Gaussian Mode Research Articles

Analytical expressions for the clipping of Laguerre- and Hermite-Gauss modes by circular apertures.

We present a closed-form analytical expression that describes the effect of clipping by circular apertures on laser beams, described in terms of an expansion in eigenmodes of the paraxial wave equation, in either the Laguerre-Gauss or Hermite-Gauss bases. This result provides a faster and more accurate way to compute the coupling between higher-order modes, compared to commonly used grid-based numerical integration.

Measuring the orbital angular momentum mode of vortex beam based on phase matching sequence

Measuring the orbital angular momentum(OAM) mode of vortex beams is of great significance in applications based on vortex beams.we propose a method of phase matching characteristics of vortex beams to measure the OAM mode. The method first use a high-speed spatial light modulator(SLM) to sequentially load a set of helical phase sequence images, so that the vortex beam is modulated by this SLM. Then obtain the modulated optical field through pinhole filtering, and then the synchronized tilt phase modulation is performed by the 4f system and high-speed SLM. When the OAM mode of vortex beam is opposite to the topological charge of helical phase image, that is, the incident vortex beam degenerates to the fundamental Gaussian mode beam,and through our optical system, the output plane obtained a indicating spot with the position related to the OAM mode. The Simulation and experimental results show that the method obtains a clear OAM mode indicating spot on the final output plane, which verifies the theoretical derivation.

Polarisation-spatial entanglement upon reflection across a dielectric

Polarisation-spatial entanglement in coherent reflected paraxial vector light fields across an infinite dielectric interface, for polarised incidence, is studied. Closed form expressions for the polarisation-spatial entanglement is obtained explicitly in the case of Hermite Gaussian and Laguerre Gaussian modes up to first order approximation, assuming arbitrary state of incident polarisation, angle of incidence, waist width, and mode indices. General observations regarding the polarisation-spatial entanglement which hold true irrespective of the aforementioned parameters are arrived at. It is observed that close to 1 ebit of polarisation-spatial entanglement can be obtained for angles near Brewster’s incidence. The feasibility of possible experimental measurement of the entanglement obtained in reflected light fields is discussed through the Laguerre Gaussian mode as an example.

High power, single-frequency, long pulse width 1064 nm laser source

We present a high power, long pulse width, high pulse repetition rate (PRR), single-frequency 1064 nm master oscillator power amplifier (MOPA). The MOPA system consists of a single-frequency 1064 nm seed laser, ytterbium-doped fiber preamplifier, and two stages of rod Nd: YVO4 amplifier. The MOPA delivers a maximum average output power up to 122.3 W with a spectral linewidth of 24.15 fm, operating at a PRR of 50 kHz with a pulse width of 10 μs. The average beam quality factor is measured to be M2=1.375, exhibiting a Gaussian TEM00 mode. The output power fluctuation of the MOPA system is less than 0.96% over one hour. Such a high power, single-frequency laser source with long pulse width and high PRR is expected to be utilized for long-distance, high-precision laser imaging.

Guided-Wave Up-Conversion Luminescence in Er3+/Yb3+ Co-doped Phosphate Glass Waveguide Produced by Direct Femtosecond Laser Writing

We report on guided-wave up-conversion luminescence in femtosecond laser writing cladding waveguides in Er3+/Yb3+ co-doped phosphate glass. The waveguides were fabricated with 30-μm- and 100-μm-diameter of the guiding cores. The guiding properties of waveguides have been investigated at 633 nm by end face coupling of free space light and physical contact of fibers. The experimental and calculated results of propagating modal profiles and losses have proved favorable performances suitable to Gaussian mode field and multi-mode applications. Under the optical pump laser at 980 nm, the guided-wave up-conversion luminescence at visible light range has been realized through the waveguides.

