Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators

Angular width and beam quality of a partially coherent standard Laguerre-Gaussian vortex beam in turbulent plasma

Analytical formulas for the angular width and propagation factor of a partially coherent standard Laguerre-Gaussian (sLG) vortex beam through anisotropic turbulent plasma were derived based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function. The evolution properties of the angular width and propagation factor of partially coherent sLG vortex beams propagating in anisotropic turbulent plasma were investigated numerically. The numerical results demonstrate the influence of the source and turbulence parameters on the normalized angular width and normalized propagation factor of the partially coherent sLG vortex beams. It can be observed that in a partially coherent sLG vortex beam with a lower beam order, topological charge, and wavelength, or a higher correlation coefficient of the source plane, and with increasing propagation distance and refractive index fluctuation variance or decreasing anisotropy parameters, the outer and inner scales of the turbulent plasma have a large angular width and propagation factor (i.e., the beam quality is worse). The results of this study will be beneficial for applications in remote sensing and optical communications.

Broadband optical vortex beam generation using flat-surface nanostructured gradient index vortex phase masks

We developed a new kind of compact flat-surface nanostructured gradient index vortex phase mask, for the effective generation of optical vortex beams in broadband infrared wavelength range. A low-cost nanotechnological material method was employed for this work. The binary structure component consists of 17,557 nano-sized rods made of two lead-bismuth-gallium silicate glasses which were developed in-house. Those small rods are spatially arranged in such a way that, according to effective medium theory, the refractive index of this internal structure is constant in the radial direction and linearly changes following azimuthal angle. Numerical results demonstrated that a nanostructured vortex phase mask with a thickness of 19 μm can convert Gaussian beams into fundamental optical vortices over 290 nm wavelength bandwidth from 1275 to 1565 nm. This has been confirmed in experiments using three diode laser sources operating at 1310, 1550, and 1565 nm. The generation of vortex beams is verified through their uniform doughnut-like intensity distributions, clear astigmatic transformation patterns, and spiral as well as fork-like interferograms. This new flat-surface component can be directly mounted to an optical fiber tip for simplifying vortex generator systems as well as easier manipulation of the generated OVB in three-dimensional space.

Enhancement of Doppler spectroscopy to transverse direction by using optical vortex

Tunable diode laser absorption spectroscopy (TDLAS) is a valuable method for measuring particle flow velocities in plasma. However, conventional TDLAS using a plane-wave beam is sensitive only to the laser propagation direction. This limitation is particularly unfavorable for the observation of the particle transportation perpendicularly incident on the material in the plasma-material interaction. In this paper, we show for the first time that flow measurements perpendicular to the beam direction are possible by replacing the probe beam with an optical vortex beam. Because an optical vortex has a helical wavefront, particles moving in its field experience an azimuthal Doppler shift in addition to the translational Doppler shift. Assuming a uniform gas flow across the optical vortex, the azimuthal Doppler shift of the absorption spectrum observed in the beam cross-section varies sinusoidally in the azimuthal direction. The transverse flow velocity is derived from the amplitude of this sinusoidal variation. At transverse velocities above 70 m/s, the measurement errors are found to be less than 15%, with a mean absolute percentage error of less than 8%.

Dual-functional metalenses for the polarization-controlled generation of focalized vector beams in the telecom infrared

The availability of static tiny optical devices is mandatory to reduce the complexity of optical paths that typically use dynamic optical components and/or many standard elements for the generation of complex states of light, leading to unprecedented levels of miniaturization and compactness of optical systems. In particular, the design of flat and integrated optical elements capable of multiple vector beams generation with high resolution in the visible and infrared range is very attractive in many fields, from life science to information and communication technology. In this regard, we propose dual-functional transmission dielectric metalenses that act simultaneously on the dynamic and geometric phases in order to manipulate independently right-handed and left-handed circularly polarized states of light and generate focused vector beams in a compact and versatile way. In the specific, starting from the mathematical fundamentals for the compact generation of vector beams using dual-functional optical elements, we provide the numerical algorithms for the computation of metaoptics and apply those techniques to the design and fabrication of silicon metalenses which are able to generate and focus different vector beams in the telecom infrared, depending on the linear polarization state in input. This approach provides new integrated optics for applications in the fields of high-resolution microscopy, optical manipulation, and optical communications, both in the classical and single-photon regimes.

Orbital angular momentum in the near-field of a fork grating

Light beams with Orbital Angular Momentum (OAM) are explored in applications from microscopy to quantum communication, while the Talbot effect revives in applications from atomic systems to x-ray phase contrast interferometry. We evidence the topological charge of an OAM carrying THz beam in the near-field of a binary amplitude fork-grating by means of the Talbot effect, which we show to persist over several fundamental Talbot lengths. We measure and analyze the evolution of the diffracted beam behind the fork grating in Fourier domain to recover the typical donut-shaped power distribution, and we compare experimental data to simulations. We isolate the inherent phase vortex using the Fourier phase retrieval method. To complement the analysis, we assess the OAM diffraction orders of a fork grating in the far-field using a cylindrical lens.

