In this work, we present a novel and practical method for generating optical vortices in high-power laser systems. Off-axis spiral phase mirrors are used at oblique angles of incidence in the beam path after amplification and compression allowing for the generation of high-power optical vortices in almost any laser system. An off-axis configuration is possible via modification of the azimuthal gradient of the spiral phase helix and is demonstrated with a simple model using a discrete spiral staircase. This work presents the design, fabrication, and implementation of off-axis spiral phase mirrors in both low and high-power laser systems.
We report on the generation of high-order optical vortices by spiral phase mirrors. The phase mirrors are produced by direct machining with a diamond tool and are shown to produce high-quality optical vortices with topological charges ranging from 1 to 1000 at a wavelength of 532 nm. The direct machining technique is flexible and offers the promise of high-precision, large-diameter spiral phase mirrors that are compatible with high optical powers.
We propose to generate optical vortices using a degenerate optical resonator with an intra-cavity spiral phase plate (SPP). The rays retracing skewed V-shaped paths in the resonator are phase-locked to form vortex laser with wavefront dislocation mirroring the topological charge of the SPP. Experimental demonstrations on diode-pumped solid state system using Nd:YAG crystal emitted randomly polarized optical vortices at a wavelength of 1064nm when the pump power went above 1.52W and the slope efficiency was 0.19. For long-term operations a power fluctuation of 2.2\% and pointing stability of 2.…
We designed a metallic programmable mirror for optical wavelengths made up of a large number of discrete steps which can be moved independently by actuators. The device is able to easily reshape an incident beam, imprinting on it an optical vortex with tunable topological charge and orbital angular momentum (OAM). Furthermore it is possible to generate almost arbitrary field profiles which can be used for spatial encoding.
In view of wide applications of structured light fields and plasmonic vortices, we propose the concept of compound plasmonic vortex and design several structured plasmonic vortex generators. This kind of structured plasmonic vortex generators consists of multiple spiral nanoslits and they can generate two or more concentric plasmonic vortices. Different from Laguerre-Gaussian beam, the topological charge of the plasmonic vortex in different region is different. Theoretical analysis lays the basis for the design of radially structured plasmonic vortex generators and numerical simulations for se…
We introduce a simple and practical method to create ultrashort intense optical vortices for applications involving high-intensity lasers. Our method utilizes femtosecond laser pulses to laser-etch grating lines into laser-quality gold mirrors. These grating lines holographically encode an optical vortex. We derive mathematical equations for each individual grating line to be etched, for any desired (integer) topological charge. We investigate the smoothness of the etched grooves. We show that they are smooth enough to produce optical vortices with an intensity that is only a few percent lower…
Square vortex lattices predicted theoretically and experimentally observed in diode-pumped solid state microchip lasers are shown to have a remarkable symmetry. These lattices are formed by counter-rotating vortices. The interaction of vortices with nonlinear gain medium leads to precession of vortices and collective excitations with dynamics identical to acoustical and optical vibrations of atomic lattices.
We exploit the vorticity, familiar from fluid mechanics and the theory of superfluids, as a tool to track the birth and subsequent development of optical vortices at a spiral phase plate.
