Resonant Filters Based on Ring Resonator With Multiple π-Phase-Shifted Fiber Bragg Grating

The ring resonator (RR) configuration with single as well as multiple
$\pi \!\!\!$
-phase-shifted fiber Bragg gratings(PSFBG) is mathematically modelled and analyzed using the delay line signal processing approach in Z domain and Mason’s gain formula. The integration of single
$\pi \!\!$
-FBG in a ring results in much sharper linewidth at Bragg wavelength compared to the resonance linewidth of the
$\pi \!\!$
-FBG alone. By proper optimization of grating length, ring length and coupling ratios of the couplers, the transmission spectrum depicts a much narrower spectral width of 62.6 MHz with virtually zero crosstalk. The dependence of the slope and bandwidth of the passband on the ratio of grating section length and grating coupling strength is also analyzed. For RR with double
$\pi \!\!$
-phase-shifted FBG, RR with triple
$\pi \!\!$
-phase-shifted FBG, RR with quadruple
$\pi \!\!$
-phase-shifted FBG and RR with pentuple
$\pi \!\!$
-phase-shifted FBG, the grating section lengths and the phase shift locations need to considered separately and incorporated in the Z domain model. With increasing number of phase-shifts, the resonant bandwidth of the composite structure decreases while the slope increases. The number of channels possible for the ring resonator with pentuple
$\pi $
-phase-shifted FBG (RRPPSFBG) having a spectral width of 15.59 MHz is estimated around 11050. Moreover, theoretical analysis demonstrates that ultra-high resolution weak strain measurement of 44.23 f
$\varepsilon ~\surd $
Hz is easily achievable using the interferometric interrogation of the proposed RRPPSFBG sensor.