Margarita Khokhlova: Analytical theory of resonant high-order harmonic generation

abstract as PDF file here: PDF file

Analytical theory of resonant high­order harmonic generation

M. A. Khokhlova1,2, V. V. Strelkov1

1. Theoretical Department, General Physics Institute of Russian Academy of Sciences,119991, 38 Vaviliva str., Moscow, Russia

2. Department of Physics, M. V. Lomonosov Moscow State University, 119991, Leninskie gory str., Moscow, Russia

Properties of resonant high­order harmonics generated in intense laser field are actively studied both 

experimentally [1­3] and theoretically [4­7]. Very efficient generation of the harmonic resonant with the 

transition from the bound to the autoionizing state was demonstrated in the experiments using plasma plumes 

[1,2] and Xe jet [3].

We suggested analytical quantum­mechanical theory describing the effect of quasi­stationary state on HHG 

[7]. We start with the time­dependent Schrodinger equation for an atom or ion in an external laser field. The 

wave function is presented as a sum of the ground state, unperturbed continuum and the quasi­stationary state. 

To solve the Schrödinger equation we derived the perturbation method in which the solution obtained in the 

absence of the quasi­stationary state by Lewenstein et al. in Ref. [5] is taken as an unperturbed solution. 

Assuming that (i) the ionization rate is low, (ii) the quasi­stationary state population is low, (iii) the quasi­

stationary state is not affected with the laser field, and (iv) the quasi­stationary state width * is much less than 

the quasi­stationary state energy, we find the following equation for the spectral complex amplitude of the 

microscopic response at the frequency Z

 (atomic units are used):

 P ( Z ) P nr ( Z ) F (Z )

a

 * / 2 o

F (Z )

 « 1 Q »

¬

 'Z i* / 2 1⁄4

where is the 

 P

 nr

 (Z

 )

 spectrum of the non­resonant contribution, * is the resonance width, Q is a complex 

parameter 

 defined by the properties of the generating atom or ion, but not 

depending on the laser field. So the resonant harmonic line is presented as a product of the F (Z ) Fano­like 

[8] factor and the harmonic line which would be emitted in the absence of the AIS. 

Our theory allows calculating not only the resonant harmonic intensity, but also its phase. We show that there 

is a rapid variation of the phase in the vicinity of the resonance. Our calculations reasonably agree with recent 

harmonic phase measurements [9]. 

The other direction of our research is the study of the phase properties of the cut­off harmonics. We study the 

harmonic phase dependence on the laser intensity both analytically and numerically. Moreover, we investigate 

the dephasing between adjacent harmonics to study the emission time of the attosecond pulses. Thus, the 

optimum conditions for the shortest attosecond pulse generation using the cut­off harmonics are suggested.

References

>1@ R. A. Ganeev, "High­order harmonic generation in a laser plasma: a review of recent achievements", J. Phys. B: At. Mol. Opt. Phys. 40, 

R213 (2007).

[2] R. A. Ganeev, V. V. Strelkov, C. Hutchison, A. Zaïr, D. Kilbane, M. A. Khokhlova, and J. P. Marangos, "Experimental and theoretical 

studies of two­color­pump resonance­induced enhancement of odd and even harmonics from a tin plasma", Phys. Rev. A 85, 023832 (2012).

[3] A. D. Shiner, B. E. Schmidt, C. Trallero­Herrero, H. J. Wörner, S. Patchkovskii, P. B. Corkum, J­C. Kieffer, F. Légaré & D. M. 

Villeneuve, "Probing collective multi­electron dynamics in xenon with high­harmonic spectroscopy", Nature Physics 7, 464 (2011).

[4] V. Strelkov, "Role of Autoionizing State in Resonant High­Order Harmonic Generation and Attosecond Pulse Production", Phys. Rev. 

Lett. 104, 123901 (2010).

[5] M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L’Huillier, and P. B. Corkum, "Theory of high­harmonic generation by low­frequency 

laser fields", Phys. Rev. A 49, 2117­2132 (1994).

[6] Jan Rothhardt, Steffen Hädrich, Stefan Demmler, Manuel Krebs, Stephan Fritzsche, Jens Limpert, and Andreas Tünnermann, "Enhancing 

the Macroscopic Yield of Narrow­Band High­Order Harmonic Generation by Fano Resonances", Phys. Rev. Lett. 112, 233002 (2014).

[7] V. V. Strelkov, M. A. Khokhlova, and N. Yu Shubin, "High­order harmonic generation and Fano resonances", Phys. Rev. A 89, 053833 

(2014).

[8] U. Fano, "Effects of Configuration Interaction on Intensities and Phase Shifts", Phys. Rev. 124, 1866­1878 (1961).

[9] S Haessler, V Strelkov, L B Elouga Bom, M Khokhlova, O Gobert, J­F Hergott, F Lepetit, M Perdrix, T Ozaki and P Salières, "Phase 

distortions of attosecond pulses produced by resonance­enhanced high harmonic generation", New J. Phys. 15, 013051 (2013).

