Airy-induced dynamics in nonlinear media

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Airy beam is a self-sustained light beam that propagates in free space along a parabolic trajectory with a constant lateral acceleration. It is a diffraction-free beam with an electric field pattern described by the Airy function containing a main lobe and side lobes. Unlike Gaussian beam that expands after the focus, a practical finite-energy Airy beam keeps its pattern without spreading over a relatively long distance during its propagation. This unique feature makes the Airy beam a great potential of designing optical systems for three-dimensional (3D) imaging. In this work, we develop a new optical 3D imaging methodology using Airy beam. The proposed imaging method has an advantage of increased depth of field (DOF) that is important in biological optical imaging. In the first step, we perform a fundamental research on specific parameters that can affect the properties of the Airy beams. The finite-energy Airy beams are generated by optical Fourier transform using a lens with the incoming plane wave that is truncated by an aperture. Our simulation and experiments showed that by changing the aperture size and the focal length of the lens, the Airy beam pattern is modified. In addition, the DOF, the beam size and the main lobe energy are changed. As a result, Airy beam can be designed for specific imaging applications. Next, we consider the phase in the cubic phase pattern for the phase modulation to generate the Airy beam. This problem is related to the wavelength dependent phase modulation since the phase in cubic phase pattern is designed for a specific wavelength whereas a broadband light source is normally used in optical coherence tomography (OCT). A liquid crystal display (LCD) panel from a projector is used as the SLM. The cubic phase patterns with different gray values displayed on the computer screen provide different phase modulations in the SLM. The experimental and simulated results show that the phase modulation affects the beam shape of the Airy beam. If the maximum phase modulation is larger than 1.7pi, the Airy beam can keep its pattern and the unmodulated Gaussian beam can be neglected. Further, we design a 3D imaging system using the phase-space method based on the Wigner distribution function (WDF). We theoretically build the WDF for the Airy beam and show that the WDF of the Airy beam is shifted in the phase-space as the transverse position of incoming Airy beam changes, and the WDF is tilted as changing the axial position (along the propagation direction). A larger truncating factor can reduce the energy contribution in WDF for the side lobes and modify the shape of the main lobe close to a straight line. In this case, the WDF of the Airy beam is similar to that of the Gaussian beam. However, the DOF of the Airy beam is greatly improved. We perform experimental measurements of WDF using the basic idea of measuring both the space and spatial frequency information in a 4-f system. Our experimental results match the simulation and validate the 3D imaging using Airy beam in the phase space.

The propagation characteristics of a single Airy beam in nonlinear Kerr media were numerically investigated by utilizing the split-step Fourier transform method. We show that in addition to normal breathing solitons, the anomalous bound states of Airy spatial solitons can also be formed, which are similar to the states formed in the interaction between two Airy beams in nonlinear media. This quasi-equilibrium state is formed by the interaction of the main soliton beam and side lobes of Airy beam due to their different propagation trajectories in the nonlinear media. Moreover, it has been shown the Airy spatial solitons in tree structure can be formed by adjusting the initial parameters in the interaction between the Airy beam and Kerr media.

Based on scintillation index of Airy beam and exponentiated Weibull channel model, analytical expressions of average channel capacity for free-space optical (FSO) communication links with Airy beam as signal carrier under weak atmospheric turbulence and on-off keying modulation scheme are derived. The average capacity at various propagation distances, transverse scale factors and exponential decay factors has been evaluated. And we compared the average capacity of FSO links with Airy beam and Gaussian beam as signal carrier. The results show that the average capacity of FSO links with Airy beam as carrier increases with the increase of mean signal-to-noise ratio and decreases uniformly with the increase of propagation distance. When the transverse scale factor of Airy beam is about 2 cm, a higher average capacity can be obtained. And the smaller the exponential decay factor of Airy beam, the larger the average capacity. Under the same source power or source width, the average capacity of FSO links with Airy beam as carrier is significantly higher than that of FSO links with Gaussian beam as carrier. The results of this research have some reference significance for the application of Airy beam in FSO communication system.

