Mathematical model for highly sensitive photonic crystal fiber sensor based on hyperbolic black holes

Abstract

In this paper, the photonic crystal fiber sensor based on the geometry of hyperbolic black holes is proposed. As the hyperbolic black hole concentrates the electromagnetic radiation in its powerful gravitational field, the designed sensor has resulted in the concentration of the most electromagnetic field in the core of fiber. The extraordinary sensitivity of the sensor is due to the topology and exact geometry, which originates from the idea of the black hole. All the parameters related to the geometry of the structure are optimized by the Nelder-Mead algorithm, also, a unique three variable equation for the behavior of the structure is provided, which allows obtaining the possible errors due to the construction based on the geometry of the structure. In addition, the calculated equation leads to saving the simulation time. The proposed sensor has an amplitude sensitivity of 4650 (RIU ^-1) and wavelength sensitivity of 7000 (nm/RIU) and covers a wide range of refractive indices (1.31–1.42) in the bio and chemical range. Because of the amazing options that represent the functionality of the sensor, its construction is highly recommended.