V.I. Krivenkov − Ph.D. (Phys.-Math.). E-mail: krivenkov.v@gmail.com

One of the main task in the theory of guided modes of optical fibers is a problem of their own waves (of guided modes) of the homo-geneous along a certain axis infinitely lengthy optical fiber made of doped quartz glass with extremely low optical losses in the infrared and visible parts of the electromagnetic spectrum. In the process of determining the waveguide characteristics of the fiber, as a rule the following, questions arise: the selection of a system of differential equations for the components of the electromagnetic fields of guided modes, the presentation of the dielectric constant tensor of anisotropic optical fiber; determination of the dispersion of the dielectric permittivity of doped quartz glass;most accurate calculation of dispersion, energy and polarization characteristics of guided modes with minimal cost of computing resources. Answers to these questions effects the efficiency of the chosen method of solving the problem, namely, the possibility of computing with a high precision of dispersion, energy, and polarization characteristics of guided modes of the considered optical fiber with a minimum expenditure of computational resources. In this paper we propose possible answers to these questions. Two systems of differential equations for components of guided modes of the optical fiber of the first order and three systems of the second order are presented in the invariant form. The dielectric constant tensor of anisotropic optical fiber is presented in an optimal form for to solve the problem on their own waves. The dispersion of the dielectric permittivity of multicomponent doped quartz glass is presented in the form of a generalized number of Sellmeier. Expressions for coefficients of the chromatic dispersion of the first and second order are obtained, whose application rovides high accuracy calculations and reduces he amount of computational work more than three times. The expression for the longitudinal flow of the power of the guided modes through the region of the cross-section of a uniaxial anisotropic a optical fiber, where the transverse and longitudinal components of the dielectric constant tensor are constant values is presented in the form of a contour integral.

 

