Abstract
High harmonic generation is a table-top laboratory-sized facility has emerged as another potential for extreme ultraviolet/X-ray coherent source in high-resolution microscopy and imaging applications. Previous research on coherence study in HHG has relied primarily on fringe visibility to characterize spatial coherence. To our knowledge, no studies have been done to calculate spatial coherence length of a high harmonic generation source. To determine the extent to which the source remain coherent, we investigated the spatial coherence properties by means of Young’s double slit experiment using slit separation from 20 to 150 μm in order to obtain interference data. An analytical method is used to estimate fringe visibility eventually be used to characterize coherence properties of each harmonic. In this work, high harmonic generation is produced in gaseous medium driven by intense laser pulses. Contrary to the assumption that coherence length may depend on harmonic intensity, however, our findings show that the spatial coherent length of the HHG source does not depend on harmonic intensity, but decreases with harmonic order, with a significant decrease in harmonics near the cut-off. This feature resembles the shape of the harmonic spectrum of a single atom.
Similar content being viewed by others
References
Abdul Aziz, N.A., Tarmizi, E.Z.M., Mansor, Y.: Coherence measurement at different spatial points across high harmonic generation source using different spatial filter. Macromol. Symp. 397, 2000292 (2021)
Born, M., Wolf, E.: Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Cambridge University Press, New York (2001)
Brabec,T.: Strong Field Laser Physics. New York: Springer, firsted., 2008
Clark, J.N., Huang, X., Harder, R., Robinson, I.K.: High-resolution three-dimensional partially coherent diffraction imaging. Nat. Commun. 3(1), 1–6 (2012)
Coisson, R.: Spatial coherence of synchrotron radiation. Appl. Opt. 34(5), 904–908 (1995)
Corkum, P.B.: Plasma perspective on strong-field multiphoton ionization. Phys. Rev. Lett. 71(13), 1994–1997 (1993)
Gaarde, M.B., Schafer, K.J.: Quantum path distributions for high-order harmonics in rare gas atoms. Phys. Rev. A 65(3), 31406 (2002)
Geloni, G., Saldin, E., Samoylova, L., Schneidmiller, E., Sinn, H., Tschentscher, T., Yurkov, M.: Coherence properties of the European XFEL. New J. Phys. 12(3), 35021 (2010)
Ghimire, S., DiChiara, A.D., Sistrunk, E., Agostini, P., DiMauro, L.F., Reis, D.A.: Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7(2), 138–141 (2011)
Ghimire, S., Reis, D.A.: High-harmonic generation from solids. Nat. Phys. 15(1), 10–16 (2019)
Hernández-García, C., Pérez-Hernández, J.A., Ramos, J., Jarque, E.C., Roso, L., Plaja, L.: High-order harmonic propagation in gases within the discrete dipole approximation. Phys. Rev. A 82(3), 33432 (2010)
Hädrich, S., Rothhardt, J., Krebs, M., Demmler, S., Klenke, A., Tünnermann, A., Limpert, J.: Single-pass high harmonic generation at high repetition rate and photon flux. J. Phys. B: At. Mol. Opt. Phys. 49(17), 172002 (2016)
Jin, C.: Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium. Springer Science & Business Media, Berlin (2013)
Kapteyn, H.C., Murnane, M.M., Christov, I.R.: Extreme nonlinear optics: a coherent X rays from lasers. Phys. Today 58(3), 39–44 (2005)
Kim, H.T., Janulewicz,K.A., Kim,C.M.,Choi,I.W., Sung,J.H., Yu,T.J., Lee,S.K., Jeong,T.M., Ko,D.K., Nickles,P.V., Tummler,J., Lee,J.: Investigation on the spatial properties of siver X-ray laser using grip schemes, pp.143–152. Belfast, UK: Springer, (2008)
Kneip, S., McGuffey, C., Martins, J.L., Martins, S.F., Bellei, C., Chvykov, V., Dollar, F., Fonseca, R., Huntington, C., Kalintchenko, G.: Bright spatially coherent synchrotron X-rays from a table-top source. Nat. Phys. 6(12), 980–983 (2010)
Kulander, K.C., Shore, B.W.: Calculations of multiple-harmonic conversion of 1064-nm radiation in Xe. Phys. Rev. Lett. 62(5), 524–526 (1989)
Lan, P., Ruhmann, M., He, L., Zhai, C., Wang, F., Zhu, X., Zhang, Q., Zhou, Y., Li, M., Lein, M.: Attosecond probing of nuclear dynamics with trajectory-resolved high-harmonic spectroscopy. Phys. Rev. Lett. 119(3), 33201 (2017)
Lewenstein, M., Balcou, P., Ivanov, M.Y., Lhuillier, A., Corkum, P.B.: Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49(3), 2117 (1994)
Lhuillier, A., Balcou, P., Candel, S., Schafer, K.J., Kulander, K.C.: Calculations of high-order harmonic-generation processes in xenon at 1064 nm. Phys. Rev. A 46(5), 2778–2790 (1992)
Lhuillier, A., Schafer, K.J., Kulander, K.C.: Theoretical aspects of intense field harmonic-generation. J. Phys. B Atom. Mol. Opt. Phys. 24(15), 3315–3341 (1991)
