Generation of phase edge singularities by coplanar three-beam interference and their detection

Abstract

In recent years singular optics has gained considerable attention in science and technology. Up to now optical vortices (phase point dislocations) have been of main interest. This paper presents the first general analysis of formation of phase edge singularities by coplanar three-beam interference. They can be generated, for example, by three-slit interference or self-imaging in the Fresnel diffraction field of a sinusoidal grating. We derive a general condition for the ratio of amplitudes of interfering beams resulting in phase edge dislocations, lateral separation of dislocations depends on this ratio as well. Analytically derived properties are corroborated by numerical and experimental studies. We develop a simple, robust, common path optical self-imaging configuration aided by a coherent tilted reference wave and spatial filtering. Finally, we propose an automatic fringe pattern analysis technique for detecting phase edge dislocations, based on the continuous wavelet transform. Presented studies open new possibilities for developing grating based sensing techniques for precision metrology of very small phase differences.

Optical design of a laser wavefront sensor applicable under strong diffraction effects by irreproducible microscale high-density plasma

“…At this point, which is called the phase singularity, the wavefronts cancelled each other and the amplitude became zero. Phase singularities occur frequently during laser interference [29] or when steep gradients are present in the refractive index [30][31][32].…”