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We experimentally demonstrate that 2D Airy wave packets can produce intense curved two-color filaments that emit terahertz (THz) radiation with unique characteristics. Due to the curvature of the plasma channel, THz waves, emitted from different longitudinal regions of the plasma, propagate in different directions resulting in non-concentric THz cones in the far-field. These cones have different cone angles and polarization which we attribute to the way the two-color 2D Airy driving fields are produced in the nonlinear crystal and then propagate to form the curved plasma filament.

Optics manufacturing technology is predicted to play a major role in the future production of integrated photonic circuits. One of the major drawbacks in the realization of photonic circuits is the damage of optical materials by intense laser pulses. Here, we report on the preparation of a series of organic–inorganic hybrid photoresists that exhibit enhanced laser-induced damage threshold. These photoresists showed to be candidates for the fabrication of micro-optical elements (MOEs) using three-dimensional multiphoton lithography. Moreover, they demonstrate pattern ability by nanoimprint lithography, making them suitable for future mass production of MOEs.

Tornado waves (ToWs) [1] were recently introduced theoretically as a new type of structured light that twists and accelerate both over the radial and the angular dimensions. Tornado waves are comprised by superimposing cylindrically symmetric accelerating beams [2] , [3] , often referred as circular Airy beams (CAB) or ring-Airy beams that carry orbital angular momentum (OAM) of opposite helicity [4] , [5] . In this work we report on the experimental observation of Tornado Waves and demonstrate their unique spatio-angular acceleration property. To generate such waves we used a single phase modulation device (SLM) and applied spatial multiplexing techniques to generate superimposing accelerating waves carrying OAM of opposite handedness [1] . For each of the superimposed fields a phase mask was designed following an approach similar to [6] , [7] .

Two-color laser filamentation constitute one of the most convenient and efficient sources of pulsed ultra-broadband terahertz (THz) radiation. In this approach, a Gaussian ultrashort laser pulse together with its second harmonic are focused into a gas medium, forming a filament, which emits THz radiation with extremely high THz electric and magnetic fields [1] . A major advantage of two-color filamentation is that one can tune the emitted THz radiation in terms of energy, spectrum, polarization and THz beam divergence by properly tailoring the filament itself [2] , [3] . One way to achieve this tailoring is with the use of robust exotic-wavepackets from the family of accelerating beams such as the ring-Airy and the 2D Airy beams. Two-color plasma channels induced by pre-engineered abruptly autofocusing ring-Airy beams have already been proposed in order to enhance the THz yield by 5.3 times compared to a Gaussian-beam-induced plasma [4] .

We report on THz generation from curved filaments produced by 2D Airy wave packets. Due to the curvature of the plasma channel, non-concentric THz beams with different polarizations are generated.

We experimentally generate Tornado Waves using a single phase modulation device. We show that, by applying spatial multiplexing techniques, such complex superimposing fields that carry orbital angular momentum of opposite handedness can be efficiently generated.

Nanoimprint lithography (NIL) is a technique suitable for the mass production of micro-optical elements using a mould. One drawback, however, is that the materials used in NIL have low laser-induced damage threshold (LIDT). Here, we present our results in the development of a series of high-LIDT organic-inorganic hybrid materials, and their application in NIL using moulds made by multiphoton lithography.

We present the theoretical analysis of a novel optical beam steering technique (OBST) for fiber to free-space to fiber coupling schemes on optical breadboards. This technique uses glass wedges and plates to correct misalignments in the position and angle of beams on the breadboard. It can be used in any application where stable and robust coupling of light from an input to an output fiber is required, such as laser distribution boards for cold atom experiments in space. We examine the optical performance in terms of coupling efficiency (CE) for a number of different OBST systems and compare the results. Coupling efficiencies above 95% and positional and angular resolution of smaller than 5 μm and 5 μrad can be achieved using this technology.

