KAIST Research Team Solves Physics Problem "That Had No Theory Before"

Development of a 3D Tomography Method for Permittivity Tensor

Liquid crystal dynamics and liquid crystal network measured by the developed method. Image provided by KAIST.

[Asia Economy Reporter Kim Bong-su] A domestic research team has solved another longstanding problem in physics. The Korea Advanced Institute of Science and Technology (KAIST) announced on the 4th that Professor Yong-Geun Park's research team in the Department of Physics has developed a three-dimensional tomographic method for dielectric tensors, one of the unsolved problems in physics for which no theoretical framework previously existed.

The dielectric tensor is an important physical quantity that fundamentally describes the interaction between light and matter and can quantitatively express the optical anisotropy of materials (the property of appearing different depending on direction). Although dielectric constant is a basic concept covered even in high school physics, until now, there has been no experimental method to measure the three-dimensional dielectric tensor. Despite its importance in various fields such as pathology, materials science, soft matter science, and displays, there was a limitation in that no direct measurement method existed. Even today, three-dimensional optical anisotropy can only be inaccurately estimated through two-dimensional polarized microscopy measurements and simulations.

Measuring the three-dimensional dielectric tensor has been one of the longstanding challenges in physics and optics. In 1967, a technology was invented that simplified the dielectric tensor by ignoring optical anisotropy and measuring it as a three-dimensional refractive index value. This technology rapidly developed and was commercialized over the past 50 years, but a method to measure the three-dimensional dielectric tensor itself has not yet been developed.

The reason this problem remained unsolved is that the dielectric tensor, which has three eigenvalues, cannot be measured because the degrees of freedom of the polarization direction of light are limited to two.

The research team overcame this limitation and succeeded in developing and implementing a theory for three-dimensional tomographic imaging of dielectric tensors in optically anisotropic structures. Departing from conventional ideas, the core idea of the research team was to slightly tilt the direction of light to utilize overlapping information, thereby increasing the degrees of freedom of the polarization direction to three and obtaining all three eigenvalues of the dielectric tensor. By controlling these three polarization degrees of freedom simultaneously and developing a holographic microscope to image the optical anisotropic structure from multiple angles?similar to X-rays and computed tomography (CT) scans used in hospitals?they directly measured the three-dimensional dielectric tensor.

Using the developed method, the research team successfully measured the three-dimensional dielectric tensor of well-known three-dimensional optical anisotropic materials such as twisted nematic liquid crystals, demonstrating the implementation of the technology. Furthermore, they achieved the first experimental measurement of three-dimensional dielectric tensors that were difficult to estimate with existing methods, such as liquid crystal dynamics growing, disappearing, and merging in thermal nonequilibrium states, and liquid crystal networks with recurring topological singularity structures.

Dr. Seung-woo Shin, first author and a physicist at KAIST, said, "It is significant that we have developed a methodology to directly measure dielectric tensors that could not be seen before." He added, "Because it can quantitatively and non-invasively observe the three-dimensional structures of various materials exhibiting optical directionality, such as liquid crystals, chiral materials, and collagen fibers inside pathological tissues like cancer tissues, it is expected to be a universally essential tool across many fields."

The research results were published on the 3rd in the international academic journal Nature Materials (IF 43.84). The English title of the paper is "Tomographic measurements of dielectric tensors at optical frequency."

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