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This paper presents a method of analysing the dispersion relation and field shape of any type of wave field for which the dispersion relation is transcendental. The method involves replacing each transcendental term in the dispersion relation by a finite-product polynomial. The finite products chosen must be consistent with the low-frequency, lowwavenumber limit; but the method is nevertheless accurate up to high frequencies and high wavenumbers. Full details of the method are presented for a non-trivial example, that of anti-symmetric elastic waves in a layer; the method gives a sequence of polynomial approximations to the dispersion relation of extraordinary accuracy over an enormous range of frequencies and wavenumbers. It is proved that the method is accurate because certain gamma-function expressions, which occur as ratios of transcendental terms to finite products, largely cancel out, nullifying Runge's phenomenon. The polynomial approximations, which are unrelated to Taylor series, introduce no spurious branches into the dispersion relation, and are ideal for numerical computation. The method is potentially useful for a very wide range of problems in wave theory and stability theory.

The electron spin coherence in n-doped and undoped, self-assembled CdSe/Zn(S,Se) quantum dots has been studied by time-resolved pump-probe Kerr rotation. Long-lived spin coherence persisting up to 13 ns after spin orientation has been found in the n-doped quantum dots, outlasting significantly the lifetimes of charge neutral and negatively charged excitons of 350 − 530 ps. The electron spin dephasing time as long as 5.6 ns has been measured in a magnetic field of 0.25 T. Hyperfine interaction of resident electrons with a nuclear spin fluctuations is suggested as the main limiting factor for the dephasing time. The efficiency of this mechanism in II-VI and III-V quantum dots is analyzed.

Development of molecular beam epitaxy (MBE) of two-dimensional (2D) layered materials is an inevitable step in realizing novel devices based on 2D materials and heterostructures. However, due to existence of numerous polytypes and occurrence of additional phases, the synthesis of 2D films remains a difficult task. This paper reports on MBE growth of GaSe, InSe, and GaTe layers and related heterostructures on GaAs(001) substrates by using a Se valve cracking cell and group III metal effusion cells. The sophisticated self-consistent analysis of X-ray diffraction, transmission electron microscopy, and Raman spectroscopy data was used to establish the correlation between growth conditions, formed polytypes and additional phases, surface morphology and crystalline structure of the III–VI 2D layers. The photoluminescence and Raman spectra of the grown films are discussed in detail to confirm or correct the structural findings. The requirement of a high growth temperature for the fabrication of optically active 2D layers was confirmed for all materials. However, this also facilitated the strong diffusion of group III metals in III–VI and III–VI/II–VI heterostructures. In particular, the strong In diffusion into the underlying ZnSe layers was observed in ZnSe/InSe/ZnSe quantum well structures, and the Ga diffusion into the top InSe layer grown at ~450 °C was confirmed by the Raman data in the InSe/GaSe heterostructures. The results on fabrication of the GaSe/GaTe quantum well structures are presented as well, although the choice of optimum growth temperatures to make them optically active is still a challenge.

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