In the visible spectrum vortex beams have found various applications, ranging from optical tweezers to super-resolution imaging. Recently, these beams have been demonstrated using X-rays and electron beams. However, so far, no in-depth discussion has been carried out on the vortex quality, which could become essential for a variety of vortex applications. Here, we investigate the mode conversion efficiency (MCE), vortex structure and stability (in terms of vortex splitting) of the vortex fields generated by spiral zone plates (SZP). We have designed and fabricated SZPs with varying topological…
Vortices are whirling disturbances commonly found in nature ranging from tremendously small scales in Bose-Einstein condensates to cosmologically colossal scales in spiral galaxies. An optical vortex, generally associated with a spiral phase, can carry orbital angular momentum (OAM). The optical OAM can either be in the longitudinal direction if the spiral phase twists in the spatial domain or in the transverse direction if the phase rotates in the spatiotemporal domain. In this article, we demonstrate the intersection of spatiotemporal vortices and spatial vortices in a wave packet. As a resu…
Optical vortices, as a kind of structured beam with helical phase wavefronts and doughnut shape intensity distribution, have been used for fabricating chiral structures in metal and spiral patterns in anisotropic polarization-dependent azobenzene polymer. However, in isotropic polymer, the fabricated microstructures are typically confined to non-chiral cylindrical geometry due to two-dimensional doughnut intensity profile of optical vortices. Here we develop a powerful strategy for realizing chiral microstructures in isotropic material by coaxial interference of a vortex beam and a plane wave,…
We present the first experimental evidence, supported by theory and simulation, of spatiotemporal optical vortices (STOVs). Quantized STOVs are a fundamental element of the nonlinear collapse and subsequent propagation of short optical pulses in material media. A STOV consists of a ring-shaped null in the electromagnetic field about which the phase is spiral, forming a dynamic torus which is concentric with and tracks the propagating pulse. Depending on the sign of the material dispersion, the local electromagnetic energy flow is saddle or spiral about the STOV. STOVs are born and evolve conse…
In optics, we can generate vortex beams using specific methods such as spiral phase plates or computer generated holograms. While, in nature, it is worth noting that water can produce vortices by a circularly symmetrical hole. So, if a light beam can generate vortex when it is diffracted by an aperture? Here, we show that the light field in the Fresnel region of the diffracted circularly polarized beam carries orbital angular momentum, which can transfer to the trapped particles and make orbital rotation.
We explore photon vortex generation in synchrotron radiations from a spiral moving electron under a uniform magnetic field along z-axis using Landau quantization. The obtained wave-function of the photon vortecies is the eigen-state of the z-component of the total angular momentum (zTAM). In m-th harmonic radiations, individual photons are the eigen-state of zTAM of m. This is consistent with previous studies. Using the presently obtained wave-functions we calculate the decay widths and the energy spectra under extremely strong magnetic fields of 10^12 - 10^13 G, which are observed in astrophy…
We demonstrate the generation of far-field propagating optical beams with a desired orbital angular momentum by using a smooth optical mode transformation between a plasmonic vortex and free space Laguerre-Gaussian modes. This is obtained by means of an adiabatically tapered gold tip surrounded by a spiral slit. The proposed physical model, backed up by the numerical study, brings about an optimized structure which is fabricated by using highly reproducible secondary electron lithography technique. Optical measurements of the structure excellently agree with the theoretically predicted far-fie…
Self-reference interferometry of optical vortices using a Michelson interferometer is investigated in this paper. It is found that the detection of topological charge (TC) for the optical vortices is constrained by some physical conditions. We present these conditions through the theoretical analyses, numerical simulation and experimental results. For different parameters, the maximal detectable TCs are different, which is helpful for the measurement of TC in the practical application. Within the range allowed by the constrained conditions, we also study the detection of TC using the interfere…
Intensity minima and maxima of speckle patterns obtained behind a diffuser are experimentally interchanged by applying a spiral phase delay of charge $\pm 1$ to the impinging coherent beam. This transform arises from the intuitive expectation that a tightly focused beam is so-changed into a vortex beam and vice-versa. The statistics of extrema locations and the intensity distribution of the so-generated "complementary" patterns are characterized by numerical simulations. It is demonstrated experimentally that the incoherent superposition of the three "complementary speckle patterns" yield a sy…