Resolution and uniformity improvement of parallel confocal microscopy based on microlens arrays and a spatial light modulator

In traditional fluorescence microscopy, it is hard to achieve a large uniform imaging field with high resolution. In this manuscript, we developed a confocal fluorescence microscope combining the microlens array with spatial light modulator to address this issue. In our system, a multi-spot array generated by a spatial light modulator passes through the microlens array to form an optical probe array. Then multi-spot adaptive pixel-reassignment method for image scanning microscopy (MAPR-ISM) will be introduced in this parallelized imaging to improve spatial resolution. To generate a uniform image, we employ an optimized double weighted Gerchberg-Saxton algorithm (ODWGS) using signal feedback from the camera. We have built a prototype system with a FOV of 3.5 mm × 3.5 mm illuminated by 2500 confocal points. The system provides a lateral resolution of ∼0.82 µm with ∼1.6 times resolution enhancement after ISM processing. And the nonuniformity across the whole imaging field is 3%. Experimental results of fluorescent beads, mouse brain slices and melanoma slices are presented to validate the applicability and effectiveness of our system.

The Longitudinal Plasma Modes of κ-Deformed Kaniadakis Distributed Plasmas Carrying Orbital Angular Momentum

Based on plasma kinetic theory, the dispersion and Landau damping of Langmuir and ion-acoustic waves carrying finite orbital angular momentum (OAM) were investigated in the κ-deformed Kaniadakis distributed plasma system. The results showed that the peculiarities of the investigated subjects relied on the deformation parameter κ and OAM parameter η. For both Langmuir and ion-acoustic waves, dispersion was enhanced with increased κ, while the Landau damping was suppressed. Conversely, both the dispersion and Landau damping were depressed by OAM. Moreover, the results coincided with the straight propagating plane waves in a Maxwellian plasma system when κ=0 and η→∞. It was expected that the present results would give more insight into the trapping and transportation of plasma particles and energy.

Direct generation of continuous-wave and passively Q-switched visible vortex beams from a doughnut-shaped diode-pumped Pr: YLF laser

We demonstrate the direct generation of visible vortex beams (LG₀₁ mode) from a doughnut-shaped diode-pumped Pr:YLF laser. In continuous-wave mode, the maximum vortex output power was 36 mW at 523 nm, 354 mW at 607 nm, 838 mW at 639 nm, 722 mW at 721 nm, respectively. Moreover, based on this operation, the orange and red passively Q-switched vortex lasers were also achieved by inserting a Co:MgAl₂O₄ crystal into the laser cavity as a saturable absorber. The shortest pulse width of Q-switched vortex laser was 58 ns for 607 nm, and 34 ns for 639 nm, respectively. Our work provides a reliable and efficient method for the direct generation of visible vortex lasers for potential applications.

Complex-Amplitude-Modulation Vectorial Excitation Beam for High-Resolution Observation of Deep Regions in Two-Photon Microscopy

In two-photon microscopy, aberration correction is an essential technique for realizing high resolution in deep regions. A spatial light modulator (SLM) incorporated into an optical system for two-photon microscopy performs pre-compensation on the wavefront of the excitation beam, restoring the resolution close to the diffraction limit even in the deep region of a biological sample. If a spatial resolution smaller than the diffraction limit can be achieved along with aberration correction, the importance of two-photon microscopy for deep region observation will increase further. In this study, we realize higher resolution observations in the deep region by combining two resolution-enhancement methods and an aberration correction method. Therefore, a z-polarizer is added to the aberration-correction optical system, and the SLM modulates the amplitude and phase of the excitation beam; in other words, complex-amplitude modulation is performed. The lateral resolution is found to be approximately 20% higher than the diffraction limit obtained using a circularly polarized beam. Verification was conducted by simulation and experimentation using model samples and ex vivo biological samples. The proposed method has the potential to be effective for live imaging and photostimulation of the deep region of the sample, although it requires only minor changes to the conventional optical system that performs aberration correction.

Coupling light to higher order transverse modes of a near-concentric optical cavity

Optical cavities in the near-concentric regime have near-degenerate transverse modes; the tight focusing transverse modes in this regime enable strong coupling with atoms. These features provide an interesting platform to explore multi-mode interaction between atoms and light. Here, we use a spatial light modulator (SLM) to shape the phase of an incoming light beam to match several Laguerre-Gaussian (LG) modes of a near-concentric optical cavity. We demonstrate coupling efficiency close to the theoretical prediction for single LG modes and well-defined combinations of them, limited mainly by imperfections in the cavity alignment.

Acoustic trapping of particles using a Chinese taiji lens

Focused acoustic vortex (FAV) beams can trap particles in a contactless and non-destructive way and the method has thereby attracted much attention. In contrast to the traditional complex and expensive transducer array, we propose a fast and cheap method to generate FAV beams in water using an ultrasonic holographic lens engraved with the Chinese taiji pattern. This method can obtain high transmission efficiency, and hence the strong trapping force makes the particles trapped stably in a straight line. The formation of the FAV beams derives from a superposition of the spiral phase of a Laguerre Gaussian beam and the focusing phase. Because of the phase singularity of this beam, the intensity of the ultrasonic field on the beam axis is zero, thereby forming a strong gradient surround the beam axis. The trapping and manipulation of polystyrene particles with a radius of 150 μm is realized in the gradient field of the FAV beam. The proposed single beam acoustic trapping method does not depend on the reflector, making it more suitable for the manipulation of cells in vivo.

