Based on the theoretical symmetry analysis of the nonlinear electric susceptibility, second harmonic generation
is examined as a probe for detection of various type of ordering: magnetic, ferroelectric, ferroelastic. The nonlinear
optical response of multiferroics is illustrated by the example of bismuth ferrite BiFeO<sub>3</sub>. It is shown that magnetically
induced second harmonic response as well as anisotropic part of ferroelectrically induced second harmonic depends on
mechanical (ferroelastic) ordering. This is one of the aspects of order parameters coupling in multiferroics.
Based on the group theoretical analysis of the nonlinear electric susceptibility second harmonic response in different magnetic states of multiferroic bismuth ferrite is considered. It is shown that nonlinear magneto-optic effect can serve as an effective tool for spin cycloid structure detection in bulk material and probing homogenous antiferromagnetic state in thin films of bismuth ferrite. The study of antiferromagnetic state that determines magnetoelectric properties of the material is important in the context of practical applications in microelectronic and magnetic storage.
Photonic band-gap structures are of interest both from fundamental and practical points of view. They are known to enhance nonlinear, magnetooptical, electrooptical and other effects in the medium when frequency is near photonic band gap [1, 2]. Second harmonic generation is observed when phase-matching conditions are fulfilled,
i.e. phase velocities of first and second harmonics are equal. Homogeneous media have their own material dispersion, so phase mismatch always presents. Anisotropy in some materials can compensate dispersion in specific directions, and such nonlinear crystals are commonly used in lasers and parametric light generators . Photonic crystals are attractive for practical applications because of a large diversity of their dispersion properties comparing to homogeneous media. Varying photonic crystal parameters, such as lattice period, filling factor and refractive indices of media, one can manipulate
its band structure.
Multiferroics, i.e. the materials with electric and magnetic subsystems coexisting, are considered. The possible future application of materials in spintronics, storage devices and microwave technique are discussed. The results of the research devoted to the elaboration of new efficient multiferroics are presented.