Vector beam, with a spatial nonuniform polarization distribution, is important for many applications due to its unique field characteristics and novel effects when interacting with matter. Here through three-dimensional particle-in-cell simulations, we demonstrate that intense vector beams in the extreme-ultraviolet to x-ray spectral region can be generated by means of high harmonic generation (HHG) in the relativistic regime. The vector features of the fundamental laser beam can be transferred to the higher frequency emission coherently during the extreme nonlinear HHG dynamics from relativis…
The analytical solution for the propagation of the laser beam with optical vortex through the system of lenses is presented. The optical vortex is introduced into the laser beam (described as Gaussian beam) by spiral phase plate. The solution is general as it holds for the optical vortex of any integer topological charge, the off-axis position of the spiral phase plate and any number of lenses. Some intriguing conclusions are discussed. The higher order vortices are unstable and split under small phase or amplitude disturbance. Nevertheless, we have shown that off-axis higher order vortices ar…
Understanding the near-field electromagnetic interactions that produce optical orbital angular momentum (OAM) is central to the integration of twisted light into nanotechnology. Here, we examine the cathodoluminescence (CL) of plasmonic vortices carrying OAM generated in spiral nanostructures through scanning transmission electron microscopy (STEM). The nanospiral geometry defines the photonic local density of states (LDOS) sampled by STEM-CL, which provides access to the phase and amplitude of the plasmonic vortex with nanometer spatial and meV spectral resolution. We map the full spectral di…
We report on efficient nonlinear generation of ultrafast, higher order "perfect" vortices at the green wavelength. Based on Fourier transformation of the higher order Bessel-Gauss beam generated through the combination of spiral phase plate and axicon we have transformed the Gaussian beam of the ultrafast Yb-fiber laser at 1060 nm into perfect vortices of power 4.4 W and order up to 6. Using single-pass second harmonic generation (SHG) of such vortices in 5-mm long chirped MgO-doped, periodically poled congruent LiNbO$_3$ crystal we have generated perfect vortices at green wavelength with outp…
Based on the Kirchhoff-Fresnel approximation, we consider behavior of the optical vortices (OV) upon propagation of the diffracted Laguerre-Gaussian (LG) beams with topological charge |m| = 1, 2. Under conditions of weak diffraction perturbation (i.e. the diffraction obstacle covers only the far transverse periphery of the incident LG beam), the OVs describe almost perfect 3D spirals within the diffracted beam body, which is an impressive demonstration of the helical nature of an OV beam. The far-field OV positions within the diffracted beam cross section depend on the wavefront curvature of t…
In this work, an analytic expression is derived for the optical field generated by an off-axis Gaussian beam diffracted by a Discrete Vortex-Producing Lens. With this system, a multifocal arrangement of asymmetric optical vortices is obtained whose topological charge values change with the position along the optical axis. This scheme allows obtaining a principal asymmetric vortex corresponding with the topological charge value of the phase mask and secondary ones with different charges. With the analytical expression, the effects induced by the discretization and misalignment on the irradiance…
We report on the experimental realization of flat mirrors enabling the broadband generation of optical vortices upon reflection. The effect is based on the geometric Berry phase associated with the circular Bragg reflection phenomenon from chiral uniaxial media. We show the reflective optical vortex generation from both diffractive and nondiffractive paraxial light beams using spatially patterned chiral liquid crystal films. The intrinsic spectrally broadband character of spin-orbit generation of optical phase singularities is demonstrated over the full visible domain. Our results do not rely …
High-order optical vortices are inherently unstable, as they tend to split up under perturbation to a series of vortices with unity charge. Control over the perturbation opens up a new degree of freedom to control and tune their location in a 2D-space, with immediate implications on trapping, light-matter interactions and super-resolution imaging. Here, we present a continuous nano-scale tuning of the spatial location of plasmonic vortices on metal-air interface achieved by varying the polarization state of the light coupled to the surface plasmons through a spiral slit. We demonstrate such a …
As a new degree of freedom for optical manipulation, recently spatiotemporal optical vortices (STOVs) carrying transverse orbital angular momentums have been experimentally demonstrated with pulse shapers. Here a spatiotemporal differentiator is proposed to generate STOVs with transverse orbital angular momentum. In order to create phase singularity in the spatiotemporal domain, the spatiotemporal differentiator is designed by breaking spatial mirror symmetry. In contrast to pulse shapers, the device proposed here is a simple one-dimensional periodic nanostructure and thus it is much more comp…