Second-harmonic computer-generated holographic imaging through monolithic lithium niobate crystal by femtosecond laser micromachining

The computer-generated holography technique is a powerful tool for three-dimensional display, beam shaping, optical tweezers, ultrashort pulse laser parallel processing, and optical encryption. We have realized nonlinear holography in ferroelectric crystals by utilizing spatial light modulators in our previous works. Here, we demonstrate an improved method to realize second-harmonic (SH) holographic imaging through a monolithic lithium niobate crystal based on binary computer-generated holograms (CGHs). The CGH patterns were encoded with the detour phase method and fabricated by femtosecond laser micromachining. By the use of the birefringence phase-matching process in the longitudinal direction, bright nonlinear holograms can be obtained in the far-field. The realization of SH holography through monolithic crystal opens wide possibilities in the field of high power laser nonlinear holographic imaging.

Experimental demonstration of structural robustness of spatially partially coherent fields in turbulence

Structured fields that are spatially completely coherent have been extensively studied in the context of long-distance optical communication, as the structure in the intensity profile of such fields is used for encoding information. This method of doing optical communication works very well in the absence of turbulence. However, in the presence of turbulence, the intensity structures of such fields start to degrade because of the complete spatial coherence of the field, and this structural degradation increases with the increase in turbulence strength. On the other hand, several theoretical studies have now shown that the structured fields that are spatially only partially coherent are less affected by turbulence. However, to the best of our knowledge, no such experimental demonstration has been reported until now. In this Letter, we experimentally demonstrate the structural robustness of partially coherent fields in the presence of turbulence, and we show that for a given turbulence strength, the structural robustness of a partially coherent field increases as the spatial coherence length of the field is decreased.

Airy transform of Laguerre-Gaussian beams

Airy transform of Laguerre-Gaussian (LG) beams is investigated. As typical examples, the analytic expressions for the Airy transform of LG₀₁, LG₀₂, LG₁₁, and LG₁₂ modes are derived, which are special optical beams including the Airy and Airyprime functions. Based on these analytical expressions, the Airy transform of LG₀₁, LG₀₂, LG₁₁, and LG₁₂ modes are numerically and experimentally investigated, respectively. The effects of the control parameters α and β on the normalized intensity distribution of a Laguerre-Gaussian beam passing through Airy transform optical systems are investigated, respectively. It is found that the signs of the control parameters only affect the location of the beam spot, while the sizes of the control parameters will affect the characteristics of the beam spot. When the absolute values of the control parameters α and β decrease, the number of the side lobes in the beam spot, the beam spot size, and the Airy feature decrease, while the Laguerre-Gaussian characteristic is strengthened. By altering the control parameters α and β, the performance of these special optical beams is diversified. The experimental results are consistent with the theoretical simulations. The Airy transform of other Laguerre-Gaussian beams can be investigated in the same way. The properties of the Airy transform of Laguerre-Gaussian beams are well demonstrated. This research provides another approach to obtain special optical beams and expands the application of Laguerre-Gaussian beams.

Space-selective crystallization of glass by an optical vortex beam

We report on the improvement of ultrafast laser-written track quality by using an optical vortex.

Theoretical Prediction of Umbilics Creation in Nematic Liquid Crystals with Positive Dielectric Anisotropy

Optically assisted electrical generation of umbilic defects, arising in homeotropically aligned nematic liquid crystal cells and known as topological templates for the generation of optical vortices, are reported in nematic liquid crystals with positive dielectric anisotropy in detail. It is shown that nematic liquid crystals with positive dielectric anisotropy can serve as a stable and efficient medium for the optical vortex generation from both linearly and circularly polarized input Gaussian beams. Hybrid cells made from a thin layer of nematic liquid crystal confined between a photoresponsive slab of iron-doped lithium niobate and a glass plate coated with an active material, i.e., indium tin oxide, were studied. Exposure to a laser beam locally induces a photovoltaic field in the iron-doped lithium niobate substrate, which can penetrate into the liquid crystal film and induce realignment of molecules. The photovoltaic field drives charge carrier accumulation at the interface of indium tin oxide with the liquid crystal, which effectively modifies the shape and symmetry of the electric field. The photovoltaic field has a continuous radial distribution in the transverse xy-plane, weakening with increasing distance from the light irradiation center, where the electric field is normal to the cell plane. Umbilics are created as a result of the liquid crystal tendency to realign parallel to the electric field. Numerical studies of the transmitted intensity profiles in between linear polarizers reveal optical vortex pattern (of four and eight brushes) characteristics for the umbilical defects. The application of crossed circular polarizers results in annular-shaped intensity patterns as a result of spin-to-orbital angular momentum conversions, which give rise to the optical vortices.

