Time-resolved investigation of nanometer scale deformations induced by a high flux x-ray beam

J. Gaudin; B. Keitel; A. Jurgilaitis; R. Nüske; L. Guérin; J. Larsson; K. Mann; B. Schäfer; K. Tiedtke; A. Trapp; Th. Tschentscher; F. Yang; M. Wulff; H. Sinn; B. Flöter

doi:10.1364/OE.19.015516

Time-resolved investigation of nanometer scale deformations induced by a high flux x-ray beam

J. Gaudin, B. Keitel, A. Jurgilaitis, R. Nüske, L. Guérin, J. Larsson, K. Mann, B. Schäfer, K. Tiedtke, A. Trapp, Th. Tschentscher, F. Yang, M. Wulff, H. Sinn, and B. Flöter

Optics Express
Vol. 19,
Issue 16,
pp. 15516-15524
(2011)
•https://doi.org/10.1364/OE.19.015516

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J. Gaudin, B. Keitel, A. Jurgilaitis, R. Nüske, L. Guérin, J. Larsson, K. Mann, B. Schäfer, K. Tiedtke, A. Trapp, Th. Tschentscher, F. Yang, M. Wulff, H. Sinn, and B. Flöter, "Time-resolved investigation of nanometer scale deformations induced by a high flux x-ray beam," Opt. Express 19, 15516-15524 (2011)

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Abstract

We present results of a time-resolved pump-probe experiment where a Si sample was exposed to an intense 15 keV beam and its surface monitored by measuring the wavefront deformation of a reflected optical laser probe beam. By reconstructing and back propagating the wavefront, the deformed surface can be retrieved for each time step. The dynamics of the heat bump, build-up and relaxation, is followed with a spatial resolution in the nanometer range. The results are interpreted taking into account results of finite element method simulations. Due to its robustness and simplicity this method should find further developments at new x-ray light sources (FEL) or be used to gain understanding on thermo-dynamical behavior of highly excited materials.

