Using a complex optical orbital-angular-momentum spectrum to measure object parameters

Revealing the Incidence-Angle-Independent Frequency Shift in the Acoustic Rotational Doppler Effect

The Doppler effect is a universal wave phenomenon that has inspired various applications due to the induced frequency shift. In the case of the linear Doppler effect, the frequency shift depends on the incident frequency and angle. Here, we unveil the frequency shift dependence induced by the acoustic rotational Doppler effect in the wave-object scattering process. We experimentally demonstrate that this frequency shift is exclusively determined by the angular speed and rotational symmetry of the spinning scatterer while remaining independent of the incident angular momentum and angle. We derive the analytical relationship between the frequency shift and the scatterer's helicity, presenting a novel approach for helical feature recognition. The angle-independent nature of the frequency shift inherently prevents spectrum broadening and offers a solution for precise motion measurement through the rotational Doppler effect. This work provides a rigorous and comprehensive understanding of the acoustic Doppler effect, enriching its applications in helicity and motion detection.

Optical ranging and vibration sensing based on the lagging propagation phase of structured beams

Recently, studies have shown that the spatial confinement on waves or photons with beam shaping techniques would modify the propagation speed of optical fields including both group and phase velocities. Particularly, for the monochromatic spatially structured beams, the reduced longitudinal wave vector enables the phase velocity to be superluminal, causing a lagging propagation phase. In this Letter, we propose a novel, to the best of our knowledge, scheme for optical ranging and vibration sensing with the lagging propagation phase of structured beams. We experimentally demonstrate the extraction of displacement from the rotating angles of interfering fringes of superposed Gaussian and higher-order Bessel beams with lagging propagation phase difference. The measuring range is 0.2 m with the limitation of the tested moving stage, but it can be extended to tens of meters in principle. The measuring resolution can reach sub-millimeters, which can be further improved by carefully designing the probe beam and using a finer camera. The results may provide potential applications in position sensing and monitoring.

Fragmental optical vortex for the detection of rotating object based on the rotational Doppler effect

Rotational Doppler effect (RDE), as a counterpart of the conventional linear Doppler effect in the rotating frame, has attracted increasing attention in recent years on rotational object detection. Many previous works have investigated the RDE based on the whole optical vortex field. In this work, we report on the RDE of the partially obstructed optical vortex and the corresponding rotational speed extraction method. Based on the orbital angular momentum (OAM) mode analysis theory, we establish the relationship between the OAM spectrum and the RDE frequency shift of fragmental optical vortex (FOV). The mechanism of the rotational speed extraction is analysed and validated by the numerical simulation and experiments. Further, a dual Fourier transformation method is proposed to accurately obtain the rotational speed which successfully overcomes the problem of the discrete distribution of the RDE signals. Our work may be useful for practical remote sensing based on the optical RDE metrology.

Quantum-inspired protocol for measuring the degree of similarity between spatial shapes

We put forward and demonstrate experimentally a quantum-inspired protocol that allows us to quantify the degree of similarity between two spatial shapes embedded in two optical beams without the need to measure the amplitude and phase across each beam. Instead the sought-after information can be retrieved by measuring the degree of polarization of the combined optical beam, a measurement that is much easier to implement experimentally. The protocol makes use of non-separable optical beams, whose main trait is that different degrees of freedom (polarization and spatial shape here) cannot be described independently. One important characteristic of the method described is that it allows us to compare two unknown spatial shapes.

Over-Two-Octave Supercontinuum Generation of Light-Carrying Orbital Angular Momentum in Germania-Doped Ring-Core Fiber

In this paper, we design a silica-cladded Germania-doped ring-core fiber (RCF) that supports orbital angular momentum (OAM) modes. By optimizing the fiber structure parameters, the RCF possesses a near-zero flat dispersion with a total variation of <±30 ps/nm/km over 1770 nm bandwidth from 1040 to 2810 nm for the OAM1,1 mode. A beyond-two-octave supercontinuum spectrum of the OAM1,1 mode is generated numerically by launching a 40 fs 120 kW pulse train centered at 1400 nm into a 12 cm long designed 50 mol% Ge-doped fiber, which covers 2130 nm bandwidth from 630 nm to 2760 nm at −40 dB of power level. This design can serve as an efficient way to extend the spectral coverage of beams carrying OAM modes for various applications.

Sensing optical phase distortion via beatnote detection of a dual probe beam encoded with orbital angular momentum

Laser based optical applications such as imaging, ranging, and wireless communications are susceptible to environmental distortions. Inferring the strength of these optical distortions is crucial to obtaining information about the environment in which the system is operating. Our technique of inferring environmental distortion strength leverages the spreading of light's orbital angular momentum (OAM) spectrum combined with heterodyne detection. A laser encoded with OAM can be decomposed into a basis set of helical modes that spreads upon interaction with optical distortions. This mode spreading is quantified using the OAM spectrum that can be measured using mode projection or mode sorting techniques. This new technique, to the best of our knowledge, provides benefits compared to the latter two OAM detection methods such as: low-frequency noise rejection, a simpler optical receiver, lower noise floor, and an inherent optical phase component. Central to the method is the heterodyne detection of the zeroth-order OAM coefficient of a superimposed two-beam, two-frequency, probe. The measured heterodyne signal power is seen to be proportional to the coupling power of each beam's OAM spectra. To test the idea, wave-optic simulations and experiments using spatial light modulators are implemented using a simplified optical turbulence model to represent the environment. The experimental implementation agrees well with simulated and theoretical results.