Low-loss and small-cross-section waveguide for compact terahertz free-electron laser

The demand for terahertz (THz) sources that can be used in practical implementations has not yet been fully met. Through the development of small-scale free-electron lasers (FEL), we investigated a solution to overcome the low lasing gain of the FEL, which is caused by a small-current accelerator and a short-length undulator. To enhance the FEL gain, the FEL interaction between the electron beam and radiation was increased by reducing the cross-sectional area of the FEL oscillator mode. We developed a waveguide for the FEL oscillator, which has a remarkably small eye-shaped cross section with low wave loss. The mode cross-sectional area was calculated to be just 4 mm2 (full width at half maximum), which is considerably smaller than those of the free-space Gaussian mode and other waveguide modes. Using COMSOL Multiphysics simulation code, we calculated and analyzed the attenuation loss and mode cross-section area for waveguides of different shapes and sizes, and we observed that the dielectric coated eye-shaped waveguide has the lowest attenuation loss, that is, less than 2.5% for 1-m propagation at an operating wavelength of 300–600 µm. These results are in good agreement with our requirements for the tabletop THz FEL. Finally, we showed that the calculated operating wavelength range of the waveguide-mode THz FEL is 300–600 µm using the machine parameters of an accelerator and undulator that were developed by considering the dispersion relations of the eye-shaped waveguide and undulator radiation.

Twisted Waves near a Plasma Cutoff

This work considers twisted wave propagation in inhomogeneous and unmagnetised plasma, and discusses the wave properties in the cutoff region. The qualitative differences between twisted waves described by a single Laguerre–Gauss (LG) mode, and light springs resulting from the superposition of two or more LG modes with different frequency and helicity are studied. The peculiar properties displayed by these waves in the nonuniform plasma are discussed. The pulse envelope of a light-spring shows a contraction at reflection, which resembles that of a compressed mechanical spring. The case of normal incidence is examined, and nonlinear ponderomotive effects are discussed, using theory and simulations.

Tunable, high-power, high-order optical vortex beam generation in the mid-infrared.

We report the generation of tunable high-order optical vortices in the mid-infrared (mid-IR) using a picosecond optical parametric oscillator (OPO). The OPO is based on MgO:PPLN as the nonlinear gain medium and synchronously pumped by a mode-locked Yb-fiber laser at 1064 nm. Using a singly-resonant oscillator configuration for the OPO, we have achieved direct transfer of pump optical vortices to the non-resonant idler beam, with the resonant signal in the Gaussian cavity mode. We demonstrate the successful transfer of pump optical vortices of order, lp = 1 to 5, to the idler beam of the same order across the mid-IR, with an output power of 630 mW to 130 mW across 2538 nm to 4035 nm for the highest idler vortex order, li = 5. To the best of our knowledge, this is the first report of an OPO pumped by a vortex beam of order as high as lp = 5 and generating idler vortices of high order in the mid-IR.

Phase locking of lasers with Gaussian coupling.

A unique approach for steady in-phase locking of lasers in an array, regardless of the array geometry, position, orientation, period or size, is presented. The approach relies on the insertion of an intra-cavity Gaussian aperture in the far-field plane of the laser array. Steady in-phase locking of 90 lasers, whose far-field patterns are comprised of sharp spots with extremely high power density, was obtained for various array geometries, even in the presence of near-degenerate solutions, geometric frustration or superimposed independent longitudinal modes. The internal phase structures of the lasers can also be suppressed so as to obtain pure Gaussian mode laser outputs with uniform phase and overall high beam quality. With such phase locking, the laser array can be focused to a sharp spot of high power density, useful for many applications and the research field.

