Experimental Demonstration of the Effect of Magnetic Polaritons on the Radiative Properties of Deep Aluminum Gratings

Yang, Peiyan; Ye, Hong; Zhang, Zhuomin M.

doi:10.1115/1.4042698

Title: Experimental Demonstration of the Effect of Magnetic Polaritons on the Radiative Properties of Deep Aluminum Gratings

Abstract

Despite the abundant theoretical studies of magnetic polaritons (MPs) in tailoring the radiative properties of nanostructures, experimental investigation of MPs in deep metal gratings is still lacking. This work experimentally demonstrates the excitation of MP from several microfabricated aluminum gratings in the mid-infrared region by measuring the specular reflectance (zeroth-order diffraction) of the specimen using a Fourier-transform infrared (FTIR) spectrometer. The rigorous coupled-wave analysis (RCWA) and an LC-circuit model are employed to elucidate the mechanism of various resonant modes and their coupling effect. The influence of incidence angle, plane of incidence, polarization, and the trench depth on the spectral reflectance is also discussed. Moreover, the MP dispersion for off-plane layout has been investigated and demonstrated for the first time. Finally, the insight gained from this work may facilitate future design and applications of subwavelength periodic structures with desired radiative properties.

Authors:

Yang, Peiyan ^[1]; Ye, Hong ^[2]; Zhang, Zhuomin M. ^[1]

Georgia Inst. of Technology, Atlanta, GA (United States)
Univ. of Science and Technology of China, Hefei (China)

Publication Date:: Wed Mar 27 00:00:00 EDT 2019

Research Org.:: Georgia Institute of Technology, Atlanta, GA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); National Science Foundation of China

OSTI Identifier:: 1594775

Grant/Contract Number:: SC0018369; CBET-1603761; 51576188

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Heat Transfer

Additional Journal Information:: Journal Volume: 141; Journal Issue: 5; Journal ID: ISSN 0022-1481

Publisher:: ASME

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; deep gratings; FTIR; magnetic polariton; radiative properties

Citation Formats


                    Yang, Peiyan, Ye, Hong, and Zhang, Zhuomin M. Experimental Demonstration of the Effect of Magnetic Polaritons on the Radiative Properties of Deep Aluminum Gratings.  United States: N. p., 2019. 
Web.  doi:10.1115/1.4042698.

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                    Yang, Peiyan, Ye, Hong, & Zhang, Zhuomin M. Experimental Demonstration of the Effect of Magnetic Polaritons on the Radiative Properties of Deep Aluminum Gratings.  United States.  https://doi.org/10.1115/1.4042698

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                    Yang, Peiyan, Ye, Hong, and Zhang, Zhuomin M. Wed .  
"Experimental Demonstration of the Effect of Magnetic Polaritons on the Radiative Properties of Deep Aluminum Gratings".  United States.  https://doi.org/10.1115/1.4042698.  https://www.osti.gov/servlets/purl/1594775.

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@article{osti_1594775,

  title        = {Experimental Demonstration of the Effect of Magnetic Polaritons on the Radiative Properties of Deep Aluminum Gratings},

  author       = {Yang, Peiyan and Ye, Hong and Zhang, Zhuomin M.},

  abstractNote = {Despite the abundant theoretical studies of magnetic polaritons (MPs) in tailoring the radiative properties of nanostructures, experimental investigation of MPs in deep metal gratings is still lacking. This work experimentally demonstrates the excitation of MP from several microfabricated aluminum gratings in the mid-infrared region by measuring the specular reflectance (zeroth-order diffraction) of the specimen using a Fourier-transform infrared (FTIR) spectrometer. The rigorous coupled-wave analysis (RCWA) and an LC-circuit model are employed to elucidate the mechanism of various resonant modes and their coupling effect. The influence of incidence angle, plane of incidence, polarization, and the trench depth on the spectral reflectance is also discussed. Moreover, the MP dispersion for off-plane layout has been investigated and demonstrated for the first time. Finally, the insight gained from this work may facilitate future design and applications of subwavelength periodic structures with desired radiative properties.},

  doi          = {10.1115/1.4042698},

  journal      = {Journal of Heat Transfer},

  number       = 5,

  volume       = 141,

  place        = {United States},

  year         = {Wed Mar 27 00:00:00 EDT 2019},

  month        = {Wed Mar 27 00:00:00 EDT 2019}

}

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Works referenced in this record:

