Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer Waveguides
This paper describes the algorithm for the numerical solution of the diffraction problem of waveguide modes at the joint of two open planar waveguides. For planar structures under consideration, we can formulate a scalar diffraction problem, which is a boundary value problem for the Helmholtz equati...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2018-01-01
|
| Series: | MATEC Web of Conferences |
| Online Access: | https://doi.org/10.1051/matecconf/201818601010 |
| _version_ | 1818645549608337408 |
|---|---|
| author | Divakov Dmitriy Tiutiunnik Anastasiia Sevastianov Anton |
| author_facet | Divakov Dmitriy Tiutiunnik Anastasiia Sevastianov Anton |
| author_sort | Divakov Dmitriy |
| collection | DOAJ |
| description | This paper describes the algorithm for the numerical solution of the diffraction problem of waveguide modes at the joint of two open planar waveguides. For planar structures under consideration, we can formulate a scalar diffraction problem, which is a boundary value problem for the Helmholtz equation with a variable coefficient in two-dimensional space. The eigenmode problem for an open three-layer waveguide is the Sturm-Liouville problem for a second-order operator with piecewise constant potential on the axis, where the potential is proportional to the refractive index. The described problem is singular and has a mixed spectrum and therefore the Galerkin method can not be used in this definition. One way to adapt the Galerkin method for the problem solution is to artificially limit the area, which is equivalent to placing the open waveguide in question in a hollow closed waveguide whose boundaries are remote from the real boundaries of the waveguide layer of the open waveguide. Thus, we obtain a diffraction problem on a finite interval and with a discrete spectrum, which can be solved by the projection method, as done in this paper. |
| first_indexed | 2024-12-17T00:32:31Z |
| format | Article |
| id | doaj.art-9467cd29ab84462e80b52f592b8e5cea |
| institution | Directory Open Access Journal |
| issn | 2261-236X |
| language | English |
| last_indexed | 2024-12-17T00:32:31Z |
| publishDate | 2018-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | MATEC Web of Conferences |
| spelling | doaj.art-9467cd29ab84462e80b52f592b8e5cea2022-12-21T22:10:14ZengEDP SciencesMATEC Web of Conferences2261-236X2018-01-011860101010.1051/matecconf/201818601010matecconf_icemp2018_01010Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer WaveguidesDivakov DmitriyTiutiunnik AnastasiiaSevastianov AntonThis paper describes the algorithm for the numerical solution of the diffraction problem of waveguide modes at the joint of two open planar waveguides. For planar structures under consideration, we can formulate a scalar diffraction problem, which is a boundary value problem for the Helmholtz equation with a variable coefficient in two-dimensional space. The eigenmode problem for an open three-layer waveguide is the Sturm-Liouville problem for a second-order operator with piecewise constant potential on the axis, where the potential is proportional to the refractive index. The described problem is singular and has a mixed spectrum and therefore the Galerkin method can not be used in this definition. One way to adapt the Galerkin method for the problem solution is to artificially limit the area, which is equivalent to placing the open waveguide in question in a hollow closed waveguide whose boundaries are remote from the real boundaries of the waveguide layer of the open waveguide. Thus, we obtain a diffraction problem on a finite interval and with a discrete spectrum, which can be solved by the projection method, as done in this paper.https://doi.org/10.1051/matecconf/201818601010 |
| spellingShingle | Divakov Dmitriy Tiutiunnik Anastasiia Sevastianov Anton Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer Waveguides MATEC Web of Conferences |
| title | Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer Waveguides |
| title_full | Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer Waveguides |
| title_fullStr | Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer Waveguides |
| title_full_unstemmed | Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer Waveguides |
| title_short | Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer Waveguides |
| title_sort | algorithm for numerical solution of diffraction problem on the joint of two open three layer waveguides |
| url | https://doi.org/10.1051/matecconf/201818601010 |
| work_keys_str_mv | AT divakovdmitriy algorithmfornumericalsolutionofdiffractionproblemonthejointoftwoopenthreelayerwaveguides AT tiutiunnikanastasiia algorithmfornumericalsolutionofdiffractionproblemonthejointoftwoopenthreelayerwaveguides AT sevastianovanton algorithmfornumericalsolutionofdiffractionproblemonthejointoftwoopenthreelayerwaveguides |