Comparative assessment of automated algorithms for the separation of one-dimensional Gaussian mixtures

MotivationGaussian mixture models (GMMs) are probabilistic models commonly used in biomedical research to detect subgroup structures in data sets with one-dimensional information. Reliable model parameterization requires that the number of modes, i.e., states of the generating process, is known. However, this is rarely the case for empirically measured biomedical data. Several implementations are available that estimate GMM parameters differently. This work aims to provide a comparative evaluation of automated GMM fitting methods. Results and conclusionsThe performance of commonly used algorithms for automatic parameterization and mode number determination was compared with respect to reproducing the ground truth of generated data derived from multiple normal distributions. Four main variants of Gaussian mode number detection algorithms and five variants of GMM parameter estimation methods were tested in a combinatory scenario. The combination of best performing mode number determination algorithms and GMM parameter estimation methods was then tested on artificial and real-live data sets known to display a GMM structure. None of the tested methods correctly determined the underlying data structure consistently. The likelihood ratio test had the best performance in identifying the mode number associated with the best GMM fit of the data distribution while the Markov chain Monte Carlo (MCMC) algorithm was best for GMM parameter estimation while. The combination of the two methods of number determination algorithms and GMM parameter estimation was consistently among the best and overall outperformed the available implementations. ImplementationAn automated tool for the detection of GMM based structures in (biomedical) datasets was created based on the present results and made freely available in the R library “opGMMassessment” at https://cran.r-project.org/package=opGMMassessment.

Mode Coupling in a Fabry-Perot Open Resonator

A Fabry-Perot open resonator (FPOR) is a tool dedicated to broadband accurate microwave and millimeter-wave characterization of dielectric sheets. Despite the various advantages of that method, one of the major challenges limiting its applicability is unintentional coupling of Gaussian modes of interest with a particular family of parasitic higher order modes. The coupling affects the resonance frequency of the resonator loaded with the material under test, thus disturbing the extracted permittivity. It has already been shown that spectral properties of these parasitic modes can be predicted using a recently developed electromagnetic model of a FPOR based on the scattering matrix method. It is shown in this article that the systematic analysis of experimental results supplemented with accurate numerical computations allows us to suppress the impact of mode coupling on the measured permittivity.

Low-loss and Small-cross-section Waveguide for Compact Terahertz Free -electron Laser

The demand for terahertz (THz) sources that can be used in practical implementations has not yet been fully met. Through the development of small-scale free-electron lasers (FEL), we investigated a solution to overcome the low lasing gain of the FEL, which is caused by a small-current accelerator and a short-length undulator. To enhance the FEL gain, the FEL interaction between the electron beam and radiation was increased by reducing the cross-sectional area of the FEL oscillator mode. We developed a waveguide for the FEL oscillator, which has a remarkably small eye-shaped cross section with low wave loss. The mode cross-sectional area was calculated to be just 4 mm2 (full width at half maximum), which is considerably smaller than those of the free-space Gaussian mode and other waveguide modes. Using COMSOL Multiphysics simulation code, we calculated and analyzed the attenuation loss and mode cross-section area for waveguides of different shapes and sizes, and we observed that the dielectric coated eye-shaped waveguide has the lowest attenuation loss, that is, less than 2.5% for 1-m propagation at an operating wavelength of 300–600 µm. These results are in good agreement with our requirements for the tabletop THz FEL. Finally, we showed that the calculated operating wavelength range of the waveguide-mode THz FEL is 300–600 µm using the machine parameters of an accelerator and undulator that were developed by considering the dispersion relations of the eye-shaped waveguide and undulator radiation.

Direct generation of mid-infrared pulsed optical vortices at ∼ 2.7 µm

We present the first, to the best of our knowledge, direct generation of pulsed optical vortices in the 2.7-µ m spectral range by employing polycrystalline Fe:ZnSe as a saturable absorber (SA). A modified theoretical model taking into account the propagation features of the reshaped annular pump beam is elaborated to accurately determine the excitation conditions of the Laguerre–Gaussian (LG0,l) modes, yielding a lasing efficiency comparable to the fundamental TEM00 mode in continuous-wave (CW) regime. Nanosecond scalar optical vortices with well-defined handedness are successfully produced by taking advantages of designated mode-matching, high polarization extinction ratio (PER), and the "spatial filter" effect of the SA on other transverse modes. Such scalar vortex laser pulses in the mid-infrared region will enable new applications such as frequency down conversion to produce optical vortices at longer (far-infrared) wavelengths, structuring organic materials, novel molecular spectroscopy, etc.