[10] J. Seres, E. Seres, D. Hochhaus, B. Ecker, D. Zimmer, V. Bagnoud, T. Kuehl and C. Spielmann, "Laser­driven amplification of soft X­

rays by parametric stimulated emission in neutral gases", Nature Physics 6, 455–461 (2010)

JC: Daniel: Disclosing intrinsic molecular dynamics on the 1-fs scale through extreme-ultraviolet pump-probe measurements

Through frequency up-conversion of polarization-shaped, femtosecond laser pulses nonlinearly interacting with xenon atoms, energetic, broadband, coherent, XUV continuum radiation is generated. By exploiting the thus-formed short-duration XUV pulses, all the optically allowed excited states of H2are coherently populated. Nuclear and electronic 1-fs-scale dynamics are subsequently investigated by means of XUV-pump–XUV-probe measurements, which are compared to the results of ab initiocalculations. The revealed dynamics reflects the intrinsic molecular behavior, as the XUV probe pulse hardly distorts the molecular potential.

http://journals.aps.org/pra/abstract/10.1103/PhysRevA.89.023420

Dane: DM: Recent results TBC

Peter: JC: Effect of multiple conduction bands on high-harmonic emission from dielectrics

We find that, for sufficiently strong mid-IR fields, transitions between different conduction bands play an important role in the generation of high-order harmonics in a dielectric. The transitions make a significant contribution to the harmonic signal, and they can create a single effective band for the motion of an electron wave packet. We show how high harmonic spectra produced during the interaction of ultrashort laser pulses with periodic solids provide a spectroscopic tool for understanding the effective band structure that controls electron dynamics in these media.

http://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.013405

No JC, but OSA/SPIE student chapter seminar

No Jc today, but please go to Blackett 630 for 15:00 for this seminar organised by the local OSA/SPIE student chapter!

Microcirculation imaging with light and sound

Martin J. Leahy, Haroon Zafar, Sean O’Gorman, Aedán Breathnach,  and Hrebesh M. Subhash

Tissue Optics & Microcirculation Imaging Facility, National University of Ireland, Galway, Ireland and National Biophotonics & Imaging Platform, Ireland.

Structural and functional imaging of the microcirculation is necessary to understand many diseases such as diabetes mellitus, heart disease, peripheral vascular disease and arteriosclerosis. We have developed several methods for assessment of both the structural and dynamic properties of the capillaries in the upper dermis and the vessels which supply them.

We have developed 2D devices based on polarisation spectroscopy which output colour-coded maps which are sensitive to the concentration of red blood cells in the skin tissue. The hardware design consists of two orthogonally placed polarisation filters over the light source and sensor of a standard digital camera and utilises the video mode to provide 15/30 frames per second at a resolution of ~ 200 mm. We have also developed correlation mapping optical coherence tomography (cmOCT) to render the 3D microcirculation. To obtain microvascular maps without motion artefact, we used the full-field technique and applied the cmOCT algorithm to the data. We are developing miniature low cost OCT. and nanosensitive OCT [3&4]. Since the depth is limited to one or two millimetres with OCT and much less with full-field OCT, we have recently begun to work with photoacoustic tomography where we find a backscatter type probe, similar to existing clinical ultrasound, has advantages of ease of use, speed and familiarity for radiographers.


References:
1. Microcirculation Imaging. (Wiley-VCH), Leahy, M.J. editor, 2012.
2. Enfield, J., Jonathan, E. and Leahy, M.J., 2011. In vivo imaging of the microcirculation of the volar forearm using correlation mapping optical coherence tomography (OCT). Biomedical Optics Express 2 (5) 1184-1193.
3. Dsouza, R., Subhash, H.M., Neuhaus, K., Hogan, J., Wilson, C., and Leahy, M.J. 2014, Dermascope guided multiple reference optical coherence tomography, Biomedical Optics Express, 5(9) 2870-2882. http://dx.doi.org/10.1364/BOE.5.002870
4. Alexandrov, S., Subhash, H.M., Zam, A. and Leahy M.J. 2014, Nano-sensitive optical coherence tomography, Nanoscale, 6, 3545-3549, DOI: 10.1039/C3NR06132A

Daniel: DM: Experimental methods for time-resolved measurements of molecular electron dynamics

In the ‘attosecond lab’ we can now generate synchronised attosecond pulses at 20eV and 90eV, which we hope to use to make time resolved measurements of ultrafast electronic processes in atoms and molecules, such as charge migration. In conjunction, a new electron-ion particle detector has been installed (the ‘VMI-TOF’) in order to be able to get as much information as possible from the probe step in a ‘pump-probe’ measurement. I will try to give a brief overview of the theory of charge migration (from a non-theorist stand point!) and the challenges of making attosecond pump - attosecond probe measurements. I will then discuss the experimental implementation of spLEAD (single photon Laser Enabled Auger Decay) , a scheme to measure electron dynamics in the glycine molecule, and the operation of the VMI-TOF, with a view to informing future experiments .

Christian: JC: Efficient generation of below-threshold harmonics for high-fidelity multi- photon physics in the VUV spectral range

We demonstrate the generation of microjoule level, sub-20-fs, Ti:Sa fifth-harmonic pulses utilizing a loose-focusing geometry in a long Ar gas cell. The VUV pulses centered at 161.8 nm reach pulse energies of 1.1 μJ per pulse, while the corresponding pulse duration is measured with a second-order, fringe-resolved autocorrelation scheme to be 18±1  fs . Nonresonant, two-photon ionization of Kr and three-photon ionization of Ne verify the fifth-harmonic pulse high-intensity content and indicate the feasibility of multi-photon VUV pump-VUV probe studies of ultrafast atomic and molecular dynamics.

http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-40-8-1675