Intensity patterns of a focused electromagnetic spherical wave with aberration.

The laser pulse focused by a relativistic flying parabolic mirror can exceed the laser intensity focused by conventional physical focusing optics. Depending on the Lorentz γ-factor, the focal length of the relativistic flying mirror in the boosted frame of reference becomes much shorter than the incident beam size. The 4π-spherical focusing scheme is applied to describe such a focused field configuration. In this paper, a theoretical formalism has been developed to describe the field configuration focused by the 4π-spherical focusing scheme with an arbitrary phase error of an incident electromagnetic wave. The focused field configuration is described by the linear combination of the product of the spherical Bessel function and the spherical harmonics, resulting in the same expression as the multipole radiation. The mathematical expression showing the focused field for the femtosecond laser pulse, as well as the continuous wave, has been derived for the application to the femtosecond high-power laser. We show the three-dimensional intensity distribution near focus for the 4π-spherically focused electromagnetic field with phase error.

Towards bright gamma-ray flash generation from tailored target irradiated by multi-petawatt laser.

One of the remarkable phenomena in the laser-matter interaction is the extremely efficient energy transfer to [Formula: see text]-photons, that appears as a collimated [Formula: see text]-ray beam. For interactions of realistic laser pulses with matter, existence of an amplified spontaneous emission pedestal plays a crucial role, since it hits the target prior to the main pulse arrival, leading to a cloud of preplasma and drilling a narrow channel inside the target. These effects significantly alter the process of [Formula: see text]-photon generation. Here, we study this process by importing the outcome of magnetohydrodynamic simulations of the pedestal-target interaction into particle-in-cell simulations for describing the [Formula: see text]-photon generation. It is seen that target tailoring prior the laser-target interaction plays an important positive role, enhancing the efficiency of laser pulse coupling with the target, and generating high energy electron-positron pairs. It is expected that such a [Formula: see text]-photon source will be actively used in various applications in nuclear photonics, material science and astrophysical processes modelling.

Superluminal-subluminal orbital angular momentum femtosecond laser focus.

The interplay between the frequency chirping of a broadband laser pulse and the longitudinal chromatic aberration of a focusing optic introduces the superluminal or subluminal behavior to a laser focus. In this paper, we present an analytic expression for an electric field describing a superluminal or subluminal femtosecond laser focus with orbital angular momentum. The analytic expression for a superluminal or subluminal laser focus is obtained through a diffraction integral, in which the focal length is replaced by a time-dependent focal length under the paraxial approximation, and the Fourier transformation. The speed and pulse duration of a laser focus are determined by the total group delay dispersion and a chromaticity parameter defined by the longitudinal chromatic aberration of a dispersive focusing optic. It is shown that it is possible to generate a several femtosecond superluminal orbital angular momentum laser focus in the focal region.

Relativistic flying forcibly oscillating reflective diffraction grating.

Relativistic flying forcibly oscillating reflective diffraction gratings are formed by an intense laser pulse (driver) in plasma. The mirror surface is an electron density singularity near the joining area of the wake wave cavity and the bow wave; it moves together with the driver laser pulse and undergoes forced oscillations induced by the field. A counterpropagating weak laser pulse (source) is incident at grazing angles, being efficiently reflected and enriched by harmonics. The reflected spectrum consists of the source pulse base frequency and its harmonics, multiplied by a large factor due to the double Doppler effect.

4π-spherically focused electromagnetic wave: diffraction optics approach and high-power limits.

The focused field and its intensity distribution achieved by the 4π-spherical focusing scheme are investigated within the framework of diffraction optics. Generalized mathematical formulas describing the spatial distributions of the focused electric and magnetic fields are derived for the transverse magnetic and transverse electric mode electromagnetic waves with and without the orbital angular momentum attribute. The mathematical formula obtained shows no singularity in the field in the focal region and satisfies the finite field strength and electromagnetic energy conditions. The 4π-spherical focusing of the transverse magnetic mode electromagnetic wave provides the highest field strength at the focus and the peak intensity reaches 1026 W/cm2 for the laser power of 100 PW at 800 nm wavelength. As an example of using the mathematical formula, the electron-positron pair production via the Schwinger mechanism is analyzed and compared with previous results.

Analysis on the longitudinal field strength formed by tightly-focused radially-polarized femtosecond petawatt laser pulse.

