Helical Wavefront Research Articles

Multi-User Nonlinear Optical Cryptosystem Based on Polar Decomposition and Fractional Vortex Speckle Patterns

In this paper, we propose a new multiuser nonlinear optical cryptosystem using fractional-order vortex speckle (FOVS) patterns as security keys. In conventional optical cryptosystems, mostly random phase masks are used as the security keys which are prone to various attacks such as brute force attack. In the current study, the FOVSs are generated optically by the scattering of the fractional-order vortex beam, known for azimuthal phase and helical wavefronts, through a ground glass diffuser. FOVSs have a remarkable property that makes them almost impossible to replicate. In the input plane, the amplitude image is first phase encoded and then modulated with the FOVS phase mask to obtain the complex image. This complex image is further processed to obtain the encrypted image using the proposed method. Two private security keys are obtained through polar decomposition which enables the multi-user capability in the cryptosystem. The robustness of the proposed method is tested against existing attacks such as the contamination attack and known-plaintext attack. Numerical simulations confirm the validity and feasibility of the proposed method.

Optical characteristics of radially-polarised twisted light

Recent work has confirmed that radially-polarised optical modes, specifically those endowed with helical wave fronts can now be routinely generated in the laboratory. Here we show that such a paraxial mode carries only an axial total optical angular momentum (AM) where is the winding number and is a constant. This mode, however, is shown to have zero spin angular momentum (SAM), so it is endowed only with orbital angular momentum (OAM) and no SAM. The helicity is found to be proportional to , hence this kind of mode displays chirality. When applied to a Laguerre–Gaussian (LG) mode our treatment leads to a total helicity equal to , where is the action constant. The factor , depends on the sign, not the magnitude of and so the result holds for any radially-polarised LG mode however large the magnitude of its winding number is. The magnitude of the action constant and hence the helicity are diminished for all such LG modes of large beam waist w 0.

Optical Imaging Using Orbital Angular Momentum: Interferometry, Holography and Microscopy

Light with helical phase wavefront carries orbital angular momentum, a unique feature widening the horizon of optical imaging applicability. Here, we take particular interest in the common but important imaging techniques of interferometry, holography and microscopy using orbital angular momentum of light. In contrast to the conventional imaging techniques that rely on the plane-wave or fundamental Gaussian beam, the orbital angular momentum of light introduces a new physical dimension into the play to enrich the applicable imaging mechanism. Indeed, we revisit the milestone achievements that exploit the orbital angular momentum of light as the essential roles of the interference reference, multiplexing channel, spatial-filter, or excitation source. These methods bestow the imaging applications with many new and various benefits.

Guest Editorial Special Issue on Progress in Photonic Spin-Orbit Interaction (SOI)

The papers in this special section focus on progress in photonic spin-order interaction (SOI). Spin and orbital angular momenta (SAM and OAM) are two distinct components of light beams. The SAM is associated with polarization of the light, whereas the OAM is related to a helical wave front, which has an azimuthal dependence of phase and can be described by a topological charge. These two different forms of AM are independent of each other within the boundaries of paraxial propagation in space. However, they become intertwined when the light beam is traveling through inhomogeneous and anisotropic media, or is tightly focused beyond the paraxial condition, leading to the photonic SOI. The photonic SOI underpins many optical processes, thus playing a significant role in the modern optics. The photonic SOI has led to such intriguing optical phenomena, as photonic spin Hall effect, orbit Hall effect, spin-orbit Hall effect, optical Skyrmion, and interconversions between the spin and the orbital terms, among others. Importantly, the photonic SOI also holds promise for potential applications in nanophotonic devices, quantum information processing, precise metrology, and optical (including quantum) sensing.

