The polarization properties of monochromatic light beams are studied. In contrast to the idealization of an electromagnetic plane wave, finite beams which are everywhere linearly polarized in the same direction do not exist. Neither do beams which are everywhere circularly polarized in a fixed plane. It is also shown that transversely finite beams cannot be purely transverse in both their electric and magnetic vectors, and that their electromagnetic energy travels at less than c. The electric and magnetic fields in an electromagnetic beam have different polarization properties in general, but there exists a class of steady beams in which the electric and magnetic polarizations are the same (and in which energy density and energy flux are independent of time). Examples are given of exactly and approximately linearly polarized beams, and of approximately circularly polarized beams.
We investigate the mechanism of the nonparaxial propagation of the tightly focused beams in the view of Fourier optics. It shows that it is the phase of the angular spectrum which induces the interesting evolution of the tightly focused beams. Based on the theory of Fourier optics, we propose an approach on controlling and detecting the focusing spot of the tightly focused beams.
Fully analytic expressions, for the electric and magnetic fields of an ultrashort and tightly focused laser pulse of the radially polarized category, are presented to lowest order of approximation. The fields are derived from scalar and vector potentials, along the lines of our earlier work for a similar pulse of the linearly polarized variety. A systematic program is also described from which the fields may be obtained to any desired accuracy, analytically or numerically.
We report experiments on the generation of third and fifth harmonics of millijoule-level, tightly focused, femtosecond laser pulses at 2.2 μm wavelength in air. The measured ratio of yields of the third and fifth harmonics in our setup is about 2 \cdot 10-4. This result contradicts the recent suggestion that the Kerr effect in air saturates and changes sign in ultra-intense optical fields.
This letter is the first demonstration of material modification using tightly focused femtosecond laser vortex beams. Double-charge femtosecond vortices were synthesized with the polarization-singularity beam converter described in Ref [1] and then focused using moderate and high numerical aperture optics (viz., NA = 0.45 and 0.9) to ablate fused silica and soda-lime glasses. By controlling the pulse energy we consistently machine high-quality micron-size ring-shaped structures with less than 100 nm uniform groove thickness.
This letter is the first demonstration of material modification using tightly focused femtosecond laser vortex beams. Double-charge femtosecond vortices were synthesized with the polarization-singularity beam converter described in Ref [1] and then focused using moderate and high numerical aperture optics (viz., NA = 0.45 and 0.9) to ablate fused silica and soda-lime glasses. By controlling the pulse energy we consistently machine high-quality micron-size ring-shaped structures with less than 100 nm uniform groove thickness.
A high index dielectric nano-sphere can be excited and yet remain radiationless. A method to excite the non-radiating anapole mode of a high index isotropic dielectric nanosphere is presented. With tightly focused radially polarized beam illumination, the main-contributing electric dipole mode and magnetic modes can be zero with only a weak electric quadruple contributing to the total scattering. Further, with a standing wave illumination formed by two counter-propagating focused radially polarized beam under $4π$ configuration, the ideal radiationless ananpole can be excited.
Analytic expressions for the electromagnetic fields of an ultrashort, tightly focused, linearly polarized laser pulse in vacuum are derived from scalar and vector potentials, using a small parameter which assumes a small bandwidth of the laser pulse. The derived fields are compared with those of the Lax series expansion and the complex-source-point approaches and are shown to be well-behaved and accurate even in the subcycle pulse regime. We further demonstrate that terms stemming from the scalar potential and due to a fast varying pulse envelope are non-negligible and may significantly influe…
Light's orbital angular momentum (OAM) with inherent mode orthogonality has been suggested as a new way to the optical encryption. However, the dependence of annular intensity profiles on the topological charge complicates nanoscale light-matter interactions and hampers the ultra-secure encryption application. In this paper, we demonstrate ultra-secure image encryption by tightly focusing perfect optical vortex (POV) beams with controllable annular intensity profiles and OAM states. A simple scheme composed of single spatial light modulator is proposed to generate radius-controllable POV in ti…
We report the first measurement with no approximations of the full field of tightly focused vector beams (NA up to $1.23$) across areas of $\sim 9-49\,λ^2$. Prior to focusing, the structured laser light has a linear or circular polarization state. The transverse components are extracted directly from 12 interferograms using 4 step interferometry, while the longitudinal component is extracted from the transverse fields with Gauss law. Different structured beams are measured to demonstrate that the method works for any field geometry. In the case of circular polarization we use vortex beams to v…
The performance of the knife-edge method as a beam profiling technique for tightly focused light beams depends on several parameters, such as the material and height of the knife-pad as well as the polarization and wavelength of the focused light beam under study. Here we demonstrate that the choice of the substrate the knife-pads are fabricated on has a crucial influence on the reconstructed beam projections as well. We employ an analytical model for the interaction of the knife-pad with the beam and report good agreement between our numerical and experimental results. Moreover, we simplify t…
We derive an asymptotically accurate formula for the beam waist of ultrashort, tightly-focused fundamental linearly-polarized, radially-polarized, and azimuthally-polarized modes in free space. We compute the exact beam waist via numerical cubature to ascertain the accuracy with which our formula approximates the exact beam waist over a broad range of parameters of practical interest. Based on this, we describe a method of choosing parameters in the model given the beam waist and pulse duration of a laser pulse.
