DOI: 10.1063/1.3624603. Temperature dependence of surface phonon polaritons from a quartz grating

Temperature dependence of surface phonon polaritons from a quartz grating

10.1063/1.3624603

Crossref journal-article

AIP Publishing

Journal of Applied Physics (317)

Abstract

We report the temperature dependence of the surface phonon polariton (SPhP) spectra of α-SiO2 (quartz), propagated to the far-field by a grating, in the temperature range between 300 K and 800 K. Room temperature data for a 670 nm deep grating are compared to a simulated spectrum using a finite-difference frequency-domain approach. The inputs to the simulation are the dielectric functions measured by infrared ellipsometry and modeled as a set of damped oscillators. The simulated spectra are in good agreement with experiment. The width of the SPhP reflectivity dip depends on the depth of the grating. For a grating depth of 280 nm, the width of the reflectivity dip in the temperature range 300 &lt; T &lt; 800 K is comparable to what is expected for the SPhP excitations of a flat surface. For a grating depth of 670 nm, the width of the reflectivity dip increases significantly due to coupling to far-field radiation.

Bibliography

Hafeli, A. K., Rephaeli, E., Fan, S., Cahill, D. G., & Tiwald, T. E. (2011). Temperature dependence of surface phonon polaritons from a quartz grating. Journal of Applied Physics, 110(4).

Authors 5

Andrew K. Hafeli (first)
Eden Rephaeli (additional)
Shanhui Fan (additional)
David G. Cahill (additional)
Thomas E. Tiwald (additional)

References 31 Referenced 19

10.1038/416061a / Nature (2002)
10.1115/1.2401204 / J. Heat Transfer (2007)
10.1364/JOSAA.21.001368 / J. Opt. Soc. Am. A (2004)
10.1364/OL.30.002623 / Opt. Lett. (2005)
10.1080/108939502753428202 / Microscale Thermophys. Engin. (2002)
10.1103/PhysRevLett.104.154301 / Phys. Rev. Lett. (2010)
10.1063/1.3125453 / J. Appl. Phys. (2009)
10.1088/0034-4885/31/1/303 / Rep. Prog. Phys. (1968)
10.1088/0022-3719/7/19/015 / J. Phys. C (1974)
{'volume-title': 'Surface Polaritons: Electromagnetic Waves at Surfaces and Interfaces', 'year': '1982', 'first-page': '717', 'key': '2023080401544758700_c10'} / Surface Polaritons: Electromagnetic Waves at Surfaces and Interfaces (1982)
10.1016/0038-1098(84)91071-8 / Solid State Commun. (1984)
10.1016/0030-4018(86)90429-3 / Opt. Commun. (1986)
10.1002/pssb.2220560213 / Phys. Status Solidi B (1973)
10.1002/pssb.v69:2 / Physica Status Solidi B (1975)
10.1103/PhysRev.121.1324 / Phys. Rev. (1961)
10.1103/PhysRevB.11.3944 / Phys. Rev. B (1975)
10.1088/0960-1317/3/2/006 / J Micromech. Microeng. (1993)
10.1088/0960-1317/8/1/001 / J. Micromech. Microeng. (1998)
{'volume-title': 'Ellipsometry and Polarized Light', 'year': '1977', 'first-page': '354', 'key': '2023080401544758700_c19'} / Ellipsometry and Polarized Light (1977)
10.1063/1.358864 / J. Appl. Phys. (1995)
10.1016/0038-1098(75)90738-3 / Solid State Commun. (1975)
10.1016/0040-6090(93)90280-3 / Thin Solid Films (1993)
10.1109/TMTT.1974.1128246 / IEEE Trans. Microwave Theory Techn. (1974)
{'volume-title': 'Computational Electrodynamics: The Finite-Difference Time-Domain Method', 'year': '2005', 'edition': '3rd ed.', 'key': '2023080401544758700_c24'} / Computational Electrodynamics: The Finite-Difference Time-Domain Method (2005)
10.1016/j.surfrep.2004.12.002 / Surf. Sci. Rep. (2005)
{'volume-title': 'Electromagnetic Surface Modes', 'year': '1982', 'first-page': '776', 'key': '2023080401544758700_c26'} / Electromagnetic Surface Modes (1982)
{'key': '2023080401544758700_c27', 'first-page': '574', 'volume': '14', 'year': '1972', 'journal-title': 'Sov. Phys. Solid State'} / Sov. Phys. Solid State (1972)
{'volume-title': 'Surface Modes in Physics', 'year': '2001', 'key': '2023080401544758700_c28'} / Surface Modes in Physics (2001)
10.1103/PhysRevB.55.15 / Phys. Rev. B (1997)
10.1115/1.2955475 / J. Heat Transfer (2008)
10.1364/JOSAA.20.000569 / J. Opt. Soc. Am. A (2003)

Dates

Type	When
Created	14 years ago (Aug. 23, 2011, 6:22 p.m.)
Deposited	2 years ago (Aug. 3, 2023, 9:54 p.m.)
Indexed	1 month ago (July 30, 2025, 6:57 a.m.)
Issued	14 years ago (Aug. 15, 2011)
Published	14 years ago (Aug. 15, 2011)
Published Online	14 years ago (Aug. 23, 2011)
Published Print	14 years ago (Aug. 15, 2011)

Funders 0

None

BibTeX

@article{Hafeli_2011, title={Temperature dependence of surface phonon polaritons from a quartz grating}, volume={110}, ISSN={1089-7550}, url={http://dx.doi.org/10.1063/1.3624603}, DOI={10.1063/1.3624603}, number={4}, journal={Journal of Applied Physics}, publisher={AIP Publishing}, author={Hafeli, Andrew K. and Rephaeli, Eden and Fan, Shanhui and Cahill, David G. and Tiwald, Thomas E.}, year={2011}, month=aug }

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