Novel topology-related technologies

Optical and acoustic measurement can be used to extract a wide variety of physical properties in a non-contact and non-destructive way, by controlling wavelength, intensity, phase, direction of polarization, bandwidth, pulse width, or other parameters. This project will develop new measurement, analysis and processing technologies using light and sound; these technologies will become the basic tools for our studies in Topological Science and Technology. Take an example from the medical field: it is known that the topology of the networks produced by cancer or other tissue anomalies is different from that of normal tissue. To extract this network topology, we will develop technology to visualize tissue, making the most of the advantageous features of optical and acoustic measurement. By combining this technology with the network topology invariant analysis method of the Topology in Relation to Critical Phenomena and the Topology in the Life Sciences projects, we aim to develop non-contact and non-invasive quantitative diagnostic methods. By visualizing not only the static topology of the network, but also its time variation and in-vivo material flow, this should lead to new techniques in tissue anomaly identification and diagnosis. We will also develop other practical technologies based on the combination of topology and optical technologies: Topological Quantum Information, involving the combination of quantum information with the concepts of topology, is a project concerned with the solution of complex quantum superposition and interference problems involving photons. For example, an optical quantum gate to control the Berry phase will be constructed, a topological variable used to solve such problems.

Basic technologies for these projects have already been developed by our group members. For example, the technology for the real-time visualization of surface acoustic waves excited on a (planar) solid surface using laser pulses of femtosecond (10^-15 second) duration has been developed. This technology will be extended to allow the real time visualization and analysis of the propagation of surface acoustic waves on spherical, ring-like, or other curved surfaces. The aim in this case is to ascertain how differences in topology affect the propagation of surface acoustic waves.

Visualization of surface waves excited on a (planar) solid surface.