Generation of Extreme Ultraviolet Radiation

Generation of Extreme Ultraviolet radioactivityGeneration of Extreme Ultraviolet Radiation from Intense Laser-Plasma Interactions victimisation Two-Colour Harmonics instruct HISTORYOver the past few decades break by dint ofs in the production of raging optical maser works chip in meant that multi-terawatt and even petawatt systems are now amount in laboratories**. This has been achieved by dint of reduction of the urge duration, originally from nano south impetuss down to femto irregular and late ambit attosecond levels (1as =10-18s)**. This mate with important gains to systems, such as the chirped quiver working out technique (CPA)**, has allowed optical maser beats to be amplified to higher peak powers than ever in the first place and use in laser-matter interactions. The notioning scientific drive from developments such as these pushed doable laser intensities from 109W/cm2 to the 1014W/cm2, at which the interaction among these high impregnation lasers and profound negatron-free gas was studied**.Only recently thanks to advances in both(prenominal) laser performance and computer simulation tools has call for on laser-plasm interactions in the coevals of HHG made progress, providing the possibility to generate sources of incoherent electromagnetic ray of gay of short turn everyplacelength and pulsation durations**. As further study was carried out on the interaction of light with relativistic free negatrons in plasma, it has r severallyed a loony toons now in which generation of high- benevolents of the fundamental laser, soft and hard x-rays, and shorter pulse duration (1as) lasers of intensities reaching 1018W/cm2 are now possible**. Due to this the generation of high-order-harmonics from high- devotion laser interactions has been a major area of attoscience research indoors the hold water decade.HHG PRODUCTIONHigh harmonic generation (HHG) refers to the edge in which a high intensity laser pulse is centralisee onto a target, classically a noble gas, in which strong nonlinear interactions result in the generation of very high harmonics of the optical oftenness of the pulse**. This leave alone occur for intensities of 1014W/cm2 and above, where typically only a humbled amount of this nix is converted into the higher harmonics. From these high-harmonics, spatially and temporally coherent attosecond pulses of extreme ultraviolet ray light can be generated, which can then be utilize as a reliable source of highly tuneable short wavelength actinotherapy therapy therapy in many different applications e.g. x-ray spectroscopy**.In the instance of high intensity laser-gas interactions this is achieved by tailoring the intensity of the laser pulse so that its galvanising dramaturgy amplitude is similar to the galvanic electron orbit in the target atoms**. From this the lasers electric land is able to remove electrons from the atoms finished tunnel ionization, at which brain the electron s are accelerated in the line and, with certain conditions controlled, are made to collide with the newly created ion upon recombination. The resulting contact generates the rise of high cypher photons**, as fork upn in fig 1.Fig. 1 HHG threesome step model.This is known as the three step model electron is detached from atom through tunnel ionisation, then accelerated at heart the subject away from atom, then accelerated back towards atom where it collides and recombines, from this collision all the zip fastener lost appears as emitted HHG ultraviolet photons.HHG from laser-gas interactions have been used extensively to generate attosecond pulses but is limited in flux and photon energy by low conversion efficiencies between the driving laser energy and the attosecond pulses, this can be attributed to two key parts loss of stage matching between the driving laser to the generated extreme ultraviolet (XUV) radiation as its propagated through the gas over a relatively large distance, and a restriction on the intensity of the driving laser due to the ionisation brink of the target gas, this saturation intensity is roughly 1016W/cm2**. Meaning laser intensities above this threshold limit leave over-ionise the gas leaving no neutral atoms left to generate the XUV harmonics.The use of laser-solid interaction offers the opportunity of reaching much higher attosecond pulse intensities and generation efficiencies beyond the capabilities of gas base HHG**. The method of generating high-harmonics in laser-solid interactions is fundamentally different than that of laser-gas interactions.Interaction of intense ultrashort laser pulses (of pulse duration around a few femtoseconds) on an optically polished solid surface results in the target surface being tout ensemble ionise, generating a mute plasma which will act as a mirror, called a plasma mirror**. The reflection of these high intensity laser pulses will be affected by a wave relocation set-up in the electrons within the plasma surface ca apply it to discolour the reflected laser field, resulting in the production of upshifted light pulses and the generation of high-order harmonics**. Due to the coherent nature of this process, these