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Fano resonance is a pervasive resonance phenomenon which can be applied to high sensitivity sensing, perfect absorption, electromagnetic-induced transparency, and slow-light photonic devices. In this paper, we propose a metal–insulator–metal (MIM) waveguide structure consisting of a D-shaped cavity and a bus waveguide with a silver–air–silver barrier. The Fano resonance can be achieved by the interaction between the D-shaped cavity and the bus waveguide. The finite element method is used to analyze the transmission characteristics and magnetic-field distributions of the structure in detail. Simulation results show the Fano resonance can be adjusted by altering the geometric parameters of the MIM waveguide structure or the refractive index of the D-shaped cavity. The maximum refractive index sensitivity of the structure can reach up to 1510 nm/RIU, and there is a good linear relationship between resonance wavelength and refractive index. Since it has good sensitivity and tunability, the MIM waveguide structure can be used in bio-sensing, such as human hemoglobin detection. We show its applicability for the detection of three different human blood groups as well.

This study aims to identify the types of difficulties experienced by high school students in solving equations and trigonometric identities. The method used in this research is descriptive qualitative research method because researchers want to describe or describe the facts of students' difficulties in solving equations and trigonometric identities. The data collection technique in this study is by using respondents' ability tests and interviews. Based on the results of data analysis, there are three aspects of students 'difficulties in solving trigonometric equations and also there are three aspects of students' difficulties in solving trigonometric identity problems. The difficulties of students in solving trigonometric equations, namely the difficulty of students in deciphering the form of the problem, difficulty in factoring in the form of trigonometric quadratic equations, and difficulties using the basic trigonometric equations. Whereas, the difficulties of students in solving trigonometric identity problems, namely the difficulty of students applying general trigonometry formulas, difficulty describing each of the trigonometric comparison relationships, and difficulties in performing algebraic calculations/computation.

In this paper, a metal–insulator–metal (MIM) waveguide structure consisting of a side-coupled rectangular cavity (SCRC), a rightward opening semi-ring cavity (ROSRC), and a bus waveguide is reported. The finite element method is used to analyze the transmission characteristics and magnetic-field distributions of the structure in detail. The structure can support triple Fano resonances, and the Fano resonances can be tuned independently by altering the geometric parameters of the structure. Moreover, the structure can be applied in refractive index sensing and biosensing. The maximum sensitivity of refractive index sensing is up to 1550.38 nm/RIU, and there is a good linear relationship between resonance wavelength and refractive index. The MIM waveguide structure has potential applications in optical on-chip nano-sensing.