Frequency-Doubled High-Power Optical Vortex Beam With Sub 500 fs Pulse Duration

We report on the generation of high-power ultrashort-pulsed optical vortex beams (VBs) with orbital angular momentum (OAM) of +1 in the infrared (IR) and +2 in the visible (VIS) spectral regions. The IR vortex beam was created from a Gaussian beam by employing a nanograting (S-waveplate) mode converter. With this approach we obtained an average power of up to 802 W at a wavelength of λ = 1030 nm in the IR-VB with a pulse energy of 802 µJ, a pulse duration of 460 fs, and a mode-conversion efficiency of 90.1%. By subsequent second harmonic generation, the IR-VB was frequency-doubled inside a lithium triborate (LiB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> ) crystal. An average power of up to 320 W at λ = 515 nm was generated, with 320 µJ of pulse energy, 382 fs of pulse duration, and an IR-VB to SH-VB conversion efficiency of 39.9%. The generated IR and VIS VBs were characterized by a Mach-Zehnder type interferometric measurement, confirming the helical wavefronts at these high average powers. These results show that it is possible to efficiently generate high-quality VBs at multi hundreds of watts and confirm the OAM scaling law in harmonic generation processes.

Structured Beamforming Based on Orbital Angular Momentum Mode-Group

The structured beams, which can manipulate arbitrary intensity and phase of electromagnetic rays, are significant in communication and sensing. The vortex electromagnetic wave carrying orbital angular momentum (OAM) exhibits the phase distribution of the helical wavefront, which can be viewed as a complete set of eigenmodes for electromagnetic waves. It provides a flexible beamforming method to achieve the azimuthal pattern diversity by the spatial superposition of multiple specific OAM modes. We have proposed a novel form of OAM wave with a two-dimensional structure called plane spiral OAM (PS-OAM), which is conducive to overlapping different modes. Based on this, the PS-OAM mode-group can be employed to modify the spatial beam structure and form structured electromagnetic beams. This kind of beam not only retains the inherent vorticity and orthogonality of the OAM waves but also tackles the difficulties in applications stemming from the singularity-caused dark zone and beam divergence of conventional OAM waves. In this paper, the construction and manipulation of the structured beams are investigated, and the properties are analyzed. The potential applications in multiple-input multiple-output (MIMO) communication, orthogonal multiplexing communication, and spatial field digital modulation (SFDM) communication are envisioned.

Angular momentum-carrying radially-polarised twisted light

It is well-known that the fields of pure radially-polarised optical vortex modes do not possess the usual phase function eiℓϕ of typical twisted light and so they do not carry angular momentum. However, recent work has confirmed that radially-polarised modes with helical wave fronts have been created in the laboratory by several groups and they can now be readily generated using commercially available devices. They are endowed with the phase function eiℓϕ for arbitrary values of the winding number ℓ. Crucially, the original theoretical treatments disregard the longitudinal electric and magnetic field components. We show here that the longitudinal components must be included, not just for the consistency of the treatment, but because only this can lead to angular momentum. We show that for such created modes the cycle-averaged angular momentum is αħℓ where α=(Pw02)/(ħc2) is a dimensionless constant, with P the power in the mode and w0 the mode width at focus.

Ray tracing of long-range underwater acoustic vortex wave propagation

The underwater acoustic communications environment is severely band-limited, which leads to a bottleneck in data transfer. Existing methods of data transfer in underwater acoustic communications applications typically rely primarily on conventional temporal and frequency modulation techniques and achieve bit rates peaking at approximately 40 kb/s. One method of easing the bottleneck and increasing the data rate is to explore further potential degrees of freedom which may be utilized. Acoustic orbital angular momentum (OAM) is a physical quantity that characterizes the rotation in a propagating helical pressure wavefront. The unique phase patterns of OAM carrying vortex waves form an orthogonal basis which may be useful as an additional degree of freedom in acoustics communications applications; however, the long-distance propagation of these waves is largely unstudied. By employing BELLHOP’s ray tracing algorithm, the dominant features of a propagating OAM carrying vortex wave are tracked over long ranges (to and beyond 1 km) under various environmental conditions. This provides essential guidance in the design of the sending and receiving arrays of high-speed underwater communications systems, which rely on multiplexing acoustic OAMs.

