Beam-quality measurements using a spatial light modulator

Spectral-broadness simulation of a Littman/Metcalf external cavity diode laser with a dynamic-curvature end mirror

We propose a dynamic-spectral-broadness Littman/Metcalf external cavity diode laser, which replaces the flat end mirror of the external cavity with a curved one with a tunable radius of curvature (RoC). The concept was verified via simulation; first, the frequency selectivity of the cavity was calculated for each RoC using Gaussian-beam optics combined with ray tracing, and second, laser oscillation and amplified spontaneous-emission (ASE) spectra were obtained using the transmission-line laser model. The simulation revealed a tuning range with spectral broadness: 250 kHz for single-mode operation, 1.2-47 GHz for multi-mode operation, and 50 GHz-3.9 THz for ASE.

Synthetic spin dynamics with Bessel-Gaussian optical skyrmions

Skyrmions are topologically stable fields that cannot be smoothly deformed into any other field configuration that differs topologically, that is, one that possesses a different integer topological invariant called the Skyrme number. They have been studied as 3-dimensional and 2-dimensional skyrmions in both magnetic and, more recently, optical systems. Here, we introduce an optical analogy to magnetic skyrmions and demonstrate their dynamics within a magnetic field. Our optical skyrmions and synthetic magnetic field are both engineered using superpositions of Bessel-Gaussian beams, with time dynamics observed over the propagation distance. We show that the skyrmionic form changes during propagation, exhibiting controllable periodic precession over a well defined range, analogous to time varying spin precession in homogeneous magnetic fields. This local precession manifests as the global beating between skyrmion types, while still maintaining the invariance of the Skyrme number, which we monitor through a full Stokes analysis of the optical field. Finally, we outline, through numerical simulation, how this approach could be extended to create time varying magnetic fields, offering free-space optical control as a powerful analogue to solid state systems.

Transverse energy flow in an optical Skyrmionic Hopfion

The energy flow of light represents a natural way of investigating complex light fields with respect to their applicability. With the generation of a three-dimensional Skyrmionic Hopfion structure in light, which is a topological 3D field configuration with particle-like nature, we paved the way to employ optical, topological constructs. In this work, we present an analysis of the transverse energy flow in the optical Skyrmionic Hopfion, showing the transfer of the topological properties to the mechanical attributes such as the optical angular momentum (OAM). Our findings thus prepare topological structures to be applied in optical traps and data storage or communication.

Switchable optical ring lattice in free space

Optical lattices with spatially regular structures have recently attracted considerable attention across physics and optics communities. In particular, due to the increasing emergence of new structured light fields, diverse lattices with rich topology are being generated via multi-beam interference. Here, we report a specific ring lattice with radial lobe structures generated via superposition of two ring Airy vortex beams (RAVBs). We show that the lattice morphology evolves upon propagation in free space, switching from a bright-ring lattice to dark-ring lattice and even to fascinating multilayer texture. This underlying physical mechanism is related to the variation of the unique intermodal phase between the RAVBs as well as topological energy flow with symmetry breaking. Our finds provide an approach for engineering customized ring lattices to inspire a wide variety of new applications.

Versatile all-digital transport-of-intensity based wavefront sensor and adaptive optics using a DMD

Measuring and correcting wavefront aberrations is an important process in a wide variety of disciplines, from ophthalmology, laser cutting, and astronomy to free-space communication and microscopy, and always relies on measuring intensities to infer phase. One approach is to use the transport-of-intensity as a means for phase retrieval, exploiting the connection between observed energy flow in optical fields and their wavefronts. Here we present a simple scheme, using a digital micro-mirror device (DMD), to perform angular spectrum propagation and extract the wavefront of optical fields at various wavelengths, dynamically, with high resolution and tuneable sensitivity. We verify the capability of our approach by extracting common Zernike aberrations, turbulent phase screens, and lens phases under static and dynamic conditions at multiple wavelengths and polarizations. We use this setup for adaptive optics, correcting distortion using a second DMD to apply conjugate phase modulation. We observed effective wavefront recovery under a variety of conditions which allowed for convenient real-time adaptive correction in a compact arrangement. Our approach provides an all-digital system that is versatile, cheap, fast, accurate, broadband and polarization invariant.

