For an application to the optical signal processing devices, we propose the optical X coupler which consists of two bending waveguides and a nonlinear dielectric region. To analyze this structure accurately we utilized the iterative finite difference beam propagation method (iterative FD-BPM). In this paper the formulation of the iterative FD-BPM for one wave and two waves cases are presented, respectively. We investigate following two cases. First, we consider the case that the light is launched into one of the input ports. We calculate the evolutions of the field amplitude and the transmission characteristics for the input power. Second, we consider the case that the signal light with the constant power is launched into one of the input ports and that the control light with the wavelength different from that of the signal light is launched into another input port. We calculate the evolutions of the field amplitude and the transmission characteristics of the signal light for the power of control light. As a result of the analysis, we show that all-optical switching operation is possible in the proposed structure.

Although intervention practices like mindfulness meditation have proven effective in treating psychosis, there is no clarity on the mechanism of information propagation in the brain. In this study, we formulated a network optimization problem and searched for the optimal solution using Digital Annealer developed by Fujitsu Ltd. This is inspired by quantum computing and is effective in solving large-scale combinatorial optimization problems to find the information propagation pathway in the brain that contributes to the realization of mindfulness. Specifically, we defined the optimal network state as the state of the brain network that is considered to be associated with the mindfulness state. We formulated the problem into two network optimization problems — the minimum vertex-cover problem and the maximum-flow problem — to search for the information propagation pathway that is important for realizing the state. In the minimum vertex-cover problem, we aimed to identify brain regions that are important for the realization of the mindfulness state, and identified eight regions, including four that were suggested to be consistent with previous studies. We formulated the problem as a maximum-flow problem to identify the information propagation pathways in the brain that contribute to the activation of these four identified regions. As a result, approximately 30% of the connections in the brain network structure of this study were identified, and the pathway with the highest flow rate was considered to characterize the bottom-up emotion regulation during mindfulness. The findings of this study could be useful for more direct interventions in the context of mindfulness, which are being investigated by neurofeedback and other methods. This is because existing studies have not clarified the information propagation pathways that contribute to the realization of the brain network states that characterize mindfulness states. In addition, this approach may be useful as a methodology to identify information propagation pathways in the brain that contribute to the realization of higher-order human cognitive activities, such as mindfulness, within large-scale brain networks.