Elementary Optical Catastrophes and Caustic-Based Photonic Structures

Significant interest has been devoted to tailoring optical fields that transversely accelerate during propagation in the form of Airy, Weber and Mathieu beams. In this work, we introduce a new type of optical field that exhibits controlled angular acceleration during propagation which is achieved by superpositions of Bessel beams with non-canonical phase functions. We demonstrate these angular accelerating fields by modulating the phase and amplitude of a supercontinuum source with the use of a phase-only spatial light modulator (SLM). We illustrate that by considering only the first diffraction order when the SLM is encoded with a blazed grating, the SLM is capable of tailoring the spatial profile of broadband sources without any wavelength dependence. By digitally simulating free-space propagation on the SLM, we compare the effects of real and digital propagation on the angular rotation rates of the resulting optical fields for various wavelengths. The development of controlled angular accelerating optical fields will be useful in areas such as particle manipulation, plasma control, material processing and non-linear optics.

Based on a geometric caustic argument and diffraction catastrophe theory, we generate a novel form of accelerating beams using a symmetric 3/2 phase-only pattern. Such beams can be called accelerating quad Airy beams (AQABs) because they look very much like four face-to-face combined Airy beams. Optical characteristics of AQABs are subsequently investigated. The research results show that the beams have axial-symmetrical and centrosymmetrical transverse intensity patterns and quasi-diffraction-free propagation features for their four main lobes while undergoing transverse shift along parabolic trajectories. Moreover, we also demonstrate that AQABs possess self-construction ability when local areas are blocked. The unique optical properties of these beams will make them useful tools for future scientific applications.

From the Fresnel approximation to the Rayleigh–Sommerfeld solution for scalar wave propagation it follows that the field generated by a focused wave passing through an arbitrary aperture is simply related to the field generated by a collimated beam that is diffracted by any aperture of the same shape—the transverse intensity patterns are simply scaled and shifted. In fact, this result provides a simple, diffraction-based model for the action of a lens. A closed-form expression is found for the width of the beam generated by a focused uniform field that is diffracted by a circular aperture and, as an illustrative application, the beam of smallest maximum width over a fixed scanning depth is investigated.

Main lobe shifting and splitting phenomena of Airy beams are theoretically investigated based on the spatial light modulator (SLM) method. By digitally modulating the phase masks on the SLM, the single main lobe of the 2D symmetric Airy beam shifts to its neighboring side lobe. This results in the main-lobe splitting and the formation of a two-main-lobe state. These two main lobes further split into four while appropriately setting the phase modulation parameters. Meanwhile, the main lobe intensity decreases from 1.529 to 0.361a.u. as the incident Gaussian beam's amplitude is 1. Therefore, one, two, or four main lobes can be obtained in Airy beams, and the corresponding intensity can be flexibly modulated by digital phase masks without moving the obstacle. Furthermore, a set of Airy beams with single main lobes and their corresponding splitting are realized by periodically setting the propagation distance. This further improves the modulation flexibility of the main lobe intensity. In our work, the number and intensity modulations of main lobes in Airy beams may have significant potentials for optical communication devices, such as tunable lasers and optical demultiplexers.

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.

It is well known that large spherical drops of water in air give enhanced scattering at angles close to the rainbow angle θ r ≃ 138°. Near θ r , diffraction provides an essential correction to geometric optics and the scattering is a simple example of a fold diffraction catastrophe.1 We observed2 the scattering from spheroidal drops into the rainbow region and we find other diffraction catastrophes can be produced depending on the drop's axis ratio q = D/H. Here the drop's diameter is D in the equatorial plane and it is H along the vertical axis of rotational symmetry. An acoustic standing wave was used to levitate the drop and to control q. The drops were oblate (q > 1 ) and they were horizontally illuminated. With q ≃ 1.31, the observed scattering pattern corresponds to the focal section of a hyperbolic-umbilic diffraction catastrophe. For q differing somewhat from this value, the pattern was observed to separate into fold and cusp diffraction catastrophes. These novel manifestations of far-field diffraction catastrophes are applicable to inverse problems.

Airy beams showing curved paths have found extensive applications in fields such as optical trapping, biomedical analysis, and material processing. Despite their utility, dynamic control of Airy beams poses a significant challenge. This work investigates the experimental realization of dynamic steering of Airy beams by utilizing computer-generated holograms with phase-amplitude encoding on a phase-only spatial light modulator (SLM). We successfully generated and controlled Airy beams by imposing dynamic phase masks that manipulated both the phase and amplitude of the field, which sets our approach apart from conventional methods with only phase manipulation. By directly encoding in situ such a hologram and transferring it to an SLM, we are able to control the initial position and rotational orientation of Airy beams without relying on mechanical movement or traditional optical setups involving lenses and apertures. Generating Airy beams in any initial position and rotational direction is anticipated to significantly impact applications such as optical trapping, optical communication, and biomedical imaging by providing a flexible platform for dynamic Airy beam manipulation.