Stimulated slowing of Yb atoms on the narrow 1S0 → 3P1 transition

We analyzed bichromatic and polychromatic stimulated forces for laser cooling and trapping of Yb atoms using only the narrow ${}^{1}{S}_{0}\phantom{\rule{4pt}{0ex}}\ensuremath{\rightarrow}{\phantom{\rule{4pt}{0ex}}}^{3}{P}_{1}$ transition. Our model is based on numerical solutions of optical Bloch equations for two-level atoms driven by multiple time-dependent fields combined with Monte Carlo simulations, which account for realistic experimental conditions such as atomic beam divergence, geometry, and Gaussian laser modes. Using 1 W of laser power, we predict a loading rate of $\ensuremath{\approx}\phantom{\rule{4pt}{0ex}}{10}^{8}$ atoms/s into a 556-nm magneto-optical trap (MOT) with a slowing force of $\ensuremath{\approx}60{F}_{\text{rad}}$. We show that a square-wave modulation can produce similar stimulated forces with almost twice the velocity range and improve the MOT loading rate of Yb atoms by up to 70%.

Direct generation of ultrafast vortex beam from a Tm:CaYAlO4 oscillator featuring pattern matching of a folded-cavity resonator.

Optical vortices, beams with spiral wavefronts and screw phase dislocations have been explored in applications in optical manipulation, quantum optics, and the next generation of optical communications. In traditional methods, optical vortices are generated using space light modulators or spiral phase plates, which would sharply decrease the integration of optical systems. Different from previous transverse mode conversion outside the cavity, here we experimentally demonstrate a direct generation of ultrafast vortex beam from a Tm:CaYAlO4 oscillator by pattern matching of a six-mirror-folded-cavity resonator. By accurately adjusted the angle of the end mirror and the distance L between the M4 and the SESAMs to control the beam diameter of laser incidence on the gain medium in the sagittal and tangential planes, a stable 2 µm ultrafast vortex laser emission of annular Laguerre-Gaussian (LG) mode was obtained with a maximum output power of 327 mW and pulse duration of 2.1 ps. A simple YAG crystal plate was used as handedness selector and a homemade Mach-Zehnder (MZ) interferometer has verified the vortical property of the LG01 mode. By furtherly controlling the cavity mode pattern matching, other stable transverse-mode operations for TEM00, high-order Hermite-Gaussian (HG) transverse mode and doughnut-shaped beams were successfully realized. This work provides a flexible and reliable way to generate mid-infrared ultrafast vortex beams and is of special significance for applications in the areas of molecular spectroscopy and organic material processing amongst others.

High-peak-power structured beams by an Nd:YAG/Cr4+:YAG laser in a near-hemispherical cavity.

An Nd:YAG/Cr4+:YAG passively Q-switched (PQS) laser in a near-hemispherical cavity is exploited to generate high-order structured pulsed fields. Under tightly focused on-axis pumping, radial-order Laguerre-Gaussian (LG) modes with controllable mode orders by the input pump power are realized to exhibit quite stable temporal behavior. The pulse repetition rates of radial-LG modes can reach up to 78 kHz with an average output power of 0.57 W and peak power beyond 300 W under a 5-W pump level. Furthermore, by introducing 1D off-axis pumping into the PQS laser, various structured pulsed fields with transverse morphologies as high-order Ince-Gaussian (IG) modes are further created. With clean and well-defined beam structures, the IG pulsed fields can be nicely reconstructed by the resonant modes of the inhomogeneous Helmholtz equation for spherical cavities. More importantly, these high-order PQS IG modes reveal highly regular pulse trains with the maximum pulse repetition rate beyond 20 kHz and overall peak power higher than 1.5 kW.

