In recent years, fractal gratings have been widely used in the fields of optics, materials etc. In this paper, the diffraction characteristics of the two-dimensional Cantor fractal grating diffraction are discussed from three aspects: theory, simulation and experiment. Firstly, the analytical formulation of light intensity distribution is derived according to the scalar diffraction theory. Then, a graphical interface is developed based on Python for experimental simulation, and the simulated diffraction pattern is obtained. Finally, the grating is prepared for experiment. Our results show that the diffraction patterns obtained from experiments and theoretical simulations are consistent with each other. Our work could help undergraduates to understand the diffraction rule of two-dimensional Cantor fractal grating, and the obtained rule also has some application prospects in optics and materials.

In this paper, we design a scheme of measuring the natural frequency of fixed beam by fiber grating sensor and measure the first to fourth order natural frequency of fixed beam. In particular, we analyzed the structural characteristics of clamped beams and derived theoretical formulas for their first to fourth-order natural frequencies. Then, with the clamped beam as the basic frame, the beam body is excited by the shaker to make the beam body produce forced vibration. When the beam body generates standing waves, the fiber Bragg grating (FBG) is used as the sensitive element to measure the deflection change of the specific position of the beam body. The wavelength variation of the FBG is measured by Micron Optic fiber grating demodulator, the data is then collected and processed by MOI software to obtain the natural frequency of fixed beams. The experimental results show that the measured natural frequencies of the clamped beam are in good agreement with theoretical values, with minimal error. The experimental scheme is simple in structure, highly sensitive, and robust against external interference, demonstrating strong practicality and promising applications.