Abstract
We present numerical modeling based on a combination of the Bidirectional Beam Propagation Method and Finite Element Method that completely describes the wavelength spectra of point by point femtosecond laser inscribed fiber Bragg gratings, showing excellent agreement with experiment. We have investigated the dependence of different spectral parameters such as insertion loss, all dominant cladding and ghost modes and their shape relative to the position of the fiber Bragg grating in the core of the fiber. Our model is validated by comparing model predictions with experimental data and allows for predictive modeling of the gratings. We expand our analysis to more complicated structures, where we introduce symmetry breaking; this highlights the importance of centered gratings and how maintaining symmetry contributes to the overall spectral quality of the inscribed Bragg gratings. Finally, the numerical modeling is applied to superstructure gratings and a comparison with experimental results reveals a capability for dealing with complex grating structures that can be designed with particular wavelength characteristics.
Highlights
The development of fiber Bragg grating (FBG) inscription using femtosecond lasers has resulted in two key approaches: the interferometric or phase mask method [1] and point-bypoint (PbP) inscription [2,3,4,5]
This local confinement of the index change can be a drawback, as a small lateral shift of the focal point can displace the inscribed grating from the fiber axis, resulting in symmetry breaking and changing the grating spectrum in strength and shape
As a result of our initial study we conclude that finite element method (FEM) has improved accuracy on the effective refractive indices calculation compared to the beam propagation method (BPM)
Summary
The development of fiber Bragg grating (FBG) inscription using femtosecond lasers has resulted in two key approaches: the interferometric or phase mask method [1] and point-bypoint (PbP) inscription [2,3,4,5]. The PbP method is an innovative and flexible way of modifying the filtering properties of optical fibers, the nature of the non-linear interaction of the light and material unavoidably results in refractive index changes that are confined to the laser beam focus volume. This local confinement of the index change can be a drawback, as a small lateral shift of the focal point can displace the inscribed grating from the fiber axis, resulting in symmetry breaking and changing the grating spectrum in strength and shape. We note the strong convergence of the analysis with experimental results allowing us to accurately reproduce the physical parameters of the inscribed grating, such as the spatial extent and strength of the refractive index modulation, the grating length, its displacement from the core center and whether there is any device tilt
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