M2 factor estimation in few-mode fibers based on a shallow neural network

A high-accuracy, high-speed, and low-cost M² factor estimation method for few-mode fibers based on a shallow neural network is presented in this work. Benefiting from the dimensionality reduction technique, which transforms the two-dimension near-field image into a one-dimension vector, a neural network with only two hidden layers can estimate the M² factor directly. In the simulation, the mean estimation error is smaller than 3% even when the mode number increases to 10. The estimation time of 10000 simulation test samples is around 0.16s, which indicates a high potential for real-time applications. The experiment results of 50 samples from the 3-mode fiber have a mean estimation error of 0.86%. The strategies involved in this method can be easily extended to other applications related to laser characterization.

Modal description of paraxial structured light propagation: tutorial

Here we outline a description of paraxial light propagation from a modal perspective. By decomposing the initial transverse field into a spatial basis whose elements have known and analytical propagation characteristics, we are able to analytically propagate any desired field, making the calculation fast and easy. By selecting a basis other than that of planes waves, we overcome the problem of numerical artifacts in the angular spectrum approach and at the same time are able to offer an intuitive understanding for why certain classes of fields propagate as they do. We outline the concept theoretically, compare it to the numerical angular spectrum approach, and confirm its veracity experimentally using a range of instructive examples. We believe that this modal approach to propagating light will be a useful addition to the toolbox for propagating optical fields.

Shaping light in 3d space by counter-propagation

We extend the established transverse customization of light, in particular, amplitude, phase, and polarization modulation of the light field, and its analysis by the third, longitudinal spatial dimension, enabling the visualization of longitudinal structures in sub-wavelength (nm) range. To achieve this high-precision and three-dimensional beam shaping and detection, we propose an approach based on precise variation of indices in the superposition of higher-order Laguerre-Gaussian beams and cylindrical vector beams in a counter-propagation scheme. The superposition is analyzed experimentally by digital, holographic counter-propagation leading to stable, reversible and precise scanning of the light volume. Our findings show tailored amplitude, phase and polarization structures, adaptable in 3D space by mode indices, including sub-wavelength structural changes upon propagation, which will be of interest for advanced material machining and optical trapping.

Digital Stokes polarimetry and its application to structured light: tutorial

Stokes polarimetry is a mature topic in optics, most commonly performed to extract the polarization structure of optical fields for a range of diverse applications. For historical reasons, most Stokes polarimetry approaches are based on static optical polarization components that must be manually adjusted, prohibiting automated, real-time analysis of fast changing fields. Here we provide a tutorial on performing Stokes polarimetry in an all-digital approach, exploiting a modern optical toolkit based on liquid-crystal-on-silicon spatial light modulators and digital micromirror devices. We explain in a tutorial fashion how to implement two digital approaches, based on these two devices, for extracting Stokes parameters in a fast, cheap, and dynamic manner. After outlining the core concepts, we demonstrate their applicability to the modern topic of structured light, and highlight some common experimental issues. In particular, we illustrate how digital Stokes polarimetry can be used to measure key optical parameters such as the state of polarization, degree of vectorness, and intra-modal phase of complex light fields.

Modal analysis of structured light with spatial light modulators: a practical tutorial

A quantitative analysis of optical fields is essential, particularly when the light is structured in some desired manner, or when there is perhaps an undesired structure that must be corrected for. A ubiquitous procedure in the optical community is that of optical mode projections-a modal analysis of light-for the unveiling of amplitude and phase information of a light field. When correctly performed, all the salient features of the field can be deduced with high fidelity, including its orbital angular momentum, vectorial properties, wavefront, and Poynting vector. Here, we present a practical tutorial on how to perform an efficient and effective optical modal decomposition, with emphasis on holographic approaches using spatial light modulators, highlighting the care required at each step of the process.

Deep learning enabled superfast and accurate M2 evaluation for fiber beams

We introduce deep learning technique to predict the beam propagation factor M² of the laser beams emitting from few-mode fiber for the first time, to the best of our knowledge. The deep convolutional neural network (CNN) is trained with paired data of simulated near-field beam patterns and their calculated M² value, aiming at learning a fast and accurate mapping from the former to the latter. The trained deep CNN can then be utilized to evaluate M² of the fiber beams from single beam patterns. The results of simulated testing samples have shown that our scheme can achieve an averaged prediction error smaller than 2% even when up to 10 eigenmodes are involved in the fiber. The error becomes slightly larger when heavy noises are added into the input beam patterns but still smaller than 2.5%, which further proves the accuracy and robustness of our method. Furthermore, the M² estimation takes only about 5 ms for a prepared beam pattern with one forward pass, which can be adopted for real-time M² determination with only one supporting Charge-Coupled Device (CCD). The experimental results further prove the feasibility of our scheme. Moreover, the method we proposed can be confidently extended to other kinds of beams provided that adequate training samples are accessible. Deep learning paves the way to superfast and accurate M² evaluation with very low experimental efforts.