The knife-edge method is an established technique for profiling of even tightly focused light beams. However the straightforward implementation of this method fails if the materials and geometry of the knife-edges are not chosen carefully or in particular if knife-edges are used that are made of pure materials. In these cases artifacts are introduced in the shape and position of the reconstructed beam profile due to the interaction of the light beam under study with the knife. Hence, corrections to the standard knife-edge evaluation method are required. Here we investigate the knife-edge metho…
Recently, it was shown that a non-zero transverse angular momentum manifests itself in a polarization dependent intensity shift of the barycenter of a paraxial light beam [A. Aiello et al., Phys. Rev. Lett. 103, 100401 (2009)]. The underlying effect is phenomenologically similar to the spin Hall effect of light, but does not depend on the specific light-matter interaction and can be interpreted as a purely geometric effect. Thus, it was named the geometric spin Hall effect of light. Here, we experimentally investigate the appearance of this effect in tightly focused vector-beams. We use an exp…
Efficient optical excitation of hybridized plasmon modes in nanoantennas is vital to achieve many promising functionalities, but it can be challenging due to a field-profile mismatch between the incident light and the hybrid mode. We present a general approach for efficient hybrid-mode excitation by focusing the incident light field in the basis of cylindrically polarized vector beams of various higher-order spiral phases. Such basis vector beams are described in the higher-order polarization states and Stokes parameters (both defined locally in polar coordinates), and visualized corresponding…
Analytic expressions for the fields of a radially polarized, ultrashort and tightly focused laser pulse propagating in a linear-response plasma are derived and discussed. The fields are obtained from solving the inhomogenous wave equations for the vector and scalar potentials, linked by the Lorenz gauge, in a plasma background. First the scalar potential is eliminated using the gauge condition, then the vector potential is synthesized from Fourier components of an initial uniform distribution of wavenumbers, and the inverse Fourier transformation is carried out term-by-term in a truncated seri…
Free electrons moving in an optical standing wave field feel the ponderomotive potential, acting as a refractive-index medium in electron optics. Emerging technologies involving this potential have been proposed and realized in electron microscopy, such as electron phase-contrast imaging using a laser standing wave in an optical enhancement cavity. However, the interaction between electrons with a cylindrically distributed optical field has not been investigated although its suitability for electron-optical imaging systems. In this study, we theoretically show that the divergence and convergen…
We study the modification of the far-field cross sections and the near-field enhancement for gold and silver nanospheres illuminated by a tightly focused beam. Using a multipole-expansion approach we obtain an analytical solution to the scattering problem and provide insight on the effects of focusing on the optical response. Large differences with respect to Mie theory are found especially when the nanoparticle supports quadrupole or higher-order resonances.
Exact closed-form solutions to Maxwell's equations are used to investigate electron acceleration driven by radially polarized laser beams in the nonparaxial and ultrashort pulse regime. Besides allowing for higher energy gains, such beams could generate synchronized counterpropagating electron bunches.
