Studies And Designs Of The Multipoint Interferometers For Realizing The Manipulation Of Optical Vortices And Intensity Patterns

Vortex field is a special kind of light field, where the wave fronts have helical variations.In an optical vortex, there exist some points where the intensity vanishes, and we call suchpoints vortex cores. Both the real part and the imaginary part of the field at cores are all zeros,and the phases here are undefined. Around a vortex core, the light phase has a helical variationalong with the increase of azimuthal angle. The total phase variation may be some integermultiples of, and the integer is called the topological charge of the vortex. For a vortex withthe phase increasing strictly linearly to the azimuthal angle, every photon it carries may takethe orbital angular momentum of that is determined by the topological charge. Due to thephase characters mentioned above and the potential use in dynamics, optical vortex hasattracted great attention since proposed. Now, optical vortex has been used in a variety of fieldsranging from optical micromanipulation, material science, quantum optics, opticalcommunication to biomedicine, and so on. Therefore, it is of great practical interest to studythe optical vortex.In optics, the study of multi-beam interference has also attracted great attention. Byadjusting the positions, incident directions, amplitudes and relative phases in the interferencingbeams, we can accurately control the resultant fields. Nowadays, multipoint interferometers,which are based on the optional selection of incident wave by pinholes, have been well appliedin optical studies. The multipoint interferometers can readily offer multiple waves forinterference, and their fabrications are easy and low-cost. In application, they have been usedin the detection of topological charges, generations of both optical vortices and optical lattices,and they are now a more and more useful tool in optics.Basing on the modulation of incident wave fronts by multipoint interferometers, weproposed a multipoint interferometer with the pinholes arranged in a helical way. Due to theadjustment of radial positions of the pinholes, the optical paths from adjacent pinholes to theorigin of the observation plane may increase or decrease evenly, and the total variation may bemultiples of the incident wavelength. This results in the specific phase differences between theinterferencing waves. We have illuminated such multipoint interferometers with plane waves,and have obtained high-order optical vortices on the observation plane in Fresnel field. Wehave illuminated the spiral-slit screen with vortex beams, and have realized the conversion oftopological charges of the incident vortex. We have realized the simultaneous distinguishes ofboth the value and the sign of the incident topological charges, by using a spiral pinholeinterferometer with small pinhole numbers. We have obtained second-order vortex arrays by illuminating six-pinhole interferometers of variable radial distances. The phase-encoded photonsieves have been proposed, and we have obtained designed intensity patterns after the sieves.We have also obtained the height variation of two transmissive ruled grating surfaces, using thecombination of a microscope objective and a interferometer. The whole paper is detailed inseven chapters.Chapter1: Introduction. We describe the background of this paper, and give the generaldescriptions of optical vortices. At the beginning, we show the development of optical vortex.Second, we study the characters of optical vortex, including its mathematical description,orbital angular momentum of photon and its propagation. Third, we review the commonly usedexperimental generation of optical vortex, including mode conversion of laser,computer-generated hologram, spiral phase plate, direct input of laser and multi-beaminterference. At the last, we discuss the methods in detecting of topological charge, includinginterference of vortex and plane wave, holograms, interferometries and multipointinterferometers.Chapter2: In this chapter, we study the application of spiral multipoint interferometers ingenerating high-order optical vortex. Pinholes are arranged with even azimuthal angleincrement on the multipoint interferometer. According to the quadratic relationship between thedistances from a pinhole to the observation plane origin and the distance from this pinhole tothe interferometer origin, we adjust the pinhole position in radial directions until the opticalpaths from neighboring pinholes to the observation plane origin have constant increment. Thetotal path variation determines the total phase difference in the multiple transmitting waves,which may be integer multiples of. We obtain high-order optical vortices in the interferencefield of the waves. In numerical simulation, we demonstrate the fabrication process of theinterferometer and verify the feasibility of this mechanism. We discover that the topologicalcharge of the generated vortex is determined by the total path variation, e.g., the structure ofthe pinhole arrangement. The simulations show that the possible topological charge of thevortex is confined to be no more than half the pinhole number. We also show that the feasibilityof the interferometer is influenced by the pinhole sizes, and that smaller pinholes are better fora good vortex. In experiment, we fabricate such spiral multipoint interferometers by ablatingpinholes on flattened Coca-Cola cans. The experimental results coincide with the simulationswell.Chapter3: In this chapter, we study the conversion of topological charge with the use ofspiral-slit screens. When an optical vortex transmits from a designed spiral-slit, its topologicalcharge may be altered. The variation is determined by the structure of the slit. We also replacethe slit by small number of isolated pinholes, and show that both the value and the sign of theincident topological charge could be distinguished simultaneously by reading the differentintensity patterns on the observation plane.Chapter4: We propose the phase-encoded photon sieves and use them to generate designed intensity patterns. First, we arrange some pinholes of equal size evenly on some ringscentered at the origin. The optical paths from the rings to the observation plane origin differ bymultiples of incident wavelength, and this design eliminates the quadratic phase aberration ofthe sieve in Fresnel diffraction. Then, using the iteration in the Gerchberg-Saxton algorithm,we obtain the required phase value at each pinhole. By deviating the pinhole position fromcorresponding ring, we encode such phase values on the sieve, and obtain the phase-encodedphoton sieve. When such sieves are illuminated by plane wave, the designed intensity patternsare obtained on the observation plane. We have also discussed the influences of pinholenumbers and rings on the quality of the generated patterns. We fabricate three phase-encodedphoton sieves in experiment, and verify their feasibilities.Chapter5: In this chapter, we generate second-order vortex arrays with six-pinholeinterferometers. The six-pinhole interferometer is fabricated by combining two differentregular three-pinhole interferometers together. In the simulations, we predict the requirement ofsize ratios of the two three-pinhole interferometers to generate second-order vortex arrays. Insimulation, the feasibility of the interferometer is verified, and the influence of the pinholesizes is discussed. By using the self-made six-pinhole interferometer with ratio4:5inexperiment, we obtain second-order vortex arrays under plane wave illumination.Chapter6: In this chapter, we obtain the height variations of two transmissive ruledgrating surfaces. By using the combination of a Mach-Zende interferometer and an objectivemicroscope of high numerical aperture and high magnification, we obtain the magnified imageof grating surface in small area and distract the phase distribution of the light from theinterferogram. The height variation is deduced from the phase values. We compare the resultswith the ones obtained by a Atomic Force Microscope, and discover that the optical methodrealizes a resolution of nano-scale.Charpter7: In this chapter, we summarize the results and the innovations of this paper,and describe the future work.