Propagation trajectory measurement and autofocusing generation of Airy beams using digital propagation

We present a method of measuring the propagation trajectory of Airy beams using digital propagation based on the theory of angular spectrum. The dependence of the transverse displacement of Airy beams on artificial propagation distance in phase masks is investigated with no motion of imaging apparatus. The parabolic propagation trajectory is experimentally verified, which is consistent with theoretical predictions. On this basis, we generate autofocusing beams by combining multiple Airy beams and digital propagation. Results show that this technique can provide accurate and easy measurement of the self-accelerating characteristic in a fixed plane, as well as flexible manipulation without translating the target.

Automated translating beam profiler for in situ laser beam spot-size and focal position measurements

We present a simple and convenient, high-resolution solution for automated laser-beam profiling with axial translation. The device is based on a Raspberry Pi computer, Pi Noir CMOS camera, stepper motor, and commercial translation stage. We also provide software to run the device. The CMOS sensor is sensitive over a large wavelength range between 300 and 1100 nm and can be translated over 25 mm along the beam axis. The sensor head can be reversed without changing its axial position, allowing for a quantitative estimate of beam overlap with counter-propagating laser beams. Although not limited to this application, the intended use for this device is the automated measurement of the focal position and spot-size of a Gaussian laser beam. We present example data of one such measurement to illustrate device performance.

Suppressing the influence of charge-coupled device vertical blooming on the measurement of laser beam quality factor (M2) of a near-infrared laser

In this paper, a new method, which is based on reconstructing the original intensity distribution of a laser with images captured by a charge-coupled device (CCD) in two orthogonal directions, is proposed for suppressing the influence of CCD vertical blooming on the measurement of the laser beam quality factor (M²). A simplified theoretical model for the distribution of CCD blooming is also proposed. With the proposed method and model, the influence of CCD vertical blooming on the measurement of M² is simulated. The experimental results demonstrate that the new method can be an effective means to measure the M² of a near-infrared laser with a silicon CCD camera. The proposed method can be applied to a beam quality analyzer in order to suppress the influence of blooming on the measurement of M².

Femtosecond-Laser-Based 3D Printing for Tissue Engineering and Cell Biology Applications

Fabrication of 3D cell scaffolds has gained tremendous attention in recent years because of its applications in tissue engineering and cell biology applications. The success of tissue engineering or cell interactions mainly depends on the fabrication of well-defined microstructures, which ought to be biocompatible for cell proliferation. Femtosecond-laser-based 3D printing is one of the solution candidates that can be used to manufacture 3D tissue scaffolds through computer-aided design (CAD) which can be efficiently engineered to mimic the microenvironment of tissues. UV-based lithography has also been used for constructing the cellular scaffolds but the toxicity of UV light to the cells has prevented its application to the direct patterning of the cells in the scaffold. Although the mask-based lithography has provided a high resolution, it has only enabled 2D patterning not arbitrary 3D printing with design flexibility. Femtosecond-laser-based 3D printing is trending in the area of tissue engineering and cell biology applications due to the formation of well-defined micro- and submicrometer structures via visible and near-infrared (NIR) femtosecond laser pulses, followed by the fabrication of cell scaffold microstructures with a high precision. Laser direct writing and multiphoton polymerization are being used for fabricating the cell scaffolds, The implication of spatial light modulators in the interference lithography to generate the digital hologram will be the future prospective of mask-based lithography. Polyethylene glycol diacrylate (PEG-DA), ormocomp, pentaerythritol tetraacrylate (PETTA) have been fabricated through TPP to generate the cell scaffolds, whereas SU-8 was used to fabricate the microrobots for targeted drug delivery. Well-designed and precisely fabricated 3D cell scaffolds manufactured by femtosecond-laser-based 3D printing can be potentially used for studying cell migration, matrix invasion and nuclear stiffness to determine stage of cancer and will open broader horizons in the future in tissue engineering and biology applications.