Average Bit Error Rate (BER) expression of free-space optical (FSO) communication links with Airy beam as signal carrier under weak atmospheric turbulence and on–off keying modulation scheme is derived based on scintillation index of Airy beam and Exponentiated Weibull channel model. The average BER has been evaluated at different transverse scale factors and exponential decay factors of Airy beam and link distances. And comparison of the average BER of FSO links with Airy beam and Gaussian beam as signal carrier has been carried out. The simulation results show that the average BER of FSO links with Airy beam as carrier decreases with the increase of mean signal to noise ratio and increases with the increase of transmission distance. When the transverse scale factor is about 1.5 cm, a lower average BER can be obtained. And the smaller the exponential decay factor is, the lower the average BER is. Under the same atmospheric turbulence condition, the average BER of FSO links with Airy beam as carrier is obviously better than that of FSO links with Gaussian beam as carrier. The results of this research have some significance for the application of Airy beam in FSO system.

We compared optical scattering of Airy and Gaussian beams, generated simultaneously using a LCD panel, through a turbid medium. The Airy beam had a smaller speckle size due to its self-healing property.

Two-photon flow cytometry with laser scanning two-dimensional airy beams

A high-efficiency laser coherent combination method based on the virtue of the self-transverse acceleration effect of Airy beams is proposed and demonstrated by converting an array of Gaussian beams into Airy beams array to reduce laser beams separation distance. The coherent combination procedures of circular array for both Airy and Gaussian beams are theoretically and experimentally studied. The results show that the central intensity of the laser coherent combination of the circular array of Airy beams is 14.33 times higher than that of the Gaussian beams array, and the combined efficiency of the circular array of Airy beams is 1.64 times higher than that of the Gaussian beams circular array. The method may provide an efficient way to increase combination efficiency of laser coherent combination array and may have a broad application prospect in optical communication, particle capture, material processing.

Structured light – electromagnetic waves with a strong spatial inhomogeneity of amplitude, phase, and polarization – has occupied far-reaching positions in both optical research and applications. Terahertz (THz) waves, due to recent innovations in photonics and nanotechnology, became so robust that it was not only implemented in a wide variety of applications such as communications, spectroscopic analysis, and non-destructive imaging, but also served as a low-cost and easily implementable experimental platform for novel concept illustration. In this work, we show that structured nonparaxial THz light in the form of Airy, Bessel, and Gaussian beams can be generated in a compact way using exclusively silicon diffractive optics prepared by femtosecond laser ablation technology. The accelerating nature of the generated structured light is demonstrated via THz imaging of objects partially obscured by an opaque beam block. Unlike conventional paraxial approaches, when a combination of a lens and a cubic phase (or amplitude) mask creates a nondiffracting Airy beam, we demonstrate simultaneous lensless nonparaxial THz Airy beam generation and its application in imaging system. Images of single objects, imaging with a controllable placed obstacle, and imaging of stacked graphene layers are presented, revealing hence potential of the approach to inspect quality of 2D materials. Structured nonparaxial THz illumination is investigated both theoretically and experimentally with appropriate extensive benchmarks. The structured THz illumination consistently outperforms the conventional one in resolution and contrast, thus opening new frontiers of structured light applications in imaging and inverse scattering problems, as it enables sophisticated estimates of optical properties of the investigated structures.

In this paper, by analyzing the main lobe of the Airy beam and its fitting Gaussian beam, we define the Rayleigh range of Airy beam based on the width of FEABs main lobe for scaling the propagation characteristic of the Airy beam. The similar diffraction-free distance of FEAB (here, the width of the main lobe expanding to times) can be scaled by Rayleigh range, but it is from infinite (Pure non-diffraction beam) to one Rayleigh range (the same with Gaussian beam) when decay factor is from 0 to 1. On the contrary, although the FEAB with smaller decay factor () can propagate more Rayleigh ranges keeping diffraction-free, the effective energy in the main lobe is low by studying the power in the bucket (PIB). If more energy needing in the main lobe, the FEAB need bigger decay factor () will become more similar with Gaussian beam which can propagate about one Rayleigh range.

