Project topics and materials
Get Complete Project Material File(s) Now! »
Summary
This thesis focuses on two topics about optical vortices in strongly scintillated beams. One is optical vortex detection with a conventional Shack-Hartmann wavefront sensor. The other is the correction of strongly scintillated beams through forced vortex dipole annihilation.
Based on vortex detection with a line integral over the phase gradient around a vor- tex, circulation is implemented over the outputs of a Shack-Hartmann wavefront sensor to detect optical vortices. The output of the wavefront sensor is computed with an area integration to obtain an analytical expression for vortex circulation. The vortex locations and topological charges can be determined from the peaks of the circulation. In these investigations, it is shown that this circulation value for a vortex is not §2¼ as is ob- tained from a line integral, but a smaller value depending on the relative positions and its morphologies of the vortex in the wavefront sensor subaperture. Since the outputs
of a Shack-Hartmann wavefront sensor computed with area integrations approximate the outputs computed from the bright spots centroid shifts in a real Shack-Hartmann wave- front sensor, the vortex circulation values may be much closer to the results of physical experiments. At the same time, the in°uence of the morphology as the vortex is detected with a Shack-Hartmann wavefront sensor is also investigated.
In a strongly scintillated beam, there are generally numerous optical vortices. They are in general created and annihilated as vortex dipoles. Due to the cancellation e®ects in the circulations, the in°uence of a vortex dipole on the Shack-Hartmann vortex detection is also investigated in this thesis. Investigations are carried out in a Gaussian beam fo simplicity. Although the morphology of a vortex changes when the vortex is close to the annihilation point, it is shown that the vortex morphology evolution during beam propagation does not have a signi¯cant impact on Shack-Hartmann vortex detection.
When two oppositely charged vortices approach each other, the vortex circulation peaks may cancel each other out. This cancellation e®ect is especially strong when the separation distance in a vortex dipole is smaller than twice the size of the Shack-Hartmann wavefront sensor subaperture. Therefore a small separation distance makes Shack-Hartmann vortex detection more di±cult. Statistical results obtained from numerical simulations for Shack- Hartmann vortex detection in strongly scintillated beams show good agreement with the investigations in a Gaussian beam.
For the correction of strongly scintillated beams, the continuous phase °uctuations can be corrected with a conventional adaptive optics (AO) system by removing the least- squares reconstructed phase. This leaves behind the solenoidal phase distortions cause by optical vortices. The only way to correct the strongly scintillated beams with numerous optical vortices is to get rid of these optical vortices by forcing them to annihilate in oppo- sitely charged pairs. Since vortices are annihilated in pairs, the global background phase prior to dipole annihilation is investigated. This background phase shows the potential offorcing a vortex dipole to annihilate. However, the extraction of this background phas before dipole annihilation may introduce errors due to the ¯nite resolutions. Therefore, the background phase after dipole annihilation is taken into consideration. Since the phase changes gradually during beam propagation, the background phase after dipole annihilation is assumed to retain the power of forcing a vortex dipole to annihilate. Therefore, a background phase can be created based on the locations of any vortex dipole, and in turn use it to remove vortex dipoles. Numerical simulations show that the background phase after dipole annihilation can e±ciently accelerate the annihilation of a vortex di- pole. Even if two oppositely charged vortices will move apart from each other and never annihilate each other during beam propagation, this background phase can force them to annihilate.
Based on the concept of accelerating the annihilation of a vortex dipole through con- tinuous background phase modulation, a beam correction system is proposed. It consists of a few conventional AO systems using dipole annihilation and least-squares (DALS) phase correction. The least-squares phase correction scheme is also used to remove the continuous phase °uctuations. We ¯nd that the removal of the least-squares reconstructed phase in a strongly scintillated beam may cause some vortex dipoles with short separa- tion distance to annihilate by themselves after a short distance of free-space propagation.
However, it does not have an impact on the dipoles with large separation distances. An algorithm is proposed to identify the vortex dipoles according to the vortex locations. A background phase is created based on these dipoles, and is in turn used to force these dipoles to annihilate. In the beam correction system, the least-squares reconstructed phase together with this background phase is used to get rid of optical vortices and remove the continuous phase °uctuations in a strongly scintillated beam. Numerical simulations show that the number of optical vortices are reduced signi¯cantly after a few steps of DALS phase corrections. Several statistical results and curves are obtained and compared with least-squares phase correction, which indicate that the system’s performance is improved signi¯cantly.
1 Introduction
1.1 Literature review and motivations
1.2 Goals and objectives
1.3 Contributions
1.4 Outline of thesis
2 Beam propagation, beam correction and optical vortices
2.1 Introduction
2.2 Beam propagation in a turbulent atmosphere
2.3 Adaptive optics .
2.3.1 Principle of adaptive optics
2.3.2 Shack-Hartmann wavefront sensor
2.3.3 Deformable mirror
2.3.4 Phase reconstruction
2.4 Optical vortices
3 Optical vortex detection with a Shack-Hartmann wavefront sensor
3.1 Introduction
3.2 Theory of vortex detection
3.3 Vortex detection with a Shack-Hartmann wavefront sensor
3.3.1 Canonical vorte
3.3.2 Noncanonical vortex
3.4 Numerical investigation
3.4.1 Vortex detection in a scintillated beam
3.4.2 Noise circulations
3.5 Conclusion
4 Dipole in°uence on Shack-Hartmann vortex detection
4.1 Introduction .
4.2 In°uences of dipole on vortex detection in a
Gaussian beam
4.2.1 Morphology
4.2.2 Separation distance
4.2.3 Vortex dipole in a Gaussian beam .
4.3 Numerical simulations .
4.4 Conclusion
5 Accelerating the annihilation of an optical vortex dipole
6 Strongly scintillated beam correction through forced dipole annihilation
7 Conclusions