Direct generation of orthogonally polarized dual-wavelength continuous-wave and passively Q-switched vortex beam in diode-pumped Pr:YLF lasers

We report on direct generation of an orthogonally polarized dual-wavelength vortex laser, for the first time to our knowledge, by means of a diode-pumped V-shaped Pr:YLF laser platform. A method of misaligning the folded mirror is proposed to realize the simultaneous orthogonally polarized dual-wavelength laser, while a method of orthogonally rotating the laser gain medium is proposed to generate an intracavity vortex beam (LG₀₁ mode). With the two methods, in continuous-wave (CW) mode, we have achieved simultaneous lasing of an orthogonally polarized dual-wavelength vortex laser at 604 and 607 nm with maximum output power of 237.7 mW. Moreover, based on this operation, a simultaneous orthogonally polarized dual-wavelength passively Q-switched vortex laser is also realized by inserting a Co:ASL crystal into the laser resonator as a saturable absorber. This work provides the simplest way for direct generation of an orthogonally polarized dual-wavelength vortex laser for potential applications.

2.7 μm optical vortex beam directly generated from an Er:Y2O3 ceramic laser

We demonstrate, to the best of our knowledge, the first direct vortex beam generation in the 3 μm spectral region by employing an Er:Y₂O₃ ceramic laser. Controllable handedness with high purity is achieved by introducing asymmetric cavity loss and reducing the number of longitudinal modes. The average orbital angular momentum of the produced scalar vortex beam is quantitatively evaluated to be 0.95ħ for the LG_0,+1 mode and -0.94ħ for the LG_0,-1 mode. The corresponding optical spectrum is centered at 2710.8 and 2710.5 nm, respectively.

Spatial light modulator phase calibration based on spatial mode projection

Spatial light modulators (SLMs), which are devices used to manipulate the phase of an incident wave front, are prolific in fields such as optical trapping, dynamic diffractive optical elements, and display technology. Of the many challenges inherent to using SLMs, one of the most ubiquitous is the calibration of the device's phase-shifting mechanism. In this paper, we present a new SLM calibration method based on spatial mode projection. We also implement a data processing technique to our data to generate accurate look-up tables from our calibration curves. We then evaluate the success of our method by propagating Laguerre-Gauss beams with computer-generated holograms. Our results show that the qualitative analysis of modes propagated using the SLM is a viable method of assessing performance. On the whole, we show that spatial mode projection provides clear performance improvements in the SLM's phase-modulating capabilities.

Comprehensive quantitative analysis of vector beam states based on vector field reconstruction

We demonstrate a comprehensive quantitative analysis of vector beam states (VBSs) by using a vector field reconstruction (VFR) technique integrating interferometry and imaging polarimetry, where the analysis is given by a cylindrically polarized Laguerre-Gaussian (LG) mode expansion of VBSs. From test examples of cylindrically polarized LG mode beams, we obtain the complex amplitude distributions of VBSs and perform their quantitative evaluations both in radial and azimuthal directions. The results show that we generated (l, p) = (1, 0) LG radially polarized state with a high purity of 98%. We also argue that the cylindrically polarized LG modal decomposition is meaningful for the detail discussion of experimental results, such as analyses of mode purities and mode contaminations. Thus the VFR technique is significant for analyses of polarization structured beams generated by lasers and converters.

Direct generation of red and orange optical vortex beams from an off-axis diode-pumped Pr3+:YLF laser

We demonstrate the direct generation of visible vortex beams at 640 nm and 607 nm by employing an off-axis pumping scheme in a diode end-pumped Pr³⁺:YLF laser. A detailed numerical analysis, based on the coherent superposition of Hermite-Gaussian modes with different amplitudes and phases, is perfectly consistent with the experimentally observed lasing modes. The maximum vortex output powers have been measured to be 808 mW and 211 mW at a pump power of 3.16 W, for the wavelengths of 640 nm and 607 nm, respectively. We also demonstrate the handedness control of the generated vortex beam. Such a visible vortex laser can potentially be applied in super-resolution fluorescent microscopes and micro-fabrication research.

Hermite-Gaussian mode detection via convolution neural networks

Hermite-Gaussian (HG) laser modes are a complete set of solutions to the free-space paraxial wave equation in Cartesian coordinates and represent a close approximation to physically realizable laser cavity modes. Additionally, HG modes can be mode-multiplexed to significantly increase the information capacity of optical communication systems due to their orthogonality. Because cavity tuning and optical communication applications benefit from a machine vision determination of HG modes, convolution neural networks were implemented to detect the lowest 21 unique HG modes with an accuracy greater than 99%. As the effectiveness of a CNN is dependent on the diversity of its training data, extensive simulated and experimental data sets were created for training, validation, and testing.