Determination of the laser beam quality factor (M2) by stitching quadriwave lateral shearing interferograms with different exposures

A complete complex amplitude reconstruction method for the determination of the laser beam quality factor M² based on the multiple exposure of a quadriwave lateral shearing interferometer (QWLSI) is presented. The theoretical analysis and simulation of the influence of the information in the small signal area on the calculation of the M² factor is provided. The experimental results demonstrate that the new method can be an accurate means to measure the M² factor. The proposed method can avoid the influence of phase inaccuracy in the small signal area of the interferogram, during the measurement of the M² factor.

Real-time complex amplitude reconstruction method for beam quality M2 factor measurement

We present a real-time complex amplitude reconstruction method for determining the beam propagation ratio M² of laser beams based on the transport of intensity equation (TIE). In this work, a synchronous acquisition system consisting of two identical CCDs is established. Once two beam intensity images at different cross-section positions along the optical axis are captured simultaneously by the system, the complex amplitude of the laser beam can be rapidly reconstructed using TIE algorithm. Then the beam intensity distribution at any section position along its propagation direction can be obtained by using angular spectrum (AS) theory. The beam quality M² factor is therefore calculated utilizing the second-order moments and hyperbola fitting methods, which conform to the ISO standard. The suitability of this method is verified by the numerical analysis and experiments with the He-Ne and high-power fiber laser sources, respectively. The experimental technique is simple and fast, which allows to investigate laser beams under conditions inaccessible to other methods.

Real and virtual propagation dynamics of angular accelerating white light beams

Accelerating waves have received significant attention of late, first in the optical domain and later in the form of electron matter waves, and have found numerous applications in non-linear optics, material processing, microscopy, particle manipulation and laser plasma interactions. Here we create angular accelerating light beams with a potentially unlimited acceleration rate. By employing wavelength independent digital holograms for the creation and propagation of white light beams, we are able to study the resulting propagation in real and virtual space. We find that dephasing occurs for real propagation and that this can be compensated for in a virtual propagation scheme when single plane dynamics are important. Our work offers new insights into the propagation dynamics of such beams and provides a versatile tool for further investigations into propagating structured light fields.

Radially dependent angular acceleration of twisted light

While photons travel in a straight line at constant velocity in free space, the intensity profile of structured light may be tailored for acceleration in any degree of freedom. Here we propose a simple approach to control the angular acceleration of light. Using Laguerre-Gaussian modes as our twisted beams carrying orbital angular momentum, we show that superpositions of opposite handedness result in a radially dependent angular acceleration as they pass through a focus (waist plane). Due to conservation of orbital angular momentum, we find that propagation dynamics are complex despite the free-space medium: the outer part of the beam (rings) rotates in an opposite direction to the inner part (petals), and while the outer part accelerates, the inner part decelerates. We outline the concepts theoretically and confirm them experimentally. Such exotic structured light beams are topical due to their many applications, for instance in optical trapping and tweezing, metrology, and fundamental studies in optics.

Complex amplitude reconstruction for dynamic beam quality M2 factor measurement with self-referencing interferometer wavefront sensor

A real-time complex amplitude reconstruction method for determining the dynamic beam quality M² factor based on a Mach-Zehnder self-referencing interferometer wavefront sensor is developed. By using the proposed complex amplitude reconstruction method, full characterization of the laser beam, including amplitude (intensity profile) and phase information, can be reconstructed from a single interference pattern with the Fourier fringe pattern analysis method in a one-shot measurement. With the reconstructed complex amplitude, the beam fields at any position z along its propagation direction can be obtained by first utilizing the diffraction integral theory. Then the beam quality M² factor of the dynamic beam is calculated according to the specified method of the Standard ISO11146. The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment, including the static and dynamic beam process. The experimental method is simple, fast, and operates without movable parts and is allowed in order to investigate the laser beam in inaccessible conditions using existing methods.

