspond to the highest, lowest, and average reflectance modes, respectively. The H and V polarization components were superposed at the incident plane. (d), (e) and (f): Experimentally recorded intensity maps of reflected waves for the cases of (a), (b) and (c), respectively. (g), (h) and (i): Measured intensity maps of transmitted waves for the case of (a), (b) and (c), respectively. Scale bar, 5 μm. The color bar next to (c) indicates intensity in an arbitrary unit and applies also to (a) and (b). The other two color bars follow the same rule.


Preferential coupling of an incident wave to reflection eigenchannels of disordered media, Wonjun Choi, Moonseok Kim, Donggyu Kim, Changhyeong Yoon, Christopher Fang-Yen, Q-Han Park, and Wonshik Choi, Scientific Reports 5:11393 (2015)

Exploring anti-reflection modes in disordered media, Moonseok Kim, Wonjun Choi, Changhyeong Yoon, Guang Hoon Kim, Seung-hyun Kim, Gi-Ra Yi, Q-Han Park, and Wonshik Choi, Optics Express 23, 12740 (2015) 

The transmission matrix of a scattering medium and its applications in biophotonics, Moonseok Kim, Wonjun Choi, Youngwoon Choi, Changhyeong Yoon, and Wonshik Choi, Optics Express 23, 12648 (2015)

Measurement of the time-resolved reflection matrix for enhancing light energy delivery into a scattering medium, Youngwoon Choi, Timothy R. Hillman, Wonjun Choi, Niyom Lue, Ramachandra R. Dasari, Peter T. C. So, Wonshik Choi, and Zahid Yaqoob, Physical Review Letters 111, 243901 (2013)

Maximal energy transport through disordered media with the implementation of transmission eigenchannels, Moonseok Kim, Youngwoon Choi, Changhyeong Yoon, Wonjun Choi, Jaisoon Kim, Q-Han Park and Wonshik Choi, Nature Photonics 6, 581 (2012)

Transmission eigenchannels in a disordered medium, Wonjun Choi, Allard P. Mosk, Q-Han Park and Wonshik Choi, Physical Review B 83, 134207 (2011)

Scattering tensor of a nonlinear scattering medium

Complex scattering media can serve as a platform for spatially mixing incoming waves through numerous randomly interconnected channels, making it act as a unique linear optical operator. We developed methods to measure the transfer functions of the scattering medium, which enables us to use it as an effective lens. Furthermore, we demonstrated that the scattering medium can be used as a special lens, allowing us to achieve resolution surpassing the diffraction limit (Physical Review Letters, 2011). Recently, we extended this framework to a nonlinear scattering medium and demonstrated that the disordered nonlinear medium can be used as a highly scalable nonlinear optical operator for optical encryptions and machine learning.

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Solving the inverse of the scattering tensor. (a) Input wave with specific amplitude and phase patterns in the k-space were projected to the SHG scattering layer, and the generated SHG wave ESHG were recorded. The original input wave was retrieved by the inverse of the scattering tensor. Scale bar, 10 μm. (b-c) Magnitude of squeezed vector obtained by the inverse of the scattering tensor. (d-e) Amplitude and phase maps of the input wave, respectively, obtained by solving the tensor inverse.


Moon, J., Cho, Y.-C., Kang, S., Jang, M. & Choi, W. Measuring the scattering tensor of a disordered nonlinear medium. Nat. Phys. 19, 1709–1718 (2023).

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