Tight Focusing Research Articles

Sub-surface modifications in silicon with ultra-short pulsed lasers above 2 µm

Nonlinear optical phenomena in silicon such as self-focusing and multi-photon absorption are strongly dependent on the wavelength, energy, and duration of the exciting pulse, especially for wavelengths > 2 µ m . We investigate the sub-surface modification of silicon using ultra-short pulsed lasers at wavelengths in the range of 1950–2400 nm, at a pulse duration between 2 and 10 ps and pulse energy varying from 1 µJ to 1 mJ. We perform numerical simulations and experiments using fiber-based lasers built in-house that operate in this wavelength range for the surface and sub-surface processing of Si-wafers. The results are compared to the literature data at 1550 nm. Due to a dip in the nonlinear absorption spectrum and a peak in the spectrum of the third-order nonlinearity, the wavelengths between 2000 and 2200 nm prove to be more favorable for creating sub-surface modifications in silicon. This is the case even though those wavelengths do not allow as tight focusing as those at 1550 nm. This is compensated for by an increased self-focusing due to the nonlinear Kerr-effect around 2100 nm at high light intensities, characteristic for ultra-short pulses.

Optimization of ultrafast axial scanning parameters for efficient pulsed laser micro-machining

Abstract In order to achieve high-resolution micro-machined features, tight focusing is traditionally adopted in laser micro-machining systems, at the cost of a narrow axial machining range. As the laser energy is confined in a single, fixed focal spot, machining throughput is significantly constrained by the writing speed of either translation stages or galvanometer scanners. We study an ultrafast axial scanning technique that asynchronously distributes laser pulses along the axial direction. Oscillation of the focal spot induced by the tunable acoustic gradient index lens is visualized in borosilicate glass with femtosecond laser pulses. By tuning frequency and amplitude of the acoustic field, machining parameters can be optimized, as demonstrated by the case of line machining on silicon. Multi-pass groove machining with axial scanning on silicon as well as femtosecond laser cutting of battery separators exhibit an extended effective machining range and an improved machining efficiency for both focused and defocused surfaces.

Tailoring Antenna Focal Plane Characteristics for a Compact Free-Space Microwave Complex Dielectric Permittivity Measurement Setup

This article presents a compact precision free-space microwave measurement setup with a choice of three dielectric lenses to tailor the antenna focal plane characteristics for extracting complex dielectric permittivity of small samples. Custom designed spot-focusing horn antenna pairs were used to achieve a compact setup with antenna separation distance, 2 f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sub> :4λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> -8λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> and focal spot size, f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> :1λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> -1.5λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , where λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> is the wavelength at center frequency. Using the compact free-space setup, relative complex permittivity (e' - je'') was extracted over 8-12 GHz for lowand high-loss dielectrics with lateral dimensions, 3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> and 10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . For large materials under test (MUTs), i.e., 10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , measurement accuracy in dielectric constant, Δe'% was <; 0.65% and <; 1.14% for low- and high-loss dielectrics, respectively. For smaller MUTs (3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ), Ae'% was <; 0.89% and <; 2.29% for low- and high-loss MUTs, respectively. The error in loss tangent (Δtanδ) varied over 0.002-0.016 and 0.015-0.056 for large (10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ) and small MUTs (3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ), respectively. For large MUTs, biconvex lens pair with the smallest f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> (1λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ) and f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sub> (4λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ) among the three lenses yielded the best accuracy in dielectric constant (e') due to tight field focusing at the focal plane. The plano-convex lens pair yielded the best accuracy in loss tangent (tanδ = e''/e') for large MUTs due to slow variation in the phase of the local plane wave. By tailoring antenna focal plane characteristics, a compact free-space setup that is 6×-10× smaller than the classical setup for handling MUTs that are 1/5th of the size used in classical setup is demonstrated without compromising the measurement accuracy.