Experimental realization of dark and antidark diffraction-free beams

We report the first, to the best of our knowledge, experimental realization of high-quality dark and antidark diffraction-free beams, first theoretically proposed by Ponomarenko et al. [Opt. Lett.32, 2508 (2007)OPLEDP0146-959210.1364/OL.32.002508]. Our method employs a single spatial light modulator (SLM) and is based on superposing mutually uncorrelated but spatially coherent in the time domain Bessel modes with modal weights proportional to the SLM display times of the corresponding modes. We also experimentally verify diffraction-free properties of the generated beams upon their free space propagation.

Mode-selective image upconversion

We study selective upconversion of optical signals according to their detailed transverse electromagnetic modes and demonstrate its proof of operation in a nonlinear crystal. The mode selectivity is achieved by preparing the pump wave in an optimized spatial profile to drive the upconversion. For signals in the Laguerre-Gaussian modes, we show that a mode can be converted with up to 60 times higher efficiency than an overlapping, but orthogonal, mode. This nonlinear optical approach may find applications in compressive imaging, pattern recognition, quantum communications, and others, where the existing linear optical methods are limited.

Wave front control with SLM and simulation of light wave diffraction

With the development of microfabrication technology, it has become possible to modulate the optical wavefront with high accuracy by a device such as a liquid crystal spatial light modulator (SLM). In this study, we conducted a theoretical analysis and experimental study on the generation of Laguerre Gaussian beam of vortex light wave using phase modulation SLM. Numerical simulation and experimental results on the generation of Laguerre Gaussian beam by both binary and phase only modulation are discussed based on the angular spectrum method and the Fresnel transformation method in hologram (CGH) diffraction. The experimental results show that Fresnel diffraction calculation based on Fourier transform method can simulate the light diffraction of SLM very well. This method is very suitable for the action simulation of digital optical wavefront control devices such as SLM. It can be imagined that the simulation method in this study can also play an important role in the design and development of digital optical diffraction elements.

Kaleidoscope vortex lasers generated from astigmatic cavities with longitudinal-transverse coupling

We propose an efficient and robust method to generate the kaleidoscope vortex beam by employing an astigmatic laser cavity with an extra-cavity cylindrical lens. The kaleidoscope vortex beam is arising from the superposition of Laguerre-Gaussian modes with the longitudinal-transverse coupling effect in the laser cavity. The superposed Laguerre-Gaussian mode leads to the formation of complex phase singularities and implies the participation of different optical orbital angular momentum involved in a single kaleidoscope vortex beam. We experimentally demonstrate that a series of kaleidoscope vortex beams with different symmetry are systematically achieved by using a simple setup. The output power of the laser is dependent on the cavity length. This approach is expected to create high-order optical vortex beams and pave the way for optical entanglement.

Generating high-power asymmetrical Laguerre-Gaussian modes and exploring topological charges distribution

We employ an off-axis pumped Nd:YVO₄ laser and control the reflectance of output coupler to directly generate asymmetrical Hermite-Gaussian (HG) modes with various transverse orders. By using an astigmatic mode converter, the generated asymmetrical HG modes are straightforwardly transformed into asymmetrical Laguerre-Gaussian (LG) modes with a crescent-like shape. The average output power of all the crescent-shaped LG modes can exceed 1W at the pump power of 4W. Furthermore, experimental results are theoretically verified by resonant modes derived from the inhomogeneous Helmholtz equation with the localized source distribution. Theoretical resonant modes are also used to explore the dependence of the phase structures of LG modes on the system loss. As the loss increases, it is found that the singularities at the origin will be rearranged and new singularities are formed in the outside region with average orbital angular momentum remaining unchanged.

Extending a set of well-focused beams described by gamma and gamma-coupled functions

A set of rotationally symmetric, paraxial gamma and gamma-coupled beams [introduced in Appl. Opt.57, 3653 (2018)APOPAI0003-693510.1364/AO.57.003653] is extended with other well-focused higher-order beams described by the gamma and gamma-coupled functions with extra free parameters. A computer simulation of the propagation characteristics of some new parametrically optimized higher-order beams with a sharp central peak demonstrates that, in relation to the previous gamma and gamma-coupled beams, most of the new beams have elevated levels of sidelobes in the waist plane. At the same time, the new beams have far more propagation stability over an extended depth of field. In relation to similar Bessel-Gauss beams, these beams have a much better spatial localization of their energy.

Direct generation of vortex beams from a double-end polarized pumped Yb:KYW laser

Double-end polarized pumping scheme combined with off-axis pumping technique has been first introduced to generate vortex beams in a z-type cavity. By employing double-end pumping, two different transverse modes can be excited simultaneously. The phase delay between these two modes can be finely tuned by manipulating the cavity structure. Direct emission of a chirality controllable Laguerre Gaussian LG₀₁ vortex beam with slope efficiency of more than 40% has been realized by a double-end polarized pumped Yb:KYW laser. Other modes, such as dual-LG₀₁ mode, cross-shaped mode, and LG₁₀ mode, have also been demonstrated from our laser setup.

