Laser-assisted photoionization for attosecond pulse measurements Z. X. Zhao Thanks Zenghu, CD and XM. KSU AMO seminar 9-29-2004

Review on ultrashort pulse measurements Outline Motivation Review on ultrashort pulse measurements Theory of laser assisted photoionization Spectra of circularly polarized laser assisted XUV photoionization of argon Pulse retrieving Summary By the way, measuring fs using as is simple.

Motivation Attosecond pulse generated by Zenghu’s group using polarization gating Measure it? In this work: Using circularly polarized laser pulses laser-assisted photoionization of Argon Study the procedures of measuring attosecond pulses Left circularly polarized IR Right circularly polarized IR Polarization gating Gas target as pulse IR Gas Spectra ? as pulses? Attosecond pulses have been generated by a couple of groups. Zenghu’s group is one of them. They use polarization gating to produce attosecond pulses. The idea can be illustrated by this cartoon. We have two circularly polarized laser pulses with certain time delay, one is left polarized and the other one is right polarized. If we overlap them temporally, at the time that the instantaneous intensities of the two pulses are comparable, the combined electric field will be linearly polarized, the time duration of the linear part can be controlled by the time delay. If we focus them into gas target, harmonics will be emitted through the rescattering or recombination processes. If the linear part is shorter than one optical cycle, the emitted light will have broad and continuum spectrum which implies it is an attosecond pulse, here we assume only the linear part gives harmonic generation. Once the attosecond pulse is generated, the first thing you want to do is to measure it to make sure its duration is really in attosecond region. It has been suggested by Canadian and Austrian group that attosecond pulses can be measured through laser assisted photoionizaton so called attosecond streak camera. In fact, attosecond pulses have been measured by Austria group using linearly polarized light assisted photoioniztion. Then, why are we doing this work? First, since the generation of attoseocnd pulses starts with circularly polarized light, we are going to measure it using CPLAPI. Second, Detail study on laser-assisted photoionization of Argon to provide general ideas of the spectra for the experimentalist. Third, …

Review on ultrashort pulse measurement Autocorrelation The pulse is split into two parts and then overlapped temporally in a nonlinear medium. Limitation on wavelength. X-ray pulses generated too weak. Cross-correlation Laser-modified photoionization spectrum provides the nonlinearity linking the x-ray to the laser pulse The atomic gas serves as the nonlinear medium. For long XUV pulses (>T0): For sub-laser-cycle pulses (this talk) Traditional method of measuring pulse duration relies on the principle of autocorrelation. So far the XUV/x-ray pulses generated by high harmonics are too weak to induce measurable nonlinearities of atomic media. Created in 2-18-04 modified 8/20/04 In order to measure a short pulse in time, we have to use a shorter one. What if we can not find a shorter one, we can use the pulse to measure itself, that is autocorrelation. However, autocorrelation is actually a fairly difficult measurement to make. It requires splitting the pulse into two replicas and then focusing and recombining them (overlapping them in space and time) in a second-harmonic-generation (SHG) crystal. So FROG and SPIDER are developed, In their simplest form, FORG and SPIDER can be considered as autocorrelation setup, but all these methods can not be applied to attosecond pulse measurement directly First it is the limitation on wavelength, difficult to find nonlinear medium working at soft X-ray region Second, so far the xuv pulses are still too weak to produced measurable nonlinear effect. Thus the concept of attosecond streak camera is developed. By the way, measuring fs using as is simple. This involves carefully aligning three sensitive degrees of freedom (two spatial and one temporal). It is also necessary to maintain this alignment while scanning the delay. Worse, the phase-matching-bandwidth condition mandates a thin SHG crystal, yielding a very weak signal and poor measurement sensitivity. This latter problem compounds alignment difficulties. As a result, an autocorrelator is a time-consuming and high-maintenance undertaking; it requires significant table space; and commercial devices cost ~ $20,000 or more. Using a longer pulse to do cross-correlation measurement. In time we can only get resolution upto a quarter of laser cycle. Which is based on laser-assisted photoionization. Attosecond pulses are cross correlated with Ti-Sapphire laser pulse, the atomic gas serves as the nonlinear medium. There are two scenario one is for long pulses with duration larger than laser optical cycle and for sublaser-cycle pulse, we are going to focus on latter. If we do time-delay measurement, we can get resolution upto a quarter of laser cycle. By mapping the duration to spectra, (argon, I=6.3x10^14W/cm^2) can be upto 100 as.