Tight focusing of radially- or azimuthally-polarized electromagnetic waves becomes attractive because of the strong field generation in the longitudinal direction. In this paper, we investigate the strength of longitudinal electric field when a radially-polarized femtosecond PW laser pulse is tightly focused by a parabolic surface. From the calculation using the vector diffraction approach, it has been shown that the highest strength of 2.2 × 1013 V/cm can be reached for the longitudinal field with a radially-polarized 11.2-fs, 11.2-J uniform-beam-profile laser pulse. The difference in the strength of longitudinal field with different beam profile and the spectrum of a laser pulse has been also carefully examined. The propagation of a laser spot has been simulated under an extremely-tight-focusing condition (0.25 in terms of f-number) and an achievable field strength for a standing longitudinal field has been examined by colliding two radially-polarized fs PW-level laser pulses.

Spatio-temporal modification of femtosecond focal spot under tight focusing condition.

The focusing property of a focal spot of a femtosecond laser pulse is presented under tight focusing conditions (below f-number of 1). The spatial and temporal intensity distributions of a focused electric field are calculated by vector diffraction integrals and coherent superposition method. The validity of the calculation method is examined by comparing the intensity distribution obtained under a high f-number condition to that obtained with the fast Fourier transform method that assumes the scalar paraxial approximation. The spatial and temporal modifications under tight focusing conditions are described for a focused femtosecond laser pulse. The calculation results show that a peak intensity of about 2.5x10(24) W/cm2 can be achievable by tightly focusing a 12-fs, 10 PW laser pulse with a f/0.5 parabolic optic. The precise information on intensity distributions of a femtosecond focal spot obtained under a tight focusing condition will be crucial in assessing a focused intensity and in describing the motion of charged particles under an extremely strong electric field in ultra-relativistic and/or relativistic laser matter-interaction studies.

Enhancement of electron energy to the multi-GeV regime by a dual-stage laser-wakefield accelerator pumped by petawatt laser pulses.

Laser-wakefield acceleration offers the promise of a compact electron accelerator for generating a multi-GeV electron beam using the huge field gradient induced by an intense laser pulse, compared to conventional rf accelerators. However, the energy and quality of the electron beam from the laser-wakefield accelerator have been limited by the power of the driving laser pulses and interaction properties in the target medium. Recent progress in laser technology has resulted in the realization of a petawatt (PW) femtosecond laser, which offers new capabilities for research on laser-wakefield acceleration. Here, we present a significant increase in laser-driven electron energy to the multi-GeV level by utilizing a 30-fs, 1-PW laser system. In particular, a dual-stage laser-wakefield acceleration scheme (injector and accelerator scheme) was applied to boost electron energies to over 3 GeV with a single PW laser pulse. Three-dimensional particle-in-cell simulations corroborate the multi-GeV electron generation from the dual-stage laser-wakefield accelerator driven by PW laser pulses.

Transition of proton energy scaling using an ultrathin target irradiated by linearly polarized femtosecond laser pulses.

Particle acceleration using ultraintense, ultrashort laser pulses is one of the most attractive topics in relativistic laser-plasma research. We report proton and/or ion acceleration in the intensity range of 5×10(19) to 3.3×10(20) W/cm2 by irradiating linearly polarized, 30-fs laser pulses on 10-to 100-nm-thick polymer targets. The proton energy scaling with respect to the intensity and target thickness is examined, and a maximum proton energy of 45 MeV is obtained when a 10-nm-thick target is irradiated by a laser intensity of 3.3×10(20) W/cm2. The proton acceleration is explained by a hybrid acceleration mechanism including target normal sheath acceleration, radiation pressure acceleration, and Coulomb explosion assisted-free expansion. The transition of proton energy scaling from I(1/2) to I is observed as a consequence of the hybrid acceleration mechanism. The experimental results are supported by two- and three-dimensional particle-in-cell simulations.

Relativistic frequency upshift to the extreme ultraviolet regime using self-induced oscillatory flying mirrors.

Coherent short-wavelength radiation from laser-plasma interactions is of increasing interest in disciplines including ultrafast biomolecular imaging and attosecond physics. Using solid targets instead of atomic gases could enable the generation of coherent extreme ultraviolet radiation with higher energy and more energetic photons. Here we present the generation of extreme ultraviolet radiation through coherent high-harmonic generation from self-induced oscillatory flying mirrors--a new-generation mechanism established in a long underdense plasma on a solid target. Using a 30-fs, 100-TW Ti:sapphire laser, we obtain wavelengths as short as 4.9 nm for an optimized level of amplified spontaneous emission. Particle-in-cell simulations show that oscillatory flying electron nanosheets form in a long underdense plasma, and suggest that the high-harmonic generation is caused by reflection of the laser pulse from electron nanosheets. We expect this extreme ultraviolet radiation to be valuable in realizing a compact X-ray instrument for research in biomolecular imaging and attosecond physics.

