Ultrashort Laguerre-Gaussian pulses with angular and group velocity dispersion compensation

Wavefront control of subcycle vortex pulses via carrier-envelope-phase tailoring

The carrier-envelope phase (CEP) of an ultrashort laser pulse is becoming more crucial to specify the temporal characteristic of the pulse's electric field when the pulse duration becomes shorter and attains the subcycle regime; here, the pulse duration of the intensity envelope is shorter than one cycle period of the carrier field oscillation. When this subcycle pulse involves a structured wavefront as is contained in an optical vortex (OV) pulse, the CEP has an impact on not only the temporal but also the spatial characteristics owing to the spatiotemporal coupling in the structured optical pulse. However, the direct observation of the spatial effect of the CEP control has not yet been demonstrated. In this study, we report on the measurement and control of the spatial wavefront of a subcycle OV pulse by adjusting the CEP. To generate subcycle OV pulses, an optical parametric amplifier delivering subcycle Gaussian pulses and a Sagnac interferometer as a mode converter were integrated and provided an adequate spectral adaptability. The pulse duration of the generated OV pulse was 4.7 fs at a carrier wavelength of 1.54 µm. To confirm the wavefront control with the alteration of the CEP, we developed a novel [Formula: see text]-2[Formula: see text] interferometer that exhibited spiral fringes originating from the spatial interference between the subcycle OV pulse and the second harmonic of the subcycle Gaussian pulse producing a parabolic wavefront as a reference; this resulted in the successful observation of the rotation of spiral interference fringes during CEP manipulation.

High-order femtosecond vortices up to the 30th order generated from a powerful mode-locked Hermite-Gaussian laser

Femtosecond vortex beams are of great scientific and practical interest because of their unique phase properties in both the longitudinal and transverse modes, enabling multi-dimensional quantum control of light fields. Until now, generating femtosecond vortex beams for applications that simultaneously require ultrashort pulse duration, high power, high vortex order, and a low cost and compact laser source has been very challenging due to the limitations of available generation methods. Here, we present a compact apparatus that generates powerful high-order femtosecond vortex pulses via astigmatic mode conversion from a mode-locked Hermite-Gaussian Yb:KGW laser oscillator in a hybrid scheme using both the translation-based off-axis pumping and the angle-based non-collinear pumping techniques. This hybrid scheme enables the generation of femtosecond vortices with a continuously tunable vortex order from the 1st up to the 30th order, which is the highest order obtained from any femtosecond vortex laser source based on a mode-locked oscillator. The average powers and pulse durations of all resulting vortex pulses are several hundred milliwatts and <650 fs, respectively. In particular, 424-fs 11th-order vortex pulses have been achieved with an average power of 1.6 W, several times more powerful than state-of-the-art oscillator-based femtosecond vortex sources.

Generation of spatiotemporal optical vortices in ultrashort laser pulses using rotationally interleaved multispirals

Ultrashort optical vortex pulses carrying spatiotemporal orbital angular momentum (OAM) have inspired versatile applications such as the micromachining of integrated quantum chips and discoveries such as optical toroidal structures and OAM-carrying X-waves. Generating high-quality ultrashort vortices with controllable topological charges remains a crucial issue. Thus, we propose a rotationally interleaved multispiral to generate such vortices. A multispiral comprises multiple identical spirals rotated around the center in the equal-azimuthal interval and interleaved in equal-radius increments; this structure overcomes the previous structural asymmetry of the single spiral and improves the vortex quality. Accordingly, we conducted theoretical analyses, numerical simulations, and experimental investigations that demonstrated the feasibility of multispirals in generating the ultrashort vortices with symmetric distributions and flexibly controlling the topological charges. The proposed study is significant for broader applications involving ultrashort vortices and extensive investigations in related areas such as research on electron vortices, plasmonic vortices, and other matter vortices.

Angular dispersion compensation for ultra-broadband pulses by using a cascaded prism and hollow-core fiber configuration

In this paper, we report that the angular dispersion of the output pulses in a nonlinear process can be efficiently compensated by using a cascaded prism(s) and short hollow-core fiber (HCF) configuration. Here, the prism(s) is used to suppress the angular dispersion and transform it into spatial chirp, while the HCF is used for removing this spatial chirp and the residual angular dispersion, which can also significantly improve the beam quality. The feasibility of this novel method is numerically and experimentally investigated with the ultra-broadband idler pulses centered at 1250 nm wavelength and generated by an LBO crystal based non-collinear optical parametric amplifier. The proof-of-principle experiment shows that the angular dispersion can be effectively removed and ultra-broadband idler pulses with good spectral quality and spatial profile can be obtained. The total transmission efficiency in the experiment is around 67% and the measured M x2 and M y2 can reach 1.12 and 1.04, respectively. To the best of our knowledge, this is the first reported ultra-broadband angular dispersion compensation scheme combining prism(s) and HCF, which can remarkably eliminate the angular dispersion while simultaneously possesses high efficiency, good spectral and beam spatial quality.