Resonance enhanced absorption in a graphene monolayer using deep metal gratings
journal, January 2015

Zhao, B.; Zhao, J. M.; Zhang, Z. M.
Journal of the Optical Society of America B, Vol. 32, Issue 6
DOI: 10.1364/JOSAB.32.001176

Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film
journal, January 2008

Lee, B. J.; Wang, L. P.; Zhang, Z. M.
Optics Express, Vol. 16, Issue 15
DOI: 10.1364/OE.16.011328

Blocking-assisted infrared transmission of subwavelength metallic gratings by graphene
journal, February 2015

Liu, X. L.; Zhao, B.; Zhang, Z. M.
Journal of Optics, Vol. 17, Issue 3
DOI: 10.1088/2040-8978/17/3/035004

Resonance transmission or absorption in deep gratings explained by magnetic polaritons
journal, September 2009

Wang, L. P.; Zhang, Z. M.
Applied Physics Letters, Vol. 95, Issue 11
DOI: 10.1063/1.3226661

Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model
journal, December 2014

Sakurai, Atsushi; Zhao, Bo; Zhang, Zhuomin M.
Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 149
DOI: 10.1016/j.jqsrt.2014.07.024

Anisotropic Polarized Emission of a Doped Silicon Lamellar Grating
journal, June 2006

Marquier, F.; Laroche, M.; Carminati, R.
Journal of Heat Transfer, Vol. 129, Issue 1
DOI: 10.1115/1.2360594

Design of tungsten complex gratings for thermophotovoltaic radiators
journal, January 2007

Chen, Y. -B.; Zhang, Z. M.
Optics Communications, Vol. 269, Issue 2
DOI: 10.1016/j.optcom.2006.08.040

Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure
journal, December 2013

Zhao, Bo; Wang, Liping; Shuai, Yong
International Journal of Heat and Mass Transfer, Vol. 67
DOI: 10.1016/j.ijheatmasstransfer.2013.08.047

Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators
journal, January 2009

Liu, H.; Li, T.; Wang, Q. J.
Physical Review B, Vol. 79, Issue 2
DOI: 10.1103/PhysRevB.79.024304

Taming the thermal emissivity of metals: A metamaterial approach
journal, May 2012

Mattiucci, N.; D’Aguanno, G.; Alù, A.
Applied Physics Letters, Vol. 100, Issue 20
DOI: 10.1063/1.4719582

Spatial and temporal coherence of thermal radiation in asymmetric Fabry–Perot resonance cavities
journal, June 2009

Wang, L. P.; Lee, B. J.; Wang, X. J.
International Journal of Heat and Mass Transfer, Vol. 52, Issue 13-14
DOI: 10.1016/j.ijheatmasstransfer.2009.01.042

Narrow-Band Thermal Radiation with Low Directivity by Resonant Modes inside Tungsten Microcavities
journal, August 2004

Kusunoki, Fuminori; Kohama, Tatsuro; Hiroshima, Takeshi
Japanese Journal of Applied Physics, Vol. 43, Issue 8A
DOI: 10.1143/JJAP.43.5253

Measurement of Coherent Thermal Emission Due to Magnetic Polaritons in Subwavelength Microstructures
journal, July 2013

Wang, L. P.; Zhang, Z. M.
Journal of Heat Transfer, Vol. 135, Issue 9
DOI: 10.1115/1.4024469

Unifying approach to left-handed material design
journal, January 2006

Zhou, Jiangfeng; Economon, Eleftherios N.; Koschny, Thomas
Optics Letters, Vol. 31, Issue 24
DOI: 10.1364/OL.31.003620

Narrow-band spectral features of structured silver surface with rectangular resonant cavities
journal, March 2011

Huang, Jinguo; Xuan, Yimin; Li, Qiang
Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 112, Issue 5
DOI: 10.1016/j.jqsrt.2010.11.007

Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings
journal, January 1995

Moharam, M. G.; Gaylord, T. K.; Grann, Eric B.
Journal of the Optical Society of America A, Vol. 12, Issue 5
DOI: 10.1364/JOSAA.12.001068

Coupling between gap plasmon polariton and magnetic polariton in a metallic-dielectric multilayer structure
journal, August 2011

Chen, Junxue; Wang, Pei; Zhang, Zhuomin M.
Physical Review E, Vol. 84, Issue 2
DOI: 10.1103/PhysRevE.84.026603