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S. Qian, W. Jark, G. Sostero, A. Gambitta, F. Mazzolini, and A. Savoia, “Precise measuring method for detecting the in situ distortion profile of a high-heat-load mirror for synchrotron radiation by use of a pentaprism long trace profiler,” Appl. Opt. 36(16), 3769–3775 (1997).
[Crossref] [PubMed]
J. Susini, R. Baker, M. Krumrey, W. Schwegle, and I. Kvick, “Adaptive x-ray mirror prototype: first results,” Rev. Sci. Instrum. 66(2), 2048–2052 (1995).
[Crossref]
P. Revesz and A. Kazimirov, “In situ measurements of thermal distortions in synchrotron optics under high heat load,” Synchrotron Radiation News 23(1), 32–35 (2010).
[Crossref]
W. Ackermann, G. Asova, V. Ayvazyan, A. Azima, N. Baboi, J. Bähr, V. Balandin, B. Beutner, A. Brandt, A. Bolzmann, R. Brinkmann, O. I. Brovko, M. Castellano, P. Castro, L. Catani, E. Chiadroni, S. Choroba, A. Cianchi, T. Costello, D. Cubaynes, J. Dardis, W. Decking, H. Delsim-Hashemi, A. Delserieys, G. Di Pirro, M. Dohlus, S. Düsterer, A. Eckhardt, T. Edwards, B. Faatz, J. Feldhaus, K. Flöttmann, J. Frisch, L. Fröhlich, T. Garvey, U. Gensch, Ch. Gerth, M. Görler, N. Golubeva, H.-J. Grabosch, M. Grecki, O. Grimm, K. Hacker, U. Hahn, J. H. Han, K. Honkavaara, T. Hott, M. Hüning, Y. Ivanisenko, E. Jaeschke, W. Jalmuzna, T. Jezynski, R. Kammering, V. Katalev, K. Kavanagh, E. T. Kennedy, S. Khodyachykh, K. Klose, V. Kocharyan, M. Körfer, M. Kollewe, W. Koprek, S. Korepanov, D. Kostin, M. Krassilnikov, G. Kube, M. Kuhlmann, C. L. S. Lewis, L. Lilje, T. Limberg, D. Lipka, F. Löhl, H. Luna, M. Luong, M. Martins, M. Meyer, P. Michelato, V. Miltchev, W. D. Möller, L. Monaco, W. F. O. Müller, O. Napieralski, O. Napoly, P. Nicolosi, D. Nölle, T. Nuñez, A. Oppelt, C. Pagani, R. Paparella, N. Pchalek, J. Pedregosa-Gutierrez, B. Petersen, B. Petrosyan, G. Petrosyan, L. Petrosyan, J. Pflüger, E. Plönjes, L. Poletto, K. Pozniak, E. Prat, D. Proch, P. Pucyk, P. Radcliffe, H. Redlin, K. Rehlich, M. Richter, M. Roehrs, J. Roensch, R. Romaniuk, M. Ross, J. Rossbach, V. Rybnikov, M. Sachwitz, E. L. Saldin, W. Sandner, H. Schlarb, B. Schmidt, M. Schmitz, P. Schmüser, R. Schneider, A. Schneidmiller, S. Schnepp, S. Schreiber, M. Seidel, D. Sertore, V. Shabunov, C. Simon, S. Simrock, E. Sombrowski, A. Sorokin, P. Spanknebel, R. Spesyvtsev, L. Staykov, B. Steffen, F. Stephan, F. Stulle, H. Thom, K. Tiedtke, M. Tischer, S. Toleikis, R. Treusch, D. Trines, I. Tsakov, E. Vogel, T. Weiland, H. Weise, M. Wellhöfer, M. Wendt, I. Will, A. Winter, K. Wittenburg, W. Wurth, P. Yeates, V. Yurkov, I. Zagorodnov, and K. Zapfe, “Operation of a free-electron laser from the extreme ultraviolet to the water window,” Nat. Photonics 1(6), 336–342 (2007).
[Crossref]
P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, Ph. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]
A. Barty, R. Soufli, T. McCarville, S. L. Baker, M. J. Pivovaroff, P. Stefan, and R. Bionta, “Predicting the coherent X-ray wavefront focal properties at the Linac Coherent Light Source (LCLS) X-ray free electron laser,” Opt. Express 17(18), 15508–15519 (2009).
[Crossref] [PubMed]
G. Geloni, E. Saldin, L. Samoylova, E. Schneidmiller, H. Sinn, Th. Tschentscher, and M. Yurkov, “Coherence properties of the European XFEL,” N. J. Phys. 12(3), 035021 (2010).
[Crossref]
F. Siewert, J. Buchheim, and T. Zeschke, “Characterization and calibration of 2nd generation slope measuring profiler,” Nucl. Instrum. Meth. Phys. Res. Sect. A 616(2-3), 119–127 (2010).
[Crossref]
A. R. B. de Castro, A. R. Vasconcellos, and R. Luzzi, “Thermoelastic analysis of a silicon surface under x-ray free-electron-laser irradiation,” Rev. Sci. Instrum. 81(7), 073102 (2010).
[Crossref] [PubMed]
A. R. B. de Castro, A. R. Vasconcellos, and R. Luzzi, “Erratum: ‘Thermoelastic analysis of a silicon surface under x-ray free-electron-laser irradiation’,” Rev. Sci. Instrum. 82(4), 049901 (2011).
[Crossref]
B. Schäfer, J. Gloger, U. Leinhos, and K. Mann, “Photo-thermal measurement of absorptance losses, temperature induced wavefront deformation and compaction in DUV-optics,” Opt. Express 17(25), 23025–23036 (2009).
[Crossref] [PubMed]
J. Hartmann, “Bemerkungen über den Bau und die Justirung von Spektrographen,” Z. Instrumentenkd 1900(20), 47 (1900).
J. Hoszowska, J.-S. Migliore, V. Mocella, C. Ferrero, A. K. Freund, and L. Zhang, “Performance of synchrotron X-ray monochromators under heat load Part 1: finite element modeling,” Nucl. Instrum. Meth. Phys. Res. Sect. A 467-468, 409–413 (2001).
[Crossref]
T. K. Kim, J. H. Lee, M. Wulff, Q. Kong, and H. Ihee, “Spatiotemporal kinetics in solution studied by time-resolved X-ray liquidography (solution scattering),” ChemPhysChem 10(12), 1958–1980 (2009).
[Crossref] [PubMed]
M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge University Press, Cambridge, 1985)
D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]
B. Schäfer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71(7), 2663–2668 (2000).
[Crossref]
J. J. Wortman and R. A. Evans, “Young's modulus, shear modulus, and Poisson's ratio in silicon and germanium,” J. Appl. Phys. 36(1), 153–156 (1965).
[Crossref]