Direct observation of the effects of spin dependent momentum of light in optical tweezers

We demonstrate that tight focusing of a circularly polarized Gaussian beam in optical tweezers leads to spin-momentum locking—with the transverse momentum density (Poynting vector) being helicity-dependent, while the transverse spin angular momentum density becomes independent of helicity. We further use a stratified medium in the path of the trapping beam in our optical tweezers setup to enhance the magnitude of the transverse momentum and the electric field intensity in the radial direction with respect to the beam axis and cause them to significantly overlap. This overlap allows us to experimentally observe the circular motion of a birefringent particle, trapped off-axis, in response to an input circularly polarized fundamental Gaussian beam carrying no intrinsic orbital angular momentum (OAM). The circular motion is dependent on the helicity of the input beam so that we can identify it as the signature of the elusive Belinfante spin in propagating light beams obtained in our optical tweezers configuration. Our results can be extended to beams carrying intrinsic OAM leading to simple routes for achieving complex manipulation of micro-machines or other mesoscopic matter using optical tweezers.

Theoretical Diversity: Economies of Affection and Their Implications for Management Studies

This panel symposium brings together Indigenous and non- Indigenous scholars to address the issues of global and theoretical diversity within the Academy of Management and meaningful trans- and inter-disciplinary collaborations, through a tight focus on Indigenous philosophies of management often described as ‘gift exchange’ practices and economies. Among the dichotomies this symposium will recognise and address are distinctions between Indigenous and non-Indigenous economic philosophies and their researchers; methods and outputs of management studies compared to other social sciences; and the management of relationships within and beyond the Academy predicated on reciprocal exchange. Our overall premise is that what the academy usually sees as ‘the anthropological study of gift economies’ is a modern-day reality for Indigenous societies who maintain time-honoured protocols for managing inseparable economies and ecologies.

Enhanced laser wakefield acceleration using dual-color relativistic pulses

In a recent article by Li et al (2019 Sci. Adv. 5. eaav7940), experimental results from a dual-color laser wakefield acceleration (LWFA) were presented. In the present paper we, primarily, focus on detailed simulation studies of such a scheme in the self-injection and ionization injection regimes, respectively. The spatiotemporally-overlapped 30 fs dual-color laser pulses are at fundamental (FL, 800 nm, ‘red’) and second-harmonic (SH, 400 nm, ‘blue’) wavelengths. They are (a) co-propagating in an under-dense plasma, (b) relativistically intense (I > 1018 W cm−2) and (c) having relatively high-energy (multi-Joule, loose focusing) and low-energy (sub-Joule, tight focusing), respectively. The basic concept of the scheme is the fact that the depletion length (Lpd) for a relativistic laser pulse in an under-dense plasma has an inverse quadratic dependence on the laser wavelength (∝1/λ2). Here, first by using a single FL 77 TW/30 fs laser pulse to drive a LWFA, an electron beam was accelerated up to ∼400 MeV from a background plasma having an electron density of 1019 cm−3. Then, by driving the same LWFA by co-propagating ‘blue’ 7 TW/30 fs and ‘red’ 70 TW/30 fs laser pulses, the electron energy reached ∼700–800 MeV (maximum). The simulations confirm that in such a dual-color LWFA scheme, the role of the SH laser pulse is post-accelerating electrons after a rapid depletion of the FL laser pulse in the plasma. Furthermore, the SH pulse assists the ionization-injection of the electrons which is an additional benefit of the dual-color LWFA scheme.

Theoretical analysis based on mirror symmetry for tightly focused vector optical fields.

A theoretical analysis based on mirror symmetry is proposed to analyze and predict the symmetry in intensity, phase and polarization distributions of the tightly focused vector optical field (VOF). We extend the analysis to more cases including more complicated polarization states and weak focusing cases. We further show the symmetric tightly focused fields of the eccentric cylindrical VOF and the redesigned VOF with a radially variant polarization state, which are achieved by redesigning the polarization state of the incident VOF based on the symmetry analysis. We also take the laser fabrication as an example to further show how to apply this symmetry analysis in a specific application area. Such a theoretical analysis can improve the calculation efficiency, provide new insights into the tight focusing process and offer a convenient way to engineer the field distributions in the focal plane, which may have potential applications in areas needing flexibly controllable tightly focused fields, such as laser fabrication, optical trapping, and optical storage.

