Design, fabrication, and analysis of chirped multilayer mirrors for reflection of extreme-ultraviolet attosecond pulses

Chirped Mo/Si multilayer coatings have been designed, fabricated, and characterized for use in extreme-ultraviolet attosecond experiments. By numerically simulating the reflection of the attosecond pulse from a multilayer mirror during the optimization procedure based on a genetic algorithm, we obtain optimized layer designs. We show that normal incidence chirped multilayer mirrors capable of reflecting pulses of approximately 100 attoseconds (as) duration can be designed by enhancing the reflectivity bandwidth and optimizing the phase-shift behavior. The chirped multilayer coatings have been fabricated by electron-beam evaporation in an ultrahigh vacuum in combination with ion-beam polishing of the interfaces and in situ reflectivity measurement for layer thickness control. To analyze the aperiodic layer structure by hard-x-ray reflectometry, we have developed an automatic fitting procedure that allows us to determine the individual layer thicknesses with an error of less than 0.05 nm. The fabricated chirped mirror may be used for production of 150-160 as pulses.     

Isolated attosecond pulse generation with the chirped two-color laser field

We propose a scheme to generate isolated attosecond pulse using a linearly chirped two-color laser field, which includes a fundamental laser field and a weak infrared control laser field in the multicycle regime. The fundamental laser field consists of one linearly up-chirped and one linearly down-chirped pulses. The control pulse is chirped free. We compare the attosecond pulse generated in the chirped two-color field and the chirp-free field. It is found that an IAP can be generated even without carrier envelop phase stabilization in the chirped two-color laser field with a duration of 40 fs. We also discuss the influence of the relative intensity, relative phase, time delay, and chirping parameters on the generation of IAPs.     

Recent development and new ideas in the field of dispersive multilayer optics

A dispersive-mirror-based laser permits a dramatic simplification of high-power femtosecond and attosecond systems and affords promise for their further development toward shorter pulse durations, higher peak powers, and higher average powers with user-friendly systems. The result of the continuous development of dispersive mirrors permits pulse compression down to almost single cycle pulses of 3?fs duration. These design approaches together with the existing modern deposition technology pave the way for the manufacture of dielectric multilayer coatings able to compress pulses of tens of picoseconds duration down to a few femtoseconds.     

Group delay dispersion measurement of a dispersive mirror by spectral interferometry: comparison of different signal processing algorithms

We built a dispersive white-light spectral interferometer for precisely measuring the dispersion properties of a multilayer thin-film structure. A novel algorithm with improved robustness to measurement errors is presented by combining a windowed Fourier transformation with wavelet-based differentiation. Compared with previously published algorithms, this method shows substantial resistance to measurement errors. The group delay dispersion properties of bulk materials and a homemade chirped mirror are measured by our apparatus, and the measurement result manifests considerable accuracy and robustness. The technique shows reasonable potential for the characterization of ultrabroadband chirped mirrors.     

Design of aperiodic multilayer structures for attosecond pulses in the extreme ultraviolet

The design of aperiodic reflecting multilayer (ML) structures for attosecond physics in the extreme ultraviolet spectral region is presented. An optimization procedure based on "evolutive strategy" has been developed in order to get coating structures reflecting high photon fluxes in ultrashort duration pulses. The MLs are designed for a specific (75-105 eV) spectral interval with suitable reflectance and phase characteristics, in particular high total spectral reflectivity coupled with very wide bandwidth, spectral phase compensation, and amplitude reshaping. Furthermore, to take into account manufacturing tolerances, solutions stable with respect to random layer thickness variations are selected. To test the reliability of the proposed design procedure, examples of Mo/Si ML structures designed to reflect ultrashort pulses with different amplitude profiles and phase behavior are considered. The performances of the various structures are analyzed.     

Chirped optical X-shaped pulses in material media

We analyze the properties of chirped optical X-shaped pulses propagating in material media without boundaries. We show that such ("superluminal") pulses may recover their transverse and longitudinal shapes after some propagation distance, whereas the ordinary chirped Gaussian pulses can recover their longitudinal width only (since Gaussian pulses suffer a progressive transverse spreading during their propagation). We therefore propose the use of chirped optical X-type pulses to overcome the problems of both dispersion and diffraction during pulse propagation.     

