Interferometric methods for aberration-insensitive imaging and generation of light beams with controlled group velocity

Optical interferometry has many important applications in science and technology. For example, it is used to improve the performance of interferometric imaging systems, to detect weak signals in cosmology, to measure surface profiles and vibrations in metrology, and to visualize the amplitude and phase profiles of optical fields in holography. The main goal of the research presented in this thesis is to study static and dynamic interference effects and use them to develop novel methods for optical imaging and detection, as well as to create new structured optical beams with controlled group velocity in free space.A variety of imaging systems utilizing the intensity or field correlations of light have in the past few decades significantly extended their range of applications towards non-invasive scanning of three-dimensional objects and imaging through turbid media. However, the existing techniques are often not robust and have a relatively low resolution. In the thesis, we introduce novel interferometric imaging systems that combine the advantages of optical coherence tomography and classical ghost imaging to exhibit a high transverse resolution and insensitivity to optical aberrations. These systems are able to reveal a sharp image of the object even if its intensity image is completely destroyed by aberrations. The method can be used in optical microscopy, endoscopy, and three-dimensional imaging systems. The thesis also describes a method to create non-diverging multifrequency optical beams with controlled group velocity in free space. These beams exhibit the wave beating phenomenon, and the control of the group velocity in them is based on dynamic interference effects. We show that by adjusting the angular dispersion of the beam's plane-wave components, essentially arbitrary values of the group velocity can be achieved. We demonstrate theoretically that continuous-wave and pulsed Bessel beams with superluminal, subluminal and negative group velocities can be created. Furthermore, we find that the on-axis group velocity of a beam can be a function of both spatial and temporal coordinates. We demonstrate experimentally a longitudinally accelerating optical beam that shows both negative and positive group velocities with a magnitude several times higher than the speed of light in vacuum. The fact that the group velocity of the beam depends on the on-axis phase distribution of its frequency components allows one to measure the local group velocity interferometrically. The measured group velocities in the conducted experiments agree well with the theoretical predictions. Such optical beams can find applications in intensity interferometry, ultrafast optics, optical tweezers, and nonlinear optics.