Generation of high-contrast, 30 fs, 1.5 PW laser pulses from chirped-pulse amplification Ti:sapphire laser.

High-contrast, 30 fs, 1.5 PW laser pulses are generated from a chirped-pulse amplification (CPA) Ti:sapphire laser system at 0.1 Hz repetition rate. The maximum output energy of 60.2 J is obtained, at a pump energy of 120 J, from a booster amplifier that is pumped by four frenquency-doubled Nd:glass laser systems. During amplification, parasitic lasing is suppressed by index matching fluid with absorption dye and the careful manipulation of the time delay between the seed and pump pulses. An amplified pulse passes through a pulse compressor consisting of four gold-coated gratings. After compression, the measured pulse duration is 30 fs, and the output energy is 44.5 J, yielding a peak power of about 1.5 PW. The output energy of 44.5 J and output power of 1.5-PW are the highest values ever achieved from the femtosecond CPA Ti:sapphire laser system. To maintain a sufficiently high temporal contrast, a saturable absorber is installed in the front-end system with two ultrafast Pockels cells in order to minimize the amplified spontaneous emission (ASE) and pre-pulse intensity. An adaptive optics system is implemented for PW laser pulses and a focused intensity of about 1 × 10(22) W/cm(2) can be obtained when an f/3 optic is used.

0.1 Hz 1.0 PW Ti:sapphire laser.

We report on the generation of 1.0 PW, 30 fs laser pulses at a 0.1 Hz repetition rate from a chirped-pulse amplification Ti:sapphire laser system. The energy of the laser pulses is amplified up to 47 J in a final three-pass booster amplifier having 96 J pump energy. To the best of our knowledge, this is the first petawatt Ti:sapphire laser system at a 0.1 Hz repetition rate. The shot-to-shot energy fluctuation of the laser pulses is as low as 0.53% in rms value, and the laser pulses have homogeneous flattop spatial beam profiles.

Direct reconstruction of an object from dual exposure Fourier intensity measurements.

The reconstruction of an object with a method using a dual exposure single inverse Fourier transform is investigated. The method calculates phase information in the Fourier plane to perform the inverse Fourier transform. The phase information in the Fourier plane is calculated from the intensity distributions formed by an object with and without a reference electric field. The method successfully reconstructs an object in a simple and fast manner. For the practical use of the method, the effects of the intensity digitization and the noise in the intensity distributions are examined in reconstructing an object.

Method of reconstructing wavefront aberrations from the intensity measurement.

A method for reconstructing wavefront aberrations from intensity measurements in the focal plane of a focusing optic is presented. This reconstruction method is simple, fast, and accurate in reconstructing wavefront aberrations because it uses the inverse Fourier transform of an intensity distribution in the focal plane with a reference electric field. The validity of the reconstruction method is demonstrated by computing a wavefront aberration from the intensity distributions in the focal plane.

Characterizing the wave aberration in eyes with keratoconus or penetrating keratoplasty using a high-dynamic range wavefront sensor.

PURPOSE: The purpose of this study was to characterize aberrations in 2 populations of eyes, namely those with keratoconus (KC) and those having undergone penetrating keratoplasty (PK), using a large-dynamic range Shack-Hartmann wavefront sensor. DESIGN: Prospective comparative case series. PARTICIPANTS: Twenty-one people with ocular pathologic features (either KC or PK) were recruited for this study. A previously compiled population of 190 people with no pathologic features other than refractive error was used as a means for comparison. METHODS: Thirty-three abnormal eyes (19 with KC and 14 PK) were measured using a high-dynamic range wavefront sensor, and Zernike coefficients were computed over a 6-mm pupil. The data then were used to characterize the populations by themselves, as well as to compare them with the population of normal eyes. MAIN OUTCOME MEASURES: Root mean square (RMS) higher-order aberration (HOA), percent of higher-order or total aberration variance, and magnitude of individual Zernike modes (in micrometers). Visual benefit of correcting higher-order aberrations was used when comparing pathologic and normal populations. RESULTS: The keratoconic eyes exhibited 2.24 microm of HOA RMS on average. Vertical coma accounted for 53+/-32% (mean+/-standard deviation [SD]) of the HOA variance and was the most dominant higher-order aberration. The PK subjects had an average higher-order RMS of 2.25 microm, and trefoil dominated in this population with an average HOA variance contribution of 38+/-23% (mean+/-SD). The KC and PK higher-order aberrations represented 16+/-20% and 16+/-13% (mean+/-SD) of the total aberration variance, whereas the ratio was only 1+/-1% in the normal population. A visual benefit calculation on 15 KC eyes and 14 PK eyes yielded a result of 4.4+/-2.0 and 6.0+/-1.5 (mean+/-SD), respectively, whereas the normal population had a visual benefit of only 2.1+/-0.4. CONCLUSIONS: Eyes with KC and PK have higher-order aberrations that are approximately 5.5 times more than what is typical in normal eyes. Vertical coma is the dominant higher-order aberration in people with KC, whereas PK eyes are dominated by trefoil, spherical aberration, and coma. Correcting these aberrations may provide substantial improvements in vision beyond what is possible with conventional correction methods.