Effects of the Coupling between the Orbital Angular Momentum and the Temporal Degrees of Freedom in the Most Intense Ring of Ultrafast Vortices

It has recently been shown that the temporal and the orbital angular momentum (OAM) degrees of freedom in ultrafast (few-cycle) vortices are coupled. This coupling manifests itself with different effects in different parts of the vortex, as has been shown for the ring surrounding the vortex where the pulse energy is maximum, and also in the immediate vicinity of the vortex center. However, in many applications, the ring of maximum energy is not of primary interest, but the one where the peak intensity of the pulse is maximum, which is particularly true in nonlinear optics applications such as experiments with ultrafast vortices that excite high harmonics and attosecond pulses that also carry OAM. In this paper, the effects of the OAM-temporal coupling on the ring of maximum pulse peak intensity, which do not always coincide with the ring of maximum pulse energy, are described. We find that there is an upper limit to the magnitude of the topological charge that an ultrafast vortex with a prescribed pulse shape in its most intense ring can carry, and vice versa, a lower limit to the pulse duration in the most intense ring for a given magnitude of the topological charge. These limits imply that, with a given laser source spectrum, the duration of the synthesized ultrafast vortex increases with the magnitude of the topological charge. Explicit analytical expressions are given for the ultrafast vortices that contain these OAM-temporal couplings effects, which may be of interest in various applications, in particular in the study of their propagation and interaction with matter.

Fractional vortex ultrashort pulsed beams with modulating vortex strength

In most papers about the fractional vortex continuous beams (FVCBs), the relationship between the total vortex strength S_α and the propagation distance is not analyzed since the vortex structure is not stable in the near field. In this paper, we theoretically study the fractional vortex ultrashort pulsed beams (FVUPBs) possessing non-integer topological charges α at arbitrary plane and find that the vortex structure is propagation-distance-dependent. Both the intensity and phase distributions are calculated to analyze the vortex structure. To evaluate the propagation properties of FVUPBs, we focus on the total vortex strength (TVS) of FVUPBs to investigate the number of vortex, and demonstrate that the birth of a vortex is at α = m + ɛ, where m is an integer, ɛ is a changing fraction depending on the pulse durations, peak wavelengths and propagation distances. Furthermore, we discover that the FVUPBs carry decreasing TVS along the propagation axis in free space. This special vortex structure for FVUPBs appears due to the mixture weight of vortex pulsed beam with different integer topological charges (TCs) n. However, the total orbital angular momentum is invariant during propagation. The above phenomenon presented in our paper are totally particular and intriguing compared with the FVCBs.

Comprehensive quantitative analysis of vector beam states based on vector field reconstruction

We demonstrate a comprehensive quantitative analysis of vector beam states (VBSs) by using a vector field reconstruction (VFR) technique integrating interferometry and imaging polarimetry, where the analysis is given by a cylindrically polarized Laguerre-Gaussian (LG) mode expansion of VBSs. From test examples of cylindrically polarized LG mode beams, we obtain the complex amplitude distributions of VBSs and perform their quantitative evaluations both in radial and azimuthal directions. The results show that we generated (l, p) = (1, 0) LG radially polarized state with a high purity of 98%. We also argue that the cylindrically polarized LG modal decomposition is meaningful for the detail discussion of experimental results, such as analyses of mode purities and mode contaminations. Thus the VFR technique is significant for analyses of polarization structured beams generated by lasers and converters.

Effects of orbital angular momentum on few-cycle and sub-cycle pulse shapes: coupling between the temporal and angular momentum degrees of freedom

We describe the effects of the coupling between the orbital angular momentum (OAM) and the temporal degrees of freedom in pulsed Laguerre-Gauss beams as a significant increase of the duration of few-cycle pulses when the OAM carried by the pulse is large, and as an enhancement to other previously known spatiotemporal couplings as radial red- and blue-shift of the mean frequency. In contrast to other detrimental, but retrievable, effects in the generation and propagation of ultrashort vortices such as spatial, group velocity, and topological charge dispersions, the OAM-temporal coupling effect is unavoidable and, therefore, has an impact on applications such as OAM-based optical communications, or on the generation of vortex-carrying attosecond pulses.