Deep-learning-based recognition of multi-singularity structured light

Abstract Structured light with customized topological patterns inspires diverse classical and quantum investigations underpinned by accurate detection techniques. However, the current detection schemes are limited to vortex beams with a simple phase singularity. The precise recognition of general structured light with multiple singularities remains elusive. Here, we report deep learning (DL) framework that can unveil multi-singularity phase structures in an end-to-end manner, after feeding only two intensity patterns upon beam propagation. By outputting the phase directly, rich and intuitive information of twisted photons is unleashed. The DL toolbox can also acquire phases of Laguerre–Gaussian (LG) modes with a single singularity and other general phase objects likewise. Enabled by this DL platform, a phase-based optical secret sharing (OSS) protocol is proposed, which is based on a more general class of multi-singularity modes than conventional LG beams. The OSS protocol features strong security, wealthy state space, and convenient intensity-based measurements. This study opens new avenues for large-capacity communications, laser mode analysis, microscopy, Bose–Einstein condensates characterization, etc.

Coherent superposition of orthogonal Hermite–Gauss modes

The coherent superposition of orthogonal modes can result in phase dependent transverse offsets, shifts of the focus position, variations of the Rayleigh length and a reduction of the beam quality factor of the coherent sum of modes in comparison to the incoherent sum. Relations for first and second order moments, the beam quality and the Rayleigh length for the superposition of Hermite–Gauss modes are derived. The Courant–Snyder formalism, which was originally developed in the context of charged particle optics, is applied to propagate an arbitrary coherent sum of orthogonal modes through a lens system. Relations of generating and observable optical functions are highlighted. In the last part of the report the elegant Hermite–Gauss solution is interpreted in terms of generating and observable functions and the solution is decomposed into a sum of standard Hermite–Gauss modes.

Visible and Online Detection of Near‐Infrared Optical Vortices via Nonlinear Photonic Crystals

AbstractNear‐infrared (NIR) optical vortices (OVs), which carry specific orbital angular momentum, are believed to greatly increase the capacity of conventional optical communication systems. However, due to the equipment limits in invisible wavelengths, NIR OVs detection remains a great difficulty. Here, the up‐conversion imaging technology is exploited to circumvent using NIR detectors. A lithium niobate crystal with its quadratic susceptibility modulated by a specially designed Dammann vortex grating is fabricated to realize the frequency conversion—from NIR to the visible region—while converting multiplexed OVs to Gaussian modes in specific multichannels. During the detection process, the most of energies of the detected OVs are preserved, which can be considered as online detection. Additionally, at least 400 nm applicable wavelength range of this method is experimentally demonstrated, as well as up to 25 independent detection channels. Compared with existing solutions, this scheme enables a large‐broadband wavelength, low energy loss, and multiprocessing channels platform for visible detection of NIR OVs, showing great potential to be applied in optical communication systems.

Turbulence-resilient pilot-assisted self-coherent free-space optical communications using automatic optoelectronic mixing of many modes

In free-space optical communications that use both amplitude and phase data modulation (for example, in quadrature amplitude modulation (QAM)), the data are typically recovered by mixing a Gaussian local oscillator with a received Gaussian data beam. However, atmospheric turbulence can induce power coupling from the transmitted Gaussian mode to higher-order modes, resulting in a significantly degraded mixing efficiency and system performance. Here, we use a pilot-assisted self-coherent detection approach to overcome this problem. Specifically, we transmit both a Gaussian data beam and a frequency-offset Gaussian pilot tone beam such that both beams experience similar turbulence and modal coupling. Subsequently, a photodetector mixes all corresponding pairs of the beams’ modes. During mixing, a conjugate of the turbulence-induced modal coupling is generated and compensates the modal coupling experienced by the data, and thus the corresponding modes of the pilot and data mix efficiently. We demonstrate a 12 Gbit s−1 16-QAM polarization-multiplexed free-space optical link that is resistant to turbulence.