Extension of an FFT-Based Beam Propagation Method to Plasmonic and Dielectric Waveguide Discontinuities and Junctions
We adapted a fast Fourier transform-based Beam Propagation Method (FFT-BPM) to investigate waveguide discontinuities in plasmonic waveguides. The adaptation of the FFT-BPM to treat transverse magnetic (TM) fields requires the circumvention of two major difficulties: the mixed derivatives of the magn...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-10-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/9/20/4362 |
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| author | Adel Shaaban Yi-Chun Du Lotfy Rabeh Gomaa |
| author_facet | Adel Shaaban Yi-Chun Du Lotfy Rabeh Gomaa |
| author_sort | Adel Shaaban |
| collection | DOAJ |
| description | We adapted a fast Fourier transform-based Beam Propagation Method (FFT-BPM) to investigate waveguide discontinuities in plasmonic waveguides. The adaptation of the FFT-BPM to treat transverse magnetic (TM) fields requires the circumvention of two major difficulties: the mixed derivatives of the magnetic field and waveguide refractive index profile in the TM wave equation and the step-like index change at the transverse metal-dielectric boundary of the plasmonic guide and the transverse boundaries of the dielectric waveguide as well. An equivalent-index method is adopted to transform TM fields to transverse electric (TE) ones, thus enabling the benefit of the full power and simplicity of the FFT-BPM. Moreover, an appropriate smoothing function is used to approximate the step-like refractive index profile in the transverse direction. At the junction plane, we used an accurate combined spatial-spectral reflection operator to calculate the reflected field. To validate our proposed scheme, we investigated the modal propagation in a silicon waveguide terminated by air (like a laser facet in two cases: with and without a coating layer). Then we considered a subwavelength plasmonic waveguide (metal-insulator-metal MIM) butt-coupled with a dielectric waveguide, where the power transmission efficiency has been calculated and compared with other numerical methods. The comparison reveals good agreement. |
| first_indexed | 2024-12-10T05:32:37Z |
| format | Article |
| id | doaj.art-331cf1673cff42d1a28d08b91dc3a559 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-12-10T05:32:37Z |
| publishDate | 2019-10-01 |
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| record_format | Article |
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| spelling | doaj.art-331cf1673cff42d1a28d08b91dc3a5592022-12-22T02:00:30ZengMDPI AGApplied Sciences2076-34172019-10-01920436210.3390/app9204362app9204362Extension of an FFT-Based Beam Propagation Method to Plasmonic and Dielectric Waveguide Discontinuities and JunctionsAdel Shaaban0Yi-Chun Du1Lotfy Rabeh Gomaa2Department of Electrical Engineering, Southern Taiwan University of Science and Technology, Tainan 71005, TaiwanDepartment of Electrical Engineering, Southern Taiwan University of Science and Technology, Tainan 71005, TaiwanFaculty of Engineering at Shobra, Banha University, Cairo 11672, EgyptWe adapted a fast Fourier transform-based Beam Propagation Method (FFT-BPM) to investigate waveguide discontinuities in plasmonic waveguides. The adaptation of the FFT-BPM to treat transverse magnetic (TM) fields requires the circumvention of two major difficulties: the mixed derivatives of the magnetic field and waveguide refractive index profile in the TM wave equation and the step-like index change at the transverse metal-dielectric boundary of the plasmonic guide and the transverse boundaries of the dielectric waveguide as well. An equivalent-index method is adopted to transform TM fields to transverse electric (TE) ones, thus enabling the benefit of the full power and simplicity of the FFT-BPM. Moreover, an appropriate smoothing function is used to approximate the step-like refractive index profile in the transverse direction. At the junction plane, we used an accurate combined spatial-spectral reflection operator to calculate the reflected field. To validate our proposed scheme, we investigated the modal propagation in a silicon waveguide terminated by air (like a laser facet in two cases: with and without a coating layer). Then we considered a subwavelength plasmonic waveguide (metal-insulator-metal MIM) butt-coupled with a dielectric waveguide, where the power transmission efficiency has been calculated and compared with other numerical methods. The comparison reveals good agreement.https://www.mdpi.com/2076-3417/9/20/4362plasmonicsphotonicsbi-directional bpmoptical propagationtm fieldsfft-bpmplasmonic waveguidebutt-couplersensorsreflection formalism |
| spellingShingle | Adel Shaaban Yi-Chun Du Lotfy Rabeh Gomaa Extension of an FFT-Based Beam Propagation Method to Plasmonic and Dielectric Waveguide Discontinuities and Junctions Applied Sciences plasmonics photonics bi-directional bpm optical propagation tm fields fft-bpm plasmonic waveguide butt-coupler sensors reflection formalism |
| title | Extension of an FFT-Based Beam Propagation Method to Plasmonic and Dielectric Waveguide Discontinuities and Junctions |
| title_full | Extension of an FFT-Based Beam Propagation Method to Plasmonic and Dielectric Waveguide Discontinuities and Junctions |
| title_fullStr | Extension of an FFT-Based Beam Propagation Method to Plasmonic and Dielectric Waveguide Discontinuities and Junctions |
| title_full_unstemmed | Extension of an FFT-Based Beam Propagation Method to Plasmonic and Dielectric Waveguide Discontinuities and Junctions |
| title_short | Extension of an FFT-Based Beam Propagation Method to Plasmonic and Dielectric Waveguide Discontinuities and Junctions |
| title_sort | extension of an fft based beam propagation method to plasmonic and dielectric waveguide discontinuities and junctions |
| topic | plasmonics photonics bi-directional bpm optical propagation tm fields fft-bpm plasmonic waveguide butt-coupler sensors reflection formalism |
| url | https://www.mdpi.com/2076-3417/9/20/4362 |
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