The orbital angular momentum (OAM) of light holds great promise for applications in optical communication, super-resolution imaging, and high-dimensional quantum computing. However, the spatio-temporal coherence of the light source has been essential for generating OAM beams, as incoherent ambient light would result in polychromatic and obscured OAM beams in the visible spectrum. Here, we extend the applications of OAM to ambient lighting conditions. By miniaturizing spiral phase plates and integrating them with structural color filters, we achieve spatio-temporal coherence using only an incoh…
An optical vortex (OV) is a beam with spiral wave front and screw phase dislocation. This kind of beams is attracting rising interest in various fields. Here we theoretically proposed and experimentally realized a novel but easy approach to generate optical vortices. We leverage the inherent topological vortex structures of polarization around bound states in the continuum (BIC) in the momentum space of two dimensional periodic structures, e.g. photonic crystal slabs, to induce Pancharatnam-Berry phases to the beams. This new class of OV generators operates in the momentum space, meaning that …
The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schroedinger equation including fractional one- or two-dimensional diffraction and cubic or cubic-quintic nonlinear terms, as well as linear potentials. The fractional diffraction is represented by fractional-order spatial derivatives of the Riesz type, defined in terms of the direct and inverse Fourier transform. In this form, it can be realized by spatial-domain light propagation in optical setups with a specially devised combination o…
Generation of few-cycle optical vortex pulses is challenging due to the large spectral bandwidths, as most vortex generation techniques are designed for monochromatic light. In this work, we use a spiral phase plate to generate few-cycle optical vortices from an ultrafast titanium:sapphire oscillator, and characterize them in the spatiotemporal domain using a recently introduced technique based on spatially resolved Fourier transform spectrometry. The performance of this simple approach to the generation of optical vortices is analyzed from a wavelength dependent perspective, as well as in the…
The design and implementation of a multiplexed spiral phase mask in an experimental optical tweezer setup are presented. This diffractive optical element allows the generation of multiple concentric vortex beams with independent topological charges. The generalization of the phase mask for multiple concentric vortices is also shown. The design for a phase mask of two multiplexed vortices with different topological charges is developed. We experimentally show the transfer of angular momentum to the optically trapped microparticles by enabling orbiting dynamics around the optical axis independen…
Deterministic control of coherent random light is highly important for information transmission through complex media. However, only a few simple speckle transformations can be achieved through diffusers without prior characterization. As recently shown, spiral wavefront modulation of the impinging beam allows permuting intensity maxima and intrinsic $\pm 1$-charged optical vortices. Here, we study this cyclic-group algebra when combining spiral phase transforms of charge $n$, with $D_3$- and $D_4$-point-group symmetry star-like amplitude modulations. This combination allows statistical streng…
We report on generation and control of tunable, broad orbital angular momentum (OAM) spectrum of a vortex beam. Using two spiral phase plates (SPPs), we have converted the Gaussian beam of Yb-fiber femtosecond laser at 1064 nm into optical vortices of orders, l=1-6, with conversion efficiency >95%. By adjusting the transverse shift of the SPPs with respect to the incident Gaussian beam axis, we have transformed the symmetric (intensity distribution) optical vortex of order, l, into an asymmetric vortex beam of broad OAM spectrum of orders, l, l-1, l-2,..,0. While the position of the SPPs deter…
Using the concept of an ideal phase-conjugating mirror we demonstrate that regardless of internal physical mechanism the phase-conjugation of a singular laser beam is accompanied by excitation within the mirror of internal waves which carry doubled angular momentum in order to match angular momentum conservation. For a Brillouin hypersound wavefront-reversal mirror this means that each elementary optical vortex belonging to a speckle pattern emits an acoustical vortex wave with doubled topological charge. The exact spatial profiles of light intensity and the intensity of hypersound in the vici…
Recently, it has been shown that spiral-shaped microdisk cavities support highly nonorthogonal pairs of copropagating modes with a preferred sense of rotation (spatial chirality) [Wiersig et al., Phys. Rev. A 78, 053809 (2008)]. Here, we provide numerical evidence which indicates that such pairs are a common feature of deformed microdisk cavities which lack mirror symmetries. In particular, we demonstrate that discontinuities of the cavity boundary such as the notch in the spiral cavity are not needed. We find a quantitative relation between the nonorthogonality and the chirality of the modes …