Investigation of laser matter interaction with electromagnetic codes requires to implement sources for the electromagnetic fields. A way to do so is to prescribe the fields at the numerical box boundaries in order to achieve the desired fields inside the numerical box. Here we show that the often used paraxial approximation can lead to unexpected field profiles with strong impact on the laser matter interaction results. We propose an efficient numerical algorithm to compute the required laser boundary conditions consistent with the Maxwell's equations for arbitrarily shaped, tightly focused la…
Spin-orbital coupling and interaction as intrinsic light fields characteristics have been extensively studied. Previous studies involve the spin angular momentum (SAM) carried by circular polarization and orbital angular momentum (OAM) associated with a spiral phase wavefront within the beam cross section, where both the SAM and OAM are in parallel with the propagation direction. In this work, we study a new type of spin-orbital coupling between the longitudinal SAM and the transverse OAM carried by a spatiotemporal optical vortex (STOV) wavepacket under tight focusing condition. Intricate spa…
In this work we present a simple code to calculate tightly focused vectorial light fields (propagating and evanescent) generated by input fields that have arbitrary amplitude, phase and polarization. The program considers results from previous studies, like integration via fast Fourier transforms to speed up the integration. The calculations are done in a Cartesian coordinate system that is convenient to compare with experimental results for beams that are shaped with programmable optical elements like spatial light modulators or digital micromirror arrays. We also discuss how to avoid divergi…
Highly confined vectorial electromagnetic field distributions represent an excellent tool for detailed studies in nano-optics and high resolution microscopy, such as nonlinear microscopy, advanced fluorescence imaging or nanoplasmonics. Such field distributions can be generated, for instance, by tight focussing of polarized light beams. To guarantee high quality and resolution in the investigation of objects with sub-wavelength dimensions, the precise knowledge of the spatial distribution of the exciting vectorial field is of utmost importance. Full-field reconstruction methods presented so fa…
The spin-orbit interaction (SOI) of light generated by tight focusing in optical tweezers has been regularly employed in generating angular momentum - both spin and orbital - in trapped mesoscopic particles. Specifically, the transverse spin angular momentum (TSAM), which arises due to the longitudinal component of the electromagnetic field generated by tight focusing, is of special interest, both in terms of fundamental studies and associated applications. We provide an effective and optimal strategy for generating TSAM in optical tweezers by tightly focusing radially and azimuthally polarize…
Recently, it was shown that vector beams can be utilized for fast kinematic sensing via measurements of their global polarization state [Optica 2(10), 864 (2015)]. The method relies on correlations between the spatial and polarization degrees of freedom of the illuminating field which result from its nonseparable mode structure. Here, we extend the method to the nonparaxial regime. We study experimentally and theoretically the far-field polarization state generated by the scattering of a dielectric microsphere in a tightly focused vector beam as a function of the particle position. Using polar…
Spin-orbit interaction (SOI) have provided a new viable roadmap for the development of spin-based photonics devices. However, existing strategies to control the SOI focus commonly on tailoring the spatial dimension of light fields yet neglecting the inherent temporal one. Herein, we first present ultrafast temporal effects on both spin-to-orbit and orbit-to-local-spin conversions based on the time-assistant vectorial diffractive theory and the fast Fourier transformation. Such interconversions depend upon whether the incident hybridly vectorial light pulse carries vortex phase or not in a sing…
We report on an experimental measurement of the pulse front tilt (PFT) of spatiotemporally focused femtosecond laser pulses in the focal plane in both air and bulk transparent materials, which is achieved by examination of the interference pattern between the spatiotemporally focused pulse and a conventional focused reference pulse as a function of time delay between the two pulses. Our simulation results agree well with the experimental observations.
We study two-photon scattering of a tightly focused weak light beam from a small atomic ensemble of two-level atoms (2LAs). This is similar to the scattering of photons from an atomic ensemble in a one-dimensional waveguide. The scaling of two-photon nonlinearity at single-photon resonance shows a non-monotonic behaviour with an increasing number of few identical 2LAs. The two-photon nonlinearity decays monotonically with an increasing number of atoms for incident photons detuned from single-photon resonance. Single-photon transport in two 2LAs is similar to that in a single V-type three-level…
Femtosecond laser micromachining provides high precision and less thermal diffusion in surface structuring as a result of the ultrashort temporal duration and ultrahigh peak intensity of the femtosecond laser pulses. To increase the throughput of surface patterning, the focal spot size can be expanded with loose focusing, which, however, could lead to nonlinear self-focusing of the pulses when the pulses propagate in air. We solve the problem by use of spatiotemporally focused femtosecond laser pulses for ablation of metal surfaces, which gives rise to improved surface quality as compared with…
We analytically and numerically investigate the propagation of ultrashort tightly focused laser pulses in vacuum, with particular emphasis on Hermite-Gaussian and Laguerre-Gaussian modes. We revisit the Lax series approach for forward-propagating linearly-polarized laser pulses, in order to obtain Maxwell-consistent and symmetry-preserving analytical solutions for the propagation of all field components beyond the paraxial approximation in four-dimensional geometry (space and time). We demonstrate that our solution conserves the energy, which is set by the paraxial-level term of the series. Th…
We report on experimental observations of formation and evolution of transient plasma produced in fused silica glass with spatiotemporally focused (STF) femtosecond laser pulses using a pump-probe shadow imaging technique. Surprisingly, the observation shows that the track of the plasma is significantly curved, which is attributed to an asymmetric density distribution of the transient plasma produced in the focal volume caused by the pulse front tilt of the STF laser field.