2011 (1)

A. R. B. de Castro, A. R. Vasconcellos, and R. Luzzi, “Erratum: ‘Thermoelastic analysis of a silicon surface under x-ray free-electron-laser irradiation’,” Rev. Sci. Instrum. 82(4), 049901 (2011).
[Crossref]

2010 (5)

P. Revesz and A. Kazimirov, “In situ measurements of thermal distortions in synchrotron optics under high heat load,” Synchrotron Radiation News 23(1), 32–35 (2010).
[Crossref]

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, Ph. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

G. Geloni, E. Saldin, L. Samoylova, E. Schneidmiller, H. Sinn, Th. Tschentscher, and M. Yurkov, “Coherence properties of the European XFEL,” N. J. Phys. 12(3), 035021 (2010).
[Crossref]

F. Siewert, J. Buchheim, and T. Zeschke, “Characterization and calibration of 2nd generation slope measuring profiler,” Nucl. Instrum. Meth. Phys. Res. Sect. A 616(2-3), 119–127 (2010).
[Crossref]

A. R. B. de Castro, A. R. Vasconcellos, and R. Luzzi, “Thermoelastic analysis of a silicon surface under x-ray free-electron-laser irradiation,” Rev. Sci. Instrum. 81(7), 073102 (2010).
[Crossref] [PubMed]

2009 (3)

A. Barty, R. Soufli, T. McCarville, S. L. Baker, M. J. Pivovaroff, P. Stefan, and R. Bionta, “Predicting the coherent X-ray wavefront focal properties at the Linac Coherent Light Source (LCLS) X-ray free electron laser,” Opt. Express 17(18), 15508–15519 (2009).
[Crossref] [PubMed]

B. Schäfer, J. Gloger, U. Leinhos, and K. Mann, “Photo-thermal measurement of absorptance losses, temperature induced wavefront deformation and compaction in DUV-optics,” Opt. Express 17(25), 23025–23036 (2009).
[Crossref] [PubMed]

T. K. Kim, J. H. Lee, M. Wulff, Q. Kong, and H. Ihee, “Spatiotemporal kinetics in solution studied by time-resolved X-ray liquidography (solution scattering),” ChemPhysChem 10(12), 1958–1980 (2009).
[Crossref] [PubMed]

2007 (1)

W. Ackermann, G. Asova, V. Ayvazyan, A. Azima, N. Baboi, J. Bähr, V. Balandin, B. Beutner, A. Brandt, A. Bolzmann, R. Brinkmann, O. I. Brovko, M. Castellano, P. Castro, L. Catani, E. Chiadroni, S. Choroba, A. Cianchi, T. Costello, D. Cubaynes, J. Dardis, W. Decking, H. Delsim-Hashemi, A. Delserieys, G. Di Pirro, M. Dohlus, S. Düsterer, A. Eckhardt, T. Edwards, B. Faatz, J. Feldhaus, K. Flöttmann, J. Frisch, L. Fröhlich, T. Garvey, U. Gensch, Ch. Gerth, M. Görler, N. Golubeva, H.-J. Grabosch, M. Grecki, O. Grimm, K. Hacker, U. Hahn, J. H. Han, K. Honkavaara, T. Hott, M. Hüning, Y. Ivanisenko, E. Jaeschke, W. Jalmuzna, T. Jezynski, R. Kammering, V. Katalev, K. Kavanagh, E. T. Kennedy, S. Khodyachykh, K. Klose, V. Kocharyan, M. Körfer, M. Kollewe, W. Koprek, S. Korepanov, D. Kostin, M. Krassilnikov, G. Kube, M. Kuhlmann, C. L. S. Lewis, L. Lilje, T. Limberg, D. Lipka, F. Löhl, H. Luna, M. Luong, M. Martins, M. Meyer, P. Michelato, V. Miltchev, W. D. Möller, L. Monaco, W. F. O. Müller, O. Napieralski, O. Napoly, P. Nicolosi, D. Nölle, T. Nuñez, A. Oppelt, C. Pagani, R. Paparella, N. Pchalek, J. Pedregosa-Gutierrez, B. Petersen, B. Petrosyan, G. Petrosyan, L. Petrosyan, J. Pflüger, E. Plönjes, L. Poletto, K. Pozniak, E. Prat, D. Proch, P. Pucyk, P. Radcliffe, H. Redlin, K. Rehlich, M. Richter, M. Roehrs, J. Roensch, R. Romaniuk, M. Ross, J. Rossbach, V. Rybnikov, M. Sachwitz, E. L. Saldin, W. Sandner, H. Schlarb, B. Schmidt, M. Schmitz, P. Schmüser, R. Schneider, A. Schneidmiller, S. Schnepp, S. Schreiber, M. Seidel, D. Sertore, V. Shabunov, C. Simon, S. Simrock, E. Sombrowski, A. Sorokin, P. Spanknebel, R. Spesyvtsev, L. Staykov, B. Steffen, F. Stephan, F. Stulle, H. Thom, K. Tiedtke, M. Tischer, S. Toleikis, R. Treusch, D. Trines, I. Tsakov, E. Vogel, T. Weiland, H. Weise, M. Wellhöfer, M. Wendt, I. Will, A. Winter, K. Wittenburg, W. Wurth, P. Yeates, V. Yurkov, I. Zagorodnov, and K. Zapfe, “Operation of a free-electron laser from the extreme ultraviolet to the water window,” Nat. Photonics 1(6), 336–342 (2007).
[Crossref]