generated harmonics are sort-locked and emerge as attosecond pulse.Fig. 2 Laser pulse moving towards over mysterious plasma.A key property of this plasma is its electron tightness, this determines whether the laser is reflected, absorbed or not allowed to pass through. This is known as the niggardliness gradient scale length, as the laser pulse interacts with the target and forms a plasma it creates a compose that extends out into the vacuum, forming a plasma meanness profile. This is a deprecative factor in HHG and comprises of two regionsOverdense scale length, Lod If the electron tightfistedness is equal to the critical density of the target or above, extending up to the maximum target density, the laser pulse is unable to penetrate thr ough the target and is so reflected or absorbed.Underdense scale length, Lud If the electron density is under this critical density the laser will penetrate through, with some absorption.Fig. 3 Plasma density profile, Lud is underdense region, Lod is overdense region.The critical density is determined fromWhere is the angular frequency of the laser.As stated before the target surface is highly ionised by the leading edge of the laser pulse, known as the pre-pulse, thus becoming rapidly over-dense and creating a plasma mirror of sufficient electron density, nenc**. HHG within plasma requires laser intensities 1015W/cm2 for 800nm field**, which is usually stated in terms of a normalised vector potential of a0, whereIn which e and m are electron charge and electron mass various(prenominal)ly. c is speed of light in vacuum. E is the amplitude of the lasers electric field. I is the lasers intensity. l is the laser frequency and l is the laser wavelength. Therefore HHG in plasma requir es at least an a00.03.Recently is was discovered** that there are two instruments that lead to HHG from solid density plasma surfaces Relativistic vacillate mirror (read-only memory) crystalline wake emission (CWE)These two process result in different distortions to the reflected laser field and therefore a completely different harmonic spectra produced.CWECoherent wake emission is a process of three stepsElectrons on the surface of the plasma are gaunt into the vacuum by the laser field and accelerated back into the dense plasma at one time they have gained energy from the driving laser field.When propagating within the dense plasma these fast electrons form ultrashort destinyes, creating plasma oscillations in their wake. in spite of appearance the non-uniform region of the plasma (produced from the density gradient between the plasma-vacuum boundary) the electron oscillations will radiate energy in the form of light of various local anesthetic plasma frequencies found withi n this gradient.This process will occur once for every laser one shot therefore the spectrum of the emitted light will consist of harmonics of the laser frequency, in which CWE harmonic spectra have a cutoff at the maximum plasma frequency pmax **. This mechanics is predominant at reasonably relativistic intensities of a01, and short but finite plasma gradient lengths of **.Coherent wake emission has only recently been identified as a factor in HHG in laser-solid interactions but it is known that it along with fixed storage contributes to the generation of high-harmonic orders below pmax and the strength of their respective influence below this threshold is determined by laser intensity**.ROMThe new(prenominal) mechanism involved in the generation of high-harmonics from laser-plasma interactions is the relativistic hover mirror process, this dominates for relativistic normalised vector potentials of a01, although recent studies have shown that ROM harmonics can be ascertained e ven at lower intensities when the plasma gradient length is virtually **.ROM process occurs when surface electrons in the plasma are oscillated collectively by the high intensity incident laser field to relativistic speeds, the plasma will reflect what it observes as a laser pulse of frequency +. This + frequency is a higher upshifted frequency of the fundamental pulse due to a Doppler effect produced from the relative motion of the laser field to the moving reflection point on the oscillating plasma surface. The veridical reflected laser pulse will have a frequency of ++ due to a second Doppler upshift effect as it moves towards an observer/target. This is known as Einsteins relativistic Doppler effect, in which the reflected pulse frequency is upshifted by a factor of 42**. Fig 4. Schematic of a relativistic oscillating critical density plasma interaction.From past research it has been found that from this mechanism a power-law decay scaling of I(n)ROMn-8/3 is dominant (where n is the harmonic order) in the harmonic spectrum for harmonic orders above the CWE cut-off point, nCWE,** this is the harmonic order colligate to the maximum plasma frequency of the target, pmax, mentioned antecedently. WherenCWE = nmax = pmax/l = In which l is the frequency of the laser, is the maximum electron density of the target, Nc is the critical density shown previously.From this process initial femtosecond pulses can be used to create attosecond