We present a novel optical beam steering technique (OBST) for fiber to free-space to fiber coupling schemes on optical breadboards, which uses glass wedge pairs and plates to correct for angular and translational misalignments respectively. This technique finds application in proposed missions for atom quantum experiments in space, e.g. where laser beams are used to cool and manipulate atomic clouds. The key advantage compared to the conventional beam steering is that OBST permits extremely fine adjustments whilst being far less sensitive to alignment errors and mechanical drifts. Beam steering resolutions of better than 5 μrad and 2 μm are achieved, resulting in a resolution in coupling efficiency (CE) of 0.1%. The inclusion of OBST on an optical breadboard reduces the requirements on the pointing and position precision adjustment of the fiber couplers, leading to a much-simplified design. The simpler construction of the couplers combined with the reduced sensitivity to drifts increases the stability-reliability of the breadboard and reduces the production duration and cost. We demonstrate CE of up to 90%, with a stability of 0.2% in a stable temperature environment and 2% over a temperature range from 10-40 degrees Celsius. We do not observe any change in the performance after large temperature changes.

Optical wave packets are often used as means of energy delivery on a remote target in various applications. The use of shaped optical wave packets can, in principle, enable us to control the intensity distribution and the focus position in the linear and the non-linear propagation regimes. An ideal template for this tailored control is the recently introduced family of cylindrically symmetric accelerating beams [1,2], often referred as circular Airy (CAB) or ring-Airy beams. These wave packets propagate in curved trajectories, exhibit abrupt auto-focus, while at high intensities they reshape into nonlinear intense light-bullets with extremely well defined focal position [3].

Generation of ultra-broadband beams with a non-trivial wave-front is a major challenge [1,2]. Such beams are of interest in many fields ranging from bio-medical applications to materials processing and optical telecommunications. Recently a novel type of accelerating, non diffracting beams where the distribution is described by an Airy function, was introduced [3,4]. In order to generate such complex beams, a Gaussian beam is spatially shaped by imprinting a cubic phase [3]. Usually this is performed by using a phase spatial light modulator (SLM) which although tunable it lucks in spectral bandwidth and intensity threshold.

In laser material processing optical wave packets are used as means to efficiently deliver energy on a remote target. The scalability both in power and focal dimensions is an important problem in such applications. For example, higher powers ignite nonlinear propagation effects that dynamically reshape the wave packet [1]. Likewise, diffraction dominates when the focal voxel dimensions become comparable to the wavelength [2].

By superimposing vortex ring-Airy beams of opposite handedness spiral accelerating optical wave-packets are generated. The superimposed beams are tuned to abruptly auto-focus at overlapping focal regions while following distinct trajectories.

We theoretically study the evolution of ring-Airy beams during harmonic generation with the focus on the regime of pump energy depletion. We demonstrate that in this regime, ring-Airy beams still preserve their abrupt autofocusing properties, while transforming to a multiple ring-Airy structure. A similar transformation is observed on the beam of the generated harmonic. We suggest a simple analytical model that explains and predicts with precision our numerical findings.

We show that through the use of optical aberrations, a reflective cylindrical beam expander can be properly adjusted to perform as a tunable ultra-broadband continuous phase modulation device. We demonstrate the effectiveness of such a device for the case of a net cubic phase modulation that is used to generate ultra-broadband white light 2D Airy beams. In this case, the nature of our device enables all spectral components to copropagate, following the same accelerating trajectory. The scalability of our approach, both in respect of input power and bandwidth, makes it possible to be used in any part of the electromagnetic spectrum.

We demonstrate both theoretically and experimentally that the harmonics from abruptly auto-focusing ring-Airy beams present a surprising property, they preserve the phase distribution of the fundamental beam. Consequently, this "phase memory" inherits to the harmonics the abrupt autofocusing behavior, while, under certain conditions, their foci coincide in space with the one of the fundamental. Experiments agree well with our theoretical estimates and detailed numerical calculations. Our findings open the way for the use of such beams and their harmonics in strong field science., Comment: 5 pages, 6 figures

In this paper, we compare two well-established techniques, namely the BASEX and the Fourier–Hankel, as regards their efficiency of retrieving the three-dimensional distribution of cylindrically symmetric objects in the presence of noise. This situation is commonly encountered in pump–probe experiments where the refractive index profile of elongated structures, such as plasma strings or transient refractive index changes, is under study. We performed numerical experiments for a variety of objects, with respect to the spatial distribution and size, and for various statistical distributions and levels of noise. In this area of application, the BASEX can surpass the Fourier–Hankel technique in respect of reconstruction quality, spatial resolution and robustness to noise especially after proper tuning of the basis set functions width.

