Generation and Characterization of Spatially Controlled Structured Light with Exotic Propagation Properties

Abstract

Light possesses various spatial and temporal degrees of freedom, such as amplitude, phase, polarization, time, and frequency. Controlling these aspects for generating light with complex field distributions possessing exotic propagation properties, has renewed its interest in numerous applications both in fundamental science as well in applied fields. Due to this there has been growing interest in synthesizing such complex light field dis tributions, also called as structured light. Typically, the output from a laser consists of a Gaussian distribution, which exhibits physical limitations for various applications. How ever, with continuous advancements, it has become possible to control the distribution of light in di↵erent degrees of freedom. In this thesis, our aim has been to develop sim ple, cost-e↵ective, and e cient outer-cavity and intra-cavity methods for generation and characterization of novel spatially structured light with customised intensity and phase distributions as well as possessing exotic propagation properties. In addition to these, our emphasis has also been to improve the quality, resolution, resilience against perturbations, and spectral range of spatially controlled structured light. Chapter 1 is an introduction to the thesis, where we begin with the role of structured light in the modern world by mentioning its applications in fundamental and applied fields where conventional Gaussian beams pose physical limitations. We have discussed various types of spatially structured light along with their propagation properties, obtained by tailoring light in its various spatial degrees of freedom. Further, we have discussed the generation of spatially structured light based on various outer-cavity and intra-cavity methods. We have also described the analytical and numerical methods for modeling the laser cavities as well as the propagation and quantification of spatially structured light. We have also provided a brief overview of spatial light modulators including the mechanism for modulating light in the amplitude and phase degrees of freedom. Chapter 2 emphasizes the tailoring of amplitude degree of freedom of light to gener ate uniform-intensity distribution with customized spatial shapes, such as square, annular, hollow-square, rectangular, and plus-sign, based on an outer-cavity method. Such struc tured light beams are non-trivial, as these are not the regular modes of conventional laser systems. We have generated such beams from di↵ractive optical elements (DOEs) whose phase distributions are obtained from an iterative algorithm that involves Fresnel propagation and spatial Fourier filtering. Particularly, an input Gaussian beam from a laser illuminates the DOE, and after propagating a certain distance (working distance) transforms into a desired structured light output. In our method, the spatial Fourier f iltering enables to obtain a relatively simple design of DOE (smooth phase distribution), and produces a high-quality uniform-intensity output beam. The simple smooth phase distribution o↵ers the possibility of easy manufacturing of DOEs. We have simulated dif ferent DOEs, and demonstrated the generation of uniform-intensity beams with di↵erent spatial shapes. We have characterized the quality of shaped output beams by the root mean square error, and show that the shaped output beams are generated with high quality. Further, we have performed a detailed robustness analysis of our method, where the quality of shaped output beam is investigated against the various imperfections in an input beam, such as misalignment with respect to DOE, e↵ect of asymmetry, speckle noise, presence of higher-order transverse modes, and mismatch of beam sizes. We have found that for imperfections < 10%, the quality of shaped output beams remains reason ably good. We have also shown that the quality of shaped output beams can be further improved by additional external spatial Fourier filtering. We have also demonstrated the generation of shaped output beam over a broad spectral range using a single DOE. In Chapter 3,wepresent thetailoringof amplitudeandphasedegreesof freedom of light based on an outer-cavity method for generating aberration laser beams (ALBs) containing multiple bright lobes in a transverse plane and possessing unique propagation properties, such as controlled autofocusing and self-healing in both free space as well as in turbulent media. The ALBs are generated using a DOE whose phase distribution consists of radial (rq)andperiodicangulardependence(sin(m)). Owing to the radial phase term, the ALBs possess autofocusing properties, and the periodic angular dependence generates di↵raction pattern with mth order symmetry. We have given a detailed mathematical formulation for describing the propagation of ALBs in turbulent media by solving Huygen Fresnel integral using stationary phase method. Further, the numerical and experimental investigations for the generation and propagation of ALBs are also carried out. We have