Vision improvement by correcting higher-order aberrations with customized soft contact lenses in keratoconic eyes.

Higher-order aberration correction in abnormal eyes can result in significant vision improvement, especially in eyes with abnormal corneas. Customized optics such as phase plates and customized contact lenses are one of the most practical, nonsurgical ways to correct these ocular higher-order aberrations. We demonstrate the feasibility of correcting higher-order aberrations and improving visual performance with customized soft contact lenses in keratoconic eyes while compensating for the static decentration and rotation of the lens. A reduction of higher-order aberrations by a factor of 3 on average was obtained in these eyes. The higher-order aberration correction resulted in an average improvement of 2.1 lines in visual acuity over the conventional correction of defocus and astigmatism alone.

Method of reconstructing wavefront aberrations by use of Zernike polynomials in radial shearing interferometers.

A novel method of reconstructing wavefront aberrations by use of Zernike polynomials for radial shearing interferometers is discussed. This method uses matrix formalism to calculate the Zernike coefficients of a wavefront under test and shows the validity of reconstructing an arbitrary wavefront aberration from an interferogram taken by a radial shearing interferometer. We also propose a new interferometer setup to determine the shape and the direction (concave or convex) of wavefront aberration in a single measurement.

Generalized ray-transfer matrix for an optical element having an arbitrary wavefront aberration.

A generalized ray-transfer matrix for describing the action of an optical element having an arbitrary wavefront aberration is obtained. In this generalized ray-transfer matrix, the action of the aberrated optical element is represented by the product of radial ray-transfer matrices and tangential ray-transfer matrices. The refraction angle of an incident ray is calculated from the gradient of the wavefront aberration at the point of incidence, and the radial and tangential ray-transfer matrices directly use the gradient as a matrix component. To show the validity of the generalized ray-transfer matrix, intercept heights from a spot diagram are calculated with the generalized ray-transfer matrix and compared with those calculated with commercial ray-tracing software.

Measurement of wave-front aberration in soft contact lenses by use of a Shack-Hartmann wave-front sensor.

Lower- and higher-order wave-front aberrations of soft contact lenses were accurately measured with a Shack-Hartmann wave-front sensor. The soft contact lenses were placed in a wet cell filled with lens solution to prevent surface deformation and desiccation during measurements. Aberration measurements of conventional toric and multifocal soft contact lenses and a customized soft contact lens have proved that this method is reliable. A Shack-Hartmann wave-front sensor can be used to assess optical quality of both conventional and customized soft contact lenses and to assist in enhancing lens quality control.

Vision improvement by correcting higher-order aberrations with phase plates in normal eyes.

PURPOSE: To psychophysically demonstrate vision improvement when correcting higher-order aberrations with phase plates in normal eyes. METHODS: The wavefront aberrations of three nonsurgical normal eyes were measured with a Shack-Hartmann wavefront sensor. With these measured aberrations, phase plates were fabricated using a lathing technique. Theoretical improvement in retinal image quality was estimated by calculating the optical modulation transfer functions under the white light condition. Visual acuity measurements were also conducted to demonstrate improvement in visual performance after correcting higher-order aberrations with the phase plate. In this visual acuity measurement, a tumbling "E" with high (100%) and low (10%) contrast was used. RESULTS: The phase plate reduced the higher-order root mean square (RMS) wavefront error from 0.39 +/- 0.09 to 0.15 +/- 0.02 microm (mean +/- standard deviation from three eyes) for a 6-mm pupil. With the phase plate, retinal image quality based on the volume of modulation transfer function under 60 cycles per degree (c/deg) was improved by a factor of 1.8 +/- 0.4 over that of the eyes with spherocylindrical correction only. Average improvement in visual acuity achieved by correcting the higher-order aberration was 0.23 lines with high-contrast letters and 1.12 lines with low-contrast letters. All subjects reported subjective improvement in image quality of the letter with the phase plate. CONCLUSION: The phase plate effectively corrected the higher-order aberrations in normal eyes. As a result, both retinal image quality and visual acuity especially with the low-contrast letters were improved. This study demonstrated the feasibility of correcting higher-order aberrations and improving vision with customized optics.