A Generalization of the Mie Theory for a Sphere with Spatially Dispersive Permittivity
DOI:
https://doi.org/10.15407/ujpe56.2.122Keywords:
-Abstract
The Mie theory is generalized to the case of a sphere with spatially dispersive permittivity with regard for longitudinal electromagnetic waves and transverse ones with a single-valued dependence of the wavenumber on the frequency. The generalized Mie coefficients are determined with the help of the method of additional boundary conditions using the condition of electron opacity of the surface. The theory is applicable for the modeling of optical processes involving metals, does not require to simplify the dependence of the permittivity on the light frequency and wavenumber, and does not apply the electrostatic approximation. A relative error of this approximation in calculating the extinction cross-section of a 10 nm-radius silver sphere is shown to exceed 50% in a wide frequency interval.
References
B.B. Dasgupta and R. Fuchs, Phys. Rev. B 24, 554 (1981).
https://doi.org/10.1103/PhysRevB.24.554
R. Fuchs and F. Claro, Phys. Rev. B 35, 3722 (1987).
https://doi.org/10.1103/PhysRevB.35.3722
P.T. Leung, Phys. Rev. B 42, 7622 (1990).
https://doi.org/10.1103/PhysRevB.42.7622
J. Vielma and P.T. Leung, J. Chem. Phys. 126, 194704 (2007).
https://doi.org/10.1063/1.2734549
P.T. Leung and M.H. Hider, J. Chem. Phys. 98, 5019 (1993).
https://doi.org/10.1063/1.464955
M.H. Hider and P.T. Leung, Phys. Rev. B 66, 195106 (2002).
https://doi.org/10.1103/PhysRevB.66.195106
P.T. Leung and W.S. Tse, Sol. State Comm. 95, 39 (1995).
https://doi.org/10.1016/0038-1098(95)00144-1
Z.E. Goude and P. T. Leung, Sol. Stat. Comm. 143, 416 (2007).
https://doi.org/10.1016/j.ssc.2007.06.015
R. Chang, P.T. Leung, S.H. Lin, and W.S. Tse, Phys. Rev. B 62, 5168 (2000).
https://doi.org/10.1103/PhysRevB.62.5168
R. Chang, H.-P. Chiang, P.T. Leung, D.P. Tsai, and W.S. Tse, Sol. State Commun. 133, 315 (2005).
https://doi.org/10.1016/j.ssc.2004.11.014
R. Chang and P.T. Leung, Phys. Rev. B 73, 125438 (2006).
https://doi.org/10.1103/PhysRevB.73.125438
C. Girard, Phys. Rev. B 45, 1800 (1992).
https://doi.org/10.1103/PhysRevB.45.1800
C. Girard and A. Dereux, Phys. Rev. B 49, 11344 (1994).
https://doi.org/10.1103/PhysRevB.49.11344
B. Labani, M. Boustimi, and J. Baudon, Phys. Rev. B 55, 4745 (1997).
https://doi.org/10.1103/PhysRevB.55.4745
C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
J.A. Stratton, Electromagnetic Theory (McGraw Hill, New York, 1941).
H.C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
М. Born and E.W. Wolf, Principles of Optics (Pergamon Press, Oxford, 1991).
A. Yildiz, Nuovo Cimento 30, 5740 (1963).
https://doi.org/10.1007/BF02828781
V.B. Gildenburg and I.G. Kondratyev, Radiotekhn. Elektron. 10, 658 (1965).
V.S. Gvozdetskii, A.G. Zagorodnii, I.V. Krivtsun, and I.P. Yakimenko, Preprint ITP 83-167R (Kyiv, 1983).
A. Moroz, Ann. Phys. 315, 352 (2005).
https://doi.org/10.1016/j.aop.2004.07.002
H.T. Dung, L. Kn¨oll, and D.-G. Welsch, Phys. Rev. A 62, 053804 (2000).
https://doi.org/10.1103/PhysRevA.62.053804
L. Novotny, B. Hecht, Principles of Nano-Optics (Cambridge University Press, New York, 2006).
https://doi.org/10.1017/CBO9780511813535
D.D. Smith, K.A. Fuller, J. Opt. Soc. Am. B 19, 2449 (2002).
https://doi.org/10.1364/JOSAB.19.002449
R. Ruppin, Phys. Rev. B 11, 2871 (1975).
https://doi.org/10.1103/PhysRevB.11.2871
R. Ruppin, Opt. Commun. 30, 380 (1979).
https://doi.org/10.1016/0030-4018(79)90375-4
Yu.V. Kryuchenko and V.I. Sugakov, Phys. Stat. Sol. B 111, 177 (1982).
https://doi.org/10.1002/pssb.2221110119
G.S. Agarwal and S. V. ONeil, Phys. Rev. B 28, 487 (1983).
https://doi.org/10.1103/PhysRevB.28.487
S.I. Pekar, Zh. Eksp. Teor. Fiz. 33, 1022 (1957).
S. I. Pekar, Crystal Optics and Additional Light Waves (Benjamin, Menlo Park, CA, 1983).
G.H. Cocoletzi and W.L. Moch'an, Surf. Sci. Rep. 57, 1 (2005).
A. Pack, Ph.D. thesis, Technischen Universit¨at Chemnitz, 2001.
A. Pack, M. Hietschold, and R. Wannemacher, Opt. Commun. 194, 277 (2001).
https://doi.org/10.1016/S0030-4018(01)01310-4
A. Hilger, M. Tenfelde, and U. Kreibig, Appl. Phys. B 73, 361 (2001).
https://doi.org/10.1007/s003400100712
V.P. Drachev, U.K. Chettiar, A.V. Kildishev, H.-K. Yuan, W. Cai, and V.M. Shalaev, Opt. Express 16, 1186 (2008).
https://doi.org/10.1364/OE.16.001186
P.M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
J.M. G'erardy and M. Ausloos, Phys. Rev. B 25, 4204 (1982).
https://doi.org/10.1103/PhysRevB.25.4204
J.D. Eversole and H.P. Broida, Phys. Rev. B 15, 1644 (1977).
https://doi.org/10.1103/PhysRevB.15.1644
A. Curry, W. L. Hwang, and A. Wax, Opt. Express 14, 6536 (2006).
https://doi.org/10.1364/OE.14.006535
C. S¨onnichsen, Ph.D. thesis (Ludwig-Maximilians-Universit¨at, M¨unchen, 2001).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