Optimization of chirped mirrors

We demonstrate that a highly efficient global optimization of chirped mirrors can be performed with the memetic algorithm. The inherently high sensitivity of chirped-mirror characteristics to manufacturing errors can be reduced significantly by means of the stochastic quasi-gradient algorithm. The applicability of these algorithms is not limited to chirped mirrors.     

Single attosecond light pulses from multi-cycle laser sources

High harmonic generation provides a means of producing attosecond pulses of light which are the shortest, controllable probes available to science for time-resolving ultrafast dynamics. We review techniques based on high harmonic generation for generating single attosecond pulses using high-power, multi-cycle laser sources, including optical-, polarisation-, and ionisation-gating schemes as well as techniques based on field synthesis. By significantly reducing the technical demands placed on the driving laser, these techniques have the potential to greatly broaden the application base for attosecond pulses.     

Characterization of ultrashort pulses by a modified grating-eliminated no-nonsense observation of ultrafast incident laser light E fields (GRENOUILLE) method

The measurement and characterization of ultrashort laser pulses remains an arduous task. The most commonly used pulse-measurement method is known as frequency-resolved optical gating (FROG), and another version with great experimental simplification and low-priced setup is known as grating-eliminated no-nonsense observation of ultrafast incident laser light E fields (GRENOUILLE). Nevertheless, there is interest in elaborating other, more accessible or simpler and cheaper, setups with equal or better assets. We explored modification of the GRENOUILLE method in which we replaced the original Fresnel biprism with a beam splitter and two mirrors and used a cheap webcam to measure the pulse traces. We have evaluated our system, and we propose a method to correct border effects caused by the beam intensity's profile based on the characterization of three pulse classes: Fourier-transform limited, double, and chirped. We compare the recovered electric field with further spectral and second-order correlation data of the corresponding pulses.     

Femtosecond dispersion compensation with multilayer coatings: toward the optical octave

Dispersive multilayer coatings have found widespread use, particularly in the compensation of material dispersion in femtosecond oscillators and amplifiers. Other than prism or grating sequences, only chirped mirrors allow for the compensation of a much more general spectral dependence of the dispersion. The current state of the art in ultrabroadband mirror design for dispersion compensation is reviewed. Approaches to expand the utility of chirped-mirror coatings toward the coverage of an even-wider bandwidth beyond the optical octave are discussed.     

On the possibility of obtaining attosecond pulse trains during second harmonic generation by high-intensity femtosecond pulses

The possibility of obtaining attosecond pulse trains during second harmonic generation by high-intensity femtosecond pulses is demonstrated by means of computer simulation. The attosecond pulses are formed at the basic frequency with a low efficiency (≤8%) of the energy conversion from first to second harmonic. The regimes of attosecond pulse generation at the double frequency are considered.     

Optimal control of high harmonics for the generation of double attosecond pulses by using a chirped laser pulse

An efficient scheme for the optimization of ultrashort femtosecond pulse shapes interacting with an atom to control high harmonics spectrum and double attosecond pulse generation is presented. The time-dependent Schrödinger equation of one-dimensional hydrogen atom is solved numerically to obtain electric field emission. The genetic algorithm optimization method is used to control the phase and amplitude of ultrashort excitation laser pulses to generate the desired attosecond-shaped pulses. An appropriate cost function is introduced for genetic algorithm optimization of double attosecond pulse generation. It is shown that the relative intensity of two generated pulses, their delay time and duration can be controlled in this approach. Finally, the parameters of the optimized emitted attosecond pulse are compared with those of desired pulses, and the underlying physical mechanisms are discussed in detail.     

Thermally invariant dielectric coatings for micromirrors

Thermal expansion-induced curvature becomes a major effect in micromirrors as the mirror diameter exceeds 100 microm. Such mirrors are used for optical switching, scanning, and many other applications. By using multilayer coatings instead of a single metal reflector, one can use the mechanical properties of the multilayer to create mirrors with zero curvature across temperature. We demonstrate the fabrication of such thermally invariant mirrors using dielectric coatings. A semianalytic model based on free-plate elastic theory is developed that uses empirical parameters in place of the true thermal expansion coefficients of the coating materials. Micromirrors are demonstrated that maintain their design curvature to within lambda/60 for lambda = 633 nm across an operating range from 21 degrees C to 58 degrees C.     

