Modeling and analysis of an extrinsic Fabry-Perot interferometer performance using MATLAB

In this paper block diagram representation of optical feedback between two resonator mirrors suffering a phase shift in each round trip during propagation depending on the separation is studied and transfer function model of the loss less Fabry-parot cavity(EFPI) is developed in S-domain. An extrinsic Fabry-Perot interferometer with perfectly parallel surface between the cavity shows efficient interference [1-3]. Block diagram model of the interferometer is determined using the proposed transfer function model of the Fabry -parot cavity. Frequency response analysis was carried out in MATLAB environment of the developed model to explains the behavior of the interferometer. Nyquist stability criterion is employed to analyse the behavior of the interferometer considering the conditions, (i) two surfaces are perfectly parallel in the cavity and (ii) with some tilt angle of the second mirror in the cavity. The results indicates efficient interference in case (i) and restricted interference occurs for case (ii). To explain the case (ii) a new parameter is introduced. An attempt is made to analyse the stability of resonant interference pattern with a slight tilt in one of the mirror. The analysis indicates that reflection from two slightly tilt surface may be used to form a Fabry-Parot cavity with certain restrictions. Modified modes in the cavity is characterized with real positive multiplier(‘p’). Analysis reveled stable solutions at some discrete values of 'p' and the cavity is very much sensitive to variation of 'p' value .