Upper Bound to the Orbital Angular Momentum Carried by an Ultrashort Pulse

Photons in a ring-shaped vortex light beam can have an arbitrarily high orbital angular momentum (OAM) lℏ, in addition to the spin angular momentum ±ℏ. For a pulsed vortex beam, there is, however, an upper bound to the integer units l of OAM, or topological charge of the vortex, and a lower bound to the pulse duration to carry OAM. These limits have implications in experiments with ultrashort vortices, e.g., in the generation of twisted attosecond bursts in the extreme ultraviolet, in the temporal resolution in ultrafast spectroscopy, or in the performance of OAM-based optical communications or cryptographic systems, as well as in other areas of physics as acoustics or electron waves.

Temporally shaped Laguerre-Gaussian femtosecond laser beams

Femtosecond vortex beams with adjustable temporal pulse shapes are generated. These shaped laser pulses are characterized in the spectral domain by determination of the spectral amplitude and phase as well as in the spatial domain by expansion of the beam profile in a superposition of Laguerre-Gaussian transversal laser modes. The experiments demonstrate that the temporal pulse shapes impressed with a pulse shaper based on a programmable liquid-crystal spatial light modulator are basically unaltered by subsequent transmission through a spiral phase plate, while a high-quality optical vortex is imposed. The combination of programmable pulse shapes and optical vortices in femtosecond laser beams opens new possibilities for applications in micromachining, high harmonic generation, and microscopy.

Generation of arbitrary axisymmetrically polarized pulses by using the combination of 4-f spatial light modulator and common-path optical system

We proposed and constructed a system to realize broadband generation of arbitrary axisymmetrically polarized (AP) pulses with spatial complex amplitude modulation. This system employs the combination of a spatial light modulator in the 4-f configuration (4-f SLM), and a space variant wave plate as a common path interferometer. The 4-f SLM and the common path interferometer offer compensation for spatial dispersion with respect to wavelength and stability to perturbation, respectively. We experimentally demonstrated the various AP pulses generation by applying modulations of fundamental and higher-order Laguerre-Gauss modes, whose radial indices were, respectively, p = 0 and 1, with high purity, which showed that we were able to generate arbitral AP pulses with spatial complex amplitude modulation. This technique is expected to be applied in both classical and quantum communications with higher-order modes.

Focused apodized forked grating coupler

The forked grating coupler (FGC) is an optical vortex interface for silicon photonics. Using the structure of a Bragg grating coupler with a calculated forked hologram, the FGC couples optical vortex modes into confined waveguide modes of a photonic integrated circuit. Design methodologies are given, as well as measured performance data from fabricated devices. Data are analyzed with a variety of metrics. The effectiveness of design features are evaluated. Advanced FGC designs are demonstrated with focused forked gratings, allowing feed length to be reduced, and with apodization improving vortex mode fidelity. Some configurations achieve over 25 dB multiplexing crosstalk isolation.

Spectral anomalies and Gouy rotation around the singularity of ultrashort vortex pulses

Spectral anomalies of femtosecond pulses with orbital angular momentum were studied in the vicinity of singularities. Bessel-Gauss (BG) beams were generated with mode-locked Ti:sapphire oscillators and dispersion-compensated diffractive axicons acting as spiral phase plates (SPPs). High-resolution two-dimensional spectral mapping was performed with a scanning fiber probe. Progressive rotation of the most pronounced features, known as "spectral eyes", in the maps of spectral moments was found at increasing propagation distance. The phenomenon is explained by a wavelength-dependent Gouy phase shift of interfering spectral components in the twisted wavefront. Spatial "spectral switching" was detected for few-cycle pulses. Possible improvements of selectivity are proposed.

Ultraclean femtosecond vortices from a tunable high-order transverse-mode femtosecond laser

Femtosecond optical vortices open a variety of fascinating applications, ranging from femtosecond micro-nano manipulation to vortex strong-field physics. A basic requirement for these applications is that the femtosecond vortex has a clean intensity node for capturing or trapping particles. Thus far, the generation of clean femtosecond vortices remains a challenge. Here, we report on ultraclean femtosecond vortex generation by a femtosecond mode-locked laser operating in a single high-order transverse mode. By controlling the oscillation thresholds of various-order transverse modes in a laser, a pure and mode-order-tunable femtosecond Hermite-Gaussian beam is generated from the mode-locked laser and, subsequently, is converted into the femtosecond vortex by a cylindrical lens mode converter. The obtained femtosecond vortex has an unprecedented ring-to-center intensity contrast of 36 dB measured with a near wavelength-spatial-resolution detecting device, which approaches the theoretical limit of an ideal vortex beam. This Letter may open a wide range of application prospects for femtosecond vortices and motivate novel femtosecond structured beam generation directly from mode-locked lasers.

