Laser beams and resonators

Absorption cross section of gas phase isoprene in the infrared-visible range

We have recorded the gas phase spectrum of isoprene at room temperature from the mid-infrared range and into the visible range (600 cm-1 to 17050 cm-1). Absorption spectra were obtained by Fourier transform infrared, conventional dispersion ultraviolet-visible-near-infrared and cavity ring-down spectroscopy to cover the entire range with a resolution comparable to that of the instruments on the James Webb Space Telescope. We have assigned the CH-stretching fundamental and overtone bands corresponding to the ΔvCH=1-6 transitions based on anharmonic vibrational calculations using normal mode and local mode models, for the lower- and higher-energy regions, respectively. We have determined accurate absolute intensities of the observed CH-stretching regions and compare with existing experimental values and with theoretical results. The accuracy of our absolute band intensity is about 2% in the fundamental region and about 10% in the 6 orders of magnitude weaker highest overtone region. Our spectrum can facilitate the detection and possibly quantification of isoprene in planetary atmospheres.

A highly efficient hybrid fiber optic laser using a cesium atom vapor cell as an optical gain medium

A new scheme of a highly efficient hybrid laser cavity is proposed and experimentally demonstrated utilizing a hot cesium (Cs) vapor cell as an optical gain medium. The laser cavity consists of a macroscopic concave reflector (> 99% reflectivity) and a 4% Fresnel-reflecting facet of a single mode fiber (SMF). The cesium gain cell is located between these two reflectors. The SMF serves multiple roles: (1) a passive mode-matching component to approximate the pump beam diameter to that of the laser cavity mode within the cesium cell, (2) an output coupler with a low reflectivity, and (3) a low loss laser delivery with a high beam-quality. Optimizing the pump beam waist diameter and the cesium vapor cell temperature, a high slope efficiency of 86% and an optical-to-optical conversion efficiency of 71% were achieved in the pump power range of 400-600 mW. The unique multi-functional role of the SMF in the hybrid cavity is fully described, which can also be applied to other high optical gain media.

710 kW stable average power in a 45,000 finesse two-mirror optical cavity

Very high-average optical enhancement cavities (OECs) are being used both in fundamental and applied research. The most demanding applications require stable megawatt level average power of infrared picosecond pulses with repetition rates of several tens of MHz. Toward reaching this goal, we report on the achievement of 710 kW of stable average power in a two-mirror hemispherical optical enhancement cavity. This result further improves the state of the art. So far, in compact high-power systems, cavity geometry optimization has been driven by the need to limit the deformation of radii of curvatures due to thermal effects. Here we explicitly demonstrate that thermal lensing must be accounted for, too, and that it can be used to assess the absorption of coatings. Experimental observations are matched with a simple model of thermal effects in the mirror's coatings. These results set a further stage for designing an optimized optical system for several applications where very high-average power enhancement cavities are expected to be operated.

Experimental confirmation of phase profile of Hermite-Gauss beams

Phase distribution of Hermite-Gauss (HG) beams generated by a gas laser is investigated experimentally by studying their interference with a plane wave and diffraction by a single slit by selecting pairs of bright lobes with different phases. Experimentally recorded interference and diffraction profiles support HG mode phase profiles expounded on in this paper. We find that the phase difference between one bright lobe and another is not simply zero or π but increases (or decreases) uniformly in steps of π as the number of zeros between them increases, in agreement with analytic function theory. An immediate application of this phase profile is that an HG mode can serve as a phase ruler with bright lobes as markers in steps of π.

Ultrafast structured light through nonlinear frequency generation in an optical enhancement cavity

The generation of shaped laser beams, or structured light, is of interest in a wide range of fields, from microscopy to fundamental physics. There are several ways to make shaped beams, most commonly using spatial light modulators comprised of pixels of liquid crystals. These methods have limitations on the wavelength, pulse duration, and average power that can be used. Here we present a method to generate shaped light that can be used at any wavelength from the UV to IR, on ultrafast pulses, and a large range of optical powers. By exploiting the frequency difference between higher-order modes, a result of the Gouy phase, and cavity mode matching, we can selectively couple into a variety of pure and composite higher-order modes. Optical cavities are used as a spatial filter and then combined with sum-frequency generation in a nonlinear crystal as the output coupler to the cavity to create ultrafast, frequency comb structured light.

Open-Path Cavity Ring-Down Spectroscopy for Simultaneous Detection of Hydrogen Chloride and Particles in Cleanroom Environment

The present study addresses advanced monitoring techniques for particles and airborne molecular contaminants (AMCs) in cleanroom environments, which are crucial for ensuring the integrity of semiconductor manufacturing processes. We focus on quantifying particle levels and a representative AMC, hydrogen chloride (HCl), having known detrimental effects on equipment longevity, product yield, and human health. We have developed a compact laser sensor based on open-path cavity ring-down spectroscopy (CRDS) using a 1742 nm near-infrared diode laser source. The sensor enables the high-sensitivity detection of HCl through absorption by the 2-0 vibrational band with an Allan deviation of 0.15 parts per billion (ppb) over 15 min. For quantifying particle number concentrations, we examine various detection methods based on statistical analyses of Mie scattering-induced ring-down time fluctuations. We find that the ring-down distributions' 3rd and 4th standard moments allow particle detection at densities as low as ~105 m-3 (diameter > 1 μm). These findings provide a basis for the future development of compact cleanroom monitoring instrumentation for wafer-level monitoring for both AMC and particles, including mobile platforms.

