An analytical approach is presented to comprehensively describe a meticulously designed gold nanoarray situated on a silicon waveguide(length (L) and width(W) are 12 µm and 3 µm). The incorporation of a glass substrate with an L and W of 12 µm is proposed as a means to achieve broadband focusing. At the same time, a demultiplexing element utilizing surface plasmon polariton (SPP) waves is introduced, employing a novel phase modulation method that uses in-plane diffraction processes. The analytical calculations are focused on the sublattice arrays, which are currently under investigation to enhance the performance of demultiplexers and confocal SPP beams. The suggested method exhibits various functionalities that make it a promising approach. Its planar construction ensures a streamlined and integrated design, and the absence of SPP coupling processes adds to its practicality for implementation in photonic integrations. By leveraging the unique properties of the gold nanoarray on the silicon waveguide, combined with the glass substrate for broadband focusing and the novel phase modulation method for demultiplexing SPP waves, this approach holds great potential for advancing the field of photonics.
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