Broadband Variable Meta-Axicons Based on Nano-Aperture Arrays in a Metallic Film

Metasurfaces are two-dimensional metamaterials composed of a carefully designed series of subwavelength meta-atom (antenna or aperture) arrays. These surfaces can manipulate the phase, amplitude and polarization of output light by changing the shapes and orientations of the meta-atoms on a subwavelength scale. Using these properties, we experimentally demonstrate variable meta-axicons composed of rectangular nano-apertures arranged in several concentric rings that can focus left circularly polarized (LCP) light into a real Bessel beam and defocus right circular polarized (RCP) light to form a virtual beam. A desired phase discontinuity in cross-polarized transmitted light is introduced along the interface by controlling the orientations of the nano-apertures. In addition, the meta-axicons can generate Bessel beams of arbitrary orders by suitable design of the phase profile along the surface. The meta-axicons demonstrate broadband optical properties that can switch the wavelength of the incident light from 690 nm to 1050 nm. These variable meta-axicons open a path towards the development of new applications using integrated beam shaping devices.

Goos-Hänchen and Imbert-Fedorov shifts of higher-order Laguerre-Gaussian beams reflected from a dielectric slab

We consider reflection of the Laguerre-Gaussian light beams by a dielectric slab. In view of the unified operator approach, the higher-order Laguerre-Gaussian beams represent a parametric family with the transverse beam profile given by an arbitrary generating parameter. Relying on the Fourier expansion in the focal plane of the beam, we compute the Goos-Hänchen and the Imbert-Fedorov shifts for light beams with non-zero order and azimuthal index. It is demonstrated that both shifts exhibit resonant behavior as functions of the angle of incidence due to the interference between the waves reflected from the upper and lower interfaces. The centroid shifts strongly depend on the order and azimuthal index of the beam. Most interestingly, it is found that the generating parameter of the higher-order beam families strongly affects the shifts. Thus, reshaping of the incident wavefront with fixed order and azimuthal index changes the linear Goos-Hänchen shift up to one half of the beam radius, both negative and positive.

All-fiber stable orbital angular momentum beam generation and propagation

An all-fiber scheme for stable orbital angular momentum (OAM) beam generation and propagation is proposed and demonstrated. This scheme is based on a self-designed and manufactured graded-index few mode fiber (GI-FMF) and compatible mode selection coupler (MSC). The MSC, which consists of a conventional single mode fiber (SMF) and the GI-FMF, can effectively couple the fundamental mode in the SMF to the desired OAM mode in the GI-FMF based on phase matching condition. Meanwhile, the GI-FMF breaks the degeneracy between the desired eigenmodes and neighboring vector modes, thereby allowing the preservation and propagation of the selectively excited OAM modes. As a proof-of-principle, we have implemented an all-fiber device operating in stable OAM modes with |l| = 1. The experimental results show stable propagation of OAM beams with the mode purity of ∼95% and bandwidth of 100 nm. This all fiber device could be useful for further development of wide bandwidth OAM mode division multiplexed application.

Aberration correction considering curved sample surface shape for non-contact two-photon excitation microscopy with spatial light modulator

In this paper, excitation light wavefront modulation is performed considering the curved sample surface shape to demonstrate high-quality deep observation using two-photon excitation microscopy (TPM) with a dry objective lens. A large spherical aberration typically occurs when the refractive index (RI) interface between air and the sample is a plane perpendicular to the optical axis. Moreover, the curved sample surface shape and the RI mismatch cause various aberrations, including spherical ones. Consequently, the fluorescence intensity and resolution of the obtained image are degraded in the deep regions. To improve them, we designed a pre-distortion wavefront for correcting the aberration caused by the curved sample surface shape by using a novel, simple optical path length difference calculation method. The excitation light wavefront is modulated to the pre-distortion wavefront by a spatial light modulator incorporated in the TPM system before passing through the interface, where the RI mismatch occurs. Thus, the excitation light is condensed without aberrations. Blood vessels were thereby observed up to an optical depth of 2,000 μm in a cleared mouse brain by using a dry objective lens.

Single-molecule techniques in biophysics: a review of the progress in methods and applications

Single-molecule biophysics has transformed our understanding of biology, but also of the physics of life. More exotic than simple soft matter, biomatter lives far from thermal equilibrium, covering multiple lengths from the nanoscale of single molecules to up to several orders of magnitude higher in cells, tissues and organisms. Biomolecules are often characterized by underlying instability: multiple metastable free energy states exist, separated by levels of just a few multiples of the thermal energy scale k _B T, where k _B is the Boltzmann constant and T absolute temperature, implying complex inter-conversion kinetics in the relatively hot, wet environment of active biological matter. A key benefit of single-molecule biophysics techniques is their ability to probe heterogeneity of free energy states across a molecular population, too challenging in general for conventional ensemble average approaches. Parallel developments in experimental and computational techniques have catalysed the birth of multiplexed, correlative techniques to tackle previously intractable biological questions. Experimentally, progress has been driven by improvements in sensitivity and speed of detectors, and the stability and efficiency of light sources, probes and microfluidics. We discuss the motivation and requirements for these recent experiments, including the underpinning mathematics. These methods are broadly divided into tools which detect molecules and those which manipulate them. For the former we discuss the progress of super-resolution microscopy, transformative for addressing many longstanding questions in the life sciences, and for the latter we include progress in 'force spectroscopy' techniques that mechanically perturb molecules. We also consider in silico progress of single-molecule computational physics, and how simulation and experimentation may be drawn together to give a more complete understanding. Increasingly, combinatorial techniques are now used, including correlative atomic force microscopy and fluorescence imaging, to probe questions closer to native physiological behaviour. We identify the trade-offs, limitations and applications of these techniques, and discuss exciting new directions.