Proposed experiment to measure nonlinear optical susceptibilities in the saturated regime

When an optical beam passes through a thin slice of a homogeneous material, the change of its phase and amplitude is characterized by the material's linear and nonlinear susceptibility, the latter also known as the hyperpolarizability. The standard method for measuring the nonlinear susceptibility is the Z scan. This widely used method is sometimes applied outside of its range of validity, leading to systematic errors. These errors are illustrated for a two-level system with parameters taken from atomic rubidium. The present paper proposes a method called the phase retrieval of modes to determine the nonlinear susceptibility without an assumption about its functional form, in contrast to both the Z -scan method and variants intended to apply in cases of saturation. In brief, a Gaussian beam passes through a thin sample and is detected on three planes in a focal scan. Phase retrieval methods are used to find coefficients of the modes which in turn determine the optical nonlinear susceptibility. Nearly exact recovery of the nonlinear susceptibility is shown numerically in the no-noise case. Additionally, two types of noise are considered: shot noise on the detector and intensity fluctuations of the input.

Compact low-repetition-rate femtosecond optical parametric oscillators enabled by Herriott cells

We report the design and characterization of a femtosecond optical parametric oscillator containing an intracavity Herriott cell. Pumped by a 49.16-MHz Yb:fiber laser, the signal wavelength could be tuned over 1440-1530 nm, with the Herriott cell containing 81% of the free-space cavity length required for synchronous operation. We also report a 12.29-MHz OPO using a sub-harmonic pumping approach, extending the Herriott cell OPO concept to low-repetition-rate cavities.

Study on Bottom Distributed Bragg Reflector Radius and Electric Aperture Radius on Performance Characteristics of GaN-Based Vertical-Cavity Surface-Emitting Laser

This article presents the results of a numerical analysis of a nitride-based vertical-cavity surface-emitting laser (VCSEL). The analyzed laser features an upper mirror composed of a monolithic high-contrast grating (MHCG) and a dielectric bottom mirror made of SiO2 and Ta2O5 materials. The emitter was designed for light emission at a wavelength of 403 nm. We analyze the influence of the size of the dielectric bottom mirrors on the operation of the laser, including its power-current-voltage (LIV) characteristics. We also study the effect of changing the electrical aperture radius (active area dimensions). We demonstrate that the appropriate selection of these two parameters enables the temperature inside the laser to be reduced, lowering the laser threshold current and increasing its optical power output significantly.

Stochastic ray tracing for Fresnel diffraction

We propose stochastic ray tracing for laser beam propagation in Fresnel diffraction to find the duality between wave and ray representations. We transform from the Maxwell equations to the Schrödinger equation for a monochromatic laser beam in the slowly varying envelope approximation. The stochastic ray tracing method interprets this Schrödinger equation as a stochastic process, of an analogy of Nelson's stochastic mechanics. It can illustrate the stochastic paths and the wavefront of an optical beam. This ray tracing method includes Fresnel diffraction effects naturally. We show its general theoretical construction and numerical tests for a Gaussian laser beam with diffraction, that stochasticity realizes the beam waist around the Rayleigh range.

How good are collimated Gaussian beams produced with engineered diffusers?

Collimating a Gaussian beam from an uncollimated laser source has been achieved via the deployment of engineered diffusers (EDs)-also referred to as light shaping diffusers. When compared to conventional pinhole-based optical collimation systems, this method of beam collimation ensures high optical transmission efficiency at the expense of the introduction of additional speckle and a resulting reduction in spatial coherence. Despite a lower collimation quality, these ED-produced collimated beams are attractive and promising in terms of their deployment in various benchtop or tabletop systems that involve shorter beam propagation distances of up to a few meters while requiring a high optical power throughput. This paper aims to further the understanding of collimation quality and propagation properties of ED-produced Gaussian collimated beams via carefully designed experiments and accompanying analysis. We measure and document the beam divergence, Rayleigh distance, and M 2 factor, as well as evolution of the wavefront radius of curvature (RoC), of these ED-generated beams over a few meters of propagation-a propagation distance which encapsulates a vast majority of optical systems. We further investigate the changes in the beam profile with the addition of a laser speckle reducer (SR) and compare the ED-produced beams with a near-ideal collimated beam produced with spatial filtering systems.

