<i>Q</i> Factor Enhancement of Open 2D Resonators by Optimal Placement of a Thin Metallic Rod in Front of the Longitudinal Slot
A rigorous approach was employed for the accurate evaluation of the electromagnetic interaction between a thin metallic rod and a two-dimensional (2D) slotted cavity. The problem was posed as a classical boundary value problem for the Helmholtz equation in which a 2D slotted open cavity is bounded b...
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/15/2774 |
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| author | Elena D. Vinogradova Paul D. Smith |
| author_facet | Elena D. Vinogradova Paul D. Smith |
| author_sort | Elena D. Vinogradova |
| collection | DOAJ |
| description | A rigorous approach was employed for the accurate evaluation of the electromagnetic interaction between a thin metallic rod and a two-dimensional (2D) slotted cavity. The problem was posed as a classical boundary value problem for the Helmholtz equation in which a 2D slotted open cavity is bounded by an arbitrary but otherwise smooth contour with a longitudinal slit. Using the <i>method of analytical regularization</i>, the problem was transformed to well-conditioned coupled infinite systems of linear algebraic equations for the Fourier coefficients in the expansions of induced surface currents on the rod and slotted cavity. When truncated to finite size, their solutions exhibit fast convergence to the exact solution as the order is increased. This feature makes it possible to investigate the spectral and scattering characteristics of the coupled cavity and rod to within any desired accuracy. In this paper, the complex eigenvalues for a slotted cavity in the presence of a thin rod and the dependence upon their relative location were investigated, particularly to find where there is significant or optimal enhancement of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>Q</mi></semantics></math></inline-formula> factor. Such optimisation may be exploited in the design of advanced slot antennas and slotted waveguides. |
| first_indexed | 2024-03-09T05:11:44Z |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:11:44Z |
| publishDate | 2022-08-01 |
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| spelling | doaj.art-25b64ffa48084c78bbd1da7f5efc88d52023-12-03T12:48:30ZengMDPI AGMathematics2227-73902022-08-011015277410.3390/math10152774<i>Q</i> Factor Enhancement of Open 2D Resonators by Optimal Placement of a Thin Metallic Rod in Front of the Longitudinal SlotElena D. Vinogradova0Paul D. Smith1School of Mathematical and Physical Sciences, Macquarie University, Sydney 2109, AustraliaSchool of Mathematical and Physical Sciences, Macquarie University, Sydney 2109, AustraliaA rigorous approach was employed for the accurate evaluation of the electromagnetic interaction between a thin metallic rod and a two-dimensional (2D) slotted cavity. The problem was posed as a classical boundary value problem for the Helmholtz equation in which a 2D slotted open cavity is bounded by an arbitrary but otherwise smooth contour with a longitudinal slit. Using the <i>method of analytical regularization</i>, the problem was transformed to well-conditioned coupled infinite systems of linear algebraic equations for the Fourier coefficients in the expansions of induced surface currents on the rod and slotted cavity. When truncated to finite size, their solutions exhibit fast convergence to the exact solution as the order is increased. This feature makes it possible to investigate the spectral and scattering characteristics of the coupled cavity and rod to within any desired accuracy. In this paper, the complex eigenvalues for a slotted cavity in the presence of a thin rod and the dependence upon their relative location were investigated, particularly to find where there is significant or optimal enhancement of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>Q</mi></semantics></math></inline-formula> factor. Such optimisation may be exploited in the design of advanced slot antennas and slotted waveguides.https://www.mdpi.com/2227-7390/10/15/2774open cylindrical cavities in presence of the wiresrigorous method of analytical regularization solutioncomplex <i>TM</i> oscillationscomplex eigenvaluesenhancement of the <i>Q</i> factor |
| spellingShingle | Elena D. Vinogradova Paul D. Smith <i>Q</i> Factor Enhancement of Open 2D Resonators by Optimal Placement of a Thin Metallic Rod in Front of the Longitudinal Slot Mathematics open cylindrical cavities in presence of the wires rigorous method of analytical regularization solution complex <i>TM</i> oscillations complex eigenvalues enhancement of the <i>Q</i> factor |
| title | <i>Q</i> Factor Enhancement of Open 2D Resonators by Optimal Placement of a Thin Metallic Rod in Front of the Longitudinal Slot |
| title_full | <i>Q</i> Factor Enhancement of Open 2D Resonators by Optimal Placement of a Thin Metallic Rod in Front of the Longitudinal Slot |
| title_fullStr | <i>Q</i> Factor Enhancement of Open 2D Resonators by Optimal Placement of a Thin Metallic Rod in Front of the Longitudinal Slot |
| title_full_unstemmed | <i>Q</i> Factor Enhancement of Open 2D Resonators by Optimal Placement of a Thin Metallic Rod in Front of the Longitudinal Slot |
| title_short | <i>Q</i> Factor Enhancement of Open 2D Resonators by Optimal Placement of a Thin Metallic Rod in Front of the Longitudinal Slot |
| title_sort | i q i factor enhancement of open 2d resonators by optimal placement of a thin metallic rod in front of the longitudinal slot |
| topic | open cylindrical cavities in presence of the wires rigorous method of analytical regularization solution complex <i>TM</i> oscillations complex eigenvalues enhancement of the <i>Q</i> factor |
| url | https://www.mdpi.com/2227-7390/10/15/2774 |
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