1. Unger KH.-G. Planarnye i volokonnye opticheskie volnovody / Per. s angl. pod red. V.V. SHevchenko. M.: Mir. 1980. 656 s.
2. Listvin A.V., Listvin V.N., SHvyrkov D.V. Opticheskie volokna dlja linijj svjazi. M.: LESARart. 2003. 288 s.
3. Markuze D. Opticheskie volnovody / Per. s angl. pod red. V.V. SHevchenko. M.: Mir. 1974. 576 s.
4. Adams M. Vvedenie v teoriju opticheskikh volnovodov / Per. s angl. pod red. I.N. Sisakjana. M.: Mir. 1984. 512 s.
5. Snajjder A., Lav Dzh. Teorija opticheskikh volnovodov / Per. s angl. pod red. E.M. Dianova i V.V. SHevchenko. M.: Radio i svjaz. 1987. 656 s.
6. Kamke EH. Spravochnik po obyknovennym differencialnym uravnenijam / Per. s nem. S.V. Fomina. M.: Nauka. 1976. 576 s.
7. Korn G., Korn T. Spravochnik po matematike dlja nauchnykh rabotnikov i inzhenerov / Per. s angl. I.G. Aramanovicha, A.M. Berezmana, I.A. Vajjnshtejjna, L.Z. Rumshiskogo, L.JA. Clafa /Pod obshhejj red. I.G. Aramanovicha. M.: Nauka. 1978. 831 s.
8. Spravochnik po specialnym funkcijam s formulami, grafikami i matematicheskimi tablicami / Pod red. M. Abramovica i I. Stigan / Per. s angl. pod red. V.A. Ditkina i L.N. Karmazinojj. M.: Nauka. 1979. 832 s.
9. Louson CH., KHenson R. CHislennoe reshenie zadach metoda naimenshikh kvadratov / Per. s angl. KH.D. Ikramova. M.: Nauka. 1986. 232 s.
10. Landau L.D., Lifshic E.M. Teoreticheskaja fizika. T. 8. EHlektrodinamika sploshnykh sred. M.: FIZMATLIT. 2001. 656 s.
11. Krivenkov V.I. Napravljaemye mody anizotropnogo gradientnogo svetovoda // Vestnik Moskovskogo gosudarstvennogo universiteta. Ser. Fizika. Astronomija. 2004. № 3. S. 19-22. (Moscow University Phys. Bull. 2004. V. 59. № 3. P. 25-29).
12.  Krivenkov V.I. Anizotropnyjj ehllipticheskijj svetovod // Vestnik Moskovskogo gosudarstvennogo universiteta. Ser. Fizika. Astronomija. 2004. № 4. S. 21-24.
13. Krivenkov V.I. Tochnye dispersionnye uravnenija dlja napravljaemykh mod gradientnogo svetovoda // DAN. 2001. T. 378.  № 6. S. 751-753.
14. Krivenkov V.I. Dispersionnye uravnenija dlja napravljaemykh mod mnogoslojjnogo ehllipticheskogo svetovoda // DAN. 2002. T. 382. №1. S. 38-40.
15. Krivenkov V.I. Dispersionnye uravnenija dlja napravljaemykh mod gradientnogo ehllipticheskogo svetovoda // DAN. 2002.  T. 386. № 6. S. 749-752.
16. Belanov A.S., Krivenkov V.I. Dispersionnoe uravnenie dlja napravljaemykh mod kruglogo N-slojjnogo svetovoda // Radiotekhnika i ehlektronika. 1994. T. 39. № 1. S. 31-33.
17. Belanov A.S., Dianov E.M., Krivenkov V.I. Dispersija v svetovodakh so slozhnym profilem pokazatelja prelomlenija // DAN. 1999. T. 364. № 1. S. 37-41.
18. Eickhoff W. Stress-induced single-polarization single-mode fibers // Opt. Lett. 1982. V. 7. № 8. P. 629-631.
19. Birch R.D., Varnham M.P., Payne D.M., Okamoto K. Fabrication a stress-guiding optical fiber // Electron. Lett. 1983. V. 19. № 21. P. 866-867.
20. Belanov A.S., Krivenkov V.I., Kolomijjceva E.A. Raschet dispersii v svetovodakh so slozhnym profilem pokazatelja prelomlenija //Radiotekhnika. 1998. № 3. S. 32-35.
21. Gloge D. Dispersion in weakly guiding fibers // Appl. Opt. 1971. V. 10. № 11. P. 2442-2445.
22. Fleming J.W. Dispersion in GeO₂?SiO₂ glasses // Appl. Opt. 1984. V. 23. № 24. P. 4486-4493.
23. Fleming J.W., Wood D.L. Refractive index dispersion and related properties in fluorine doped silica // Appl. Opt. 1983. V. 22. № 19. P. 3102-3104.
24. Kapron F.P., Keck D.B. Pulse transmission through a dielectric optical waveguide // Appl. Opt. 1971. V. 10. № 7. P. 1519-1523.
25. Marcuse D. Pulse distortion in single-mode fibers // Appl. Opt. 1980. V. 19. № 10. P. 1653-1660.
26. Belanov A.S., Dianov E.M., Krivenkov V.I., Kurilov A.S. Peredacha informacii po odnomodovym svetovodam s kompen­sirovannojj dispersiejj pervogo i vtorogo porjadka // EHlektrosvjaz. 1985. № 12. S. 24-28.
27. Belanov A.S., Dianov E.M., Krivenkov V.I. i dr. Svetovody s malojj dispersiejj v shirokom diapazone dlin voln // Radio­tekhnika. 2004. № 12. S. 15-19.
28. Krivenkov V.I.Svetovody so slozhnojj formojj poperechnogo sechenija // DAN. 2002. T. 387. №2. S. 184-187.
29.  Krivenkov V.I. Napravljaemye mody fotonno-kristallicheskikh svetovodov // DAN. 2003. T. 391. №5. S. 619-622.
30. Mortensen N.A. Effective area of photonic crystal fibers // Opt. Express. 2002. V.10. №7. P. 341-348.
31. Belanov A.S., Dianov E.M., Krivenkov V.I., Solopov V.M. Linejjnost poljarizacii mody HE₁₁ v kruglykh volokonnykh svetovodakh // Radiotekhnika. 1986. № 12. S. 75-76.
32. Belanov A.S., Krivenkov V.I. Distribution of longitudinal power flow of a bound mode among layers of a multilayer optical fibre with arbitrary cross section // Sov. Lightwave Commun. 1991. V.1. №3. P. 207-210.
33. Krivenkov V.I.Potok moshhnosti napravljaemojj mody svetovoda // Vestnik Moskovskogo gosudarstvennogo universiteta. Ser. Fizika. Astronomija. 2009. № 3. S. 111-113 (Moscow University Phys. Bull. 2009. V. 64. № 5. P. 558-560).
34. Krivenkov V.I.Raspredelenie potoka moshhnosti napravljaemojj mody po slojam kruglogo i ehllipticheskogo mnogoslojjnykh svetovodov // Vestnik Moskovskogo gosudarstvennogo universiteta. Ser. Fizika. Astronomija. 2009. № 4. S. 6-8 (Moscow University Phys. Bull. 2009. V. 64. № 4. P. 362-364).
35. Belovolov M.I., Bubnov M.M., Dianov E.M. i dr. Odnomodovyjj volokonnyjj svetovod s dopolnitelnym kolcevym svetovodom dlja dvukhkanalnojj svjazi i specialnykh primenenijj // Kvantovaja ehlektronika. 2001. T. 31. № 8. S. 733-739.
36. ZHeltikov A.M.Dyrchatye volnovody // UFN. 2000. T. 170. №11. S. 1203-1215.
37. Birjukov A.S., Dianov E.M. Volokonnye svetovody na osnove fotonnykh kristallov // V sb.: Volokonno-opticheskie tekhnologii, materialy i ustrojjstva. 2002. № 5. S. 6-16.