2001 (1)

J. Hoszowska, J.-S. Migliore, V. Mocella, C. Ferrero, A. K. Freund, and L. Zhang, “Performance of synchrotron X-ray monochromators under heat load Part 1: finite element modeling,” Nucl. Instrum. Meth. Phys. Res. Sect. A 467-468, 409–413 (2001).
[Crossref]

2000 (1)

B. Schäfer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71(7), 2663–2668 (2000).
[Crossref]

1997 (1)

S. Qian, W. Jark, G. Sostero, A. Gambitta, F. Mazzolini, and A. Savoia, “Precise measuring method for detecting the in situ distortion profile of a high-heat-load mirror for synchrotron radiation by use of a pentaprism long trace profiler,” Appl. Opt. 36(16), 3769–3775 (1997).
[Crossref] [PubMed]

1996 (1)

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

1995 (1)

J. Susini, R. Baker, M. Krumrey, W. Schwegle, and I. Kvick, “Adaptive x-ray mirror prototype: first results,” Rev. Sci. Instrum. 66(2), 2048–2052 (1995).
[Crossref]

1965 (1)

J. J. Wortman and R. A. Evans, “Young's modulus, shear modulus, and Poisson's ratio in silicon and germanium,” J. Appl. Phys. 36(1), 153–156 (1965).
[Crossref]

1900 (1)

J. Hartmann, “Bemerkungen über den Bau und die Justirung von Spektrographen,” Z. Instrumentenkd 1900(20), 47 (1900).

Ackermann, W.

Akre, R.

Alford, W. J.

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

Arthur, J.

Asova, G.

Ayvazyan, V.

Azima, A.

Baboi, N.

Bähr, J.

Baker, R.

J. Susini, R. Baker, M. Krumrey, W. Schwegle, and I. Kvick, “Adaptive x-ray mirror prototype: first results,” Rev. Sci. Instrum. 66(2), 2048–2052 (1995).
[Crossref]

Baker, S. L.

Balandin, V.

Barty, A.

Beutner, B.

Bionta, R.

Bolzmann, A.

Bostedt, C.

Bozek, J.

Brachmann, A.

Brandt, A.

Brinkmann, R.

Brovko, O. I.

Buchheim, J.

Bucksbaum, P.

Castellano, M.

Castro, P.

Catani, L.

Chiadroni, E.

Choroba, S.

Cianchi, A.

Coffee, R.

Costello, T.

Cubaynes, D.

Dardis, J.

de Castro, A. R. B.

Decker, F.-J.

Decking, W.

Delserieys, A.

Delsim-Hashemi, H.

Di Pirro, G.

Ding, Y.

Dohlus, M.

Dowell, D.

Düsterer, S.

Eckhardt, A.

Edstrom, S.

Edwards, T.

Emma, P.

Evans, R. A.

J. J. Wortman and R. A. Evans, “Young's modulus, shear modulus, and Poisson's ratio in silicon and germanium,” J. Appl. Phys. 36(1), 153–156 (1965).
[Crossref]

Faatz, B.

Feldhaus, J.

Ferrero, C.

Fisher, A.

Flöttmann, K.

