вращения внеосевого параксиального оптического пучка. Рассчитаны частотные спектры для параллельно сдвинутых и отклоненных пучков, вращающихся относительно референтной оси.
Ключевые слова: дислокации волнового фронта, оптические вихри, орбитальный угловой момент, паракcиальные оптические пучки, сингулярная оптика.
Vasnetsov M. V. Optical beams with wave fronts dislocations. – Manuscript. Dissertation for a doctor of science degree in physics and mathematics with specialization 01.04.05 – optics, laser physics. – Institute of Physics, National Academy of Sciences of Ukraine, Kyiv, 2005.
The research is devoted to a systematic study of main properties of optical beams with phase singularities, or wave-front dislocations. Principles of singular optics and features of optical vortices, which appear around wave-front dislocations, are accounted in succession. The origin of appearance of orbital angular momentum (OAM) is explained for a beam with an optical vortex. Edge dislocations of wave fronts are considered on a model of interference of two two-dimensional or ordinary Gaussian beams. Scenarios of a collapse of a system of two transversal optical vortices and two lines of phase saddles are shown, as well as an unfolding of an edge dislocation in the collision with the saddle line. The direction of light flow circulation was understood being dependent on the phase velocity distribution in the beam cross-section in the waist. Model beams with different directions of the light flow circulation around the edge dislocation were analyzed.
On the basis of a holographic principle, a method of generation of laboratory beams with wave-front dislocations in the form of axial and off-axis optical vortices was developed, particularly as a superposition of two Laguerre-Gaussian modes. A term “combined beam” is introduced as a superposition of two or more Laguerre-Gaussian modes. Trajectories of optical vortices in space are considered for combined beams. A possibility for a vortex trajectory to leave the beam is demonstrated, and therefore a violation of the topological charge conservation low was established. For a combined beam an analysis of OAM distribution across the beam was performed, and a general formula of OAM interference was obtained. With the aid of laboratory beams first time in the optical experiment an annihilation of optical vortices with opposite signs of topological charges and rotation of a pair of vortices with topological charges of equal sign around optical axis were studied. In these experiments the Gouy phase shift was directly measured. An influence of a weak coherent background on optical vortices of higher orders was analyzed.
Diffraction of optical-vortex beam on a nontransparent edge was experimentally studied. The effect of optical vortex regeneration was demonstrated in the first time.
A scheme of spatial separation of components of an optical beam, which are different in the sense of orbital angular momentum value “per photon” was proposed and experimentally realized.
Experiments were performed for the study of phase dislocations formation in a beam due to light-induced lens in a nonlinear optical medium. In the first time a doubling of the topological charge of an optical vortex in the process of second-harmonic generation was shown.
In the first time a phase reversal of a beam with optical vortices was performed.
In the first time in an optical region a direct experiment was carried out for observation of the rotational Doppler effect for beams with orbital angular momentum, on the level of frequency shift 1 Hz. The source of the optical vortex beam was a spiral diffraction grating, which rotation affected the optical frequency of the diffracted beam. The frequency shift was also observed in the reciprocal transformation, when an optical-vortex beam was diffracted into a vortex-free wave by the rotating spiral grating.
One-beam interferometer was realized for the measuring of phase shift between components with zero and nonzero OAM while rotation of a combined beam. This experiment demonstrated the possibility of frequency separation of the components with different OAM. In the first time a spectral selection of OAM components was obtained for a rotating beam, created as a superposition of Gaussian and Laguerre-Gaussian LG01 components. A general case of an off-axis paraxial beam rotation was analyzed. The frequency spectra generated by rotational Doppler effect were calculated for parallelly shifted and deflected beams, rotating around the reference axis. For a rotating combined beam, the shape of measured frequency spectrum was calculated in the dependence of the observation point coordinates.
Key words: wave-front dislocations, optical vortices, orbital angular momentum, paraxial optical beams, singular optics.