Mode purities of Laguerre-Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators

Space-time wave packets with reduced divergence and tunable group velocity generated in free space after multi-mode fiber propagation

Previously, space-time wave packets (STWPs) have been generated in free space with reduced diffraction and a tunable group velocity by combining multiple frequency comb lines each carrying a single Bessel mode with a unique wave number. It might be potentially desirable to propagate the STWP through fiber for reconfigurable positioning. However, fiber mode coupling might degrade the output STWP and distort its propagation characteristics. In this Letter, we experimentally demonstrate STWP generation and propagation over 1-m graded-index multi-mode fiber. Fiber mode coupling is mitigated by pre-distortion according to the inverse matrix of the fiber mode coupling matrix. Measurement of the STWP at the fiber output shows that its group velocity can vary from 1.0042c to 0.9967c by tuning the wave number of the Bessel mode on each frequency. The measured time-averaged intensity profiles show that the beam radius remains similar after 150-mm free-space propagation after exiting the fiber.

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%.

Experimental Guesswork with Quantum Side Information Using Twisted Light

Guesswork is an information-theoretic quantity which can be seen as an alternate security criterion to entropy. Recent work has established the theoretical framework for guesswork in the presence of quantum side information, which we extend both theoretically and experimentally. We consider guesswork when the side information consists of the BB84 states and their higher-dimensional generalizations. With this side information, we compute the guesswork for two different scenarios for each dimension. We then performed a proof-of-principle experiment using Laguerre-Gauss modes to experimentally compute the guesswork for higher-dimensional generalizations of the BB84 states. We find that our experimental results agree closely with our theoretical predictions. This work shows that guesswork can be a viable security criterion in cryptographic tasks and is experimentally accessible in a number of optical setups.

Zero-order free holographic optical tweezers

Holographic optical tweezers (HOTs) use spatial light modulators (SLM) to modulate light beams, thereby enabling the dynamic control of optical trap arrays with complex intensity and phase distributions. This has provided exciting new opportunities for cell sorting, microstructure machining, and studying single molecules. However, the pixelated structure of the SLM will inevitably bring up the unmodulated zero-order diffraction possessing an unacceptably large fraction of the incident light beam power. This is harmful to optical trapping because of the bright, highly localized nature of the errant beam. In this paper and to address this issue, we construct a cost-effective, zero-order free HOTs apparatus, thanks to a homemade asymmetric triangle reflector and a digital lens. As there is no zero-order diffraction, the instrument performs excellently in generating complex light fields and manipulating particles.

Generation of OAM-carrying space-time wave packets with time-dependent beam radii using a coherent combination of multiple LG modes on multiple frequencies

Space-time (ST) wave packets, in which spatial and temporal characteristics are coupled, have gained attention due to their unique propagation characteristics, such as propagation invariance and tunable group velocity in addition to their potential ability to carry orbital angular momentum (OAM). Through experiment and simulation, we explore the generation of OAM-carrying ST wave packets, with the unique property of a time-dependent beam radius at various ranges of propagation distances. To achieve this, we synthesize multiple frequency comb lines, each assigned to a coherent combination of multiple Laguerre-Gaussian (LG_ℓ,p) modes with the same azimuthal index but different radial indices. The time-dependent interference among the spatial modes at the different frequencies leads to the generation of the desired OAM-carrying ST wave packet with dynamically varying radii. The simulation results indicate that the dynamic range of beam radius oscillations increases with the number of modes and frequency lines. The simulated ST wave packet for OAM of orders +1 or +3 has an OAM purity of >95%. In addition, we experimentally generate and measure the OAM-carrying ST wave packets with time-dependent beam radii. In the experiment, several lines of a Kerr frequency comb are spatially modulated with the superposition of multiple LG modes and combined to generate such an ST wave packet. In the experiment, ST wave packets for OAM of orders +1 or +3 have an OAM purity of >64%. In simulation and experiment, OAM purity decreases and beam radius becomes larger over the propagation.