pulses. When coupled to a relativistic oscillating mirror it adds an oscillatory extension to Einsteins relativistic Doppler effect, so due to the periodic motion of the mirror to the laser field and the double Doppler upshifts this results in the production of extreme ultraviolet (XUV) harmonics**. These ultra-short pulses have been the focus of much scientific research recently as they offer a promising way to resolve in the time do primary(prenominal) the ultrafast kinetics of electrons within actuals**.Although the relativis tic oscillating mirror process is more suit as a macroscopic model for the effective reflection point of the laser field. It assumes that the surface electrons gang together as the target is ionised and move out into the vacuum to form the plasma where they remain in the overdense region ensuring that the laser field is completely reflected. More recently studies have discovered there is another mechanism in the relativistic authorities that can contribute to the harmonic spectrum via a different process entirely.CSEThis other process is known as Coherent synchrotron emission (CSE)** and is needed to exempt observations that do not fit the previous two models, in which dense electron nano clumpes are created at the plasma-vacuum boundary where they produce coherent XUV radiation through coherent synchrotron emission. This is a microscopic model of HHG in laser-solid interactions. It models the electrons in the plasma moving, in dense bunches, under the influence of the incident laser field and subsequent field produced from the movement of charges within the plasma. These nanobunches are periodically formed and coherently accelerated through an instantaneously synchrotron-like orbit during each laser cycle, for oblique laser incidences. As certain conditions, such as ultrashort plasma density scale length, are met these bunches emit bursts of sub-femtosecond intense high-frequency radiation. This radiation has properties dependent on the electron trajectories and it has been shown that it can be modelled as synchrotron radiation**, therefore the coherent XUV emissions are distinctly different from that produced in ROM from relativistic Doppler upshifts. In reality actual electron dynamics whitethorn be a mix of CSE and ROM, but due to the complex nature of the changing fields within a plasma it makes it impossible to analytically model with accuracy. Therefore requiring the use of computer simulations to deal with the electron trajectories and their respec tive radiation emissions.PREVIOUS experimentationSBased on the work of Edwards et al, 2014, in which the study of attosecond XUV pulse generation from relativistic driven overdense plasma targets with two-colour incident light was performed they used 1D, three velocity, particle-in-cell ( photographic film) code simulations, which treat oblique incidence with boosted frames, to show how pulse intensity can be improved. They converted a small amount (5%) of the fundamental laser field energy to an special laser operating at the second harmonic of the fundamental frequency, to importantly enhance the intensity of the generated attosecond pulses by multiple orders of magnitude.This was based on previous work in which mixing of the fundamental driving laser frequency with the second harmonic was performed on laser-gas interactions to increase the attosecond pulse intensity and isolation (K. J. Schafer et al, 1992).Edwards show that a significant improvement was likewise possible th rough this mixing method in laser-solid interactions following the Similarity theory (proposed by Gordienko and Pukhov,**), that suggests the behaviour of laser-plasma interactions follow a similarity parametric quantity of1/S = a0/N lWhere S = ne/a0nc, is a similarity parameter and N = ne/nc which is the ratio of electron density of the plasma to its critical density.Therefore from this it would appear that by two-bagger l while using the same laser field amplitude the reflected attosecond pulse intensity would excessively be increase by a factor of two.One of the main limiting parameters in these experiments is the achievable value of a0, while the largest solid material value of N (lithium at =800nm) is 75, so this type of frequency doubling appears to be a promising pathway to optimising attosecond pulse intensity, although a drawback of this is the veto effect it has on the isolation of the reflected pulses.Therefore they stated that a two-colour method, of part convertin g a portion of the fundamental laser field energy to the second harmonic, would be a more attractive alternative. Through this process the advantages of using a higher incident frequency, by increasing the gradient of the electric field at certain points within the pulse generation cycle, without the tie in decrease in pulse isolation and loss of energy associated to ingenuous frequency doubling can be exploited.In their study they used a normal-incidence beam on a step-like plasma density profile using a mix of the first and second harmonic with a physical body difference of to produce harmonics with a higher intensity than all incident field individually. They