Generation of carrier-envelope phase-controlled isolated attosecond pulses using chirped femtosecond excitation lasers

ABSTRACT

We present an efficient approach for producing a carrier-envelope phase controlled isolated attosecond pulse by an optimized intense driving laser pulse. High-order harmonics are produced by numerically solving the time-dependent Schrödinger equation for the one-dimensional hydrogen atom in an ultrashort laser pulse. We define an efficient cost function to optimize the laser pulse by a genetic algorithm scheme. Our approach produces single attosecond pulses with desired properties, including the carrier-envelope phase, central frequency, and duration. Also, we analyze the time–frequency profiles of the attosecond emissions to gain a deeper insight into the underlying physical mechanism.     

Optimization of multilayer mirrors at 13.4 nm with more than two materials

The design of multilayer mirrors with more than two materials is one of the key technologies for investigating lithography. We study a new procedure for optimizing multilayer mirrors of different combinations of materials at a wavelength of 13.4 nm. By adding Be and C layers in different orders to a Si/Mo stack, we have observed enhancement of the reflectivity and a reduction in the number of layers. The Luus-Jaakola optimization procedure has been implemented for the global optimization of the multilayer mirrors. With this algorithm it is not necessary to specify initially the number of layers present in a given design.     

Correlation of sidelobe suppression between rugate filters and multilayer mirrors

We present the study of the correlation between refractive index profiles and the optical response of rugate filters and multilayer mirrors. The conventionally used method in multilayer mirrors for ripple suppression in the passband will be compared with a similar simple method to remove the rugate filter sidelobes without apodization. The resulting layers are compared in performance with a typical quintic matching layer. An example based on silicon oxynitride alloys with refractive indices ranging between 1.47 and 1.83 was designed and deposited.     

Chirped bright and double-kinked quasi-solitons in optical metamaterials with self-steepening nonlinearity

Considering the self-steepening effect in a metamaterial (MM) can significantly change its behaviour. We study the propagation of ultrashort pulses in nonlinear MMs that is governed by a generalized nonlinear Schrö dinger equation with higher order effects such as pseudo-quintic nonlinearity and self-steepening effect. A class of chirped quasi-soliton solutions is obtained in the presence of the self-steepening term, and some of which are derived for the first time. The solutions comprise chirped bright quasi-solitons on a constant and zero background, kink and anti-kink quasi-solitons, and double-kink quasi-solitons. It is found that the nonlinear chirp associated with each of these waves is directly proportional to the intensity and its amplitude can be controlled by selecting the self-steepening and dispersion coefficients. Particular cases of chirp-free quasi-solitons are discussed. The conditions on MM parameters for the formation of these structures are also presented. The obtained results are important to explore much richer localized light pulses in MMs.     

Properties of defect modes in geometrically chirped one-dimensional photonic crystals

The variation of the transmission coefficient with defect mode frequency in a geometrically chirped photonic crystal with central defect layer has been investigated theoretically using transfer matrix method and validated experimentally by fabricating and characterizing such photonic crystals. The defect mode frequency is extracted by modeling the defect layer as a Fabry-Perot resonant cavity with mirrors replaced by two geometrically chirped photonic crystals. It is shown that the structural asymmetry of the chirped photonic crystals with respect to the central defect layer affects the width of the photonic band gap and also induces coupling variation between the eigenmodes of the defect layer and those at the band edges of the constituent photonic crystals. This leads to variation in the defect mode transmittance across the photonic band gap and introduces notches at positions where the eigenmodes of the band edges have maximum transmission.     

Chromium-scandium multilayer mirrors for the nitrogen K(alpha) line in the water window region

Chromium-scandium (Cr-Sc) is a promising material combination for multilayer mirrors in the water window region. A possible x-ray source for laboratory use in this wavelength range is the nitrogen K(alpha) line at 3.16 nm. High reflectivities at this wavelength can be achieved with Cr-Sc multilayer mirrors if the interfaces between adjacent layers are smooth. The growth parameters of the magnetron sputtering process for these materials have been optimized. It is shown that the reflectivity of such mirrors can be considerably improved by the application of a proper bias voltage during film growth. The high quality of the multilayer films is demonstrated with copper K(alpha) x-ray reflection and transmission electron microscopy. The reflective properties of the multilayers close to the nitrogen K(alpha) line were measured with synchrotron radiation for different angles of incidence. Reflectivities between R = 5.9% for near-normal incidence (theta = 1.5 degrees) and R = 29.6% for theta = 59.9 degrees were measured.