Optical Constants of the Noble Metals
journal, December 1972

Johnson, P. B.; Christy, R. W.
Physical Review B, Vol. 6, Issue 12, p. 4370-4379
DOI: 10.1103/PhysRevB.6.4370

Magnetic Response of Metamaterials at 100 Terahertz
journal, November 2004

Linden, Stefan; Enkrich, Christian; Wegener, Martin
Science, Vol. 306, Issue 5700, p. 1351-1353
DOI: 10.1126/science.1105371

Transparent Metals for Ultrabroadband Electromagnetic Waves
journal, March 2012

Fan, Ren-Hao; Peng, Ru-Wen; Huang, Xian-Rong
Advanced Materials, Vol. 24, Issue 15
DOI: 10.1002/adma.201104483

Strong Plasmonic Coupling between Graphene Ribbon Array and Metal Gratings
journal, October 2015

Zhao, Bo; Zhang, Zhuomin M.
ACS Photonics, Vol. 2, Issue 11
DOI: 10.1021/acsphotonics.5b00410

Magnetism from conductors and enhanced nonlinear phenomena
journal, January 1999

Pendry, J. B.; Holden, A. J.; Robbins, D. J.
IEEE Transactions on Microwave Theory and Techniques, Vol. 47, Issue 11, p. 2075-2084
DOI: 10.1109/22.798002

Study of magnetic polaritons in deep gratings for thermal emission control
journal, March 2014

Zhao, Bo; Zhang, Zhuomin M.
Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 135
DOI: 10.1016/j.jqsrt.2013.11.016

Wavelength-selective and diffuse emitter enhanced by magnetic polaritons for thermophotovoltaics
journal, February 2012

Wang, L. P.; Zhang, Z. M.
Applied Physics Letters, Vol. 100, Issue 6
DOI: 10.1063/1.3684874

Terahertz Magnetic Response from Artificial Materials
journal, March 2004

Yen, T. J.
Science, Vol. 303, Issue 5663
DOI: 10.1126/science.1094025

Experimental Verification of a Negative Index of Refraction
journal, April 2001

Shelby, R. A.; Smith, D. R.; Schultz, S.
Science, Vol. 292, Issue 5514, p. 77-79
DOI: 10.1126/science.1058847

Organ pipe radiant modes of periodic micromachined silicon surfaces
journal, December 1986

Hesketh, Peter J.; Zemel, Jay N.; Gebhart, Benjamin
Nature, Vol. 324, Issue 6097
DOI: 10.1038/324549a0

Metamaterial Electromagnetic Cloak at Microwave Frequencies
journal, November 2006

Schurig, D.; Mock, J. J.; Justice, B. J.
Science, Vol. 314, Issue 5801
DOI: 10.1126/science.1133628

Perfect mid-infrared absorption by hybrid phonon-plasmon polaritons in hBN/metal-grating anisotropic structures
journal, March 2017

Zhao, Bo; Zhang, Zhuomin M.
International Journal of Heat and Mass Transfer, Vol. 106
DOI: 10.1016/j.ijheatmasstransfer.2016.10.074

Transmission Enhancement Through Nanoscale Metallic Slit Arrays from the Visible to Mid-Infrared
journal, February 2008

Lee, B. J.; Chen, Y. -B.; Zhang, Z. M.
Journal of Computational and Theoretical Nanoscience, Vol. 5, Issue 2
DOI: 10.1166/jctn.2008.2461

Thermal radiation from two-dimensionally confined modes in microcavities
journal, August 2001

Maruyama, S.; Kashiwa, T.; Yugami, H.
Applied Physics Letters, Vol. 79, Issue 9
DOI: 10.1063/1.1397759

Circuits with Light at Nanoscales: Optical Nanocircuits Inspired by Metamaterials
journal, September 2007

Engheta, N.
Science, Vol. 317, Issue 5845
DOI: 10.1126/science.1133268

Flatness and boundness of photonic drumhead surface state in a metallic lattice
journal, April 2021

Wang, Yu; Zhou, Xiaoxi; Li, Shanshan
Scientific Reports, Vol. 11, Issue 1
DOI: 10.1038/s41598-021-88004-1

Magnetic Response of Metamaterials at 100 Terahertz
text, January 2004

Linden, S.; Enkrich, C.; Wegener, M.
Karlsruhe
DOI: 10.5445/ir/1000010922

A unifying approach to left handed material design
text, January 2006

Zhou, Jiangfeng; Economon, Eleftherios N.; Koschny, Thomas
arXiv
DOI: 10.48550/arxiv.physics/0609207