High purity orbital angular momentum of light

We present a novel technique for generating beams of light carrying orbital angular momentum (OAM) that increases mode purity and decreases singularity splitting by orders of magnitude. This technique also works to control and mitigate beam divergence within propagation distances less than the Rayleigh length. Additionally, we analyze a tunable parameter of this technique that can change the ratio of beam purity to power to fit desired specifications. Beam generation via this technique is achievable using only phase-modulating optical elements, which reduces experimental complexity and beam energy loss.

Tunability of space-time wave packet carrying tunable and dynamically changing OAM value

Space-time (ST) wave packets have gained much interest due to their dynamic optical properties. Such wave packets can be generated by synthesizing frequency comb lines, each having multiple complex-weighted spatial modes, to carry dynamically changing orbital angular momentum (OAM) values. Here, we investigate the tunability of such ST wave packets by varying the number of frequency comb lines and the combinations of spatial modes on each frequency. We experimentally generate and measure the wave packets with tunable OAM values from +1 to +6 or from +1 to +4 during a ∼5.2-ps period. We also investigate, in simulation, the temporal pulse width of the ST wave packet and the nonlinear variation of the OAM values. The simulation results show that: (i) a pulse width can be narrower for the ST wave packet carrying dynamically changing OAM values using more frequency lines; and (ii) the nonlinearly varying OAM value can result in different frequency chirps along the azimuthal direction at different time instants.

Generation of combined half-integer Bessel-like beams using synthetic phase holograms

We discuss the generation of combined half-integer Bessel-like (CHB) beams using synthetic phase holograms (SPHs). We assess the efficiency and accuracy of the SPHs, in the task of generating CHB beams. The proposal is illustrated by the implementation of CHB beams, which are experimentally generated in a setup based on a phase spatial light modulator. Also, we analyze, numerically and experimentally, the propagation of the generated CHB beams. As the main result, the SPHs are able to generate several CHB beams with relatively high accuracy. Additionally, it is obtained that the efficiency values of the SPHs are close to the theoretical predictions.

Single-shot generation of composite optical vortex beams using hybrid binary fork gratings

We design and experimentally demonstrate a simple, single-shot method for the generation of arbitrary composite vortex (CV) beams using hybrid binary fork gratings (hBFG). These gratings were computationally generated by removing the central region around the fork-dislocation of azimuthal charge ℓ₁ and substituting it with a BFG of a different charge ℓ₂. The geometrical parameters of hBFGs were optimized for the efficient generation of CV beams. The method was further extended to the generation of CV beams consisting of three different ℓ and of higher radial charges p. This simple generation method may be useful to generate complex beam shapes with engineered phase fronts without complicated interferometry based techniques.

Reconfigurable generation of double-ring perfect vortex beam

Perfect vortex beam (PVB), whose ring radius is independent of its topological charge, play an important role in optical trapping and optical communication. Here, we experimentally demonstrate the reconfigurable double-ring PVB (DR-PVB) generation with independent manipulations of the amplitude, the radius, the width, and the topological charge for each ring. Based on complex amplitude modulation (CAM) with a phase-only spatial light modulator (SLM), we successfully verify the proposed DR-PVB generation scheme via the computer-generated hologram. Furthermore, we carry out a quantitative characterization for the generated DR-PVB, in terms of both the generation quality and the generation efficiency. The correlation coefficients of various reconfigurable DR-PVBs are above 0.8, together with the highest generation efficiency of 44%. We believe that, the proposed generation scheme of reconfigurable DR-PVB is desired for applications in both optical tweezers and orbital angular momentum (OAM) multiplexing.

Sampling a vortex from a Gaussian beam using a wedge-plate shearing interferometer

Many vortex-generation techniques have been developed to address a range of potential applications, exploiting their unique amplitude and phase profiles and their possession of orbital angular momentum. In this work, we present what may be the simplest method of vortex beam generation, requiring only a wedged optic: the wedge-plate shearing interferometer (WPSI). We show that the WPSI can reflect a first order Laguerre-Gaussian vortex beam (LG₀₁) with a theoretical purity of >99% from an input fundamental Gaussian beam, with 98% LG₀₁ purity experimentally demonstrated. We demonstrate 1% power conversion with a route to 14%. The monolithic WPSI is a simple, compact, and highly stable device, which can operate at any wavelength that the material is transparent to. We anticipate that it will be useful where sampling a robust, high-purity vortex beam from a Gaussian laser beam is required, including low-cost vortex generation for metrology or education.