Experimental focusing in the characterization of ultrashort chirped pulses in a simplified device

Grating eliminated no-nonsense observation of ultrafast incident laser light e-fields is an experimental technique for the full characterization of ultrashort laser pulses. It requires the nonlinear conversion of broadband ultrashort optical pulses into their second harmonic generation (SHG) that is relatively tightly focused on a thick SHG crystal. In this paper, the laser focusing problem is experimentally presented and demonstrated in the measurements of 780 nm chirped pulses emitted from a Ti:sapphire oscillator. In this experimental study, it has been shown how the focusing effect can cause distortions in the trace of the chirped pulses. It is demonstrated that the measurement of broadband pulses requires that the beam have a wide angular divergence. Therefore, a tight focusing is essential. A long focal length leads to a smaller range of angles incident on the crystal causing an insufficient divergence angle. Finally, the ability of this device in the characterization of double and complicated chirped pulses is described. The broadening of complex chirped pulses after passing through a thick BK7 glass is measured and the group velocity dispersion of the BK7 glass is calculated as about 47.3 fs2 mm−1. Also the train of double chirped pulses created using a Michelson interferometer is measured and the spectral fringes marked by phase jumps are observed. The experimental results of the retrieved phases and intensities are in good agreement with independently measured data.

Segmented cylindrical vector beams for massively-encoded optical data storage

The possibility to achieve unprecedented multiplexing of light-matter interaction in nanoscale is of virtue importance from both fundamental science and practical application points of view. Cylindrical vector beams (CVBs) manifested as polarization vortices represent a robust and emerging degree of freedom for information multiplexing with increased capacities. Here, we propose and demonstrate massively-encoded optical data storage (ODS) by harnessing spatially variant electric fields mediated by segmented CVBs. By tight focusing polychromatic segmented CVBs to plasmonic nanoparticle aggregates, record-high multiplexing channels of ODS through different combinations of polarization states and wavelengths have been experimentally demonstrated with a low error rate. Our result not only casts new perceptions for tailoring light-matter interactions utilizing structured light but also enables a new prospective for ultra-high capacity optical memory with minimalist system complexity by combining CVB’s compatibility with fiber optics.

Nanoexplosion initiated by short-wavelength radiation: Optical breakdown in soft matter revisited

The term “laser microexplosion” has been introduced to stress the violent character of the optical breakdown by laser radiation under conditions of tight focusing. Generally, the starting phase of the breakdown has been neglected by the assumption of absorption triggered by the presence of damage precursors. The application of the plasticity–elasticity theory in the analysis of the dynamics of this phenomenon has not been extensively examined to date. This paper formulates a phenomenological model attempting to explain the creation of nanovoids in a soft matter under irradiation by a flux of extreme ultraviolet (XUV)/soft x-ray photons. The combined action of plastic deformation and dissociation waves on soft matter is found to be responsible for the material modifications. It is suggested that localized (volume≃λ3) abundance of energy, coming most likely from photon bunching, constitutes the real onset of the photo-ablative decomposition. It is shown that the coincidental presence of some small number of energy carriers (2–3 XUV photons in the considered case) in such a small volume triggers processes denoted from now on as a laser nanoexplosion. The effect is considered to be the first step in the optical breakdown followed by an intense material removal resembling, to some extent, a phase explosion.

Focussing Protons from a Kilojoule Laser for Intense Beam Heating using Proximal Target Structures

Proton beams driven by chirped pulse amplified lasers have multi-picosecond duration and can isochorically and volumetrically heat material samples, potentially providing an approach for creating samples of warm dense matter with conditions not present on Earth. Envisioned on a larger scale, they could heat fusion fuel to achieve ignition. We have shown in an experiment that a kilojoule-class, multi-picosecond short pulse laser is particularly effective for heating materials. The proton beam can be focussed via target design to achieve exceptionally high flux, important for the applications mentioned. The laser irradiated spherically curved diamond-like-carbon targets with intensity 4 × 1018 W/cm2, producing proton beams with 3 MeV slope temperature. A Cu witness foil was positioned behind the curved target, and the gap between was either empty or spanned with a structure. With a structured target, the total emission of Cu Kα fluorescence was increased 18 fold and the emission profile was consistent with a tightly focussed beam. Transverse proton radiography probed the target with ps order temporal and 10 μm spatial resolution, revealing the fast-acting focussing electric field. Complementary particle-in-cell simulations show how the structures funnel protons to the tight focus. The beam of protons and neutralizing electrons induce the bright Kα emission observed and heat the Cu to 100 eV.

Controlled negative energy flow in the focus of a radial polarized optical beam.

