Date of Award

May 2021

Document Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering

Committee Member

Eric Johnson

Committee Member

Richard Watkins

Committee Member

Hai Xiao

Committee Member

Lin Zhu


Optical orbital angular momentum (OAM) describes orbiting photons, swirling local wave vectors, or spiraling phase distribution depending on what theory we use to explain light. If we consider light as a propagating electromagnetic wave, then light has the freedoms of frequency, magnitude, phase, and polarization. For a monochromatic light, expanding the later three freedoms spatiotemporally, numerous optical modes are solved from Maxwell’s equations and boundary conditions. OAM mode study starts from integer charge because it is in the integer form of the fundamental phase singularity structure.

Fractional OAM mode is the Fourier series of integer OAM modes. The average OAM does not conserve along with propagation for the traditional fractional OAM modes. We propose a new asymmetric fractional Bessel Gaussian mode providing the average OAM conserving along with the propagation.

To better understand the fractional OAM mode or integer OAM mode combination, we study the novel concentric vortex optics. The analytical propagation expression of the concentric vortex beam is derived and analyzed. The concentric vortex beam is essentially the OAM spectrum, with only two integer OAM components. The spectrum coefficiencies are real numbers and approximately power equalized in general cases. The concentric vortex beam is the coherent combination of incomplete Kummer beams. As the inner aperture tuning large, the beam evolves into the Kummer beam with the inner charge number. The aperture decreases, the outer charges Kummer beam dominates.

The proposed asymmetric fractional Bessel Gaussian beam’s Fourier transform is azimuthal Gaussian perfect vortex. We use log-polar coordinate mapping diffractive optics to transform the elliptical Gaussian beam into the desired azimuthal Gaussian perfect vortex beam. The generated asymmetric fractional Bessel Gaussian beam is systematically compared with Kotlyar’s asymmetric Bessel Gaussian beam. It’s found that the proposed beam has a narrower OAM spectrum, preserving average fractional OAM. Furthermore, the log-polar transform’s inherent output lateral shifting problem is addressed for the first time to our knowledge. An improved log-polar design is proposed, and we use five critical metrics to show the new log-polar generated asymmetric Bessel Gaussian beam’s quality is much improved.

The manipulation of the high order asymmetric fractional Bessel Gaussian beam is critical to applications scaling from communication, sensing, filamentation, to micromanipulation. We propose and demonstrate acousto-optical deflector (AOD) HOBBIT (Higher Order Bessel Beams Integrated in Time) system. The system can continuously tune the OAM modes on the order of 400 kHz. This speed beats the fastest spatial light modulator (SLM), and even better, the proposed system could work for high power applications.



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