This paper presents intuitive interpretations of tightly focused beams of light by drawing analogies to two-dimensional electrostatics, magnetostatics and fluid dynamics. We use a Helmholtz decomposition of the transverse polarization components in the transverse plane to introduce generalized radial and azimuthal polarization states. This reveals the interplay between transverse and longitudinal polarization components in a transparent fashion. Our approach yields a comprehensive understanding of tightly focused laser beams, which we illustrate through several insightful examples.
Synchronising ultra-short (~fs) and focussed laser pulses is a particularly difficult task, as this timescale lies orders of magnitude below the typical range of fast electronic devices. Here we present an optical technique that allows for femtosecond-scale synchronisation of the focal planes of two focussed laser pulses. This technique is virtually applicable to any focussing geometry and relative intensity of the two lasers. Experimental implementation of this technique provides excellent quantitative agreement with theoretical expectations. The proposed technique will prove highly beneficia…
Precise knowledge of the behaviour of the phase of light in a focused beam is fundamental to understanding and controlling laser-driven processes. More than a hundred years ago an axial phase anomaly for focused monochromatic light beams was discovered and is now commonly known as the Gouy phase. Recent theoretical work has brought into question the validity of applying this monochromatic phase formulation to the broadband pulses becoming ubiquitous today. Based on electron back-scattering at sharp nanometre-scale metal tips, a method is available to measure light fields with sub-wavelength sp…
Optically pumped InAs quantum dot microdisk lasers with grooves etched on their surface by a focused ion beam is studied. It is shown that the radial grooves, depending on their length, suppress the lasing of specific radial modes of the microdisk. Total suppression of all radial modes except for the fundamental radial one is also demonstrated. The comparison of laser spectra measured at 78 K before and after ion beam etching for microdisk of 8 $μ$m in diameter shows a six-fold increase of mode spacing, from 2.5 nm to 15.5 nm, without significant decrease of the dominant mode quality factor. N…
Photonic integrated circuits are indispensible for data transmission within modern datacenters and pervade into multiple application spheres traditionally limited for bulk optics, such as LiDAR and biosensing. Of particular interest are ferroelectrics such as Lithium Niobate, which exhibit a large electro-optical Pockels effect enabling ultrafast and efficient modulation, but are difficult to process via dry etching . For this reason, etching tightly confining waveguides - routinely achieved in silicon or silicon nitride - has not been possible. Diamond-like carbon (DLC) was discovered in the …
When an ultrashort laser pulse is tightly focused to a size approaching its central wavelength, the properties of the focused spot diverge from the diffraction limited case. Here we report on this change in behavior of a tightly focused Petawatt class laser beam by an F/1 off-axis paraboloid (OAP). Considering the effects of residual aberration, the spatial profile of the near field and pointing error, we estimate the deviation in peak intensities of the focused spot from the ideal case. We verify that the estimated peak intensity values are within an acceptable error range of the measured val…
InGaAsP/InP quantum wells (QW) ridge waveguide lasers were fabricated for the evaluation of Ga+ Focused Ion Beam (FIB) milling of mirrors. Electrical and optical proprieties were investigated. A 7% increment in threshold current, a 17% reduction in external quantum efficiency and 15 nm blue shift in the emission spectrum were observed after milling as compared to the as cleaved facet result. Annealing in inert atmosphere partially revert these effects resulting in 4% increment in threshold current, 11% reduction in external efficiency and 13 nm blue shift with the as cleaved result. The curren…
The Stratton-Chu integral representation of electromagnetic fields is used to study the spatio-temporal properties of large bandwidth laser pulses focused by high numerical aperture mirrors. We review the formal aspects of the derivation of diffraction integrals from the Stratton-Chu representation and discuss the use of the Hadamard finite part in the derivation of the physical optics approximation. By analyzing the formulation we show that, for the specific case of a parabolic mirror, the integrands involved in the description of the reflected field near the focal spot do not possess the str…
The optical forces in optical tweezers can be robustly modeled over a broad range of parameters using generalsed Lorenz-Mie theory. We describe the procedure, and show how the combination of experimental measurement of properties of the trap coupled with computational modeling, can allow unknown parameters of the particle - in this case, the refractive index - to be determined.