Vortex ultrasound catheter for cerebral intravenous sonothrombolysis

One treatment challenge for cerebral venous sinus thrombosis (CVST) is to achieve recanalization within a short period of time (e.g., 30 min) for significant clinical outcomes. Ultrasound-mediated thrombolysis (sonothrombolysis) presents a promising treatment for venous embolism. In this paper, a miniature vortex ultrasound transducer with frequency of 1.8 MHz was developed for sonothrombolysis. A composite transducer with 2-by-2 sub-aperture piezoelectric elements was assembled into a 9-French catheter to generate a physical helical wavefront. The prototyped vortex ultrasound catheter was characterized by measuring the acoustic pressure amplitude and phases, followed by in-vitro- sonothrombolysis tests. It was found that a vortex ultrasound field can be successfully generated by the prototype. The vortex lytic rate was increased by more than 50% compared with the nonvortex lysis with the same acoustic power input. A long (∼7.5 cm), completely occluded in-vitro- 3D model of acute CVST was fully recanalized within 8 min. The unprecedented sonothrombolysis rate was likely attributed to the vortex ultrasound-induced shear stress, which can effectively disrupt acute blood clots. Furthermore, no vessel wall damage over ex-vivo bovine veins was found after the vortex sonothrombolysis treatment.

How to compress ultrashort vortex pulses.

Potential applications of ultrashort vortex pulses (ultrashort pulses with helical wavefronts) require compact tools to compensate for dispersion during their generation and propagation. In this work, a global simulated-annealing optimization algorithm, based on analysis of the temporal properties and waveforms of femtosecond vortex pulses, is used to design and optimize chirped mirrors. Performances of the algorithm through different optimization approaches and chirped mirror designs are presented.

OAM mode purity improvement based on antenna array

Orbital Angular Momentum (OAM) waves are characterized by helical wave fronts and orthogonality between different modes. Therefore, OAM waves have huge potential in improving wireless communications' channel capacity and radar imaging's resolution. Consequently, the generation and application of OAM waves have attracted a lot of attention. And many methods are proposed to generate OAM waves. Although antenna array is the most popular method of generating OAM waves, OAM waves generated by antenna array have redundant modes. However, all advantages of OAM waves are closely related to infinite OAM modes. Thus, to better apply OAM waves to wireless communications and radar, it is very important to reduce unnecessary OAM modes and improve the OAM mode purity. In order to improve the OAM mode purity, two combined antenna arrays composed of X direction antenna and Y direction antenna array are proposed in this paper. The X direction antenna array and the Y direction antenna array are supplied by the excitations with the same amplitude and fixed phase shift. The overall phase shift of the X direction antenna array is π/2 more or less than that of the Y direction antenna array. The results of formulas and antenna models in CST show that the combined antenna arrays can generate OAM waves with less redundant modes in x component, y component and z component. Besides, the z component carries pure OAM modes.

Manipulation of Scattering Spectra with Topology of Light and Matter

AbstractStructured lights, including beams carrying spin and orbital angular momenta, radially and azimuthally polarized vector beams, as well as spatiotemporal optical vortices, have attracted significant interest due to their unique amplitude, phase front, polarization, and temporal structures, enabling a variety of applications in optical and quantum communications, micromanipulation, and super‐resolution imaging. In parallel, structured optical materials, metamaterials, and metasurfaces consisting of engineered unit cells—meta‐atoms, opened new avenues for manipulating the flow of light and optical sensing. While several studies explored structured light effects on the individual meta‐atoms, their shapes are largely limited to simple spherical geometries. However, the synergy of the structured light and complex‐shaped meta‐atoms has not been fully explored. In this paper, the role of the helical wavefront of Laguerre–Gaussian beams in the excitation and suppression of higher‐order resonant modes inside all‐dielectric meta‐atoms of various shapes, aspect ratios, and orientations, is demonstrated and the excitation of various multipolar moments that are not accessible via unstructured light illumination is predicted. The presented study elucidates the role of the complex phase distribution of the incident light in shape‐dependent resonant scattering, which is of utmost importance in a wide spectrum of applications ranging from remote sensing to spectroscopy.

