Mingzhou Chen

Detection of phase singularities with a Shack-Hartmann wavefront sensor

While adaptive optical systems are able to remove moderate wavefront distortions in scintillated optical beams, phase singularities that appear in strongly scintillated beams can severely degrade the performance of such an adaptive optical system. Therefore the detection of these phase singularities is an important aspect of strong-scintillation adaptive optics. We investigate the detection of phase singularities with the aid of a Shack-Hartmann wavefront sensor and show that, in spite of some systematic deficiencies inherent to the Shack-Hartmann wavefront sensor, it can be used for the reliable detection of phase singularities, irrespective of their morphologies. We provide full analytical results, together with numerical simulations of the detection process.

Accelerating the annihilation of an optical vortex dipole in a Gaussian beam

When a Gaussian beam with two oppositely charged vortices propagates in free space, these two vortices will move around on the transverse beam plane. They may either move toward each other and annihilate each other spontaneously or survive all the way depending on the conditions. Here, we investigate how to force vortex dipoles to annihilate. We find that the background phase function created by two oppositely charged vortices during beam propagation can cause the vortices to move together and annihilate each other. The background phase function on a transverse plane just beyond the point where a dipole annihilated is continuous and retains the potential that forces a dipole to annihilate. We use this background phase function to accelerate the annihilation of vortex dipoles. Numerical results are provided to show the acceleration of dipole annihilation in a Gaussian beam, using such a background phase function.

Evolution of the scintillation index and the optical vortex density in speckle fields after removal of the least-squares phase.

Knowledge of the behavior of stochastic optical fields can aid the understanding of the scintillation of light propagating through a turbulent medium. For this purpose, we perform a numerical investigation of the evolution of the scintillation index and the optical vortex density in a speckle field after removing its continuous phase. We find that both the scintillation index and the vortex density initially drop and then increase again to reach an equilibrium level. It is also found that the initial rate of decrease in both cases is 1 order of magnitude faster than the eventual rate of increase. Their detail shapes are however different. Therefore different empirical functions are used to fit the shapes of these curves.

Application of orbital angular momentum to simultaneous determination of tilt and lateral displacement of a misaligned laser beam.

We present an analysis of the combined effects of tilt and lateral displacement on the orbital angular momentum spectrum of a laser beam. Our theory explains the symmetries and properties of the spectrum under the influence of misalignments. We apply the theory to establish a reliable and efficient method for determining and subsequently eliminating tilt and lateral displacement. An improved technique for obtaining the orbital angular momentum spectrum employing Laguerre-Gaussian modes is proposed. Finally, a numerical experiment is carried out to verify the method.

Speckle evolution with multiple steps of least-squares phase removal

We study numerically the evolution of speckle fields due to the annihilation of optical vortices after the least-squares phase has been removed. A process with multiple steps of least-squares phase removal is carried out to minimize both vortex density and scintillation index. Statistical results show that almost all the optical vortices can be removed from a speckle field, which finally decays into a quasiplane wave after such an iterative process.

Reflections on speckle: old and new results

Speckle was re-discovered after the invention of the laser in 1960. The unpublished 1963 Stanford Electronics Laboratory report by J W Goodman was the first comprehensive derivation of the first and second order statistics of the speckle intensity. This short paper describes how the senior author came to know Professor Goodman through their mutual, and lasting, interest in laser speckle. New results in speckle continue to be discovered, and we briefly describe one of these, the elimination of phase vortices using cascade adaptive optics systems.

Optical vortices in strongly scintillated beams

Opitcal vortices can not be removed with a conventional adaptive optics system. However, vortices can annihilate in pairs after a least-squares correction. This phenomenon can be explained by vortex plasma and confirmed with numerical simulations.

Dipole influence on Shack-Hartmann vortex detection in scintillated beams

Optical vortices can appear in an optical beam that propagates over a long distance through a turbulent atmosphere. A Shack-Hartmann wavefront sensor can be used to detect such vortices. However, the morphology of these vortices, which changes with beam propagation, and nearby oppositely charged vortices will affect this vortex detection. The influence of the morphology and the separation distance from oppositely charged vortices on the Shack-Hartmann vortex detection is studied. Numerical simulations for vortex detection under these turbulent atmospheric circumstances are also provided.

Experimental observation of speckle transition

In isotropic random optical waves, each dark area may contain optical vortices or phase singularities. In this paper, we experimentally generate a speckle pattern and observe its transition along the propagation direction. Experimental results show that the vortex density changes along the propagation direction when the continuous phase part of the speckle field is removed with a spatial light modulator. The contrast ratio of the spackle field also changes due to the transition of the field. Such a transition can be interpreted to a certain extent by the self-annihilation of vortex dipoles due to the least-squares phase removal.

Evolution of vortex density in a non-diffracting speckle field with its continuous phase removed

We break down the equilibrium state and the diffraction invariant property of a non-diffracting speckle field by removing its continuous part of the phase while leaving all vortices behind. During the propagation of such a phase corrected non-diffracting speckle field, the vortex density drops down to a minimum value and then comes back to an equilibrium value which is even higher than the initial one. Before the phase corrected field returns back to its new equilibrium state, another least-squares phase removal will be applied, at the position where there is a minimum vortex density, to further remove vortices from the speckle field. Such a process of removing least-squares phase and propagating the phase corrected field over a distance can be repeated to eliminate most of optical vortices. Statistical results show that most of optical vortices can be removed from a non-diffracting speckle field. Finally, a semi-plane wave without optical vortices can be obtained from an initial non-diffracting speckle field with multiple steps of least-square phase correction.