The controlled and continuous negative energy flow (from negative to positive) on the optical axis in the focal region is obtained by adjusting the polarization distribution of the input second-order radially polarized beam (the polarization topological charge is equal to 2). Moreover, the similar evolution of negative energy flow also can be achieved for the tightly focused vector beams with polarization topological charge -2. It is because both the beams with polarization topological charges 2 and -2 can possess the same polarization and spin flow density distributions with the help of the polarization modulation. The results provide a potential method for modulating the effects induced by the spin-orbit coupling in tight focusing of optical beam.

Stimulated Raman scattering signal generation in a scattering medium using self-reconstructing Bessel beams

Scattering is a huge challenge for microscopic imaging. Indeed, it is difficult to observe target chemicals in scattering media by means of the current Gaussian beam-based stimulated Raman scattering (SRS) microscopy, since the tight focus of the Gaussian beam is destroyed after propagating through a certain distance. Bessel beams, featuring self-reconstructing property, may bring a solution to this problem. By combining Bessel beams with SRS microscopy, we can probe the SRS signal from a scattering medium. In this paper, using the beam propagation method, we first simulate the propagation of the Bessel beam as well as the generation and self-reconstruction of SRS signals. By adding glass beads along the beam propagation path in order to simulate scattering, the propagation of the Bessel beams and the generation of the SRS signals will change. Then, we design a series of simulations to investigate the influence of the size, position, number, and distribution of the added glass beads on the generation of the SRS signals. A preliminary experiment is also carried out to confirm the simulation predictions. Results demonstrate that the SRS signals can be generated or be recovered at a certain depth in scattering media, and that such signals are greatly affected by the parameters of the scatters.

Probing Intracellular Dynamics Using Fluorescent Carbon Dots Produced by Femtosecond Laser In Situ.

Fluorescent particle tracking is a powerful technique for studying intracellular transport and microrheological properties within living cells, which in most cases employs exogenous fluorescent tracer particles delivered into cells or fluorescent staining of cell organelles. Herein, we propose an alternative strategy, which is based on the generation of fluorescent species in situ with ultrashort laser pulses. Using mouse germinal vesicle oocytes as a model object, we demonstrate that femtosecond laser irradiation produces compact dense areas in the intracellular material containing fluorescent carbon dots synthesized from biological molecules. These dots have tunable persistent and excitation-dependent emission, which is highly advantageous for fluorescent imaging. We further show that tight focusing and tuning of irradiation parameters allow precise control of the location and size of fluorescently labeled areas and minimization of damage inflicted to cells. Pieces of the intracellular material down to the submicrometer size can be labeled with laser-produced fluorescent dots in real time and then employed as probes for detecting intracellular motion activity via fluorescent tracking. Analyzing their diffusion in the oocyte cytoplasm, we arrive to realistic characteristics of active forces generated within the cell and frequency-dependent shear modulus of the cytoplasm. We also quantitatively characterize the level of metabolic activity and density of the cytoskeleton meshwork. Our findings establish a new technique for probing intracellular mechanical properties and also promise applications in tracking individual cells in population or studies of spatiotemporal cell organization.

Tightly focusing terahertz wave using gradient-type slotted grating based on spoof surface plasmons.

The d1-d2-d3-d4-d5 gradient-type spoof surface plasmons (SSP) grating was designed and found to exert an obvious effect on electric field localization. Two gradient-shaped planar ports were added to the bottom of this grating to form a gradient-type slotted SSP grating and achieve tight focusing and local electric field enhancement for a terahertz wave. The size of the focal spot was optimized to 0.01λ. The single-gradient-type slotted SSP grating was considered as a unit and arranged in one and two dimensions to generate a longitudinal focal line and square focal spots array. This did not only improve the resolution of terahertz imaging, but also simultaneously scan multiple focal spots to increase the speed of terahertz imaging. This work makes the manipulation of terahertz wave more flexible and efficient which has great potential in terahertz high-resolution near-field scanning imaging.