Reflective Metasurface With Steered OAM Beams for THz Communications

The abundant spectrum resources and low beam divergence of the terahertz (THz) band, can be combined with the orthogonal propagation property of orbital angular momentum (OAM) beams to multi-fold the capacity of wireless communication systems. Here, a reflective metasurface (RMTS) is utilized to enhance the coverage of the high gain THz OAM beams by enabling the non-line-of-sight (NLoS) component by reshaping the planar wavefront of the incident wave into the helical wavefront, so that it is re-directed towards the direction of interest. This can contribute to alleviating the concern of the small aperture size, since improving the channel capacity can be achieved at the low spectrum blocks of the THz band (larger aperture size). For validation, three <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$90 \times 90$ </tex-math></inline-formula> mm RMTSs are simulated, fabricated, and tested in the frequency range 90–110 GHz, to re-direct single and dual OAM beams towards the desired location.

Vortex Speckles with Customized Symmetry and Spatial Correlations

A family of optical speckles with propagation-invariant annular morphology are generated via a phase-only mask and free-space evolution, termed vortex speckles, for which phase design is inspired by the vortex beam's helical wave front carrying orbital angular momentum. Vortex beams' graceful symmetry (central and/or axial) can be naturally inherited into vortex speckles by adjusting the parity of the topological value $\ensuremath{\ell}$ and the consistency of the initial phase angle ${\ensuremath{\phi}}_{0}$. By sequentially imprinting such a series of phase profiles onto a spatial light modulator, the resultant stochastically fluctuating vortex speckles naturally constitute an annular pseudothermal light field, and the customized symmetry in intensity profiles leads to spatial correlations, which are exploited for Hanbury Brown and Twiss interferometry and beam-splitter-free lensless ghost imaging and diffraction experiments. Symmetric annular pseudothermal light also has diverse phase correlations, so in a proposed vortex self-interferometer, we can manipulate photon correlations (parity-induced anticorrelation) and observe intriguing correlation states (spatially varying photon correlation oscillations). This work not only presents a flexible light-source option for applications requiring ring-shaped speckle illumination, but it also paves the way for the customization of nontrivial classical correlation modes.

Propagation and imaging analysis of vortex acoustic waves in ocean turbulence

AbstractVortex acoustic waves (VAW) with helical phase wavefronts could provide a new dimension for the detection and imaging of targets in the ocean. To explore the propagation characteristics of VAW under the effect of ocean turbulence (OT) and the impact on imaging, the phase screen method is used to simulate the propagation of VAW generated by a phase‐modulated uniform circular array under the effect of OT and the imaging of the target. The phase change and detection probability under the influence of the acoustic wave parameters and OT parameters during the propagation process are studied. Second, the azimuth resolution performance and focussing performance of the target imaging are studied. Under the effect of OT, the VAW of different frequencies and topological modes become scattered, and the degree of scattering is different when the parameters are different; and the resolution performance and focussing performance have also deteriorated. However, the VAW still has a reliable resolution under the effect of medium and low‐intensity OT, which provides theoretical support for the practice of the VAW in underwater target imaging.

Magnetic helicoidal dichroism with XUV light carrying orbital angular momentum

Circularly polarized light is a fundamental tool in magnetic studies, notably for magnetization dynamics. It is less common in magneto-optics to exploit the orbital angular momentum (OAM) of value ℓ carried by light beams possessing a helical wavefront. After finding many applications in the visible range, recently OAM pulses with ultra-short duration and XUV wavelengths became available, widening the range of experiments that can be envisaged. We modelled the interaction of an XUV OAM beam with non-uniform magnetic structures, showing that the far field scattered intensity profile encodes the symmetry of the magnetic structure in a way that depends on the sign and value of ℓ. In analogy with magnetic circular dichroism, this effect, named magnetic helicoidal dichroism (MHD), can be observed by inverting the sign of either the orbital momentum or of the magnetization. We obtained experimental evidence of MHD by measuring ℓ-dependent resonant scattering from a magnetic vortex. The results of recent complementary experiments match well the theoretical predictions, confirming the potential of the new toolset provided by MHD for studying the laser-triggered ultrafast dynamics of complex magnetic materials.