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.

Reduced volume and reflection for bright optical tweezers with radial Laguerre-Gauss beams

Spatially structured light has opened a wide range of opportunities for enhanced imaging as well as optical manipulation and particle confinement. Here, we show that phase-coherent illumination with superpositions of radial Laguerre-Gauss (LG) beams provides improved localization for bright optical tweezer traps, with narrowed radial and axial intensity distributions. Further, the Gouy phase shifts for sums of tightly focused radial LG fields can be exploited for phase-contrast strategies at the wavelength scale. One example developed here is the suppression of interference fringes from reflection near nanodielectric surfaces, with the promise of improved cold-atom delivery and manipulation.

Highly multimodal structure of high topological charge extreme ultraviolet vortex beams

Optical beams carrying orbital angular momentum are a very active field of research for their prospective applications, especially at short wavelengths. We consider here such beams produced through high-harmonic generation (HHG) in a rare gas and analyze the characterization of their high-charge vortex structure by an extreme ultraviolet Hartmann wavefront sensor. We show that such HHG beams are generally composed of a set of numerous vortex modes. The sensitivity of the intensity and phase of the HHG beam to the infrared laser aberrations is investigated using a deformable mirror.

Tailoring diffraction of light carrying orbital angular momenta

A unified approach to controlling the diffraction of light carrying orbital angular momenta (OAM) is developed and experimentally verified in this Letter. This approach allows one to specify not only the number of diffraction maxima, their spatial frequencies, and the intensity distribution between them, but also the OAM in each maximum. It is verified that the approach can be used for structuring both single and multiple beams carrying OAMs. Simulations reveal phase singularities in structured beams. In addition, the approach makes it possible to shape the light in regular and irregular two-dimensional arrays with addressing the OAMs at each site. This approach offers new opportunities for singular optics.

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.

Common-path off-axis incoherent Fourier holography with a maximum overlapping interference area

In this Letter, we present a new method for recording spatially incoherent common-path off-axis Fourier holograms. This method records the three-dimensional (3D) information of an object into a Fourier hologram without the need of any mechanical scanning with incoherent illumination. The proposed setup consists of two gratings to form a common-path configuration, and two customized cells to create a rotational and radial shearing interferometer. While the first grating is placed on the first image plane, the second grating shifts axially from the second image plane to build off-axis geometry. A lens is used to combine two beams to generate the maximum overlapping area at the hologram plane. Proof-of-concept experiments confirm the ability of such a system to achieve the maximum overlapping interference area, stability of the system against the vibration of surrounding environment, numerical reconstruction using only one fast Fourier transform, and 3D capability to capture a 3D object illuminated by an LED light.

Beyond the display: phase-only liquid crystal on Silicon devices and their applications in photonics [Invited]

Existing for almost four decades, liquid crystal on Silicon (LCOS) technology is rapidly growing into photonic applications. We review the basics of the technology, from the wafer to the driving solutions, the progress over the last decade and the future outlook. Furthermore we review the most exciting industrial and scientific applications of the LCOS technology.

Formation of high-quality vortex laser beams with different orbital angular momenta in the laser resonator

A scheme for forming high-quality vortex laser beams by employing spiral phase elements inside a laser resonator is presented theoretically. The calculated results show that the purity of the generated mode will decrease slightly as the mode order increases. However, the purity can achieve higher than 0.97 even for the high-order mode. More important, the value of the orbital angular momentum is controllable. Then, the influence of production and alignment errors, including the number of phase levels of the spiral phase elements, the surface roughness of the reflective mirrors, and the decenter of the reflective mirrors, is discussed in detail. The results show that the diffraction loss of the proposed system is more sensitive to production errors, and the purity of the generated mode is more sensitive to alignment errors. Thus, we estimate that the height of one step of the spiral structure should be less than one-fifteenth of the wavelength, the maximum surface fluctuation should be less than one-twentieth of the wavelength, and the vertical distance between the centers of the two reflective mirrors should be less than 20 μm if one wants to obtain high-quality vortex laser beams with high efficiency. The requirements for precision are acceptable for existing microfabrication and operation technologies.