Narrow-bandwidth tunable optical filter stabilized by Newton's rings fringe analysis

The resolution of grating spectrometers is insufficient to resolve many features present in the emission spectra of solid-state quantum emitters. Spectral resolution may be improved by inserting a Fabry-Perot interferometer (FPI) whose length is tuned by a piezoelectric actuator. Yet piezo creep and thermal fluctuations cause instability that makes this solution unsuitable for measurement times longer than tens of seconds. To overcome this challenge, we employ active feedback derived from the Newton's rings interference pattern formed by the reflection of a single-frequency laser from the FPI cavity. The resulting FPI transmission frequency is stable to within 50 MHz over several hours.

Paraxial and ray approximations of acoustic vortex beams

A compact analytical solution obtained in the paraxial approximation is used to investigate focused and unfocused vortex beams radiated by a source with a Gaussian amplitude distribution. Comparisons with solutions of the Helmholtz equation are conducted to determine bounds on the parameter space in which the paraxial approximation is accurate. A linear relation is obtained for the dependence of the vortex ring radius on the topological charge, characterized by its orbital number, in the far field of an unfocused beam and in the focal plane of a focused beam. For a focused beam, it is shown that as the orbital number increases, the vortex ring not only increases in radius but also moves out of the focal plane in the direction of the source. For certain parameters, it is demonstrated that with increasing orbital number, the maximum amplitude in a focused beam becomes localized along a spheroidal surface enclosing a shadow zone in the prefocal region. This field structure is described analytically by ray theory developed in the present work, showing that the spheroidal surface in the prefocal region coincides with a simple expression for the coordinates of the caustic surface formed in a focused vortex beam.

Eigen-function division multiplexed coherent optical transmission in time domain by using higher-order Hermite-Gaussian pulses

We describe a new multiplexing technique and its application to demultiplexing in the time domain by using higher-order Hermite-Gaussian (HG) pulses, which are solutions of the Schrödinger equation. We call this technique eigen-function division multiplexing (EDM). This method enables us to further increase the total transmission capacity by superimposing many different HG pulses in the same time slot. This technique is different from a conventional optical time domain multiplexing (OTDM) technique using interleaving, where one pulse exists only in one time slot. The transmitted EDM HG pulses can be demultiplexed by adopting the time-domain orthogonality of the HG pulses (eigen-function orthogonality). The information carried by the mth-order HG pulse (HGm pulse) can be coherently detected by a photo detector, where photo-mixing with a phase-locked HGm pulse generated by a local oscillator can realize demultiplexing. The overlap integral with a different HG pulse becomes zero due to the time domain orthogonality. First, we show numerically that such a new EDM transmission scheme in the time domain is possible. We then show experimentally that we could successfully carry out an EDM HG coherent pulse transmission with four different HG pulses (HG0, HG1, HG2, and HG3), where we report a 400∼480 Gbit/s (10 Gbaud x 4 eigen-functions x 2 pol-mux.) 32∼64 QAM EDM transmission over 300∼450 km.

Direct generation of multicolor Bessel beams from a Pr3+: WPFG fiber laser

Multicolor visible high-order Bessel (Bessel-vortex) beams which have a helical wavefront and a long confocal length have garnered significant interest for applications in materials processing and biomedical technologies. In this paper, we demonstrate the direct generation of multicolor (523, 605 and 637 nm) Bessel-vortex beams from a Pr3+-doped water-proof fluoro-aluminate glass (Pr3+: WPFG) fiber laser with an intracavity lens which induces chromatic and spherical aberration. The handedness of the generated Bessel-vortex beam is selectively controlled through lateral displacement of the intra-cavity lens.

Controlled experimental generation of perturbed high-order Ince-Gaussian laser modes

We present an experimental approach for generating perturbed high-order Ince-Gaussian laser modes by transforming the low and moderate-intensity lobes of high-order Ince-Gaussian (IG) modes into high-intensity lobes and vice versa. This perturbation reshuffles optical energy among the different lobes and generates new, to the best of our knowledge, modulated Ince-Gaussian (MIG) modes. Computer-generated holograms displayed over spatial light modulators were used to modulate the IGMs. Compared to IG modes, MIG modes are generated precisely in a sense that enhances the IG modes and provides a maximum number of highly intense lobes in a particular mode. That enables the newly generated MIG modes to be utilized more efficiently than IG modes in applications such as particle manipulation and optical trapping of microparticles, which exploit highly intense lobes.

Simple analysis of Gaussian pulses and beams in mode-locked lasers

An ABCDmatrix representation in space and time of a mode-locked laser is presented. The conventional stability concept of Gaussian beams in laser cavities implies, instead of stability, an equilibrium condition, which can be indifferent, stable, or unstable. It is further shown that when beam and pulse evolution in the laser are intertwined, stable mode locking can be the result of evolution of a noise spike in an otherwise unstable (in the conventional sense) cavity.

Test station to characterize the emission of a LiDAR

A test station setup devised to measure the emission characteristics and beam propagation parameters of a light detection and ranging (LiDAR) system is presented. The main blocks of the station to measure the accessible emission, wavelength peak and FWHM, pulse duration, pulse repetition rate, horizontal and vertical angular resolution, field of view, beam propagation factor M 2, beam waist size, waist location, and divergence are described. The performance of this test station was demonstrated using a commercial spinning LiDAR, a Velodyne VLP-16, which successfully enables these measurements for a laser beam with a wavelength of 913 nm.