Azimuth measurement based on OAM phase spectrum of optical vortices

The optical vortex is a new type of structured light field with a helical wavefront. Because of carrying orbital angular momentum (OAM), the optical vortex can be used to measure the shape and angular orientation of a static object in optical remote sensing. These measurements take advantage of variations in the intensity or phase of the OAM mode. In this paper, we propose a method of target azimuth measurement based on OAM phase spectrum of optical vortices. The OAM phase spectrum consists of helical phase terms in different OAM modes, where the helical phase is obtained by a four-step phase-shifting method. By using the approximate duality relationship between the OAM phase spectrum and the azimuth, we can accurately measure the azimuth of a single target or multiple targets. The resolution of the azimuth measurement is inversely proportional to the OAM scanning range. Experimentally, the target azimuth measurement by employing OAM phase spectrum analysis is realized and the measurement error is less than 2.5°. On this basis, the inverse relationship between the OAM scanning range and azimuth resolution is verified, where the error between experimental and theoretical azimuth resolution is less than 0.3°.

Experimental realization of neutron helical waves.

Methods of preparation and analysis of structured waves of light, electrons, and atoms have been advancing rapidly. Despite the proven power of neutrons for material characterization and studies of fundamental physics, neutron science has not been able to fully integrate these techniques because of small transverse coherence lengths, the relatively poor resolution of spatial detectors, and low fluence rates. Here, we demonstrate methods that are practical with the existing technologies and show the experimental achievement of neutron helical wavefronts that carry well-defined orbital angular momentum values. We discuss possible applications and extensions to spin-orbit correlations and material characterization techniques.

Elastic orbital angular momentum transfer from an elastic pipe to a fluid

Research into the orbital angular momentum carried by helical wave-fronts has been dominated by the fields of electromagnetism and acoustics, owing to its practical utility in sensing, communication, and tweezing. Despite the huge research effort across the wave community, only recently has elastic orbital angular momentum been theoretically shown to exhibit similar properties. Here we experimentally observe the transfer of elastic orbital angular momentum from a hollow elastic pipe to a fluid in which the pipe is partially submerged, in an elastic analogue of Durnin’s slit-ring experiment for optical beams. This transfer is achieved by coupling the dilatational component of guided flexural waves in the pipe with the pressure field in the fluid; the circumferential distribution of the normal stress in the pipe acts as a continuous phased pressure source in the fluid resulting in the generation of Bessel-like acoustic beams. This demonstration has implications for future research into a new regime of orbital angular momentum for elastic waves, as well providing an alternative method to excite acoustic beams that carry orbital angular momentum that could create a paradigm shift for acoustic tweezing.

Spin-entangled orbital angular momentum filter of photons based on a chiral long-period fiber grating.

The orbital angular momentum (OAM) of light is particularly promising for multi-channel data transmission in optical fiber communications. In the implementation, one of the impediments is the lack of an effective all-fiber method to demultiplex and filter OAM modes. To solve the problem, by utilizing the inherent spiral characteristics of a chiral long-period fiber grating (CLPG), we propose and demonstrate experimentally a CLPG-based scheme for filtering spin-entangled OAM of photons. We unveil theoretically and verify experimentally that the co-handed OAM with the same chirality of helical phase wavefront as CLPG couples to higher-order cladding modes and suffers loss, while the cross-handed OAM with the opposite chirality freely passes in CLPG. Meanwhile, by combining its grating characteristics, CLPG can realize the filtering and detection of a spin-entangled OAM with arbitrary order and chirality without exerting extra loss for other OAM. Our work has great potential in analyzing and manipulating spin-entangled OAM, paving the way for the development of all-fiber OAM applications.