Direct generation of a narrow-linewidth Laguerre-Gaussian vortex laser in a monolithic nonplanar oscillator

Vortex laser beams carrying orbital angular momentum have been attracting a lot of interest in recent years. Here we demonstrate the direct generation of a vortex laser in a monolithic nonplanar ring cavity. The unidirectional and single-frequency operation of Laguerre-Gaussian modes is observed and characterized. Fork interferograms have been obtained using a simple interferometer based on a plano-concave lens, and the topological charge of vortex beam is determined. A spectral linewidth as narrow as 2.3 kHz is measured by beating with a reference laser. We believe that such a high coherent vortex laser can be beneficial for numerous applications, including precision measurements and optical communications.

Conventional volume holography for unconventional Airy beam shapes

Utilizing multiplexed volume holography, a single optical element, enabling to shape structural variants of non-diffracting Airy wavefronts, from one-dimensional Airy mode to unconventional Airy modes such as vortex Airy and quad Airy modes, has been experimentally realized. Here, beam shaped angularly multiplexed volume holographic gratings (AMVHGs) are recorded in PQ: PMMA photopolymer, where five different spatial wavefronts of Airy beams have been sequentially recorded, for simultaneous reconstruction of different Airy modes, by a conventional Gaussian beam. Spatial and spectral mode selective properties of AMVHGs are demonstrated by narrow-band as well as by broadband light source. In addition, through wavelength degeneracy property, the maximum sensitivity wavelength of blue (488 nm) is used for recording in PQ: PMMA, but the AMVHGs are operated at a broad wavelength band of interest, all the way to longer wavelength in near infrared (850 nm). The K-sphere representation is used to explain the spectral properties of AMVHGs.

Reconfigurable and tunable twisted light laser

Twisted light, having a helical spatial phase structure and carrying orbital angular momentum (OAM), has given rise to many developments ranging from optical manipulation to optical communications. The laser excitation of twisted light in a reconfigurable and tunable way is of great interest. Here, we propose and experimentally demonstrate an OAM reconfigurable and wavelength tunable twisted light laser with achievable high-order OAM modes on a hybrid free-space and fiber platform. The excited twisted light laser is enabled by a ring resonator incorporating spatial light modulators (SLMs) and bandpass filter (BPF). By appropriately switching the phase pattern loaded onto SLMs and adjusting the BPF, twisted light laser with reconfigurable OAM and tunable wavelength is implemented. In the experiment, the OAM value is varied from -10 to +10 and the wavelength is adjusted from 1530 to 1565 nm covering the whole C band. The obtained results indicate successful implementation of a reconfigurable and tunable twisted light laser with favorable operation performance. Reconfigurable and tunable twisted light laser may open up new perspectives to more extensive OAM-enabled applications with improved flexibility and robustness.

Single-shot phase-shifting incoherent digital holography with multiplexed checkerboard phase gratings

Single-shot phase-shifting incoherent digital holography with multiplexed checkerboard phase gratings is proposed for acquiring holograms of moving objects. The gratings presented here play the following three roles: dividing the beams, modulating the curvature of spherical beams, and introducing different phase shifts. With the gratings of our proposed method, four individual holograms of a spatially incoherent light are formed on an image sensor. Therefore, it is possible to simultaneously capture four holograms and implement a phase-shifting technique. A proof-of-principle experiment was conducted to show the feasibility of the proposed method.