Ultrashort vortex from a Gaussian pulse - An achromatic-interferometric approach

The more than a century old Sagnac interferometer is put to first of its kind use to generate an achromatic single-charge vortex equivalent to a Laguerre-Gaussian beam possessing orbital angular momentum (OAM). The interference of counter-propagating polychromatic Gaussian beams of beam waist ω_λ with correlated linear phase (ϕ₀ ≥ 0.025 λ) and lateral shear (y₀ ≥ 0.05 ω_λ) in orthogonal directions is shown to create a vortex phase distribution around the null interference. Using a wavelength-tunable continuous-wave laser the entire range of visible wavelengths is shown to satisfy the condition for vortex generation to achieve a highly stable white-light vortex with excellent propagation integrity. The application capablitiy of the proposed scheme is demonstrated by generating ultrashort optical vortex pulses, its nonlinear frequency conversion and transforming them to vector pulses. We believe that our scheme for generating robust achromatic vortex (implemented with only mirrors and a beam-splitter) pulses in the femtosecond regime, with no conceivable spectral-temporal range and peak-power limitations, can have significant advantages for a variety of applications.

Conical third-harmonic generation of optical vortex through ultrashort laser filamentation in air

We experimentally generate third-harmonic (TH) vortex beams in air by the filamentation of femtosecond pulses produced in a lab-built Ti:sapphire chirped pulse amplifier. The generated TH beam profile is shown to evolve with increasing pump energy. At a sufficiently high pump energy, we observe a conical TH emission of the fundamental vortex and confirm that the conical radiation follows the conservation law for orbital angular momentum. We further investigate the far-field angularly resolved spectra of the TH wave to analyze the conical emission angle. We theoretically verify that the formation of the conical TH vortex results from the phase-matching between the fundamental and TH waves during the filamentation process.

Full Quantitative Analysis of Arbitrary Cylindrically Polarized Pulses by Using Extended Stokes Parameters

Cylindrically polarized (CP) modes are laser beam modes which have rotational symmetry of the polarization distribution around the beam axis. Considerable attention has been paid to CP modes for their various applications. In this paper, by using the extended Stokes parameters and the degree of polarization defined for the spatial distribution (DOP-SD), we fully-quantitatively characterize the spectrally-resolved polarization states of arbitrary CP (axisymmetrically polarized and higher-order cylindrically polarized) broadband pulses generated by coherent beam combining. All the generated pulse states were fully-quantitatively analyzed for the first time and proved to have high symmetry (DOP-SD ≳ 0.95) and low spectral dependence of polarization states. Moreover, we show the DOP-SD, which cannot be defined by the conventional higher-order and hybrid Stokes parameters, enables us to make a quantitative evaluation of small degradation of rotational symmetry of polarization distribution. This quantitative characterization with high precision is significant for applications of precise material processing, quantum information processing, magneto-optical storage and nonlinear spectroscopic polarimetry.

Spatio-temporal light springs: extended encoding of orbital angular momentum in ultrashort pulses

We introduce a new class of spatio-temporally coupled ultrashort laser beams, which are obtained by superimposing Laguerre-Gauss beams whose azimuthal mode index is correlated to their frequency. These beams are characterized by helical structures for their phase and intensity profiles, which both encode the orbital angular momentum carried by the light. They can easily be engineered in the optical range, and are naturally produced at shorter wavelengths when attosecond pulses are generated by intense femtosecond Laguerre-Gauss laser beams. These spatio-temporal "light springs" will allow for the transfer of the orbital angular momentum to matter by stimulated Raman scattering.

Refractive-diffractive dispersion compensation for optical vortex beams with ultrashort pulse durations

Wave fields, which are described mathematically by higher order Bessel functions, carry an orbital angular momentum and thus represent particular types of optical vortex beams with helical wavefronts. For the generation of such vortex beams, one may use, for instance, diffractive spiral axicons. Diffraction, however, leads invariably to strong dispersion, which is detrimental for ultrashort pulses since it leads to severe pulse broadening. This pulse broadening can be minimized or reduced completely (at least, in a specific plane of propagation) if the pulses propagate additionally through a medium with normal refractive dispersion. The refractive-diffractive generation of ultrashort vortex pulses was demonstrated earlier for a pulse duration of approximately 8 fs [Opt. Lett.37, 3804 (2012)10.1364/OL.37.003804OPLEDP0146-9592]. Here, we present an analytical description of the generation and propagation of these vortex beams and of the refractive-diffractive compensation of the dispersion.