Orbital angular momentum-enhanced measurement of rotation vibration using a Sagnac interferometer

We construct an experimental measurement system for rotation vibration signal detection using the orbital angular momentum (OAM) of light in a Sagnac interferometer. Inputting light beams with different OAM, we demonstrate that the measured signal and signal-to-noise ratio can be increased by the OAM mode index l. In addition, the Sagnac interferometer can further improve the vibration signal and suppress the environmental noises. Such system has potential applications in high-precision sensing and monitoring of rotation vibrations.

Controllable mode transformation in perfect optical vortices

We report a novel method to freely transform the modes of a perfect optical vortex (POV). By adjusting the scaling factor of the Bessel-Gauss beam at the object plane, the POV mode transformation can be easily controlled from circle to ellipse with a high mode purity. Combined with the modulation of the cone angle of an axicon, the ellipse mode can be freely adjusted along the two orthogonal directions. The properties of the "perfect vortex" are experimentally verified. Moreover, fractional elliptic POVs with versatile modes are presented, where the number and position of the gaps are controllable. These findings are significant for applications that require the complex structured optical field of the POV.

On-chip generation of broadband high-order Laguerre-Gaussian modes in a metasurface

With experimental results, we demonstrate the generation of high-order Laguerre-Gaussian modes with non-zero radial indices using a metal meta-surface, which is composed of a series of rectangle nanoholes with different orientation angles. The phase shift after transmission through the metasurface is determined by the orientation angle of the nanohole. This device works over a broad wavelength band ranging from 700 to 1000 nm. Moreover, we achieve a LG mode with a radial mode index of 10. Our results provide an integrated method to obtain high-order LG modes, which can be used to enhance the capacity in optical communication and manipulation.

Ultrashort vortex from a Gaussian pulse - An achromatic-interferometric approach

The more than a century old Sagnac interferometer is put to first of its kind use to generate an achromatic single-charge vortex equivalent to a Laguerre-Gaussian beam possessing orbital angular momentum (OAM). The interference of counter-propagating polychromatic Gaussian beams of beam waist ω_λ with correlated linear phase (ϕ₀ ≥ 0.025 λ) and lateral shear (y₀ ≥ 0.05 ω_λ) in orthogonal directions is shown to create a vortex phase distribution around the null interference. Using a wavelength-tunable continuous-wave laser the entire range of visible wavelengths is shown to satisfy the condition for vortex generation to achieve a highly stable white-light vortex with excellent propagation integrity. The application capablitiy of the proposed scheme is demonstrated by generating ultrashort optical vortex pulses, its nonlinear frequency conversion and transforming them to vector pulses. We believe that our scheme for generating robust achromatic vortex (implemented with only mirrors and a beam-splitter) pulses in the femtosecond regime, with no conceivable spectral-temporal range and peak-power limitations, can have significant advantages for a variety of applications.

Sub-diffraction-limited fluorescent patterns by tightly focusing polarized femtosecond vortex beams in a silver-containing glass

We report that the shape and size of fluorescent patterns can be controlled by the focused laser intensity distribution, which depends on irradiation conditions as well as on the spin and orbital angular momenta being carried by light, inducing the formation of silver cluster patterns in a silver-containing zinc phosphate glass. In particular, we demonstrate that sub-diffraction-limited inner structures of fluorescent patterns can be generated by direct laser writing (DLW) with tightly focused femtosecond laser vortex beams as Laguerre-Gauss modes (LG0l) with linear and left-handed circular polarizations. We believe this technique, further combined with dual-color DLW, can be useful and powerful for developing structured light enabled nanostructures.

Correction of spherical aberration in multi-focal multiphoton microscopy with spatial light modulator

We demonstrate that high-quality images of the deep regions of a thick sample can be obtained from its surface by multi-focal multiphoton microscopy (MMM). The MMM system incorporates a spatial light modulator to separate the excitation beam into a multi-focal excitation beam and modulate the pre-distortion wavefront to correct spherical aberration (SA) caused by a refractive index mismatch between the immersion medium and the biological sample. When fluorescent beads in transparent epoxy resin were observed using four SA-corrected focal beams, the fluorescence signal of the obtained images was ~52 times higher than that obtained without SA correction until a depth of ~1100 μm, similar to the result for single-focal multiphoton microscopy (SMM). The MMM scanning time was four times less than that for SMM, and MMM showed an improved fluorescence intensity and depth resolution for an image of blood vessels in the brain of a mouse stained with a fluorescent dye.

