To enhance sensor sensitivity and resolution, the present study proposes a biochemical sensor utilizing localized surface plasmon resonance to detect minute changes in the refractive index of the analyte. This sensor comprises a single-mode fiber located on the front and back ends of the sensor, which is responsible for the input and output of fiber optic signals, and two geometrical objects arranged in an interwoven pattern in the sensing region at the center of the sensor. In particular, the rectangular metal nanoparticles are arranged in a rectangular fashion and plated in the etched cladding layer to increase the number of nanosized metal particles on the X–Y plane. In addition, to decrease the calculation time and memory capacity while increasing the precision of simulations, a numerical calculation approach with power functions was employed. This approach comprises the finite element method, eigenmode expansion method, perfectly matched layer, perfectly reflecting boundary condition, boundary meshing method, and object meshing method. Triangular meshes were employed as the basis and sensors were divided into object boundaries, small-sized objects, medium-sized objects, and large-sized objects. The meshing ratio was set to 1:9:181:1810. Numerical simulation results indicate that the proposed localized surface plasmon resonance sensor achieved superior length (approx. 170 μm), resolution (approx. −155 dB), and sensitivity (approx. 137,664.4 nm/RIU).