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High index contrast integrated optics in the cylindrical coordinate

Recently the developments of high contrast optics, such as high contrast grating (HCG), have attracted much attention. Much of the existing work has been focused on structures that can be characterized as ‘Cartesian’, i.e., which are easily described by functions that are separable in the Cartesian coordinates. Yet optical fields with cylindrical rather than Cartesian symmetries, such as Laguerre-Gaussian (LG) modes and their relatives including both the scalar LG modes and cylindrical vectorial (CV) modes, can be more efficiently manipulated by high contrast structures that have the same kind of cylindrical symmetries, hence best described in a polar or cylindrical coordinate. An example of such a structure is the angular grating based silicon photonics micro-ring optical vortex emitter device we reported. An efficient treatment of cylindrical high contrast structures requires the decomposition of Fourier components of both the field and the structure in the cylindrical coordinates, so that the coupling process between the field Fourier components via the structure can be calculated. We have implemented a semi-analytical model that fully describes the 3D vectorial coupling process using a transverse spatial Fourier analysis in the cylindrical space. This model can deal with HCG structures in cylindrical coordinates with high precision and fast speed, enabling rapid yet accurate simulation of the coupling of planar waveguide modes with optical vortex modes carrying photonic orbital angular momenta and allowing optimization of the emission coefficient and emitted beam quality. The details of the method and optimized silicon photonics integrated OAM emitter devices will be presented.