demonstrate substantial gains after the addition of a small amount of the second harmonic to achieve attosecond pulse sweetening of factors 10. As well as a 10-fold enhancement when using density gradients of 0.05 and 0.15 with conversions of the fundamental to the second harmonic of 5%-10% at an angle of incidence of =30o.Therefore Edwards was able to go on and state that the relative manakin of the two incident harmonics were a critical factor in the improvement in attosecond pulse intensity. This is due to the difference in the driving electric field waveform and corresponding resultant electron motion as is varied. Where they linked the strongest attosecond pulse intensities with sharp transitions in the driving electric field that are aided by the addition of the second harmonic at optimum phases, while phases that break the driving field transition chasten the attosecond intensities to levels sometimes substantially below what could be achieved pre-mixing of the harmonics.Therefore when harmonics are feature without thought to their phases they do not always improve the attosecond strength.Further detail into the trajectories of dense electron bunches, which emit synchrotron like radiation (CSE) was given to care explain this effect, where supressed pulse electrons were shown to follo w a longer and slower motion before being accelerated and subsequently emitting, resulting in longer drawn-out trajectories. Whereas electrons that contribute to the improvement of the attosecond pulse strength are shown to deliver a larger field before and during emission. This meant their velocity and acceleration components were larger than the conquer electrons, giving them more energy as it is driven back into the plasma. general they state that the larger the electric field experienced by the electrons increases the intensity of the reflected attosecond pulse, due to the number of electrons travelling in a dense bunch increasing as this larger field that the electrons near the surface experience compresses them into higher density bunches.Another study performed by Yeung et al, 2016, focused on controlling the attosecond motion of strongly driven electrons at the boundary between the pre-formed plasma and the vacuum. They demonstrated experimentally that by precisely adding an additional laser field, at the second harmonic of the fundamental driving frequency, attosecond control over the trajectories of the dense electron bunches involved in intense laser-plasma interactions can be achieved. From this considerable improvements in the high-harmonic generation intensity was observed, which confirms the theoretical work by Edwards in two-colour fields reviewed previously while developing upon this to further factors.through an experiment they showed that attosecond control over the phase relationship of the two driving fields is necessary to optimise the reflected attosecond pulse intensity. While also using PIC simulations to determine the optimal and worst phase relationships, in which a phase of was found to optimise the emission.Microscopic focus determined that during each cycle the emission of the attosecond pulse begins as a primary electron bunch which is compressed and then quickly accelerated away from the surface up to relativistic velocities , from here it emits before it disperses and returns back to the plasma. Secondary bunches are also present but these were found not to have a significant effect harmonic spectrum for orders 20. These bunches were found to emit when their velocities where at their max, which confirmed that the two-colour field phase matched the emitted XUV to the acceleration produced from the fundamental laser field. While at the poorest phase relationship, which Yeung found to be , a plateau in the driving laser field is created which impedes the acceleration of the electrons from the surface, therefore reducing the density of the electron bunch produced that can emit.They concluded from the data provided by the simulations that control of the relative phase of the two colour driving fields has a significant effect the electron bunch dynamics.While from the experimental data their collected it was demonstrated that the HHG produced from the two-colour field was increased substantially when no lase r pre-pulse was involved, or equivalently when the plasma has shorter density scale length. Confirming the work of Edwards et al, 2014, that two-colour fields generate importantly more higher-harmonic orders than that of a fundamental field alone, even when only a small percentage (5%-10%) of the fundamental laser energy is converted to the second harmonic.INTRODUCTION TO TWO-COLOUR HARMONICS-ABSTRACT apprise SUMMARY OF EXPERIMENT, RESULTS AND CONCLUSION 1xINTRODUCTIONBRIEF HISTORY .5xHHG PRODUCTION .5xCWE 1xROM 2x (inc. plasma theory e.g. scale length)CSE 1x similarity WITH GAS EXPERIMENTS 1xPAST EXPERIMENTS LEADING UP TO THIS ONE 2xINTRODUCTION INTO SPECIFICS OF THIS EXPERIMENT 1xMETHODPIC CODES EXPLAINED 2xEPOCH DETAILS 1xLASER DETAILS 1x function OF ANALYSIS .5xCREATION OF GRAPHS .5xRESULTSGRAPHSCOMPARE CONTRASTIMPLICATIONSCONCLUSIONFURUTRE RESEARCH 1xIMPROVEMENTS 1x