Attosecond streak camera: cross-correlation X-ray Laser Initiate atomic process Linear or circular  A general idea of building the cross-correlation can be demonstrated by a pump-probe scheme. Atomic process is initiated by the x-ray, then the evolution of the system is assisted by laser pulse. Laser field can be either linearly or circularly polarized. By changing the time delay between two pulses and measure the observables, one may get the time-resolved spectra. From the spectra, we can either obtain the cross-correlation function of two pulses or probe the atomic dynamics. We don’t have to do the time delay, we may find the time information of the pump pulse from the spectra at one time by comparing with that in laser-free case. Cross-correlation Probe atomic dynamics Time-resolved spectra

Theory of laser-assisted photoionizaton

Quantum mechanical model Strong field approximation: neglect Coulomb field Assuming no depletion of ground state, no structure Assume : XUV: ionization Laser: modify energy Stationary phase equation: ts: Saddle point The amplitude of coming out electron with momentum p is given by LAPI formula.

Linear polarized laser assisted photoionization classical model:   x y Linear polarization: Considering photoionization of atoms by x-rays. Suppose electrons are freed with momentum p_0 without laser field present. If the photoionization process is assisted by laser pulse, the electron will gain additional drift velocity from the pulse. Based on energy conservation, we have $ with W0 as hw-Ip. T is electron born time. For linear polarization, one finds:$ Electron energy at observation angle :

Linear polarized laser assisted photoionization XUV pulse Laser-free momentum distribution t0 t1 A(t) (drift velocity)

Circularly polarized laser assisted photoionization   x y  Circular polarization: (Replace  by ’ in that of linear case and noted that the definition of  is different from PRL88,173903)

Circularly polarized laser assisted photoionization Laser-free t0 t-1 XUV pulse A(t) (drift velocity)

HOW to characterize attosecond pulses from Spectra of circularly polarized laser assisted XUV photoionization of argon?

Laser-free photoionization of Argon Starting from 3P ground state, reduced dipole moment to s and d cont.: Total cross section proportional to Angular distribution: 15.759 ev of Ar. Asymmetry parameter  can be calculated from R- and R+ Single active electron model of Ar:

Laser-free photoionization: Cross section and asymmetry parameter Ix() XUV:1012W/cm2,0.1-2fs, 35 ev (21HG)

Transform-limited vs chirped pulses Do laser assisted photoionization to get pulse information Laser:5x1013W/cm2,5fs, 1.65 eV (750 nm,2.5fs) XUV:1012W/cm2,0.1-2fs, 35 ev (21HG)

No chirp– dependence on the phase angle of circularly polarized laser no laser xuv along x axis 0.1 fs for xuv

Dependence on the Chirp

Pulse retrieving

Procedures of pulse retrieving 1) Laser-free PI spectra as input: 2) Free guess of the phases: 3) Construct XUV pulse: 4) Calculate laser-assisted spectra: 5) Compared with measured one: 6) Find best fit of the phases: 1. genetic algorithm 2. 5 parameter fitting

Straightforward Genetic Algorithm Discretize the phases: Genetic algorithm: 15 bits, 200 parameters, 200 population, 200 generation 8 hours 1fs, chirp 10 as an example

5-parameter GA Taylor expansion of the phase:

Transform limited (no chirp) XUV pulses 0.2 fs Energy width decreases as pulse duration increases The angular distribution of final momentum For given energy broader as XUV pulse duration increases For XUV duration approaching laser cycle: image expands in all direction Sidebands begin to emerge 0.5 fs 2 fs no laser

Double-pulse XUV light (a) no laser (b),(c),(d) laser phase with 0, /4 and /2

mapping

Chirp-dependence Stationary phase equation (no chirp): ts: Saddle point Linearly chirped XUV pulse (, chirp parameter): Energy center of gravity at given angles: spiral curve

Summary Calculated spectra Retrieved electric field of attosecond pulse Retrieving method can be further improved