We show the existence of a family of waves that share a common interesting property affecting the way they propagate and focus. These waves are a superposition of twin waves, which are conjugate to each other under inversion of the propagation direction. In analogy to holography, these twin "real" and "virtual" waves are related respectively to the converging and the diverging part of the beam and can be clearly visualized in real space at two distinct foci under the action of a focusing lens. Analytic formulas for the intensity distribution after focusing are derived, while numerical and experimental demonstrations are given for some of the most interesting members of this family, the accelerating Airy and ring-Airy beams, 7 pages, 5 figures

We numerically demonstrate that femtosecond ring-Airy wave packets are able to overcome the reference intensity clamping of $4\ifmmode\times\else\texttimes\fi{}{10}^{13}$ W/${\mathrm{cm}}^{2}$ for filaments generated with Gaussian beams at low numerical apertures and form an intense sharp intensity peak on axis. Numerical simulations, with unidirectional propagation models for the pulse envelope and the carrier resolved electric field, reveal that the driving mechanism for this unexpected intensity increase is due to the self-generated plasma. The plasma formation, in conjunction with the circular geometry of the beam, force the wave packet into a multistage collapse process which takes place faster than the saturating mechanisms can compensate. We report here a nonstandard mechanism that increases the intensity of a collapsing wave packet, due to the joint contributions of the cubic phase of the Airy beam and the formation of a partially reflecting plasma.

We present a simple precision-method to quickly and accurately measure the diameters of Gaussian beams, Airy spots, and central peak of Bessel beams ranging from the sub-millimeter to many centimeters without specialized equipment. Simply moving a wire through the beam and recording the relative losses using an optical power meter, one can easily measure the beam diameters with a precision of 1%. The accuracy of this method has been experimentally verified for Gaussian beams down to the limit of a commercial slit-based beam profiler (3%)., Comment: 5 pages, 4 figures, 1 table

This publisher's note corrects errors in Eq. (2) of Opt. Lett.43, 5480 (2018)OPLEDP0146-959210.1364/OL.43.005480.

It is shown that the tight focusing of short ultraviolet laser pulses (248 nm, 450 fs) in the bulk of high bandgap transparent solids (fused silica) can result in structural modifications in the material. These can vary from small changes of the refractive index to birefringence, cracks and voids. This restructuring of the medium is due to the high laser intensities attained, and the plasma that is generated through multi-photon processes. The restructuring comes in the form of a string, which is the result of the nonlinear propagation of the laser beam in the medium as a self-trapped filament. We resume the conditions for the generation of the different types of modifications and comment on the temporal evolution and the role of the plasma strings at the trail of the light filaments.

We experimentally investigated the THz emission from two-color ring-Airy beam induced plasma in the ambient air. The results show that this exotic autofocusing beam tends to form an elongated weak filamentation with a main peak at the front and a ‘tail’ with certain oscillations following, which leads to a higher THz yield and a slightly narrower THz spectrum than the emission from a Gaussian beam plasma under the same circumstances.

This work combines plasma doping implantation (PLAD) with laser annealing using excimer laser, for the formation of ultra-shallow junctions. For that purpose, high dose BF3 was implanted in n-type silicon wafers using PLAD. The as implanted material was investigated by high resolution TEM, measured by SIMS and simulated by Monte-Carlo codes. Subsequently, the samples were annealed using a KrF laser source at 248 nm with a pulse duration 20 ns and different fluence values. Laser annealing completely recrystallizes the amorphous layer as monitored by TEM measurements, fully activates the dopants achieving low sheet resistance values as shown by Van der Pauw measurements and results in box-shaped dopant profiles with movement less than 10 nm at the junction depth as measured using SIMS.

The study of the laser pulse duration effect on the silicon micro-spikes morphology is presented. The microcones were produced by ultraviolet (248 nm) laser irradiation of doped Si wafers in SF 6 environment. The laser pulse duration was adjusted at 450 fs, 5 ps and 15 ns. We have analyzed the statistical nature of the spikes’ morphological characteristics, such as periodicity and apex angle by exploiting image processing techniques, on SEM images of the irradiated samples. The correlation of the quantitative morphological characteristics with the laser parameters (pulse duration, laser fluence and number of pulses) provides new insight on the physical mechanisms, which are involved on the formation of Si microcones.