The goal of this project was to make LLNL a leader in Spatial Light Modulators (SLMs) by developing the technology that will be needed by the next generation of SLMs. We would use new lower voltage actuators and bond those actuators directly to controlling circuitry to break the fundamental limitations that constrain current SLM technology. This three-year project was underfunded in the first year and not funded in the second year. With the funding that was available, we produced actuators and designs for the controlling circuitry that would have been integrated in the second year. Spatial light modulators (SLMs) are arrays of tiny movable mirrors that modulate the wave-fronts of light. SLMs can correct aberrations in incoming light for adaptive optics or modulate light for beam control, optical communication and particle manipulation. MicroElectroMechanical Systems (MEMS) is a technology that utilizes the microfabrication tools developed by the semiconductor industry to fabricate a wide variety of tiny machines. The first generation of MEMS SLMs have improved the functionality of SLMs while drastically reducing per pixel cost making arrays on the order of 1000 pixels readily available. These MEMS SLMs however are limited by the nature of their designs to be very difficult to scale above 1000 pixels and have very limited positioning accuracy. By co-locating the MEMS mirrors with CMOS electronics, we will increase the scalability and positioning accuracy. To do this we will have to make substantial advances in SLM actuator design, and fabrication.

A study on the spatio-temporal dynamics of broad-area Nd:YAG (yttrium aluminiumgarnet), Nd-doped phosphate glass and Nd-doped silicate glass lasers is presented to showthe influence of the inhomogeneous gain profile and cross-relaxation phenomena on thespatio-temporal dynamics of the system. The suppression of the order–disorder transitionshown in Cabrera et al (2006 Opt. Lett. 31 1067) for homogeneously broadened class B lasersis found for both glass lasers, independently of the strength of the cross-relaxationmechanisms. The results obtained indicate that a higher degree of inhomogeneousbroadening leads to suppression of the filamentation in the transverse intensity pattern.

Photorefractive and computational holography in the experimental generation of Airy beams

Airy beams have attracted the attention of many researchers because of its characteristics of non-diffraction, self-bending and self-repairing. However, most studies on Airy beams are only in the optical frequency, and the devices that generate Airy beams (such as spatial light modulator, etc.) are complicated. Therefore, in this paper, a novel method for the generation of Airy beam is proposed in the microwave field by using a simple metasurface with high transmittance.

Self-accelerating beam is a kind of light beam capable of self-bending in free space without any external potential, of which a typical one is the well-known Airy beam. Such a beam has gained great attention for its extraordinary properties, including nondiffracting, self-accelerating and self-healing, which may have versatile applications in the delivery and guiding of energy, information and objects using light, such as particle manipulation, micro-machining, optical routing, super-resolution imaging, etc. However, since Airy beam can only propagate along parabolic trajectory, which reduces the flexibility in practical applications, thus how to design accelerating beams propagating along arbitrary trajectory is still a crucial problem in this area. One scheme is to keep on finding other analytical solutions of the wave equation besides Airy beam, such as semi-Bessel accelerating beams, Mathius beams, and Weber beams, moving along circular, elliptical, or parabolic trajectories, but it becomes increasingly difficult to find out any more solutions. A more effective solution to this problem is based on the caustic method, which associates the predesigned trajectory with an optical caustics and then obtains the necessary initial field distribution by performing a light-ray analysis of the caustics. This method has been implemented in real space and Fourier space based on Fresnel diffraction integral and angular-spectrum integral, respectively. It has been found recently that they can be unified by constructing Wigner distribution function in phase space. Based on the caustic method, accelerating beams were constructed to propagate along arbitrary convex trajectories in two-dimensional space at first. With continuous development of this method, the types of accelerating beams available have been extending from convex trajectories to nonconvex trajectories, from two-dimensional trajectories to three-dimensional trajectories, and from one main lobe to multiple main lobes, which opens up more possibilities for emerging applications based on accelerating beams. In future, previous researches and applications based on Airy beams will certainly be generalized to all these new types of accelerating beams, and owing to the great flexibility in designing accelerating beams, more application scenarios may emerge in this process with huge development potential. Thus in this paper, we review the principle and progress of the caustic method in designing accelerating beams.

Arrays of Gaussian vortex, Bessel and Airy beams by computer-generated hologram

With the rapid development of modern science, in particular, applied mechanics, the catastrophe theory proved to be quite effective in the analysis of classical results and the development of modern ones. This theory has developed significantly in the study of a number of issues in the theory of elastic stability, which studies the response of elastic bodies and structures to existing mechanical loads. Catastrophe theory predictions have important technical applications for estimating the critical forces that initiate the loss of stability of elastic bodies and engineering structures. The main basics of the research are analysed in this paper; based on the catastrophe theory, the problems are set; the main types of catastrophes’ functions are described; and the simplest of them, in particular the fold catastrophe, is applied. Based on the set analytical relations for the calculations of effective electrical conductivities and elastic modules by the pore concentration of the electrically conductive material, the estimation of the element strength of the composite sample is simulated in the form of a rod.