Tracing Air-Breakdown Plasma Characteristics from Single-Color Filament Terahertz Spectra

In this paper, we measure broadband terahertz spectra from a single 744-nm filament produced in tight, medium, and loose geometrical focusing conditions. Terahertz spectra are measured using interferometer coupled to a helium-cooled bolometer avoiding any cutoff frequencies. Based on THz spectrum maximum position and spectral width, we estimate electron-heavy particle (neutrals and ions) collision rate. Numerical simulations are performed using the state-of-the-art model of unidirectional femtosecond pulse propagation and convergence/divergence of optical radiation at large angles.

High-Throughput Particle Concentration Using Complex Cross-Section Microchannels.

High throughput particle/cell concentration is crucial for a wide variety of biomedical, clinical, and environmental applications. In this work, we have proposed a passive spiral microfluidic concentrator with a complex cross-sectional shape, i.e., a combination of rectangle and trapezoid, for high separation efficiency and a confinement ratio less than 0.07. Particle focusing in our microfluidic system was observed in a single, tight focusing line, in which higher particle concentration is possible, as compared with simple rectangular or trapezoidal cross-sections with similar flow area. The sharper focusing stems from the confinement of Dean vortices in the trapezoidal region of the complex cross-section. To quantify this effect, we introduce a new parameter, complex focusing number or CFN, which is indicative of the enhancement of inertial focusing of particles in these channels. Three spiral microchannels with various widths of 400 µm, 500 µm, and 600 µm, with the corresponding CFNs of 4.3, 4.5, and 6, respectively, were used. The device with the total width of 600 µm was shown to have a separation efficiency of ~98%, and by recirculating, the output concentration of the sample was 500 times higher than the initial input. Finally, the investigation of results showed that the magnitude of CFN relies entirely on the microchannel geometry, and it is independent of the overall width of the channel cross-section. We envision that this concept of particle focusing through complex cross-sections will prove useful in paving the way towards more efficient inertial microfluidic devices.

Scanless two-photon excitation with temporal focusing.

Temporal focusing, with its ability to focus light in time, enables scanless illumination of large surface areas at the sample with micrometer axial confinement and robust propagation through scattering tissue. In conventional two-photon microscopy, widely used for the investigation of intact tissue in live animals, images are formed by point scanning of a spatially focused pulsed laser beam, resulting in limited temporal resolution of the excitation. Replacing point scanning with temporally focused widefield illumination removes this limitation and represents an important milestone in two-photon microscopy. Temporal focusing uses a diffusive or dispersive optical element placed in a plane conjugate to the objective focal plane to generate position-dependent temporal pulse broadening that enables axially confined multiphoton absorption, without the need for tight spatial focusing. Many techniques have benefitted from temporal focusing, including scanless imaging, super-resolution imaging, photolithography, uncaging of caged neurotransmitters and control of neuronal activity via optogenetics.

Crystal-Configuration Considerations for Higher-Sensitivity Picosecond-Pulse SHG FROG

We experimentally compare a thick BIBO crystal, a walk-off compensating configuration of thin BBO crystals, and a thin PPLN crystal for the use as a nonlinear medium in SHG FROG, aiming for increased sensitivity required for complete pulse characterization of low-energy (below pJ) pulses a few picoseconds long at wavelengths near 1030 nm. We investigate the dependence of the spectral bandwidth of the frequency-doubled input ultrashort pulse and the conversion efficiency on focal-spot size in the nonlinear crystal. Both numerical and experimental results confirm an increase of the bandwidth with tighter focusing in a thick BIBO and a more-than-threefold increase of conversion efficiency compared to a thin BIBO crystal. A PPLN crystal is found to be the most efficient among the three, but very thin (<; 0.3 mm) crystals would be required to extend the measurement capabilities of SHG FROG to sub-ps pulses. A SHG FROG using a PPLN crystal for characterization of picosecond pulse is demonstrated with a sensitivity of 2 ×10 -3 (mW)2.

Tight focusing of a cylindrical vector beam by a hyperbolic secant gradient index lens.

In this Letter, we investigate the tight focusing of a second-order cylindrical vector beam by a hyperbolic secant gradient index lens with a thickness of 10 µm, a radius of 9.43 µm, and a refractive index on the axis of 3.47 (silicon). It is shown that the lens forms the reverse energy flow near its shadow surface. Moreover, it was obtained that the spherical hole in the center of the shadow plane with a diameter of 0.3 µm allows us to localize the direct energy flow inside the lens material and with the reverse energy flow in an area of free space.