We numerically investigate the conical emission (CE) from ultrashort laser filaments, both considering and disregarding the higher-order Kerr effect (HOKE). While the consideration of HOKE has almost no influence on the predicted CE from collimated beams, differences arise for tightly focused beams. This difference is attributed to the different relative contributions of the non-linear focus and of the modulational instability over the whole filament length.
The principle of optical trapping is conventionally based on the interaction of optical fields with linear induced polarizations. However, the optical force originating from the nonlinear polarization becomes significant when nonlinear optical nanoparticles are trapped by ultrafast laser pulses. Herein we establish the time-averaged optical forces on a nonlinear optical nanoparticle using high-repetition-rate ultrafast laser pulses, based on the linear and nonlinear polarization effects. We investigate the dependence of the optical forces on the magnitudes and signs of the refractive nonlinear…
We present a new class of exact nonsingular solutions for the Maxwell equations in vacuum, which describe the electromagnetic field of the counterpropagating focused laser beams and the subperiod focused laser pulse. These solutions are derived by the use of a modification of the "complex source method", investigated and visualized.
In this paper, focal shift of a Guassian laser beam tightly focused through several planar dielectric interfaces is discussed. It is shown that the focal shift and focus point can be changed by variation of refractive index mismatch and this shift could be positive or negative, and it is proportional to refractive index mismatch between coverglass and immersion medium. It is shown also that for every immersion medium(coverglass), focal shift could be removed for a continuous range of depths by choosing a coverglass (immersion medium) with appropriate refractive index.
In-bulk processing of materials by laser radiation has largely evolved over the last decades and still opensup new scientific and industrial potentials. The development of any in-bulk processing application relieson the knowledge of laser propagation and especially the volumetric field distribution near the focus.Many commercial programs can simulate this, but, in order to adapt them, or to develop new methods,one usually needs to create a specific software. Besides, most of the time people also need to measurethe actual field distribution near the focus to evaluate their assumptions in the si…
We propose a free-space, inverse design of nanostructure's effective mode-matching fields via a backward propagation of tightly focused vector beams to the pupil plane of an aplanatic system of high numerical aperture. First, we study the nanostructure's eigenmodes without considering any excitation fields and then extract the modal near fields in the focal plane. Each modal field is then taken as the desired focal field, the band-limited waves of which are backward propagated to the pupil plane via a reversal of the Richards--Wolf vector diffraction formula. The pupil fields can be designed t…
We use paramagnetic Faraday rotation to study spin noise spectrum from unpolarized Rb vapor in a tightly focused probe beam in the presence of N$_2$ buffer gas. We derive an analytical form for the diffusion component of the spin noise time-correlation function in a Gaussian probe beam. We also obtain analytical forms for the frequency spectrum of the spin noise in the limit of a tightly focused or a collimated Gaussian beam in the presence of diffusion. In particular, we find that in a tightly focused probe beam the spectral lineshape can be independent of the buffer gas pressure. Experimenta…
Bessel beams carry orbital angular momentum (OAM). Opening up of the Hilbert space of OAM for information coding makes Bessel beams potential candidates for utility in data transfer and optical communication. A laser bullet is the ultra-short and tightly-focused analogue of a non-diffracting and non-dispersing laser Bessel beam. Here, we show fully analytically that a Bessel-Bessel laser bullet possesses orbital angular momentum. Analytic investigation of the energy, linear momentum, energy flux, and angular momentum, associated with the fields of a Bessel-Bessel bullet, in an under-dense plas…
We present a detailed study of the fields and propagation characteristics around the focus of ultrashort radially-polarized laser beams (RPLBs) having low-order spatio-temporal couplings (STCs). The three STCs considered are the focusing of the different frequencies to different positions along the longitudinal coordinate, the focusing of the frequencies to different positions along one transverse coordinate, and the beam waist or Rayleigh range having a power-law frequency dependence. The STCs considered are deemed low-order because they are generally linear in frequency. The combination of a…