Approximate solution of diffraction integral equation of resonator

Utilizing the diffraction integral equation and the principle of slow amplitude approximation, we obtain a novel approximate solution of the transverse mode including the cavity parameters a (a is the section size of the resonator) and g = 1-L/R (L is the cavity length, R is the radius of curvature of the cavity). With this approximate solution, we can explore the influence of the resonator parameters a and g on the transverse mode. The theoretical analysis demonstrates that a and g have a certain influence on the shape and quality of the transverse mode, and selecting the appropriate a and g can effectively improve the quality of the transverse pattern. Moreover, laser experiments are conducted to validate analysis conclusion.

Classical calculation of differential cross section for a beam deflected by a concentric refractive index field

Ray tracing is a fundamental geometric-optics issue which gives a single ray path but seldom presents the collective behavior of light. The optical field distribution usually involves the calculation of an electromagnetic field and is rarely discussed from the perspective of geometric optics. However, in this paper, we show for a concentric medium with spherically symmetric refractive index, how the relative angular distribution of refractive beams can be obtained from the pure classical geometric optics method. As a measurement of the distribution, we introduce the concept of the differential cross section (DCS), which can be calculated from the relation between aiming distance and deflecting the angle of the ray. We present a general method to solve this relation from both Snell's law in a constant medium and the optical Binet equation (OBE) in a gradient-index (GRIN) medium. Even without observing the collective traces, the DCS can independently give a quantitative description for the deflected light density of concentric media at different directions. It may act as a reference index for the design of beam deflector.

Periodical properties of the ray transfer matrix and generation of sideband modes in a stable laser resonator

The paper describes a subclass of stable laser cavities, periodic stable laser cavities, in which perturbations consisting of deviations of the mode axis from the ideal direction are of a strictly periodic oscillatory nature. In such resonators, in addition to unperturbed longitudinal-transverse spatial modes with an ideal direction of the optical axis, additional modes can appear at sideband frequencies, associated with the resonant buildup of perturbation oscillations. These modes have approximately the same spatial structure as those of the unperturbed fundamental modes, and their frequency detuning from the frequencies of the fundamental modes is governed by the resonator geometry and the periodicity parameter, i.e., the number of passes in the resonator in one period of perturbation oscillations. For many repetitively pulsed laser systems emitting comb spectrum structures, such as free electron lasers, modern frequency standards using femtosecond lasers, and various comb spectrometers, it is desirable to avoid such periodic stable cavities in order to preserve the purity of the comb spectrum used in them. This may also be important for CW lasers with extreme radiation monochromaticity. In some repetitively pulsed lasers, on the contrary, it may be desirable to use such periodic stable laser cavities for a more complete frequency filling and higher quasi-continuity of their emission spectra.

Injection-seeded high-power Yb:YAG thin-disk laser stabilized by the Pound-Drever-Hall method

We demonstrate an injection-seeded thin-disk Yb:YAG laser at 1030 nm, stabilized by the Pound-Drever-Hall (PDH) method. We modified the PDH scheme to obtain an error signal free from Trojan locking points, which allowed robust re-locking of the laser and reliable long-term operation. The single-frequency pulses have 50 mJ energy (limited to avoid laser-induced damage) with a beam quality of M2 < 1.1 and an adjustable length of 55-110 ns. Heterodyne measurements confirmed a spectral linewidth of 3.7 MHz. The short pulse build-up time (850 ns) makes this laser suitable for laser spectroscopy of muonic hydrogen, pursued by the CREMA collaboration.

Accelerating finite-energy generalized Olver beams

We propose a new, to the best of our knowledge, and very general finite power beam solution to the paraxial wave equation (PWE) in Cartesian coordinates by introducing an exponential differential operator on the existing PWE solution and term it as the "finite-energy generalized Olver beam." Applying the analytical expressions for the field distributions, we study the evolution of intensity, centroid, and variance of these beams during free-space propagation. Our findings demonstrate that these new beams exhibit a diffraction-resistant profile along a curved trajectory when specific beam conditions are met. Using numerical methods, we further demonstrate the ability to adjust the self-accelerating degree, sidelobe profile, and stability of the central mainlobe by manipulating the transforming parameters. This research presents a versatile approach to controlling beam properties and holds promise for advancing applications in various fields.

Newton ring interferometry application for 2D lens array alignment with micrometer accuracy

The dense packing of two-dimensional (2D) lens arrays with high tilt and decentration accuracies is a technological challenge in coherent beam combining, as the collimator lens parameters and 2D lens array alignment must satisfy stringent requirements. A method for 2D lens array alignment based on Newton ring interferometry (NRI) is proposed. The analytical model and the algorithm presented in this study enabled the estimation of alignment sensitivity. An optical setup for alignment tests using NRI was developed and experimentally verified, and micrometer sensitivity was demonstrated. Analytical and experimental results showed that micrometer accuracy was achieved. Its limitations and prospects for improvement are also discussed.