We present experiments with sub-picosecond ultraviolet laser pulses (248 nm, 450 fs) tightly focused in the bulk of fused-silica samples. The high laser intensities attained generate plasma through multi-photon absorption and electron avalanche processes in the bulk of the material. Depending on the initial experimental conditions three distinct types of structural changes in the material are observed, from small changes of the refractive index to birefringence, and even cracks and voids. We also observe the creation of micro-channels, up to 115 μm in length, inside the material due to self-guiding and filamentation of the laser pulses in the transparent material. The selective change of the refractive index is a promising method for the fabrication of photonic structures such as waveguides and three-dimensional integrated optical devices.

The sub-picosecond laser microstructuring of multilayer gratings is presented in this paper. A micromachining system operating with a 0.5 ps KrF laser at 248 nm was used to etch grating structures with a groove width of 1–2 μm in Mo/Si and Si/Mo multilayers. Atomic force microscopy, scanning electron microscopy and X-ray reflectivity were used to characterize the microetched patterns. The ω-scans around the 1st Bragg maximum show symmetric satellites up to 3rd order, with positions corresponding to the grating period. The use of sub-picosecond laser pulses minimizes the thermally affected zone and enhances the quality of the etched features. Short pulse laser processing is advantageous for the fabrication of high spatial resolution microstructures required in X-ray optics.

Recent advances of direct printing of compound microstructures by laser induced forward technique (LIFT) using a femtosecond UV laser will be presented. LIFT is a technique enabling the direct controlled transfer of thin film materials between substrates. An ultrashort UV laser has been used to transfer compound material (e.g. InO x ) onto glass substrates in order to form optical diffractive structures. The LIFT process preserves the oxide’s structural and physical properties. The use of laser-based methods in the fabrication of optically activated microstructures initiates new possible applications in the area of optoelectronics. Furthermore, time-resolved imaging of the plume produced by the femtosecond LIFT of InO x has been performed using an image intensified CCD (ICCD) camera in the time interval up to 2 μs after the laser pulse. The velocities of the emitted particles were measured to 400 m/s.

We study the influence of the application of an external electric field on the grating formed in (1-10) and (111)-cut photorefractive sillenite crystals. Optimum conditions for application of the bias field are examined, taking into account the shift of the grating orientation for maximum diffraction efficiency along the crystal depth. The contribution of the piezoelectric effect is considered both in the electro-optic tensor and space charge field calculations. An analysis on the diffractive properties under these optimum conditions shows an increase of 30% in maximum diffraction efficiency in Bi12GeO20, and experimental verification for this is provided.

We show numerically that by using radial symmetric lattices, the focal spot characteristics and filament peak intensity of high-power autofocusing waves can be controlled. The lattice induced diffraction is able to isolate the main on-axis peak and control the focus position. In addition, at higher power the lattice can control and stabilize the peak intensity of the filament over an extended distance.

Bi12SiO20 single crystals doped with Ru, Rh, Pd, Re, Os, and Ir transition elements were obtained. Optical absorption and optical activity were measured in the visible spectral range. Strong changes were observed in transmission spectra when doping with various elements. Doping with Os and Pd causes strong bleaching to the crystals, changes the transmission curve shoulder, and decreases the absorption coefficient. Transmission spectra of Ru, Re, and Ir doped crystals are shifted to the red region and the absorption coefficient is considerably increased. Optical rotatory power remains unchanged by doping with Rh, Pd, Re, and Ir. It is increased negligibly by Pd doping, considerably increased by Os doping, and strongly decreased by Ru doping. The influence of doping elements on optical rotatory power is discussed on the basis of the two elementary structural unit cells (BiOn polyhedra and SiO4 tetrahedra) and of the transition energy of electrons located in their vicinity.

We study the diffraction efficiency of volume phase gratings in Bi12GeO20, when the grating vector, lying on a (111) plane, is at an angle with respect to the crystallographic direction. An external bias field parallel to the direction is applied during recording, thus, the recording conditions depend on the grating vector orientation. The basic parameters determining the diffraction efficiency are the grating vector orientation, the rotatory power and the field-induced linear birefringence (primary and secondary). Analytic expressions for the diffraction efficiency have been obtained by taking into account all the above-mentioned parameters, provided that linearly polarized light is incident on the crystal. In this configuration, the influence of the secondary electro-optic effect (inverse piezoelectric and photoelastic effects) to the diffraction efficiency is actually stronger than the influence of the primary effect. Experimental results are given.

