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A full‐vectorial mode solver in terms of the transverse‐magnetic field components for bending waveguides with curved dielectric interfaces is developed by using multidomain pseudospectral method based on the Chebyshev polynomials basis functions. A curvilinear coordinate transformation is used to map a subdomain with curved boundary onto a unit square. The perfectly matched layers absorption boundary conditions are incorporated into the present method for effectively demonstrating the leaky nature of the bending waveguides. A bending step‐index optical fibre with high index contrast is considered as a numerical example to validate the established method. [ABSTRACT FROM AUTHOR]