Finite Element Simulation Of Special Waveguides Transmission

In recent years,in order to operate light in higer degree of freedom,more and more special waveguides have been made.However,some finite element algorithms are still limited to Hermitian systems,such as port boundary conditions.This makes us encounter many inconveniences when simulating the transmission properties of non-Hermitian systems.In addition,there is currently no effective algorithm for calculating waveguides based on bianisotropic materials.This also hinders the development of bianisotropic materials.The finite element algorithm is a very powerful numerical calculation method that can be used to calculate huge,irregular physical models.With the substantial improvement of computer computing power,finite element algorithms are also widely used in various fields,especially optics.Therefore,in order to solve above two problems,this paper uses the finite element algorithm to give the solutions.The first work of this article is to implement non-Hermitian ports.In non-Hermitian systems,the field distribution and S-parameters obtained using the Hermitian port boundary conditions are still incorrect.Therefore,we first restore the orthogonality of the modes in the non-Hermitian system by defining a new inner product,the bi-orthogonal inner product.Then based on the finite element algorithm,the non-Hermitian port boundary conditions are proposed to obtain S parameters.Finally,the symmetry and the robustness of S parameters and quasi-energy conservation prove the correctness of our simulation results.The second work of this paper is to calculate the eigenmode of the bianisotropic waveguide.First,we derive the equation of the eigenvalue problem of the dual anisotropic waveguide.Then the finite element method is used to test the equation to obtain its weak form.Using the weak form,the mathematical form of the most critical global matrix is derived,and the integral is calculated using the Jacobian transform to obtain the numerical global matrix.Finally,the procedure to calculate the second eigenvalue problem is utilized to calculate effective refractive index and mode.