observed that the turbulence deteriorates the spatial structure of ALBs and causes the beam wandering. The e↵ect of turbulence on the propagation of ALBs is quantified by calculating an overlap integral with respect to ALB in free space. The ALBs possess good autofocusing properties both in free space as well as in turbulent media, where on-axis peak intensity becomes maximum with tight focusing. The autofocusing properties of ALBs remain invariant irrespective of turbulence strength. The autofocusing distance, both in free space and turbulent media, can be controlled from any small to large values by controlling the ALB parameters. Further, we have also investigated the spectral de pendence of autofocusing of ALBs in turbulent medium, and found that the autofocusing distance does not depend on the turbulence, however, it decreases with an increase in wavelength. Furthermore, we have performed a detailed investigation of self-healing of ALBs both in free space as well as in turbulent media. We have found that, both in free space and turbulent media, the truncated ALB self-heals by redistributing the intensity within the beam, and it can self-heal reasonably well even for a large amount of truncation ⇠60%. The maximum self-healing always occurs at autofocusing distance, which remains invariant irrespective of amount of truncation and strength of turbulence. In Chapter 4,wehavepresentedthegenerationofasymmetricaberrationlaserbeams (aALBs) with controlled intensity distribution based on an outer-cavity method employing a DOE with phase asymmetry. The asymmetry in the phase distribution is introduced by shifting the coordinates in a complex plane, which provides additional control over the spatial intensity distribution of the beam. We have derived the mathematical formulations for general aALBs as well as the special cases of it. We have explored the mechanism of asymmetric control of intensity in aALBs, and found that the asymmetry parameters control the position of indeterminate phase point of the trigonometric phase term in aALBs, which creates a controlled asymmetric intensity distribution in the near-field plane, and upon propagation further provides a controlled transfer of intensity within the aALBs. In ALBs the intensity is symmetrically distributed in all lobes, and we have shown that by introducing asymmetry most of the intensity can be transferred to any one of the single lobe, and generates a high-energy density. In general, for aALB with number of lobes m,thespatial locationofhigh-energydensitylobecanbecontrolledwith aprecisevariationintheasymmetryparameter( ), and we have determined empirical relations between and m. We show that, for specific values of , the intensity in high-energy density lobe can be increased by several times as compared to other lobes. Further, we have investigated the propagation of aALBs, and have found that similar to ALBs, the aALBs also possess good autofocusing properties, which are not a↵ected by the asymmetry. The autofocusing distance of aALBs can be varied from small to large values by changing the parameters of aALB. The aALBs provide a more general framework for controlling intensity distribution, as for the specific values of asymmetry parameters the aALB behaves as an ALB. In Chapter 5,wepresentthegenerationofhigh-energydensitiesbysuppressionof higher-order sidelobes in the far-field of phase-locked lasers in di↵erent array geometries. We have generated an array of lasers in various one-dimensional (1D) and two-dimensional (2D) array geometries in a degenerate cavity and phase-locked them in the in-phase [out of-phase] configuration using far-field coupling with Gaussian apodizer [binary circular aperture]. Owing to non-uniform amplitude the geometry of laser array, the far-field of phase-locked lasers consists of higher-order sidelobes. These sidelobes contain a significant amount of energy, which limits the use of an output beam for high-power applications. Our method relies on modifying the combined field (near-field and far-field) distribution of phase-locked lasers to obtain uniform amplitude and uniform phase distributions in the near-field plane, which enables the generation of high-energy density lobe (zeroth order) in the far-filed intensity distribution. The method is applied to various 1D and 2D array geometries, such as square, triangular, Kagome, random, and 1D ring. We have shown that for the long-range in-phase locked laser arrays, the di↵raction e ciency of zeroth-order lobe can be improved by several factors (⇠ 3 4). The improved di↵raction e ciencies are found to be in a range of 90% 95% (for 2D arrays) and ⇠ 75% (for 1D ring array). Further, the e↵ects of range of phase locking, system size, as well as topological defects are examined on the di↵raction e ciency of zeroth-order lobe in the far-field of phase-locked laser arrays. We have also investigated our method for the out-of-phase locked lasers in a square array, where the zeroth-order has no intensity. With our method, we have obtained a high-energy-density zeroth-order lobe with a di↵raction e ciency of 81%. Our results on producing