A Theoretical-Practical Study On Poles And Zeros Calculated From A Filtered Modulated Function Of An Interference Pattern

In this work, it is reported that the interference pattern produced by an interferometer can be studied on the s-plane and its modulated function having three poles and two zeros over the imaginary axis. This is corroborated theoretically and experimentally using the interference pattern produced by a Fabry- Pcerot interferometer based on Bragg gratings printed on the core of an optical fiber. From our theoretical and experimental work, it is confirmed that the poles and zeros are on the imaginary axis of the s-complex plane and their positions depend on the spatial frequency of the interference pattern. This is graphically displayed on a pole-zero map. In the theoretical analysis, three poles are localized at position s(0) = 0 and s(1,2) = +/-omega(FPi) while two zeros are localized at positions s(1,2) = +/-omega(FP)/root 2 i. In our experiments, using the Fabry-Poerot interferometer whose cavity length is L-FP approximate to 1.58mm, three poles are localized at position s(0) = 0 and s(1,2) = +/- 11.93i rad/nm while two zeros are localized at positions s(1,2) = +/- 11.93/root 2 i rad/nm, confirming the theory.Our proposal finds practical application on signal demodulation for the interferometers and quasi-distributed sensor based on the interferometry.