Projecting non-diffracting waves with intermediate-plane holography

We introduce intermediate-plane holography, which substantially improves the ability of holographic trapping systems to project propagation-invariant modes of light using phase-only diffractive optical elements. Translating the mode-forming hologram to an intermediate plane in the optical train can reduce the need to encode amplitude variations in the field, and therefore complements well-established techniques for encoding complex-valued transfer functions into phase-only holograms. Compared to standard holographic trapping implementations, intermediate-plane holograms greatly improve diffraction efficiency and mode purity of propagation-invariant modes, and so increase their useful non-diffracting range. We demonstrate this technique through experimental realizations of accelerating modes and long-range tractor beams.

Generation of arbitrary axisymmetrically polarized pulses by using the combination of 4-f spatial light modulator and common-path optical system

We proposed and constructed a system to realize broadband generation of arbitrary axisymmetrically polarized (AP) pulses with spatial complex amplitude modulation. This system employs the combination of a spatial light modulator in the 4-f configuration (4-f SLM), and a space variant wave plate as a common path interferometer. The 4-f SLM and the common path interferometer offer compensation for spatial dispersion with respect to wavelength and stability to perturbation, respectively. We experimentally demonstrated the various AP pulses generation by applying modulations of fundamental and higher-order Laguerre-Gauss modes, whose radial indices were, respectively, p = 0 and 1, with high purity, which showed that we were able to generate arbitral AP pulses with spatial complex amplitude modulation. This technique is expected to be applied in both classical and quantum communications with higher-order modes.

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.

Polarization properties of Ince-Gaussian laser beams

A consistent theoretical description of the polarization properties of Ince-Gauss (IG) laser beams is provided by constructing paraxial IG solutions to Maxwell equations. We confirm this description experimentally by recording both the dominant and cross-polarization components. Moreover, by experimentally confirming the evolution of the dominant and cross-polarization components as functions of ellipticity parameters, our paper extends further support to a unified treatment of the three (Laguerre-Gauss, Hermite-Gauss, and IG) families of paraxial laser beams.

Universal phase-only spatial light modulators

Universal phase-only spatial light modulators (UP-SLMs) are proposed and demonstrated by simulation and experiment. UP-SLMs, which consist of unitarily coupled electrically controllable wave plates, convert the optically anisotropic properties of the paired two wave plates into an effective single isotropic phase plate and can be realized with electrically tunable birefringence materials such as uniaxial liquid crystals (LCs). The universal approaches are applicable to any uniaxial anisotropic materials based cells, any LC cell operation modes and any incident light polarization states. Further the UP-SLMs are experimentally demonstrated even with commercial LCD panels having low geometrical rotational symmetry. These UP-SLMs will play significant roles in wave optics, communications, information displays, digital holography, quantum optics and quantum information technology by harnessing their unique capacity of modulating the only phase of linearly, circularly, elliptically, azimuthally, radially and even randomly polarized light.

Laguerre-Gaussian modal q-plates

We propose space-variant uniaxial flat optical elements designed to generate pure Laguerre-Gaussian modes with arbitrary azimuthal and radial indices l and p from an incident Gaussian beam. This is done via the combined use of the dynamic and the geometric phases. Optimal design protocol for the mode conversion efficiency is derived, and the corresponding characteristics are given for -6≤l≤6 and 0≤p≤5. The obtained "modal q-plates" may find many applications whenever the radial degree of freedom of a light field is at play.

In situ measurement of the topological charge of a perfect vortex using the phase shift method

We propose a method to determine the topological charge (TC) of a perfect vortex. With the phase shift technique, the perfect vortex and its conjugate beam exactly overlap and interfere. Consequently, the TC of a perfect vortex is determined by counting the number of interference fringes. This proposed method enables in situ determination of the TC of the perfect vortex without the need for additional optical elements, and it is immune to environmental vibration and parasitic interference.