Simultaneous thickness and phase index measurements with a motion-free actively tunable Twyman-Green interferometer

In this paper, we present a scheme to simultaneously measure the thickness and refractive index of parallel plate samples, involving no bulk mechanical motion, by deploying an electronically tunable Twyman-Green interferometer configuration. The active electronic control with no bulk mechanical motion is realized via the introduction of a tunable focus lens within the classical motion-based Twyman-Green interferometer configuration. The resulting interferometer is repeatable and delivers accurate estimates of the thickness and refractive index of a sample under test. Elimination of bulk motion also promises a potential for miniaturization. We develop a theoretical model for estimating sample thickness and index values using this reconfigurable interferometer setup and present detailed experimental results that demonstrate the working principle of the proposed interferometer.

Conversion and selection of Laguerre-Gaussian modes via a variable aperture in a geometric-phase-plate-assisted optical resonator

We numerically analyze the conversion and selection of intracavity modes in a two-mirror optical resonator, which is assisted by a geometric phase plate (GPP) and a circular aperture, along with its output performance of high-order Laguerre-Gaussian (LG) modes. Based on the iterative Fox-Li method and the analysis of modal decomposition, transmission losses, and spot sizes, we find that various self-consistent two-faced resonator modes could be formed by fixing the GPP but changing the size of aperture. Such a feature not only enriches transverse-mode structures inside the optical resonator, but also provides a flexible way to directly output high-purity LG modes for high-capacity optical communication, high-precision interferometers, high-dimensional quantum correlation, etc.

Estimation of dislocated phases and tunable orbital angular momentum using two cylindrical lenses

A first-order optical system consisting of two cylindrical lenses separated by a distance is considered. It is found to be non-conserving of orbital angular momentum of the incoming paraxial light field. The first-order optical system is effectively demonstrated to estimate phases with dislocations using a Gerchberg-Saxton-type phase retrieval algorithm by making use of measured intensities. Tunable orbital angular momentum in the outgoing light field is experimentally demonstrated using the considered first-order optical system by varying the distance of separation between the two cylindrical lenses.

Robust, motion-free optical characterization of samples using actively-tunable Twyman-Green interferometry

Optical interferometry-based techniques are ubiquitous in various measurement, imaging, calibration, metrological, and astronomical applications. Repeatability, simplicity, and reliability of measurements have ensured that interferometry in its various forms remains popular-and in fact continues to grow-in almost every branch of measurement science. In this paper, we propose a novel actively-controlled optical interferometer in the Twyman-Green configuration. The active beam control within the interferometer is a result of using an actively-controlled tunable focus lens in the sample arm of the interferometer. This innovation allows us to characterize transparent samples cut in the cubical geometry without the need for bulk mechanical motion within the interferometer. Unlike thickness/refractive index measurements with conventional Twyman-Green interferometers, the actively-tunable interferometer enables bulk-motion free thickness or refractive index sample measurements. With experimental demonstrations, we show excellent results for various samples that we characterized. The elimination of bulk motion from the measurement process promises to enable miniaturization of actively-tunable Twyman-Green interferometers for various applications.

Statistical modeling of atmospheric turbulence based on a low-cost experimental setup for measuring C n2 over water

The performance of communication systems based on free-space optical links depends on external factors such as weather conditions. Among many atmospheric factors, turbulence can be the greatest challenge to performance. The characterization of atmospheric turbulence usually involves expensive equipment known as a scintillometer. This work presents a low-cost experimental setup for measuring the refractive index structure constant over water, which results in a statistical model based on weather conditions. The turbulence variations with air and water temperature, relative humidity, pressure, dew point, and different watercourse widths are analyzed for the proposed scenario.

Periodic Distributions and Ultrafast Dynamics of Hot Electrons in Plasmonic Resonators

Understanding and managing hot electrons in metals are of fundamental and practical interest in plasmonic studies and applications. A major challenge for the development of hot electron devices requires the efficient and controllable generation of long-lived hot electrons so that they can be harnessed effectively before relaxation. Here, we report the ultrafast spatiotemporal evolution of hot electrons in plasmonic resonators. Using femtosecond-resolution interferometric imaging, we show the unique periodic distributions of hot electrons due to standing plasmonic waves. In particular, this distribution can be flexibly tuned by the size, shape, and dimension of the resonator. We also demonstrate that the hot electron lifetimes are substantially prolonged at hot spots. This appealing effect is interpreted as a result of the locally concentrated energy density at the antinodes in standing hot electron waves. These results could be useful to control the distributions and lifetimes of hot electrons in plasmonic devices for targeted optoelectronic applications.