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Title: Experimental Demonstration of the Effect of Magnetic Polaritons on the Radiative Properties of Deep Aluminum Gratings

Abstract

Citation Formats

Resonance enhanced absorption in a graphene monolayer using deep metal gratings journal, January 2015

Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film journal, January 2008

Blocking-assisted infrared transmission of subwavelength metallic gratings by graphene journal, February 2015

Resonance transmission or absorption in deep gratings explained by magnetic polaritons journal, September 2009

Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model journal, December 2014

Anisotropic Polarized Emission of a Doped Silicon Lamellar Grating journal, June 2006

Design of tungsten complex gratings for thermophotovoltaic radiators journal, January 2007

Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure journal, December 2013

Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators journal, January 2009

Taming the thermal emissivity of metals: A metamaterial approach journal, May 2012

Spatial and temporal coherence of thermal radiation in asymmetric Fabry–Perot resonance cavities journal, June 2009

Narrow-Band Thermal Radiation with Low Directivity by Resonant Modes inside Tungsten Microcavities journal, August 2004

Measurement of Coherent Thermal Emission Due to Magnetic Polaritons in Subwavelength Microstructures journal, July 2013

Unifying approach to left-handed material design journal, January 2006

Narrow-band spectral features of structured silver surface with rectangular resonant cavities journal, March 2011

Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings journal, January 1995

Coupling between gap plasmon polariton and magnetic polariton in a metallic-dielectric multilayer structure journal, August 2011

Optical Constants of the Noble Metals journal, December 1972

Magnetic Response of Metamaterials at 100 Terahertz journal, November 2004

Transparent Metals for Ultrabroadband Electromagnetic Waves journal, March 2012

Strong Plasmonic Coupling between Graphene Ribbon Array and Metal Gratings journal, October 2015

Magnetism from conductors and enhanced nonlinear phenomena journal, January 1999

Study of magnetic polaritons in deep gratings for thermal emission control journal, March 2014

Wavelength-selective and diffuse emitter enhanced by magnetic polaritons for thermophotovoltaics journal, February 2012

Terahertz Magnetic Response from Artificial Materials journal, March 2004

Experimental Verification of a Negative Index of Refraction journal, April 2001

Organ pipe radiant modes of periodic micromachined silicon surfaces journal, December 1986

Metamaterial Electromagnetic Cloak at Microwave Frequencies journal, November 2006

Perfect mid-infrared absorption by hybrid phonon-plasmon polaritons in hBN/metal-grating anisotropic structures journal, March 2017

Transmission Enhancement Through Nanoscale Metallic Slit Arrays from the Visible to Mid-Infrared journal, February 2008

Thermal radiation from two-dimensionally confined modes in microcavities journal, August 2001

Circuits with Light at Nanoscales: Optical Nanocircuits Inspired by Metamaterials journal, September 2007

Flatness and boundness of photonic drumhead surface state in a metallic lattice journal, April 2021

Magnetic Response of Metamaterials at 100 Terahertz text, January 2004

A unifying approach to left handed material design text, January 2006

Resonance enhanced absorption in a graphene monolayer using deep metal gratings
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Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film
journal, January 2008

Blocking-assisted infrared transmission of subwavelength metallic gratings by graphene
journal, February 2015

Resonance transmission or absorption in deep gratings explained by magnetic polaritons
journal, September 2009

Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model
journal, December 2014

Anisotropic Polarized Emission of a Doped Silicon Lamellar Grating
journal, June 2006

Design of tungsten complex gratings for thermophotovoltaic radiators
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Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure
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Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators
journal, January 2009

Taming the thermal emissivity of metals: A metamaterial approach
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Spatial and temporal coherence of thermal radiation in asymmetric Fabry–Perot resonance cavities
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Narrow-Band Thermal Radiation with Low Directivity by Resonant Modes inside Tungsten Microcavities
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Measurement of Coherent Thermal Emission Due to Magnetic Polaritons in Subwavelength Microstructures
journal, July 2013

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Narrow-band spectral features of structured silver surface with rectangular resonant cavities
journal, March 2011

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Coupling between gap plasmon polariton and magnetic polariton in a metallic-dielectric multilayer structure
journal, August 2011

Optical Constants of the Noble Metals
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Magnetic Response of Metamaterials at 100 Terahertz
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Perfect mid-infrared absorption by hybrid phonon-plasmon polaritons in hBN/metal-grating anisotropic structures
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