The additive manufacture of polymer optical elements has the promise of reducing component weight, providing new design capabilities, and enhanced performance for a wide variety of military and commercial optical systems. This paper reviews progress in the development of 3d printed Gradient Index (GRIN) lenses and optical phase masks. The 3d printing process uses a modified commercial inkjet printer and UV curable polymers that have specific nanoparticles added to them to modulate the index of refraction. Complex optical phase masks for the generation of Airy laser beams and polymer GRIN lenses to replace conventional glass lenses used in a telescope or riflescope are created. The generation and propagation of Airy beams using these polymer generated optical phase masks has been investigated and analyzed through experimentation, simulations, and comparison with recent theoretical predictions. Airy beams have been generated using the conventional approach using a spatial light modulator and compared to the 3d printed optical phase masks. The maximum non-diffracting propagation distance of an aperture truncated Airy beam was experimentally measured. The results show that the maximum non-diffracting propagation distance of a laboratory generated Airy beam is proportional to x0 2 , the Airy beam waist size squared. The size of the Gaussian envelope beam has a weaker effect on the Airy beam propagation distance. The experimental results were compared with current theoretical models. A set of 1 inch diameter 100 mm focal length polymer GRIN lenses have been made using 3d printing. Transmission and modulation transfer function (MTF) results for the lenses is reported.

The additive manufacture of polymer optical elements has the promise of reducing component weight, providing new design capabilities, and enhanced performance for a wide variety of military and commercial optical systems. This paper reviews progress in the development of 3d printed Gradient Index (GRIN) lenses and optical phase masks. The 3d printing process uses a modified commercial inkjet printer and UV curable polymers that have specific nanoparticles added to them to modulate the index of refraction. Complex optical phase masks for the generation of Airy laser beams and polymer GRIN lenses to replace conventional glass lenses used in a telescope or riflescope are created. The generation and propagation of Airy beams using these polymer generated optical phase masks has been investigated and analyzed through experimentation, simulations, and comparison with recent theoretical predictions. Airy beams have been generated using the conventional approach using a spatial light modulator and compared to the 3d printed optical phase masks. The maximum non-diffracting propagation distance of an aperture truncated Airy beam was experimentally measured. The results show that the maximum non-diffracting propagation distance of a laboratory generated Airy beam is proportional to x0 2, the Airy beam waist size squared. The size of the Gaussian envelope beam has a weaker effect on the Airy beam propagation distance. The experimental results were compared with current theoretical models. A set of 1 inch diameter 100 mm focal length polymer GRIN lenses have been made using 3d printing. Transmission and modulation transfer function (MTF) results for the lenses is reported.

Generation and investigation of terahertz Airy beam realized using parallel-plate waveguides

An Airy beam is a non-diffractive wave which propagates along a ballistic trajectory without any external force. Although it is impossible to implement ideal Airy beams because they carry infinite power, so-called finite Airy beams can be achieved by tailoring infinite side lobes with an aperture function and they have similar propagating characteristics with those of ideal Airy beams. The finite Airy beam can be optically generated by several ways: the optical Fourier transform system with imposing cubic phase to a broad Gaussian beam, nonlinear generation of Airy beams, curved plasma channel generation, and electron beam generation. In this presentation, a holographic generation of the finite Airy beams will be discussed. The finite Airy beams can be generated in virtue of holographic technique by ‘reading’ a hologram which is recorded by the interference between a finite Airy beam generated by the optical Fourier transform and a reference plane wave. Moreover, this method can exploit the unique features of holography itself such as successful reconstruction with the imperfect incidence of reference beam, reconstruction of phase-conjugated signal beam, and multiplexing, which can shed more light on the characteristics of finite Airy beams. This method has an advantage in that once holograms are recorded in the photopolymer, a bulky optics such as the SLM and lenses are not necessary to generate Airy beams. In addition, multiple Airy beams can be stored and reconstructed simultaneously or individually.

In this contribution, we experimentally demonstrate a new type of spatial solitons arising from the mutual interaction of multiple two-dimensional Airy beams in a photorefractive nonlinear refractive index medium. Thereby, we combine two important concepts of optics: the fascinating accelerated Airy beams and nonlinear beam localization such as spatial soliton formation. We investigate the generation of this novel type of solitons and soliton pairs with respect to the number and phase relation of the superimposed Airy beams and support all experiments with comprehensive numerical simulations.

Photorefractive and computational holography in the experimental generation of Airy beams