Analytical representation of a spectrum of periodic solutions in a model of Majsner–Kronig–Penney in radiating system
DOI:
https://doi.org/10.1109/ICATT.1999.1236143Abstract
The wide application of a Majsner–Kronig–Penney (MKP) model is explained by analogy between distribution of waves in periodic structures, phenomenon of parametrical instability of oscillatory systems, electron properties in a crystal potential field, by a likeness of the differential equations and possibility to present solutions by elementary functions [1–5]. Characteristic features of the zonal theory, such as prohibited and permitted power bands, superficial condition have clear analogies for electromagnetic and sound waves in stratified–periodic medium and for parametric instabilities of a oscillatory system [5, 6].References
Yakubovich, V.A.; Starzinskii, G.M. Parametric Resonance in Linear System. Мoscow: Nauka, 1987, 328 p. [in Russian].
Shmidt, G. Parametric Oscelations. Мoscow: Мir, 1978, 336 p. [in Russian].
Zaiman, Dz. Principles of the Theory Rigid Bould. Мoscow: Мir, 1974, 472 p. [in Russian].
Yariv, А.; Yuh, P. Optics of Waves in Cristal. Мoscow: Мir, 1987, 616 p. [in Russian].
Chechulin, S.L. Parametric Oscillation and Stability of Periodic Driving. Leningrad: LGU, 1983, 220 p. [in Russian].
Bass, F.G.; Bulgakov, A.A.; Teterov, A.P. High-Frequency Properties is Semiconducting with Grating. Мoscow: Nauka, 1989, 288 p. [in Russian].
Abpamovich, М.; Stigan, I. Manual on Special Functions. Мoscow: Nauka, 1979, 832 p. [in Russian].
Whittaker, E.Т.; Watson, J.Н. A Rate of the Modern Analysis, Vol. 2. Мoscow: Physmatgiz, 1964, 516 p. [in Russian].
Ulianov, V.V. Problems on a Quantum Mechanics and Quantum Statistics. Kharkov: Vysshaya Shkola, 1979, 216 p. [in Russian].