Two non-centrosymmetric mixed alkali metal and alkaline earth metal scandium borate nonlinear optical materials with short ultraviolet cutoff edges

Rare earth borates, a subset of the essential nonlinear optical (NLO) materials, have sparked a significant amount of attention in recent years. In self-fluxing systems, two non-centrosymmetric scandium borates with classical B₅O₁₀ groups, namely Rb₇SrSc₂B₁₅O₃₀ (I) and Rb₇CaSc₂B₁₅O₃₀ (II), were successfully discovered. Both I and II exhibit a short ultraviolet (UV) cutoff edge (<200 nm) and appropriate second-harmonic generation efficiency (∼0.76 × KH₂PO₄, ∼0.88 × KH₂PO₄ at 1064 nm, respectively). According to theoretical calculations, it is speculated that the band gap and NLO characteristics of these two compounds are mostly derived from the B₅O₁₀ group and the ScO₆ octahedron. Due to the short cutoff edges of I and II, they may be considered as potential NLO materials in the UV and even deep UV spectral ranges. Furthermore, the advent of I and II adds to the diversity of rare earth borates.

Ultrashort laser pulses with chromatic astigmatism

Ultrashort laser pulses are described as having chromatic astigmatism, where the astigmatic phase varies linearly with the offset from the central frequency. Such a spatio-temporal coupling not only induces interesting space-frequency and space-time effects, but it removes cylindrical symmetry. We analyze the quantitative effects on the spatio-temporal pulse structure on the collimated beam and as it propagates through a focus, with both the fundamental Gaussian beam and Laguerre-Gaussian beams. Chromatic astigmatism is a new type of spatio-temporal coupling towards arbitrary higher complexity beams that still have a simple description, and may be applied to imaging, metrology, or ultrafast light-matter interaction.

Structure and Characterization of K2Na3B2P3O13, a New Nonlinear Optical Borophosphate with One-Dimensional Chain Structure and Short Ultraviolet Cutoff Edge

Nonlinear optical (NLO) crystals, being the primary medium for laser wavelength conversion, are crucial in all-solid-state lasers. Borophosphates offer more structural varieties than pure borates and phosphates, and they have become popular as NLO crystal candidates. Through spontaneous crystallization, we acquired a noncentrosymmetric alkali metal borophosphate crystal material, K₂Na₃B₂P₃O₁₃ (KNBPO). KNBPO crystallizes in the orthorhombic Cmc2₁ space group with the following unit cell parameters: a = 13.9238(18) Å, b = 6.7673(8) Å, c = 12.1298(15) Å, and Z = 4, and its structure is characterized by a fundamental building unit 1_∞ [B₂P₃O₁₃] chain structure made up of bridging oxygen linkages between BO₄ and PO₄ tetrahedra. KNBPO has a short ultraviolet (UV) cut-off edge (<186 nm), a congruent melting characteristic, good thermal stability, and a moderate second harmonic generation response roughly 0.42 times that of KH₂PO₄. Theoretical calculations reveal that the optical properties of the compound mainly originate from BO₄ and PO₄ units. Due to the short UV cut-off edge, KNBPO can be used as a potential NLO material in the UV and even deep UV regions, and it enhances the structural variety of borophosphates, which has a reference value for scholars investigating similar materials.

Subwavelength Diffractive Optical Elements for Generation of Terahertz Coherent Beams with Pre-Given Polarization State

Coherent terahertz beams with radial polarization of the 1st, 2nd, and 3rd orders have been generated with the use of silicon subwavelength diffractive optical elements (DOEs). Silicon elements were fabricated by a technology similar to the technology used before for the fabrication of DOEs forming laser terahertz beams with pre-given mode content. The beam of the terahertz Novosibirsk Free Electron Laser was used as the illuminating beam. The experimental results are in good agreement with the results of the computer simulation.

Misalignment-free, Kerr-lens-modelocked Yb:Y2O3 2.2-GHz oscillator, amplified by a semiconductor optical amplifier

We present a fully bonded, misalignment-free, diode-pumped Yb:ceramic (Yb:Y₂O₃) oscillator producing 190-fs pulses at a repetition frequency of 2.185 GHz. Self-starting Kerr-lens-modelocked operation was obtained from both outputs of the ring cavity with an average combined output power of 14-30 mW for pump powers from 380-670 mW. The fully bonded design provided self-starting, turnkey operation, with a relative intensity noise of 0.025% from 1 Hz-1 MHz. Tuning of the pulse repetition rate over a 120 kHz range was demonstrated for a 2°C change in temperature. Chirped-pulse amplification in a semiconductor optical amplifier was shown to increase the pulse average power to 69 mW and the pulse energy (peak power) from 2.5 pJ (12 W) to 32 pJ (71 W).

Diffraction of Gaussian and Laguerre-Gauss beams from a circular aperture using the moment expansion method

A method based on the distribution theory is introduced to compute the Fresnel diffraction integral. It is applied to the diffraction of Gaussian and Laguerre-Gauss beams by a circular aperture. Expressions of the diffracting field are recast into a perturbation series describing the near- and far-field regions.

