Fano Resonanace Characterization in Ring $\pi$ -Shift Fiber Bragg Gratings Biosensors. Modeling Results

The work presents a solution to the problem of Fano resonant contour characterization in optical biosensors of refractometric type based on ring fiber Bragg gratings with $\pi$: -shift. To solve this problem a microwave-photonic method of three-frequency probing of an ultra-narrowband asymmetric Fano contour using symmetrical amplitude-modulated radiation with amplitude-unbalanced sideband components was proposed. In order to characterize the central wavelength, a functional was introduced, which is similar to the modulation index of the beating envelope between the components of the probing radiation. The paper gives the requirements for the sideband frequencies selection so that the unambiguity of the functional is maintained and the maximum sensitivity is achieved in the measurement range, which is defined by the bandwidth of a Fano contour at half-maximum. The paper demonstrates the possibility of expanding the range of sidebands and increasing measurement sensitivity using dual-frequency probing with halved frequency amplitude-unbalanced sidebands and suppressed carrier. The proposed method is compared with the previously applied microwave-photonic solution of two-frequency symmetric probing with equal amplitudes of the sidebands and the suppressed carrier. Using the results of the Fano contour characterization, it is possible to explicitly determine the central frequency, maximum amplitude and its quality factor.