Modal description of paraxial structured light propagation: tutorial

Propagation of coherence-OAM matrix of an optical beam in vacuum and turbulence

Propagation of the coherence-orbital angular momentum (COAM) matrix of partially coherent beams in homogeneous and isotropic turbulence, e.g., atmosphere, is formulated using the extended Huygens-Fresnel principle. It is found that under the effect of turbulence the elements in the COAM matrix will generally be affected by other elements, resulting in certain OAM mode dispersion. We show that if turbulence is homogeneous and isotropic, there exists an analytic "selection rule" for governing such a dispersion mechanism, which states that only the elements having the same index difference, say l - m, may interact with each other, where l and m denote OAM mode indices. Further, we develop a wave-optics simulation method incorporating modal representation of random beams, multi-phase screen method and the coordinate transformation to simulate propagation of the COAM matrix of any partially coherent beam propagating in free space or in turbulent medium. The simulation method is thoroughly discussed. As examples, the propagation characteristics of the most representative COAM matrix elements of circular and elliptical Gaussian Schell-model beams in free space and in turbulent atmosphere are studied, and the selection rule is numerically demonstrated.

Aberration-induced vortex splitting in amplified orbital angular momentum beams

Here we report the generation and power amplification of higher-order (l = 2) orbital angular momentum (OAM) beams using a compact end-pumped Nd:YAG Master-Oscillator-Power-Amplifier (MOPA) design. We analysed the thermally-induced wavefront aberrations of the Nd:YAG crystal using a Shack-Hartmann sensor as well as modal decomposition of the field and show that the natural astigmatism in such systems results in the splitting of vortex phase singularities. Finally, we show how this can be ameliorated in the far field through engineering of the Gouy phase, realising an amplified vortex purity of 94% while achieving an amplification enhancement of up to 1200%. Our comprehensive theoretical and experimental investigation will be of value to communities pursuing high-power applications of structured light, from communications to materials processing.

Complex structured beam direct generation by coherent superposition of a complete set of degenerate eigenmodes

Structured beams have played an important role in many fields due to their rich spatial characteristics. The microchip cavity with a large Fresnel number can directly generate structured beams with complex spatial intensity distribution, which provides convenience for further exploring the formation mechanism of structured beams and realizing low-cost applications. In this article, theoretical and experimental studies are carried out on complex structured beams directly generated by the microchip cavity. It is demonstrated that the complex beams generated by the microchip cavity can be expressed by the coherent superposition of whole transverse eigenmodes within the same order, thus forming the eigenmode spectrum. The mode component analysis of complex propagation-invariant structured beams can be realized by the degenerate eigenmode spectral analysis described in this article.

Semi-analytic simulation of optical wave propagation through turbulence

Split-step wave-optical simulations are useful for studying optical propagation through random media like atmospheric turbulence. The standard method involves alternating steps of paraxial vacuum propagation and turbulent phase accumulation. We present a semianalytic approach to evaluating the Fresnel diffraction integral with one phase screen between the source and observation planes and another screen in the observation plane. Specifically, we express the first phase screen's transmittance as a Fourier series, which allows us to bring phase screen effects outside of the Fresnel diffraction integral, thereby reducing the numerical computations. This particular setup is useful for simulating astronomical imaging geometries and two-screen laboratory experiments that emulate real turbulence with phase wheels, spatial light modulators, etc. Further, this is a key building block in more general semianalytic split-step simulations that have an arbitrary number of screens. Compared with the standard angular-spectrum approach using the fast Fourier transform, the semianalytic method provides relaxed sampling constraints and an arbitrary computational grid. Also, when a limited number of observation-plane points is evaluated or when many time steps or random draws are used, the semianalytic method can compute faster than the angular-spectrum method.