Generation of flower high-order Poincaré sphere laser beams from a spatial light modulator

We propose and experimentally demonstrate a new complex laser beam with inhomogeneous polarization distributions mapping onto high-order Poincaré spheres (HOPSs). The complex laser mode is achieved by superposition of Laguerre-Gaussian modes and manifests exotic flower-like localization on intensity and phase profiles. A simple optical system is used to generate a polarization-variant distribution on the complex laser mode by superposition of orthogonal circular polarizations with opposite topological charges. Numerical analyses of the polarization distribution are consistent with the experimental results. The novel flower HOPS beams can act as a new light source for photonic applications.

Optical communication beyond orbital angular momentum

Mode division multiplexing (MDM) is mooted as a technology to address future bandwidth issues, and has been successfully demonstrated in free space using spatial modes with orbital angular momentum (OAM). To further increase the data transmission rate, more degrees of freedom are required to form a densely packed mode space. Here we move beyond OAM and demonstrate multiplexing and demultiplexing using both the radial and azimuthal degrees of freedom. We achieve this with a holographic approach that allows over 100 modes to be encoded on a single hologram, across a wide wavelength range, in a wavelength independent manner. Our results offer a new tool that will prove useful in realizing higher bit rates for next generation optical networks.

Comparison of beam generation techniques using a phase only spatial light modulator

Whether in art or for QR codes, images have proven to be both powerful and efficient carriers of information. Spatial light modulators allow an unprecedented level of control over the generation of optical fields by using digital holograms. There is no unique way of obtaining a desired light pattern however, leaving many competing methods for hologram generation. In this paper, we test six hologram generation techniques in the creation of a variety of modes as well as a photographic image: rating the methods according to obtained mode quality and power. All techniques compensate for a non-uniform mode profile of the input laser and incorporate amplitude scaling. We find that all methods perform well and stress the importance of appropriate spatial filtering. We expect these results to be of interest to those working in the contexts of microscopy, optical trapping or quantum image creation.

Is there an optimal basis to maximise optical information transfer?

We establish the concept of the density of the optical degrees of freedom that may be applied to any photonics based system. As a key example of this versatile approach we explore information transfer using optical communication. We demonstrate both experimentally, theoretically and numerically that the use of a basis set with fields containing optical vortices does not increase the telecommunication capacity of an optical system.

Full Quantitative Analysis of Arbitrary Cylindrically Polarized Pulses by Using Extended Stokes Parameters

Cylindrically polarized (CP) modes are laser beam modes which have rotational symmetry of the polarization distribution around the beam axis. Considerable attention has been paid to CP modes for their various applications. In this paper, by using the extended Stokes parameters and the degree of polarization defined for the spatial distribution (DOP-SD), we fully-quantitatively characterize the spectrally-resolved polarization states of arbitrary CP (axisymmetrically polarized and higher-order cylindrically polarized) broadband pulses generated by coherent beam combining. All the generated pulse states were fully-quantitatively analyzed for the first time and proved to have high symmetry (DOP-SD ≳ 0.95) and low spectral dependence of polarization states. Moreover, we show the DOP-SD, which cannot be defined by the conventional higher-order and hybrid Stokes parameters, enables us to make a quantitative evaluation of small degradation of rotational symmetry of polarization distribution. This quantitative characterization with high precision is significant for applications of precise material processing, quantum information processing, magneto-optical storage and nonlinear spectroscopic polarimetry.

Generation of Laguerre-Gaussian LGp0 beams using binary phase diffractive optical elements

In recent years, considerable attention has been devoted to laser beams with specific intensity profile, i.e., non-Gaussian. In this work, we present a novel technique to generate high-radial-order Laguerre-Gaussian beams LG(p0) based on the use of a binary phase diffractive optical element (BPDOE). The latter is a phase plate made up of annular zones introducing alternatively a phase shift equal to 0 or π modeled on positions which do not coincide with the position of the zeros of the desired LG(p0) beam. The LG(p0) beams are obtained by transforming a fundamental Gaussian beam through an appropriate BPDOE. The design of the latter is based on the calculation of the Fresnel-Kirchhoff integral, and the diffracted intensity at the focus plane of a lens has been modeled analytically for the first time. The numerical simulations and experiment demonstrate a good beam quality transformation. Obtained LG(p0) are suitable for atom trap and pumping solid state laser applications.