Li, J., Lu, J., Chew, A., Han, S., Li, J., Wu, Y., Wang, H., Ghimire, S., Chang, Z.: Attosecond science based on high harmonic generation from gases and solids. Nat. Commun. 11(1), 1–13 (2020)
Nugent, K.A.: Coherent methods in the X-ray sciences. Adv. Phys. 59(1), 1–99 (2010)
Paterson, D., Allman, B.E., McMahon, P.J., Lin, J., Moldovan, N., Nugent, K.A., McNulty, I., Chantler, C.T., Retsch, C.C., Irving, T.H.K., Mancini, D.C.: Spatial coherence measurement of X-ray undulator radiation. Opt. Commun. 195(1–4), 79–84 (2001)
Pfeiffer, F.: X-ray ptychography. Nat. Photonics 12(1), 9–17 (2018)
Popmintchev, T., Chen, M.-C., Popmintchev, D., Arpin, P., Brown, S., Ališauskas, S., Andriukaitis, G., Balčiunas, T., Mücke, O.D., Pugzlys, A., et al.: Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers. Science 336(6086), 1287–1291 (2012)
Quiney, H.M.: Coherent diffractive imaging using short wavelength light sources. J. Mod. Opt. 57(13), 1109–1149 (2010)
Raymondson,D.A., Sandberg,R.L., Townsend,E., Seaberg,M., La-o voralkiat,C., Murnane,M.M., Kapteyn,H.C., Raines,K., Miao,J., Schlotter,W.F., Ieee.: Tabletop Coherent Diffractive Microscopy with Soft X-rays from High Harmonic Generation at 13.5 nm. 2009 Conference on Lasers and Electro-Optics and Quantum Electronics and Laser Science Conference, New York: Ieee, (2009)
Rivenson, Y., Wu, Y., Ozcan, A.: Deep learning in holography and coherent imaging. Light Sci. Appl. 8(1), 1–8 (2019)
Rundquist, A., Durfee, C.G., Chang, Z.H., Herne, C., Backus, S., Murnane, M.M., Kapteyn, H.C.: Phase-matched generation of coherent soft X-rays. Science 280(5368), 1412–1415 (1998)
Sandberg, R.L., Paul, A., Raymondson, D.A., Hädrich, S., Gaudiosi, D.M., Holtsnider, J., Ra’anan, I.T., Cohen, O., Murnane, M.M., Kapteyn, H.C.: Lensless diffractive imaging using tabletop coherent high-harmonic soft-x-ray beams. Phys. Rev. Lett. 99(9), 98103 (2007)
Sandberg, R.L., Song, C.Y., Wachulak, P.W., Raymondson, D.A., Paul, A., Amirbekian, B., Lee, E., Sakdinawat, A.E., La-O-Vorakiat, C., Marconi, M.C., Menoni, C.S., Murnane, M.M., Rocca, J.J., Kapteyn, H.C., Miao, J.W.: High numerical aperture tabletop soft x-ray diffraction microscopy with 70-nm resolution. Proc. Natl. Acad. Sci. U.S.A. 105(1), 24–27 (2008)
Shan, B., Cavalieri, A., Chang, Z.: Tunable high harmonic generation with an optical parametric amplifier. Appl. Phys. B 74(1), s23–s26 (2002)
Stein, G.J., Keathley, P.D., Krogen, P., Liang, H., Siqueira, J.P., Chang, C.-L., Lai, C.-J., Hong, K.-H., Laurent, G.M., Kärtner, F.X.: Water-window soft x-ray high-harmonic generation up to the nitrogen K-edge driven by a kHz, 2.1 μm OPCPA source. J. Phys. B: At. Mol. Opt. Phys. 49(15), 155601 (2016)
Sutherland, J.R., Christensen, E.L., Powers, N.D., Rhynard, S.E., Painter, J.C., Peatross, J.: High harmonic generation in a semi-infinite gas cell. Opt. Express 12(19), 4430–4436 (2004)
Takahashi, E.J. , Kanai, T., Ishikawa, K.L., Nabekawa, Y., Midorikawa, K.: Coherent water window X ray by phase-matched high-order harmonic generation in neutral media, Phys. Rev. Lett. vol. 101(25), 253901-1 (2008)
Teichmann, S., Chen, B., Dilanian, R.A., Hannaford, P., Dao, L.V.: Spectral characteristics across the spatial profile of a high-harmonic beam. J. Phys. D Appl. Phys. 42(13), 135108 (2009)
Vampa, G., Ghamsari, B.G., Mousavi, S.S., Hammond, T.J., Olivieri, A., Lisicka-Skrek, E., Naumov, A.Y., Villeneuve, D.M., Staudte, A., Berini, P.: Plasmon-enhanced high-harmonic generation from silicon. Nat. Phys. 13(7), 659–662 (2017)
Zhang, X., Libertun, A.R., Paul, A., Gagnon, E., Backus, S., Christov, I.P., Murnane, M.M., Kapteyn, H.C., Bartels, R.A., Liu, Y.: Highly coherent light at 13 nm generated by use of quasi-phase-matched high-harmonic generation. Opt. Lett. 29(12), 1357–1359 (2004)
Acknowledgements
This paper and the research behind it would have not been possible without the exceptional support of my supervisory committee in the University of Melbourne at the time of this research: Prof. Keith A. Nugent, Prof. Harry Quiney, Dr. Bo Chen and Dr. Ruben Dilanian. My appreciation also goes to Prof Lap Van Dao (previously at the Swinburne University of Technology) and team for providing the HHG facilities and technical support, and not forgotten Dr. Eugineu Balaur for fabricating the double slit sample.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Abdul Aziz, N.A., Tarmizi, E.Z.M. & Dinh, K.B. Analysis of spatial coherence length of high harmonic generated in argon. Opt Quant Electron 54, 54 (2022). https://doi.org/10.1007/s11082-021-03438-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-021-03438-1