Hybrid generation and analysis of vector vortex beams

A method is described for generating optical vector vortex beams carrying superpositions of orbital angular momentum states by using a tandem application of a spatial light modulator with a vortex retarder. The vortex component has a spatially inhomogeneous phase front that can carry orbital angular momentum, and the vector nature is a spatially inhomogeneous state of polarization in the laser beam profile. The vector vortex beams are characterized experimentally by imaging the beams at points across the focal plane in an astigmatic system using a tilted lens. Mathematical analysis of the Gouy phase shows good agreement with the phase structure obtained in the experimental images. The polarization structure of the vector beam and the orbital angular momentum of the vortex beam are shown to be preserved.

Simultaneous generation of multiple perfect polarization vortices with selective spatial states in various diffraction orders

We demonstrate an approach to generate multiple perfect polarization vortices (PPVs) with selective spatial polarization distribution in various diffraction orders. The key is the design of a hologram with an anisotropic polarization diffraction grating. In the experiment, a setup consisting of two spatial light modulators is built. By encoding the specially designed holograms, PPVs with various states are obtained in different diffraction orders simultaneously, for instance, in radial and azimuthal polarized states. These PPVs may have applications in laser processing, optical tweezers, and so on.

~1 mJ pulsed vortex laser at 1645 nm with well-defined helicity

We report on a millijoule level Er:YAG ceramic pulsed vortex laser resonantly pumped by an annular beam at 1532 nm. By means of an uncoated YAG crystal plate inserting into the cavity and a proper thermal gradient on the ceramic, 1.03 mJ LG_0,-1 mode and 0.97 mJ LG_{0, + 1} mode were respectively produced, and no vortex mode instability problem was observed. We believe the directly generated millijoule level optical vortex with well-defined helicity will have potential applications in material modification and processing, high-field laser physics, and nonlinear optics, etc.

Experimental study of diode pumped rubidium amplifier for single higher-order Laguerre-Gaussian modes

In this paper, we have set up a diode laser pumped rubidium amplifier for higher-order Laguerre-Gauss (LG) modes. We experimentally realized amplification of higher-order LG modes including helical and sinusoidal LG₀₃, LG₁₃, LG₂₃, and LG₃₃ modes with their high purity held. This novel scheme of generating high-purity higher-order LG beams at high laser power is preferred to the second-generation gravitational wave interferometers. To the best of our knowledge, it is the first time this scheme is formulated.

Contextual phase estimation from two-plane intensity measurements

In this work we construct examples of paraxial light fields whose intensities defined at all points in space do not have a corresponding cross-spectrally pure field amplitude reproducing the same set of transported intensities at all transverse planes. Nevertheless, two spatially separated transverse plane intensities as drawn from these examples are shown to have a corresponding cross-spectrally pure field amplitude, which, through paraxial free propagation between these two planes, reproduces the drawn transverse plane intensities. And the phase associated with such a field amplitude at a given transverse plane is found to be contextual, and intrinsically dependent on the pairing plane.

Generation of optical vortex dipole from superposition of two transversely scaled Gaussian beams

We propose a distinct concept on the generation of optical vortex through coupling between the amplitude and phase differences of the superposing beams. For the proof-of-concept demonstration, we propose a simple free-space optics recipe for the controlled synthesis of an optical beam with a vortex dipole by superposing two transversely scaled Gaussian beams. The experimental demonstration using a Sagnac interferometer introduces the desired amount of radial shear and linear phase difference between the two out-of-phase Gaussian beams to create a vortex pair of opposite topological charge in the superposed beam. Flexibility to tune their location and separation using the choice of direction of the linear phase difference and the amount of amplitude difference between the superposing beams has potential applications in optical tweezers and traps utilizing the local variation in angular momentum across the beam cross section.

Analytical investigation of optical vortices emitted from a collectively polarized dipole array

Many approaches for producing optical vortices have been developed both for fundamental interests of science and for engineering applications. In particular, the approach with direct excitation of several emitters has a potential to control the topological charges with a control of the source conditions without any modifications of structures of the system. In this paper, we investigate the propagation properties of the optical vortices emitted from a collectively polarized electric dipole array as a simple model of the several emitters. Using an analytical approach based on the Jacobi-Anger expansion, we derive a relationship between the topological charge of the optical vortices and the source conditions of the emitter, and clarify and report our new finding; there exists an intrinsic split of the singular points in the electric field due to the spin-orbit interaction of the dipole fields.

Efficient generation of Hermite-Gauss and Ince-Gauss beams through kinoform phase elements

We discuss the generation of Hermite-Gauss and Ince-Gauss beams employing phase elements whose transmittances coincide with the phase modulations of such beams. A scaled version of the desired field appears, distorted by marginal optical noise, at the element's Fourier domain. The motivation to perform this study is that, in the context of the proposed approach, the desired beams are generated with the maximum possible efficiency. A disadvantage of the method is the distortion of the desired beams by the influence of several nondesired beam modes generated by the phase elements. We evaluate such distortion employing the root mean square deviation as a figure of merit.