We study the diffraction efficiency of volume phase gratings in Bi12GeO20, when the grating vector, lying on a (110) plane, makes an angle with the (110) crystallographic direction. An external bias electric field, parallel to the (110) axis, is applied during recording, thus the recording conditions do not remain constant as we vary the grating vector orientation. The basic parameters determining the diffraction efficiency are the grating vector orientation, the optical activity, and the field induced linear birefringence (primary and secondary). Analytic expressions for the diffraction efficiency have been derived by taking into account all the above mentioned parameters, provided that linearly polarized light is incident on the crystal. Experimental results are given.

TiO20. The first two can be measured by simple and classical methods, but the coexistence of optical activity, electrogyration, field-induced linear birefringence, and piezoelectric and photoelastic effects in photorefractive materials such as Bi12TiO20 complicate the measurement of the electro-optic coefficient. For normal incidence of linearly polarized light we derive analytic expressions for the polarization of light that has passed through the crystal. The ellipticity of the polarization is a function of the electric-field-induced linear birefringence and hence of the electro-optic coefficient of the crystal. Therefore measurement of the ellipticity as a function of an electric field externally applied to the crystal leads to an electro-optic coefficient r41 of 5.3±0.1 pm/V.

Controlling the propagation of intense optical wavepackets in transparent media is not a trivial task. During propagation, low- and high-order non-linear effects, including the Kerr effect, multiphoton absorption and ionization, lead to an uncontrolled complex reshaping of the optical wavepacket that involves pulse splitting, refocusing cycles in space and significant variations of the focus. Here we demonstrate both numerically and experimentally that intense, abruptly autofocusing beams in the form of accelerating ring-Airy beams are able to reshape into non-linear intense light-bullet wavepackets propagating over extended distances, while their positioning in space is extremely well defined. These unique wavepackets can offer significant advantages in numerous fields such as the generation of high harmonics and attosecond physics or the precise micro-engineering of materials.

Recent theoretical and experimental studies have introduced the counterintuitive concept of superoscillations in the context of optics, with direct implications in superresolution [1], subwavelength focusing and imaging [2, 3] without evanescent waves. One can create superoscillatory diffractionless beams by superimposing already known stationary solutions of Helmholtz equation [4], and therefore transfer subwavelength information into the far field. It is noteworthy to mention that this is not interference but a superposition effect, where the intensity of the subwavelength regions is invariant with respect to the propagation distance. The scope of this paper is to understand how one can control and change the polarization of the subwavelength regions with respect to the surrounding high intensity lobes.

We study the diffraction efficiency of volume phase gratings in photorefractive sillenite crystals, such as Bi 12 GeO 20 , Bi 12 SiO 20 and Bi 12 TiO 20 , when the grating vector makes an angle with the 〈110〉 axis. Analytic expressions for the diffraction efficiency of the diffracted light have been derived taking into account the optical activity, field-induced linear birefringence, piezoelectric and photoelastic effects, when linearly polarized light is incident normally on the crystal. Experimental results are given.

The coexistence of optical activity, field-induced linear birefringence, piezoelectric and photoelastic effects in photorefractive materials such as Bi12GeO20 and Bi12TiO20 renders the measurement of their electro-optic coefficients quite complex. Analytic expressions are given for the ellipticity and the orientation of the emerging light vibration when linearly polarized light is incident normally on the crystal. The ellipticity is a function of the electric-field-induced linear birefringence and hence of the electro-optic coefficient of the crystal. Therefore measurement of the ellipticity as a function of electric field applied across the crystal leads to a value of the electro-optic coefficient r41. Experimental results are given.

We derive exact solutions of Maxwell's equations based on superoscillatory superpositions of vectorial Bessel beams. These novel beams are diffraction-free and can support subwavelength features in their transverse electromagnetic fields, without the presence of any evanescent waves. These features can be propagated into the far field. Approximate solutions in closed form are also derived based on asymptotic expansions of Bessel functions for simple prescribed subwavelength patterns. The superoscillatory characteristics of both electric, magnetic field components (transverse and longitudinal), and the Poynting vector, as well as, the effect of nonparaxiality are systematically investigated.