Spontaneously implemented spatial coherence in vertical-cavity surface-emitting laser dot array

We report a self-induced spatially-coherent dot array consisting of fourteen units of vertical-cavity surface-emitting modes that exhibit spatially uniform spectra. A 47.5 µm total beam width and 0.5° narrow emission are achieved using an oblong cavity enclosed with a flat top mirror, cylindrically curved bottom mirror, and side facet. Notably, terminating the side of the cavity with a perpendicular facet enhances the horizontal propagation, which couples with the vertical resonance in each dot, similar to the case of master lasers in injection-locked lasers that delocalize the modes. Conventional semiconductor lasers, edge-emitting lasers, and vertical-cavity surface-emitting lasers have a Fabry-Pérot cavity; furthermore, emission and resonance are in identical directions, limiting the beam width to micrometers. Though the present structure has the same scheme of propagation, the right-angled facet synchronizes the modes and drastically expands the beam width.

Dispersion of Ultrarelativistic Tardyonic and Tachyonic Wave Packets on Cosmic Scales

We investigate the time propagation of tachyonic (superluminal) and tardyonic (subluminal, ordinary) massive wave packets on cosmic scales. A normalizable wave packet cannot be monochromatic in momentum space and thus acquires a positional uncertainty (or packet width) that increases with travel distance. We investigate the question of how this positional uncertainty affects the uncertainty in the detection time for cosmic radiation on Earth. In the ultrarelativistic limit, we find a unified result, δx(t)/c3=m2δpt/p03, where δx(t) is the positional uncertainty, m is the mass parameter, δp is the initial momentum spread of the wave function, and p0 is the central momentum of the wave packet, which, in the ultrarelativistic limit, is equal to its energy. This result is valid for tachyons and tardyons; its interpretation is being discussed.

Design of an electron cyclotron emission diagnostics suite for COMPASS Upgrade tokamak

COMPASS Upgrade is a medium size and high field tokamak that is capable of addressing key challenges for reactor grade tokamaks, including power exhaust and advanced confinement scenarios. Electron cyclotron emission will be available among the first diagnostics to provide measurements of high spatial and temporal resolution of electron temperature profiles and electron temperature fluctuation profiles through a radial view. A separate oblique view at 12° from normal will be utilized to study non-thermal electrons. Both the radial and oblique views are envisioned to be located in a wide-angle midplane port, which has dimensions that enable simultaneous hosting of the front-end of their quasi-optical (QO) designs. Each QO design will have an in situ hot calibration source in the front-end to provide standalone and calibrated Te (R,t) measurements. The conceptual design for each QO system, the Gaussian beam analysis, and the details of the diagnostic channels are presented.

Experimental realization of modulated Hermite-Gaussian laser modes: a maximum number of highly intense lobes

Here, we present an experimental method that redistributes the optical energy among the lobes of high-order standard Hermite-Gaussian (SHG) laser modes in a controlled manner. We numerically designed diffractive optical elements, displayed over a spatial light modulator for redistribution of optical energy that converts low and moderate intense lobes into all highly intense lobes and vice versa at the Fourier plane. Such precise generation of modulated HG (MHG) laser modes offers a maximum number of highly intense lobes compared to SHG modes. Hence, we envisage that MHG beams may surpass SHG beams in many applications, such as particle manipulation and optical lithography, where highly intense lobes play a significant role.

Influence of disk aberrations on high-power thin-disk laser cavities

We present a systematic study on the influence of thin-disk aberrations on the performance of thin-disk laser oscillators. To evaluate these effects, we have developed a spatially resolved numerical model supporting arbitrary phase profiles on the intracavity components that estimates the intracavity beam shape and the output power of thin-disk laser oscillators. By combining this model with the experimentally determined phase profile of the thin-disk (measured with interferometry), we can predict the operation mode of high-power thin-disk lasers, including mode degradation, higher-order mode coupling, and stability zone shrinking, all of which are in good agreement with experiment. Our results show that one of the main mechanisms limiting the performance is the small deviation of the disk's phase profile from perfect radial symmetry. This result is an important step to scaling modelocked thin-disk oscillators to the kW-level and will be important in the design of future active multi-pass cavity arrangements.

Simplifying the Experimental Detection of the Vortex Topological Charge Based on the Simultaneous Astigmatic Transformation of Several Types and Levels in the Same Focal Plane

It is known that the astigmatic transformation can be used to analyze the topological charge of a vortex beam, which can be implemented by using various optical methods. In this case, in order to form an astigmatic beam pattern suitable for the clear detection of a topological charge, an optical adjustment is often required (changing the lens tilt and/or the detection distance). In this article, we propose to use multi-channel diffractive optical elements (DOEs) for the simultaneous implementation of the astigmatic transformations of various types and levels. Such multi-channel DOEs make it possible to insert several types of astigmatic aberrations of different levels into the analyzed vortex beam simultaneously, and to form a set of aberration-transformed beam patterns in different diffraction orders in one detection plane. The proposed approach greatly simplifies the analysis of the characteristics of a vortex beam based on measurements in the single plane without additional adjustments. In this article, a detailed study of the effect of various types of astigmatic aberrations based on a numerical simulation and experiments was carried out, which confirmed the effectiveness of the proposed approach.