Vortex algebra by multiply cascaded four-wave mixing of femtosecond optical beams

Experiments performed with different vortex pump beams show for the first time the algebra of the vortex topological charge cascade, that evolves in the process of nonlinear wave mixing of optical vortex beams in Kerr media due to competition of four-wave mixing with self-and cross-phase modulation. This leads to the coherent generation of complex singular beams within a spectral bandwidth larger than 200nm. Our experimental results are in good agreement with frequency-domain numerical calculations that describe the newly generated spectral satellites.

Few-cycle high-contrast vortex pulses

Few-cycle high-contrast vortex beams with pulse durations around 8 fs were generated from a Ti:sapphire laser oscillator with a single diffractive-refractive component. Angular and temporal pulse properties were characterized with an advanced time-wavefront sensor. The temporal transfer indicates a fairly complete self-compensation.

Ultrashort optical-vortex pulse generation in few-cycle regime

We generated a 2.3-cycle, 5.9-fs, 56-μJ ultrashort optical-vortex pulse (ranging from ~650 to ~950 nm) in few-cycle regime, by optical parametric amplification. It was performed even by using passive elements (a pair of prisms and chirped mirrors) for chirp compensation. Spectrally-resolved interferograms and intensity profiles showed that the obtained pulses have no spatial or topological-charge dispersion during the amplification process. To the best of our knowledge, it is the first generation of optical-vortex pulses in few-cycle regime. They can be powerful tools for ultrabroadband and/or ultrafast spectroscopy and experiments of high-intensity field physics.

In situ tomography of femtosecond optical beams with a holographic knife-edge

We present an in situ beam characterization technique to analyze femtosecond optical beams in a folded version of a 2f-2f setup. This technique makes use of a two-dimensional spatial light modulator (SLM) to holographically redirect radiation between different diffraction orders. This manipulation of light between diffraction orders is carried out locally within the beam. Because SLMs can withstand intensities of up to I ∼ 10(11) W/cm2, this makes them suitable for amplified femtosecond radiation. The flexibility of the SLM was demonstrated by producing a diverse assortment of "soft apertures" that are mechanically difficult or impossible to reproduce. We test our method by holographically knife-edging and tomographically reconstructing both continuous wave and broadband radiation in transverse optical modes.

Generation of femtosecond paraxial beams with arbitrary spatial distribution

We present an approach to generate paraxial laser beams with arbitrary spatial distribution in the femtosecond time regime. The proposed technique is based upon a pair of volume phase holographic gratings working in parallel arrangement. It exploits the spatial coherence properties of the incoming laser beam in a compact and robust setup that mitigates angular and spatial chirp. The gratings were recorded in a photopolymerizable glass with a high optical damage threshold and a large optical throughput. Setup performance is studied and experimentally demonstrated by generating Laguerre-Gaussian femtosecond pulses.

Generalization of helicoidal beams for short pulses

A generalization to the transient regime is developed for waves with a phase singularity of the screw type. These singular waves are commonly called vortices for all kind of waves as, for instance, optical vortex or acoustical vortex. We generalize the definition of vortices to get an azimuthal velocity invariant for all the frequency components contained in the broad spectrum of a short pulse. This generalization leads to a modification of the orbital angular momentum definition. Another generalization is introduced by considering helicoidal waves with a finite number of turns. We demonstrate that, in this last case, the topological charge is no longer an integer. This provides a physical interpretation to vortices of fractional charge that are involved here to take into account the diffraction occurring at both tips of the now finite helical wave front. We show that shortening the pulse implies an angular localization of the wave energy and, as a consequence, a spreading of the angular momentum amplitude due to the uncertainty principle.

Supercontinuum optical vortex pulse generation without spatial or topological-charge dispersion

A new achromatic method to generate the optical vortex was proposed and supercontinuum optical vortex generation ranging approximately 500 to approximately 800 nm was experimentally demonstrated without spatial nor topological-charge dispersions. In addition, polarization evolution in our system using Jones vectors and matrices was discussed and the condition of the polarizer to transfer polarizations was elucidated. This method is useful for the application to time-resolved nonlinear spectroscopy utilizing ultrabroadband optical vortex pulses in topological materials such as ring-shaped crystals or annular materials.

Dispersion-compensating beam shaper for femtosecond optical vortex beams

A beam shaper suitable for sub-20 fs pulses based on a prism pair and a computer-generated hologram was developed to produce vortex beams. Comparatively high throughput and the ability to tune the group-velocity dispersion make this shaper suitable for pulses from femtosecond oscillators and amplifiers and where there is a need for additional postchirp or prechirp compensation.