high-energy density beams with suppressed higher-order sidelobes can be exploited for various applications in di↵erent areas. In Chapter 6,wepresentanovelande cientintra-cavitymethodforthegeneration of high-power discrete optical vortices with precisely controlled topological charges (l)by phase locking one-dimensional (1D) ring array of lasers in a degenerate cavity that involves spatial Fourier filtering. Owing to the special geometry of a degenerate cavity, it enables an e cient formation of a 1D ring array of lasers, where each laser consists of a nearly fundamental Gaussian distribution, and independent from each other. Initially, the lasers consist of random phase distribution, and are equally probable. To force 1D ring array of lasers in desired phase-locked steady state of optical vortex configuration, we employ a spatial Fourier filter (amplitude mask) at the Fourier plane inside the degenerate cavity, whose transmission function is engineered by the Fourier transform of a desired discrete optical vortex. The spatial Fourier filtering mechanism helps to eliminate the undesired phase distributions by introducing additional losses to them, thereby, enables the lasers to f ind a correct phase distribution in the form of a desired discrete optical vortex. With the specifically engineered spatial Fourier filters, we have demonstrated generation of discrete optical vortices with di↵erent system sizes and precisely controlled topological charges. Further, we have performed a detailed investigation of propagation, such as diver gence and self-healing, of discrete optical vortices, and compared them with the conven tional continuous optical vortices (Laguerre-Gaussian/Bessel-Gauss beams). Unlike con ventional continuous optical vortices, we have found that for a given system size (number of lasers) and fixed distance between the neighbouring lasers, the size of a discrete optical vortex and its divergence does not depend on l. Further, we have performed a detailed investigation of self-healing by partially truncating a discrete optical vortex in the waist plane (z =0)andpropagatedplane(z>0). The results show that partially truncated discrete optical vortices can self-heal quite well. The self-healing distance is found to be dependent on the amount of truncation, particularly, it increases with an increase in the amount of truncation. We have found a good agreement between the experimental and numerical results. In Chapter 7,wepresentanovelande cientmethodforaccuratedeterminationof magnitude and sign of topological charge of an unknown discrete optical vortex, which is formed by an array of lasers in a 1D ring geometry. It relies on measuring the interference pattern of a discrete optical vortex, which is obtained by interfering a single selected laser with itself and with all the other lasers in a 1D ring array, using a Mach-Zhender interferometer. The interference pattern is quantified by analyzing the fringe visibility at each laser in a 1D ring array. The discrete laser arrays with l =0andl 6 =0havedi↵erent phase distributions, thus producing interference patterns with shifted interference fringes. The averaging of these phase shifted interference patterns gives rise to a variation in the fringe visibility as a function of laser number in a discrete optical vortex, thus enables the identification of topological charge. The magnitude of topological charge of a discrete optical vortex is found to be proportional to the number of dips observed in the fringe visibility curve. Further, for an accurate determination of sign of an unknown discrete optical vortex, we have averaged the interference pattern of an unknown discrete optical vortex (l 6 =0) with the interference pattern of a discrete optical vortex with known topological charge l =+1. Thenumberofdips inthe fringevisibilitycurvedecreasesbyone forpositive values of l, and increases byone for negativevalues of l. W ehave also in vesti gated the robustness of our method against the presence of phase disorder that may occur due to aberrations in a system. It is found that the phase disorder does not a↵ect an accurate determination of topological charge. We have demonstrated our method for discrete optical vortices with topological charges from small to large values, and accurately determined their magnitude and sign. We have provided theoretical descriptions along with the numerical and experimental results, and found an excellent agreement between them, indicating that our method is highly e cient. The interest in the field of spatially controlled structured light is growing because of its potential applications in many branches of modern technology. It has shown potential where commonly used Gaussian beams have encountered physical limitations. The results presented in this thesis will contribute in developing novel structured light sources as well as characterization tools, with widespread potential applications. Our experimental and theoretical findings will open new possibilities in the field of fundamental research, health, defense, industries, optical communications, optical computing, etc.