General formulae of designing novel photonic digital sensors with arbitrary levels of directional couplers for testing liquids

Abstract

High sensitivity and rapid detecting photonic sensors are essential devices such as in medical diagnostics and biological test. Conventional biochemical sensors based on the directional couplers need other apparatus to measure the precise output power intensities. Conversely, a digital sensor is more efficiently utilized to determine the refractive index of the liquid sample. By simple mathematics induction, the formulae of designing a general photonic digital sensor, which comprises k (k ≥ 1) levels of the directional couplers composed of the ridge waveguides, are obtained in this paper. The performance of the sensor resembles an analog-to-digital converter and distinguishes 2k liquid samples. As long as k is large enough, the sensor can lower the quantization error and precisely determine the refractive index of the liquid sample. To demonstrate the validity of our formulae and design rules, we present the beam propagation method simulation results in this paper.