Measure the arbitrary topological charge of perfect optical vortex beams by using the dynamic angular double slits

Perfect optical vortex beams (POV) have attracted considerable attention in many novel applications because they have the advantage of a radial profile that is independent of the topological charge (TC). Nowadays, there are few effective methods to measure both the integer and the fractional TCs of the POV. In this paper, we achieve the precise measurement of arbitrary TCs through the approach of dynamic angular double slits (ADS), which performs the transformation from the POV to the interference intensity patterns at the angular bisector direction of the ADS. The information of the TC can be obtained from the periodically changing interference pattern. The deviation is less than 2% by comparing the theoretical values with the fitting results, therefore the detection method is effective and reasonable.

Weak turbulence effects on different beams carrying orbital angular momentum

The study of beams carrying orbital angular momentum (OAM) has been of interest for its use in free-space optical communications (FSOC), directed energy applications, and remote sensing (RS). For FSOC and RS, it is necessary to measure the wavefront of the beam to recover transmitted or environmental information, respectively. In this computational study, common OAM beams such as the Laguerre-Gaussian (LG), Bessel-Gaussian (BG), and Bessel beams are propagated through atmospheric turbulence and compared to their Gaussian beam counterpart. The turbulence is simulated using multiple phase screens within the framework of a split-step method. Beam metrics used to quantify beam propagation will include the spatial coherence radius, OAM spectrum, on-axis intensity, spot size, divergence, and on-axis scintillation. Atmospheric turbulence along the path is limited to the weak scintillation limit, where beam parameters can be predicted analytically using the Rytov approximation. The results show that BG beams and multiplexed BG beams retain more OAM information than their LG and Bessel beam counterparts. The LG beam on-axis intensity and on-axis scintillation are seen to be independent of OAM mode. The scintillation of the LG beam is less than a BG, Bessel, and Gaussian beam across low- and high-order OAM modes. Insight into these results is discussed through studying the beam divergence, while the initial spot sizes of the Gaussian, LG, and BG beams are limited to the same spatial extent.

Non-zero dispersion-shifted ring fiber for the orbital angular momentum mode

As the dimension of orbital angular momentum (OAM) is orthogonal to the other degrees of freedom for photon, such as wavelength, it can be utilized to further increase data capacity in the wavelength division multiplexing (WDM) systems. However, the non-zero dispersion-shifted fiber (NZDSF) for the OAM mode has not yet been investigated or even proposed. In this work, we propose and design a ring fiber with low chromatic dispersion for the HE_2,1 mode, which can serve as NZDSF for its corresponding OAM_1,1 mode. A low dispersion of 3.3 ps/(nm·km) at 1550 nm and <2.9 ps/(nm·km) dispersion variation from 1530 to 1565 nm for the OAM_1,1 mode is achieved in simulation, which satisfies the standard of the ITU-T G.655.C. The designed fiber with ring width from 1.5 µm to 3.5 µm can support the OAM_1,1 mode within the C-band, and a large effective area of about 646 µm² is obtained. We also note that the fiber with larger inner radius and ring width are more tolerant to the perturbations, such as fiber ellipticity and bending. In the fiber-based optical communication systems, the designed ring fiber could be used as a candidate for supporting OAM modes with low dispersion and reduced nonlinear effects.

Rotational Doppler shift from a rotating rod

This Letter reports on a rotational Doppler effect obtained from a rotating rod illuminated by a fundamental Gaussian laser beam. More specifically, we decompose the transmitted light behind the rotating rod into Laguerre-Gaussian modes and investigate the associated frequency shifts. The main contributing modes correspond to modes having the same rotational symmetry as the rotating object. Furthermore, their shifts equal the topological charge of the beam times the rotational frequency of the object. Potential applications in pattern recognition and rotation identification are then considered.

Recent Advances in Photoalignment Liquid Crystal Polarization Gratings and Their Applications

Liquid crystal (LC) circular polarization gratings (PGs), also known as Pancharatnam–Berry (PB) phase deflectors, are diffractive waveplates with linearly changed optical anisotropy axes. Due to the high diffraction efficiency, polarization selectivity character, and simple fabrication process, photoalignment LC PGs have been widely studied and developed especially in polarization management and beam split. In this review paper, we analyze the physical principles, show the exposure methods and fabrication process, and present relevant promising applications in photonics and imaging optics.

Recent Advances in Generation and Detection of Orbital Angular Momentum Optical Beams-A Review

Herein, we have discussed three major methods which have been generally employed for the generation of optical beams with orbital angular momentum (OAM). These methods include the practice of diffractive optics elements (DOEs), metasurfaces (MSs), and photonic integrated circuits (PICs) for the production of in-plane and out-of-plane OAM. This topic has been significantly evolved as a result; these three methods have been further implemented efficiently by different novel approaches which are discussed as well. Furthermore, development in the OAM detection techniques has also been presented. We have tried our best to bring novel and up-to-date information to the readers on this interesting and widely investigated topic.