Measurement of M²-Curve for Asymmetric Beams by Self-Referencing Interferometer Wavefront Sensor

For asymmetric laser beams, the values of beam quality factor Mx2 and My2 are inconsistent if one selects a different coordinate system or measures beam quality with different experimental conditionals, even when analyzing the same beam. To overcome this non-uniqueness, a new beam quality characterization method named as M²-curve is developed. The M²-curve not only contains the beam quality factor Mx2 and My2 in the x-direction and y-direction, respectively; but also introduces a curve of Mxα2 versus rotation angle α of coordinate axis. Moreover, we also present a real-time measurement method to demonstrate beam propagation factor M²-curve with a modified self-referencing Mach-Zehnder interferometer based-wavefront sensor (henceforth SRI-WFS). The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment in multimode beams. The experimental results showed that the proposed measurement method is simple, fast, and a single-shot measurement procedure without movable parts.

Beam quality measure for vector beams

Vector beams have found a myriad of applications, from laser materials processing to microscopy, and are now easily produced in the laboratory. They are usually differentiated from scalar beams by qualitative measures, for example, visual inspection of beam profiles after a rotating polarizer. Here we introduce a quantitative beam quality measure for vector beams and demonstrate it on cylindrical vector vortex beams. We show how a single measure can be defined for the vector quality, from 0 (purely scalar) to 1 (purely vector). Our measure is derived from a quantum toolkit, which we show applies to classical vector beams.

Smartphone laser beam spatial profiler

A simple, low-cost, portable, smartphone-based laser beam profiler for characterizing laser beam profiles is reported. The beam profiler utilizes a phosphor silica glass plate to convert UV light into visible (green) light that can be directly imaged onto an existing smartphone CMOS chip and analyzed using a customized app. 3D printing enables the ready fabrication of the instrument package. The beam's diameter, shape, divergence, beam quality factor, and output power are measured for two UV lasers: a CW 244 nm frequency-doubled Ar ion laser and a pulsed 193 nm ArF exciplex laser. The availability of specialized phosphor converters can extend the instrument from the UV to the near infrared and beyond, and the smartphone platform extends the Internet of Things to map laser beam profiles simultaneously in different locations.

Scattered light imaging method (SLIM) for characterization of arbitrary laser beam intensity profiles

A laser beam characterization method is reported, which is applicable to arbitrary and ideal laser beam intensity profiles. This method, called the scattered light imaging method (SLIM), is based on scattered light imaging of a laser beam and provides a complete visualization of it in the region of interest. The method was applied to characterize an arbitrary pedestal-shaped beam and compared with a conventional method (camera scanning). The results we presented show that, for arbitrary beams, it seems much more meaningful to know the intensity profile evolution than to determine an M2 value. Therefore the SLIM is a powerful tool for a new and more complete type of laser beam characterization.

All-digital wavefront sensing for structured light beams

We present a new all-digital technique to extract the wavefront of a structured light beam. Our method employs non-homogeneous polarization optics together with dynamic, digital holograms written to a spatial light modulator to measure the phase relationship between orthogonal polarization states in real-time, thereby accessing the wavefront information. Importantly, we show how this can be applied to measuring the wavefront of propagating light fields, over extended distances, without any moving components. We illustrate the versatility of the tool by measuring propagating optical vortices, Bessel, Airy and speckle fields. The comparison of the extracted and programmed wavefronts yields excellent agreement.

Measurement of the M² beam propagation factor using a focus-tunable liquid lens

We demonstrate motion-free beam quality M² measurements of stigmatic, simple astigmatic, and general astigmatic (twisted) beams using only a focus-tunable liquid lens and a CCD camera. We extend the variable-focus technique to the characterization of general astigmatic beams by measuring the 10 second-order moments of the power density distribution for the twisted beam produced by passage through multimode optical fiber. Our method measures the same M² values as the traditional variable-distance method for a wide range of laser beam sources, including nearly TEM(00) (M²≈1) and general astigmatic multimode beams (M²≈8). The method is simple and compact, with no moving parts or complex apparatus and measurement precision comparable to the standard variable-distance method.

Modal decomposition without a priori scale information

The modal decomposition of an arbitrary optical field may be done without regard to the spatial scale of the chosen basis functions, but this generally leads to a large number of modes in the expansion. While this may be considered as mathematically correct, it is not efficient and not physically representative of the underlying field. Here we demonstrate a modal decomposition approach that requires no a priori knowledge of the spatial scale of the modes, but nevertheless leads to an optimised modal expansion. We illustrate the power of the method by successfully decomposing beams from a diode-pumped solid state laser resonator into an optimised Laguerre-Gaussian mode set. Our experimental results, which are in agreement with theory, illustrate the versatility of the approach.