Femtosecond laser writing of lithium niobate ferroelectric nanodomains

Lithium niobate (LiNbO₃) is viewed as a promising material for optical communications and quantum photonic chips^1,2. Recent breakthroughs in LiNbO₃ nanophotonics have considerably boosted the development of high-speed electro-optic modulators^3-5, frequency combs^6,7 and broadband spectrometers⁸. However, the traditional method of electrical poling for ferroelectric domain engineering in optic^9-13, acoustic^14-17 and electronic applications^18,19 is limited to two-dimensional space and micrometre-scale resolution. Here we demonstrate a non-reciprocal near-infrared laser-writing technique for reconfigurable three-dimensional ferroelectric domain engineering in LiNbO₃ with nanoscale resolution. The proposed method is based on a laser-induced electric field that can either write or erase domain structures in the crystal, depending on the laser-writing direction. This approach offers a pathway for controllable nanoscale domain engineering in LiNbO₃ and other transparent ferroelectric crystals, which has potential applications in high-efficiency frequency mixing^20,21, high-frequency acoustic resonators^14-17 and high-capacity non-volatile ferroelectric memory^19,22.

Doppler compensation for cavity-based atom interferometry

We propose and demonstrate a scheme for Doppler compensated optical cavity enhancement of atom interferometers at significantly increased mode diameters. This overcomes the primary limitations in cavity enhancement for atom interferometry, circumventing the cavity linewidth limit and enabling spatial mode filtering, power enhancement, and a large beam diameter simultaneously. This approach combines a magnified linear cavity with an intracavity Pockels cell. The Pockels cell induces a voltage-controlled birefringence allowing the cavity mode frequencies to follow the Raman lasers as they track gravitationally induced Doppler shifts, removing the dominant limitation of current cavity enhanced systems. A cavity is built to this geometry and shown to simultaneously realise Doppler compensation, a 5.8 ± 0.15 mm1/e² diameter beam waist and an enhancement factor of >5× at a finesse of 35. Tuneable Gouy phase enables the suppression of higher order spatial modes and the avoidance of regions of instability. Atom interferometers will see increased contrast at extended interferometry times along with power enhancement and the reduction of optical aberrations. This is relevant to power constrained applications in quantum technology, alongside the absolute performance requirements of fundamental science.

Clarification for the fields of different radially polarized Laguerre-Gaussian light beams

Radially polarized light beams have found many applications in particle manipulation, laser processing, and microscopy. Just as with linear polarization, radially polarized light beams can have higher-order transverse modes that involve Laguerre polynomials. Fields of a radially polarized Laguerre-Gaussian light beam have been calculated before, even beyond the paraxial approximation. However, there are in fact multiple solutions to the paraxial wave equation that involve Laguerre polynomials with different properties and propagation characteristics. We therefore clarify the discrepancies among three valid radially polarized solutions to the paraxial wave equation that involve Laguerre polynomials.

Product of Two Laguerre–Gaussian Beams

We show that a product of two Laguerre–Gaussian (pLG) beams can be expressed as a finite superposition of conventional LG beams with particular coefficients. Based on such an approach, an explicit relationship is derived for the complex amplitude of pLG beams in the Fresnel diffraction zone. Two identical LG beams of the duet produce a particular case of a “squared” Fourier-invariant LG beam, termed as an (LG)2 beam. For a particular case of pLG beams described by Laguerre polynomials with azimuthal numbers n − m and n + m, an explicit expression for the complex amplitude in a Fourier plane is derived. Similar to conventional LG beams, the pLG beams can be utilized for information transmission, as they are characterized by orthogonal azimuthal numbers and carry an orbital angular momentum equal to their topological charge.

In situ determination of the penetration depth of mirrors in Fabry-Perot refractometers and its influence on assessment of refractivity and pressure

A procedure is presented for in situ determination of the frequency penetration depth of coated mirrors in Fabry-Perot (FP) based refractometers and its influence on the assessment of refractivity and pressure. It is based on assessments of the absolute frequency of the laser and the free spectral range of the cavity. The procedure is demonstrated on an Invar-based FP cavity system with high-reflection mirrors working at 1.55 μm. The influence was assessed with such a low uncertainty that it does not significantly contribute to the uncertainties (k = 2) in the assessment of refractivity (<8 × 10^-13) or pressure of nitrogen (<0.3 mPa).

2m-distance external cavity VECSEL for wireless charging applications

We characterize laser generation in an ultralong air cavity (several meters in length) using an optical-pumped semiconductor gain chip for laser wireless charging applications. The study realizes laser generation in an external air cavity with a length of 200 cm, for the first time, and achieves a maximum output laser power of more than 86.3 mW. Furthermore, the laser oscillation can be maintained even when the output mirror of laser is off-axis within 1.6 cm. Thus, a long external cavity laser would ease the alignment between the laser beam and charging terminal, making it suitable for laser wireless charging applications.