Geodesic
Mathematical models in nanooptics and biophotonics based on the discrete sources method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 269-287 
Yu. A. Eremin; A. G. Sveshnikov. Mathematical models in nanooptics and biophotonics based on the discrete sources method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 269-287. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a9/
@article{ZVMMF_2007_47_2_a9,
     author = {Yu. A. Eremin and A. G. Sveshnikov},
     title = {Mathematical models in nanooptics and biophotonics based on the discrete sources method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {269--287},
     year = {2007},
     volume = {47},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a9/}
}
TY  - JOUR
AU  - Yu. A. Eremin
AU  - A. G. Sveshnikov
TI  - Mathematical models in nanooptics and biophotonics based on the discrete sources method
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 269
EP  - 287
VL  - 47
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a9/
LA  - ru
ID  - ZVMMF_2007_47_2_a9
ER  - 
%0 Journal Article
%A Yu. A. Eremin
%A A. G. Sveshnikov
%T Mathematical models in nanooptics and biophotonics based on the discrete sources method
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 269-287
%V 47
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a9/
%G ru
%F ZVMMF_2007_47_2_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

The state of the art of the discrete sources method is reviewed. The method can be used to construct effective numerical models for problems in nanooptics and biophotonics.

[1] Tikhonov A. M., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR

[2] Tikhonov A. N., Arsenin V. Ya., Rubashov I. B., Timonov A. A., “O reshenii problem vosstanovleniya izobrazheniya v YaMR tomografii”, Dokl. AN SSR, 263:4 (1982), 872–876 | MR

[3] Wriedt T., Generalizes multipole techniques for electromagnetic and light scattering, Elsevier, Amsterdam, 1999

[4] Kupradze V. D., “O priblizhennom reshenii zadach matematicheskoi fiziki”, Uspekhi matem. nauk, 22:2 (1967), 59–107 | MR

[5] Eremin Yu. A., Sveshnikov A. G., “Kontseptsiya kvaziresheniya zadach difraktsii”, Matem. modelirovanie, 6:6 (1994), 76–84 | MR

[6] Kolton D., Kress R., Metody integralnykh uravnenii v teorii rasseyaniya, Mir, M., 1987 | MR

[7] Doicu A., Eremin Yu., Wriedt T., Acoustic and electromagnetic scattering analysis using discrete sources, Acad. Press, New York, 2000

[8] Eremin Yu. A., Sveshnikov A. G., Metod diskretnykh istochnikov v zadachakh elektromagnitnoi difraktsii, Izd-vo MGU, M., 1992

[9] Tikhonov A. H., “O normalnykh resheniyakh priblizhennykh sistem lineinykh algebraicheskikh uravnenii”, Dokl. AN SSR, 254:3 (1980), 549–554 | MR | Zbl

[10] Agranovich M. S., “Ellipticheskie operatory na zamknutykh mnogoobraziyakh”, Itogi nauki i tekhn. Ser. Sovrem. problemy matem., 63, VINITI, M., 1990, 6–126 | MR

[11] Tikhonov A. N., “Ob odnom printsipe vzaimnosti”, Dokl. AN SSSR, 253:2 (1980), 305–308 | MR | Zbl

[12] Eremin Yu. A., Orlov N. V., Sveshnikov A. G., “Models of electromagnetic scattering problems based on discrete sources methods”, Generalizes Multipole Techniques for Electromagnetic and Light Scattering, Amsterdam, 1999, 39–79

[13] Eremin Yu. A., “The method of discrete sources in electromagnetic scattering by axially symmetric structures”, J. Communs. Techn. Electronics, 45, Suppl. 2 (2000), S268–S280

[14] Born M., Volf E., Osnovy optiki, Nauka, M., 1970

[15] Eremin Yu. A., Sveshnikov A. G., “Metod diskretnykh istochnikov v zadachakh rasseyaniya elektromagnitnykh voln”, Uspekhi sovrem. radioelektroniki, 2003, no. 10, 3–40

[16] Tikhonov A. N., “Ob asimptoticheskom povedenii integralov, soderzhaschikh besselevy funktsii”, Dokl. AN SSSR, 125:5 (1959), 982–985 | Zbl

[17] Eremin Yu. A., Stover J. C., Orlov N. V., “Modeling scatter from silicon wafers features based on discrete sources method”, Optical Engng., 38:8 (1999), 1296–1304 | DOI

[18] Eremin Yu. A., Sveshnikov A. G., “Matematicheskie modeli v zadachakh biofotoniki”, Vestn. MGU. Ser. 15. Vychisl. matem. i kibernetika, 2006, no. 3, 28–35 | MR | Zbl

[19] Grishina N. V., Eremin Yu. A., “Sootnoshenie strogikh i priblizhennykh modelei v zadache transformatsii neizluchayuschikh voln”, Optika i spektroskopiya, 97:5 (2004), 867–874