Simulating quantum state engineering in spontaneous parametric down-conversion using classical light

We present a simple method of simulating the effect of the pumping process in spontaneous parametric down-conversion (SPDC) by modulating a classical laser beam with two spatial light modulators through a back projection setup. We simulate a wide range of pump beams for quantum state engineering and confirm that the results are in agreement with theory. Our approach offers high photon count rates, is quick to yield results and can easily be converted back to a SPDC setup. It is likely to be a useful tool before starting more complicated SPDC experiments with custom pump profiles.

Self-distortion compensation of spatial light modulator under temperature-varying conditions

Conventional methods of compensating for self-distortion in liquid-crystal-on-silicon spatial light modulators (LCOS-SLM) are based on aberration correction, where the wavefront of the incident beam is modulated to compensate for aberrations caused by the imperfect optical flatness of the LCOS-SLM surface. However, the phase distribution of an LCOS-SLM varies with changes in ambient temperature and requires additional correction. We report a novel phase compensation method under temperature-varying conditions based on an orthonormal Legendre series expansion of the phase distribution. We investigated the temperature dependency by controlling the ambient temperature with an incubator and successfully corrected for self-distortion in a temperature range of 20 °C to 50 °C. Our approach has the potential to be adopted in tight-focusing applications which require wavefront modulation with very high accuracy.

Direct evidence for three-dimensional off-axis trapping with single Laguerre-Gaussian beam

Optical tweezers are often applied to control the dynamics of objects by scanning light. However, there is a limitation that objects fail to track the scan when the drag exceeds the trapping force. In contrast, Laguerre-Gaussian (LG) beams can directly control the torque on objects and provide a typical model for nonequilibrium systems such as Brownian motion under external fields. Although stable “mid-water” trapping is essential for removing extrinsic hydrodynamic effects in such studies, three-dimensional trapping by LG beams has not yet been clearly established. Here we report the three-dimensional off-axis trapping of dielectric spheres using high-quality LG beams generated by a special holographic method. The trapping position was estimated as ~ half the wavelength behind the beam waist. These results establish the scientific groundwork of LG trapping and the technical basis of calibrating optical torque to provide powerful tools for studying energy-conversion mechanisms and the nonequilibrium nature of biological molecules under torque.

Comparing efficiency and accuracy of the kinoform and the helical axicon as Bessel-Gauss beam generators

We compare two phase optical elements that are employed to generate approximate Bessel-Gauss beams of arbitrary order. These elements are the helical axicon (HA) and the kinoform of the desired Bessel-Gauss beam. The HA generates a Bessel beam (BB) by free propagation, and the kinoform is employed in a Fourier spatial filtering optical setup. As the main result, it is obtained that the error in the BBs generated with the kinoform is smaller than the error in the beams obtained with the HA. On the other hand, it is obtained that the efficiencies of the methods are approximately 1.0 (HA) and 0.7 (kinoform).

Rapid generation of light beams carrying orbital angular momentum

We report a technique for encoding both amplitude and phase variations onto a laser beam using a single digital micro-mirror device (DMD). Using this technique, we generate Laguerre-Gaussian and vortex orbital-angular-momentum (OAM) modes, along with modes in a set that is mutually unbiased with respect to the OAM basis. Additionally, we have demonstrated rapid switching among the generated modes at a speed of 4 kHz, which is much faster than the speed regularly achieved by phase-only spatial light modulators (SLMs). The dynamic control of both phase and amplitude of a laser beam is an enabling technology for classical communication and quantum key distribution (QKD) systems that employ spatial mode encoding.

Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram

A phase-only hologram applies a modal transformation to an optical transverse spatial mode via phase encoding and intensity masking. Accurate control of the optical field crucially depends on the method employed to encode the hologram. In this Letter, we present a method to encode the amplitude and the phase of an optical field into a phase-only hologram, which allows the exact control of spatial transverse modes. Any intensity masking method modulates the amplitude and alters the phase of the optical field. Our method consists in correcting for this unwanted phase alteration by modifying the phase encryption accordingly. We experimentally verify the accuracy of our method by applying it to the generation and detection of transverse spatial modes in mutually unbiased bases of dimension two and three.

