Geodesic
Zero approximation of vector model for smoothly-irregular optical waveguide
Matematičeskoe modelirovanie, Tome 22 (2010) no. 8, pp. 42-54.

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On the base of adiabatic representation for eigenmodes of integrated-optical multilayer waveguide are presented differential equations and boarder conditions to vertical distribution of electromagnetic field in the waveguide. To smoothly-irregular waveguides an asymptotic method is applied and zero approximation parts of differential equations and boarder conditions are determined. Exact expressions are considered for vertical distribution of electromagnetic field in a waveguide and for boarder conditions. Finally the problem is reduced to the solution of homogeneous system of linear algebraic equations depending on a spectral parameter and to the search of the parameter values. The method and algorithms of calculating vertical dispersion of adiabatic modes are considered in conclusion.
Keywords: integrated optics, waveguide modes, smooth three-dimensional irregularities, asymptotic method, differential equations, parametrically dependent algebraic equations. 
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A. A. Egorov; A. L. Sevastyanov; E. A. Ayrjan; K. P. Lovetskiy; L. A. Sevastianov. Zero approximation of vector model for smoothly-irregular optical waveguide. Matematičeskoe modelirovanie, Tome 22 (2010) no. 8, pp. 42-54. http://geodesic.mathdoc.fr/item/MM_2010_22_8_a3/

[1] Sevastyanov L. A., Egorov A. A., “Teoreticheskii analiz volnovodnogo rasprostraneniya elektromagnitnykh voln v dielektricheskikh plavno-neregulyarnykh integralnykh strukturakh”, Optika i spektroskopiya, 105:4 (2008), 632–640 | MR

[2] Egorov A. A., Sevastyanov L. A., Sevastyanov A. L., “Issledovanie elektrodinamicheskikh svoistv planarnoi tonkoplenochnoi linzy Lyuneberga”, Zhurnal radioelektroniki, 2008, no. 6, 1–20

[3] Egorov A. A., Sevastyanov L. A., “Struktura mod plavno-neregulyarnogo integralno-opticheskogo chetyrekhsloinogo trekhmernogo volnovoda”, Kvantovaya elektronika, 39:6 (2009), 566–574

[4] Egorov A. A., Sevastianov L. A., Sevastyanov A. L., Lovetskiy K. P., “Propagation of electromagnetic waves in thin-film structures with smoothly irregular sections”, ICO Topical Meeting on Optoinformatics, Information Photonics 2008 (September 15–18, 2008, St. Petersburg, Russia), ITMO, St. Petersburg, 2008, 231–234

[5] Khansperdzher R., Integralnaya optika: Teoriya i Tekhnologiya, Mir, M., 1985, 384 pp.

[6] Deryugin L. N., Marchuk A. N., Sotin V. E., “Svoistva ploskikh nesimmetrichnykh dielektricheskikh volnovodov na podlozhke iz dielektrika”, Izv. Vuzov. Radioelektronika, 10:2 (1967), 134–142

[7] Markuze D., Opticheskie volnovody, Mir, M., 1974, 576 pp.

[8] Adams M., Vvedenie v teoriyu opticheskikh volnovodov, Mir, M., 1984, 512 pp.

[9] Blokhintsev D. I., Osnovy kvantovoi mekhaniki, Vysshaya shkola, M., 1961, 512 pp. | MR

[10] Freman N., Freman P. U., VKB-priblizhenie, Mir, M., 1967, 168 pp.

[11] Petrovskii I. G., Lektsii po teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1970, 279 pp. | MR

[12] Sevastyanov L. A., “Polnaya sistema mod otkrytogo planarnogo volnovoda”, Trudy VI mezhdunarodn. nauchno-tekhnich. konf. “Lazery v nauke, tekhnike, meditsine”, 1995, 72–76

[13] Trikomi F., Differentsialnye uravneniya, Inostrannaya literatura, M., 1962, 442 pp.

[14] Luneburg R. K., Mathematical theory of optics, University of California Press, 1966, 448 pp. | MR

[15] Morgan S. P., “General solution of the Luneburg lens problem”, J. Appl. Phys., 29:9 (1958), 1358–1368 | DOI | MR | Zbl

[16] Forsait Dzh., Malkolm M., Mouler K., Mashinnye metody matematicheskikh vychislenii, Mir, M., 1980, 277 pp. | MR

[17] Fehlberg E., Low-order Classical Runge-Kutta formulas with stepsize control, NASA Technical Report R-315

[18] Shampine L. F., Watts H. A., Davenport S., Solving non-stiff ordinary differential equations, The State of the Art, Sandia Laboratories Report SAND75-0182

[19] Moreau J-P. http://pagesperso-orange.fr/jean-pierre.moreau/

[20] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979, 288 pp. | MR