We demonstrate, for the first time, that photonic lattices support a new type of laser filaments, called lattice filaments (LF). The LF attributes (length, width, and intensity) can be tailored by both varying the photonic lattice properties and also dynamically through the interaction between filaments. This opens the way for extensive all-optical control of the nonlinear propagation of intense ultrafast wave packets. Our approach is generic and applicable to all transparent media, with potential strong impact on various photonic applications.

We study cavitation dynamics when focusing ring-shaped femtosecond laser beams in water. This focusing geometry reduces detrimental nonlinear beam distortions and enhances energy deposition within the medium, localized at the focal spot. We observe remarkable postcollapse dynamics of elongated cavitation bubbles with high-speed ejection of microbubbles out of the laser focal region. Bubbles are ejected along the laser axis in both directions (away and towards the laser). The initial shape of the cavitation bubble is also seen to either enhance or completely suppress jet formation during collapse. In the absence of jetting, microbubble ejection occurs orthogonal to the laser propagation axis.

The nonlinear dynamics of intense truncated Airy beams in Kerr ionizing media are investigated from numerical simulations and experiments. We show numerically that a competition between the linear and nonlinear effects takes place and may be modified by tuning the width of the main lobe of the Airy beam and the size of the truncating diaphragm. Our analysis shows that the acceleration of the Airy peak, an inherent feature of linear Airy beam propagation, is preserved only for powers in the main Airy lobe below a certain threshold. Nonlinear propagation of intense Airy beams with low power in the main lobe is sustained by a continuous energy flux from its neighbors, similarly to the mechanism sustaining nonlinear Bessel beam propagation. Airy beams with higher powers in the main lobe are reshaped into a multifilamentary pattern induced by Kerr and multiphoton nonlinearities. The nucleation of new filaments and their interaction affect the acceleration of the main Airy lobes. We finally show that the size of the truncation constitutes a control parameter for the energy flux that features the Airy beam acceleration. Experiments performed in water corroborate the existence of these two distinct nonlinear propagation regimes.

We show that high-angle Bessel beams may significantly reduce nonlinear pulse distortions due, for example, to nonlinear Kerr effects (self-phase-modulation and self-focusing) yet enhance ionization and plasma generation. Holographic reconstruction of Bessel beams in water show intensity clamping at increased intensities and evidence of nontrivial plasma dynamics as the input energy is increased. The solvated electron density increases significantly and the cavitation-induced bubbles are ejected from the focal region indicating a significant excess plasma heating in the Bessel-pulse wake.

High-angle Bessel beams significantly reduce nonlinear pulse distortion yet enhance ionisation and plasma generation. Digital holographic reconstruction of Bessel beams in water show clamping at increased intensities and excess plasma heating in the pulse wake.

The subpicosecond laser-induced forward transfer process (LIFT) was investigated by means of time-resolved shadowgraphic imaging. The dynamics of the subpicosecond LIFT process of InOx was investigated for time delays between 0.01 and 10 μs following laser irradiation pulse. Measured values of the velocities of the ejected material were to 400±10 m/s, depending on the laser fluence. The fraction of the material ejected by the subpicosecond LIFT process, which is visible to the shadowgraphic technique was measured to be highly directional with narrow angular divergence (3°). Such direct dynamic transfer of the material opens up application possibilities for the fabrication of high-spatial-resolution microstructures.

We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.

The recent interpretation of experiments on the nonlinear non-resonant birefringence induced in a weak probe beam by a high intensity pump beam in air and its constituents has stimulated interest in the non-resonant birefringence due to higher-order Kerr nonlinearities. Here a simple formalism is invoked to determine the non-resonant birefringence for higher-order Kerr coefficients. Some general relations between nonlinear coefficients with arbitrary frequency inputs are also derived for isotropic media. It is shown that the previous linear extrapolations for higher-order birefringence (based on literature values of n2 and n4) are not strictly valid, although the errors introduced in the values of the reported higher- order Kerr coefficients are a few percent.

Femtosecond laser filaments leave plasma strings at their trail as they propagate through any transparent medium including glasses and polymers. This initial plasma string and the energy deposited from the electrons to the lattice play a fundamental role in the creation of permanent structural modifications in these media.

Using the sum-over-states model for linear symmetric molecules we derive expressions for the frequency dispersion of n_2 of air molecules. The measured sign of non-resonant n_2 shows the recently published extended Miller formula is incorrect.