Abstract
In this paper, we explicitly show a complete analysis and detailed calculation of propagation characteristics of the effective refractive indices of the core and cladding for a long period grating employing both the Two-Layer and Three-Layer Geometries. The results are achieved employing graphical solution methods and presented in terms of the effective refractive indices of the core and cladding. Then, we compare the results with OptiGrating (Optiwave Systems Inc., Ottawa, Canada). Finally, we point the best model to evaluate the effective refractive indices, avoiding incorrect designs of the long period gratings.
Highlights
Nowadays, long period gratings (LPGs) has a growing importance in the fields of optical communications and fiber sensors technologies [1,2,3,4]
LPGs couple energy from the fundamental guided mode propagating in the core to different co-propagating symmetric cladding modes
Where is the differential propagation constant, is the grating period, and are the propagation constants for the fundamental and mth cladding modes, respectively. These cladding modes have different propagation characteristics that are dependent upon the host fiber and the refractive index of the external medium [6]
Summary
Long period gratings (LPGs) has a growing importance in the fields of optical communications and fiber sensors technologies [1,2,3,4]. Where is the differential propagation constant, is the grating period, and are the propagation constants for the fundamental and mth cladding modes, respectively These cladding modes have different propagation characteristics that are dependent upon the host fiber and the refractive index of the external medium [6]. The first method, reported by Vengsarkar [9], is the Two-Layer Geometry model, which simplifies the analysis and calculation of the propagation characteristics of the cladding modes by ignoring the effect of the core. The model treats interaction between the fundamental LP01 mode and high-azimutal-order cladding modes with arbitrary azimuthal and radial refractive index variations This method is an excellent choice for the complete analysis of LPGs with different profiles but the graphical method presents less computational costs and can be used for simple LPG geometry applications. We define which geometry model will provide correct results, and avoid erroneous design of the LPGs characteristics
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