3D simulation of hybrid Fabry-Pérot for single mode fibre

Abstract

3D modal simulation of Hybrid Fabry Pérot (H-FP) consisting of a Bragg grating (Bg) and a multilayer mirror between single-mode optical fibres shows that diffraction in their multilayer is negligible, but that multimode 3D S-matrix calculation is essential in the multilayer to determine the adequate thickness of the interface layer with the Bg. The single-mode approximation made in 1D calculation is justified for their sinusoidal profile Bg, but is not at the top of the transmission peak for their high step profile Bg. The study of manufacturing constraints shows that feasible H-FPs, with rejection broad of several hundred nanometers, provide access to bandpass widths as low as 15 fm, but that the control of the bandwidth shift remains delicate for the realization of large series. The principle of H-FP with a high refraction index step reflector and a low step one is also valid for integrated optics. All weak spectral oscillations in the rejection band of H-FPs have been interpreted. Finally, the simulation of H-FPs with Interleaved Fibre (IF) between their 2 mirrors makes it possible to deduce also for H-FPs without IF and for some of their properties a quantitative model of equivalent cavity filled with homogeneous medium and with localized mirrors equidistant by a fraction of the length of the Bg depending only on its reflection coefficient. This equivalent cavity is used to evaluate the line width. This model also applies to 2 Bg-FPs without IF with a double length of the equivalent cavity for the same grating.

Keywords

• Narrow bandpass filter
• Optical fibre
• Integrated optics
• Modal simulation
• S Matrix