Wide variety of applications have been developed using structured light due to its flexibility especially in the visible wavelength. For natural user interface, structured light, typically stripes or grids, are illuminated onto objects to derive their three-dimensional shape by analyzing the distorted reflected image. Several different types of the state-of-the-art super resolution microscopes are realized using structured light and have been the key equipment for accelerating the biological cell imaging. The structured light introducing singularity or so-called topological defects in the light waves, such as edges or vortices, helps us to realize the super resolution scheme. Optical vortex is known to host integer number of helical turns on its wavefront, carry discrete orbital angular momentum and provides multiple degree of freedom for communication. Besides, they can be realized in a wide frequency range. To date, numerous methods have been used to diagnose the topological charges or winding numbers of optical vortices, especially in the visible light region. Nevertheless, it has been sparsely characterized in the X-ray region despite the potential practical implications.
To this note, Japanese researchers at RIKEN SPring-8 Center: Professor Yoshiki Kohmura, Professor Kei Sawada, and Professor Tetsuya Ishikawa together with Professor Masaichiro Mizumaki from Japan Synchrotron Radiation Research Institute, and Professor Kenji Ohwada and Tetsu Watanuki from National Institutes for Quantum and Radiological Science and Technology (QST) explored the distribution of topological charges of X-ray orbital angular momentum formed by chiral materials. The main aim was to verify whether a differential radial Hilbert transform (RHT) microscope with reversed spiral phase filter is useful for visualizing topological charges on the X-ray vortices. Their research work is currently published in the journal, Optics Express.
In their approach, the research team characterized the X-ray structured light. A differential Fourier space filtering microscope was adopted to measure the topological charges of the X-ray vertices. The microscope contained a spiral phase filter based on the radial Hilbert transform principle. The radial Hilbert transform is generalization of the Hilbert transform developed for signal processing of complex-valued data, such as calculation of the temporal derivative of radio signals. The RHT microscope visualizes the 2D distribution of the derivative of the “phase and amplitude” of a wave passing through a sample. The feasibility of the differential radial Hilbert transform microscope in visualizing the distribution of topological charges was validated.
Experimental results showed that a single image of X-ray RHT microscope provided edge-enhanced imaging over a wide field of view. On the other hand, the differential RHT microscope with reversed spiral phase filter could visualize the topological charge of orbital angular momentum downstream of the chiral materials, thus confirming the accuracy of the initial theoretical predictions. This was attributed to its high sensitivity to azimuthal derivative of the X-ray wave. Similar to the theoretical calculations, a pair of bright and dark spots were exhibited at the center of the spiral phase plate when two images were differentiated to derive the distribution of the topological charges. Furthermore, the topological charges were theoretically proved to be proportional to the Berry curvature, the rotation of the generalized vector potential on the parameter space.
In summary, the study was the first to experimentally determine the distribution of the topological charges of X-ray orbital angular momentum downstream of chiral materials. This included the visualization of topological charges on the X-ray vortices using a differential RHT microscope with a reversed spiral phase filter. The RHT microscope enabled a high sensitivity necessary to detect the topological defects in the wave-field downstream. In a statement to Advances in Engineering, the authors said the high-performance microscope would be of great significance in the future investigation of the properties and dynamical interactions of dislocations that mainly affect material properties.
Kohmura, Y., Sawada, K., Mizumaki, M., Ohwada, K., Watanuki, T., & Ishikawa, T. (2020). X-ray microscope for imaging topological charge and orbital angular momentum distribution formed by chirality. Optics Express, 28(16), 24115.