Laguerre-Gaussian transform for rotating image processing

In practical applications, it is often crucial to track high-speed rotating objects. However, the traditional Fourier transform techniques are not applicable under such circumstances because the Fourier spectrum of a rotating object is changing. Here, we propose a Laguerre-Gaussian (LG) transform to analyze the rotating object. The rotation provides a feasible way to acquire a LG-mode spectrum, which does not change even the object working at a high rotating speed. By analyzing the LG spectrum, one can perform image processing such as reconstruction, edge enhancement, and pattern replication. The LG transform makes it convenient for real-time monitoring of industrial and astronomical objects.

Utilizing adaptive optics to mitigate intra-modal-group power coupling of graded-index few-mode fiber in a 200-Gbit/s mode-division-multiplexed link

We experimentally demonstrate the utilization of adaptive optics (AO) to mitigate intra-group power coupling among linearly polarized (LP) modes in a graded-index few-mode fiber (GI FMF). Generally, in this fiber, the coupling between degenerate modes inside a modal group tends to be stronger than between modes belonging to different groups. In our approach, the coupling inside the LP₁₁ group can be represented by a combination of orbital-angular-momentum (OAM) modes, such that reducing power coupling in OAM set tends to indicate the capability to reduce the coupling inside the LP₁₁ group. We employ two output OAM modes l=+1 and l=-1 as resultant linear combinations of degenerate LP_11a and LP_11b modes inside the LP₁₁ group of a ∼0.6-km GI FMF. The power coupling is mitigated by shaping the amplitude and phase of the distorted OAM modes. Each OAM mode carries an independent 20-, 40-, or 100-Gbit/s quadrature-phase-shift-keying data stream. We measure the transmission matrix (TM) in the OAM basis within LP₁₁ group, which is a subset of the full LP TM of the FMF-based system. An inverse TM is subsequently implemented before the receiver by a spatial light modulator to mitigate the intra-modal-group power coupling. With AO mitigation, the experimental results for l=+1 and l=-1 modes show, respectively, that (i) intra-modal-group crosstalk is reduced by >5.8dB and >5.6dB and (ii) near-error-free bit-error-rate performance is achieved with a penalty of ∼0.6dB and ∼3.8dB, respectively.

Special Issue on Novel Insights into Orbital Angular Momentum Beams: From Fundamentals, Devices to Applications

It is well-known now that angular momentum carried by elementary particles can be categorized as spin angular momentum (SAM) and orbital angular momentum (OAM) [...]

Laguerre-Gaussian mode expansion for arbitrary optical fields using a subspace projection method

Laguerre-Gaussian (LG) mode decomposition has found applications in various optics fields. However, numerical LG mode expansion for arbitrary field is still a problem, since the physical dimension of LG modes would vary with three parameters-the beam waist width w, the radial index p, and the azimuthal index m, which make it difficult to determine the optimal value of w and the truncation order on p. Here a general method of LG mode expansion for an arbitrary field is developed. It is found that the local frequency distribution of the LG function consists of two parts, the quasi-periodic part and the chirped part. The effective space-bandwidth product of the LG function is defined as the product of the spatial width and frequency-domain width of the quasi-periodic part. Then, based on this space-bandwidth product definition, the criteria for determining the beam waist parameter and the truncation order of LG series expansion are given. The scheme is tested for the representation of off-axis Hermite-Gaussian mode, which shows that our method is of high accuracy.

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

Talbot effect on orbital angular momentum beams: azimuthal intensity repetition-rate multiplication

We propose and experimentally demonstrate the azimuthal Talbot effect on orbital angular momentum (OAM) beams. By applying predetermined phases to a number of OAM beams carrying different topological charges, the intensity petal is self-imaged in the azimuthal angle, with arbitrary azimuthal repetition-rate multiplication. The close analogy between temporal and azimuthal Talbot self-imaging is studied. In addition, the effect of amplitude apodization of the OAM spectrum on the resulting intensity pattern, and the azimuthal Talbot effect on Laguerre-Gaussian beams of the same radial indices, are experimentally investigated. All of our experimental images are in excellent agreement with simulation results.

Investigation of propagation dynamics of truncated vector vortex beams

In this Letter, we experimentally investigate the propagation dynamics of truncated vector vortex beams generated using a Sagnac interferometer. Upon focusing, the truncated vector vortex beam is found to regain its original intensity structure within the Rayleigh range. In order to explain such behavior, the propagation dynamics of a truncated vector vortex beam is simulated by decomposing it into the sum of integral charge beams with associated complex weights. We also show that the polarization of the truncated composite vector vortex beam is preserved all along the propagation axis. The experimental observations are consistent with theoretical predictions based on previous literature and are in good agreement with our simulation results. The results hold importance as vector vortex modes are eigenmodes of the optical fiber.