Position measurement of non-integer OAM beams with structurally invariant propagation

We present a design to generate structurally propagation invariant light beams carrying non-integer orbital angular momentum (OAM) using Hermite-Laguerre-Gaussian (HLG) modes. Different from previous techniques, the symmetry axes of our beams are fixed when varying the OAM; this simplifies the calibration technique for beam positional measurement using a quadrant detector. We have also demonstrated analytically and experimentally that both the OAM value and the HLG mode orientation play an important role in the quadrant detector response. The assumption that a quadrant detector is most sensitive at the beam center does not always hold for anisotropic beam profiles, such as HLG beams.

Holographic generation of a class of nondiffracting fields with optimum efficiency

We discuss the accurate generation of complex optical fields using phase holograms that provide the optimum diffraction efficiency. In each considered case, the phase modulation of the employed hologram is identical to the phase of the desired optical field. We show that periodic and quasiperiodic nondiffracting optical fields, mathematically obtained through the superposition of multiple plane waves, can be generated with high fidelity using this approach.

Diffractive generalized phase contrast for adaptive phase imaging and optical security

We analyze the properties of Generalized Phase Contrast (GPC) when the input phase modulation is implemented using diffractive gratings. In GPC applications for patterned illumination, the use of a dynamic diffractive optical element for encoding the GPC input phase allows for on-the-fly optimization of the input aperture parameters according to desired output characteristics. For wavefront sensing, the achieved aperture control opens a new degree of freedom for improving the accuracy of quantitative phase imaging. Diffractive GPC input modulation also fits well with grating-based optical security applications and can be used to create phase-based information channels for enhanced information security.

Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections

In this work, we propose a robust and versatile approach for the characterization of the complex field amplitude of holographically generated coherent-scalar paraxial beams. For this purpose we apply an iterative algorithm that allows recovering the phase of the generated beam from the measurement of its Wigner distribution projections. Its performance is analyzed for beams of different symmetry: Laguerre-Gaussian, Hermite-Gaussian and spiral ones, which are obtained experimentally by a computer generated hologram (CGH) implemented on a programmable spatial light modulator (SLM). Using the same method we also study the quality of their holographic recording on a highly efficient photopolymerizable glass. The proposed approach is useful for the creation of adaptive CGH that takes into account the peculiarities of the SLM, as well as for the quality control of the holographic data storage.

Microparticle movements in optical funnels and pods

Three-dimensional microparticle movements induced by laser beams with a funnel- and tubular pod-like structure, in the neighbourhood of the focal plane of an optical trapping setup, are experimentally studied. The funnel and pod beams constructed as coherent superpositions of helical Laguerre-Gaussian modes are synthesized by a computer generated hologram using a phase-only spatial light modulator. Particle tracking is achieved by in-line holography method which allows an accurate position measurement. It is experimentally demonstrated that the trapped particle follows different trajectories depending on the orbital angular momentum density of the beam. In particular applying the proposed pod beam the particle rotates in opposite directions during its movement in the optical trap. Possible applications of these single-beam traps for volumetric optical particle manipulation are discussed.

Structure of optical singularities in coaxial superpositions of Laguerre-Gaussian modes

We investigate optical singularities in coaxial superpositions of two Laguerre-Gaussian (LG) modes with a common beam waist from the viewpoints of a general formulation of phase structure, experimental generation of various superposition beams, and evaluation of the generated beams' fidelity. By applying a holographic phase-amplitude modulation scheme using a phase-modulation-type spatial light modulator, output fidelity beyond 0.960 was observed under several typical conditions. Additionally, an elliptic-type folded singularity, which provides a different class of phase structures from familiar helical singularities, was predicted and observed in a superposition involving two LG modes of both radially and azimuthally higher orders.