Freund, A. K.

Frisch, J.

Fröhlich, L.

Galayda, J.

Gambitta, A.

Garvey, T.

Geloni, G.

G. Geloni, E. Saldin, L. Samoylova, E. Schneidmiller, H. Sinn, Th. Tschentscher, and M. Yurkov, “Coherence properties of the European XFEL,” N. J. Phys. 12(3), 035021 (2010).
[Crossref]

Gensch, U.

Gerth, Ch.

Gilevich, S.

Gloger, J.

Golubeva, N.

Görler, M.

Grabosch, H.-J.

Grecki, M.

Grimm, O.

Gruetzner, J. K.

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

Hacker, K.

Hahn, U.

Han, J. H.

Hartmann, J.

J. Hartmann, “Bemerkungen über den Bau und die Justirung von Spektrographen,” Z. Instrumentenkd 1900(20), 47 (1900).

Hastings, J.

Hays, G.

Hering, Ph.

Honkavaara, K.

Hoszowska, J.

Hott, T.

Huang, Z.

Hüning, M.

Ihee, H.

Ivanisenko, Y.

Iverson, R.

Jaeschke, E.

Jalmuzna, W.

Jark, W.

Jezynski, T.

Kammering, R.

Katalev, V.

Kavanagh, K.

Kazimirov, A.

P. Revesz and A. Kazimirov, “In situ measurements of thermal distortions in synchrotron optics under high heat load,” Synchrotron Radiation News 23(1), 32–35 (2010).
[Crossref]

Kennedy, E. T.

Khodyachykh, S.

Kim, T. K.

Klose, K.

Kocharyan, V.

Kollewe, M.

Kong, Q.

Koprek, W.

Korepanov, S.

Körfer, M.

Kostin, D.

Krassilnikov, M.

Krumrey, M.

J. Susini, R. Baker, M. Krumrey, W. Schwegle, and I. Kvick, “Adaptive x-ray mirror prototype: first results,” Rev. Sci. Instrum. 66(2), 2048–2052 (1995).
[Crossref]

Kube, G.

Kuhlmann, M.

Kvick, I.

J. Susini, R. Baker, M. Krumrey, W. Schwegle, and I. Kvick, “Adaptive x-ray mirror prototype: first results,” Rev. Sci. Instrum. 66(2), 2048–2052 (1995).
[Crossref]

Lee, J. H.

Leinhos, U.

Lewis, C. L. S.

Lilje, L.

Limberg, T.

Lipka, D.

Löhl, F.

Loos, H.

Luna, H.

Luong, M.

Luzzi, R.

Mann, K.

B. Schäfer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71(7), 2663–2668 (2000).
[Crossref]

Martins, M.

Mazzolini, F.

McCarville, T.

Messerschmidt, M.

Meyer, M.

Miahnahri, A.

Michelato, P.

Migliore, J.-S.

Miltchev, V.

Mocella, V.

Moeller, S.

Möller, W. D.

Monaco, L.

Müller, W. F. O.

Napieralski, O.

Napoly, O.

Neal, D. R.

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

Nicolosi, P.

Nölle, D.

Nuhn, H.-D.

Nuñez, T.

Oppelt, A.

Pagani, C.

Paparella, R.

Pchalek, N.

Pedregosa-Gutierrez, J.

Petersen, B.

Petrosyan, B.

Petrosyan, G.

Petrosyan, L.

Pflüger, J.

Pile, G.

Pivovaroff, M. J.

Plönjes, E.

Poletto, L.

Pozniak, K.

Prat, E.

Proch, D.

Pucyk, P.

Qian, S.

Radcliffe, P.

Ratner, D.

Redlin, H.

Rehlich, K.

Revesz, P.

P. Revesz and A. Kazimirov, “In situ measurements of thermal distortions in synchrotron optics under high heat load,” Synchrotron Radiation News 23(1), 32–35 (2010).
[Crossref]

Richter, M.

Roehrs, M.

Roensch, J.

Romaniuk, R.

Ross, M.

Rossbach, J.

Rybnikov, V.

Rzepiela, J.

Sachwitz, M.

Saldin, E.

G. Geloni, E. Saldin, L. Samoylova, E. Schneidmiller, H. Sinn, Th. Tschentscher, and M. Yurkov, “Coherence properties of the European XFEL,” N. J. Phys. 12(3), 035021 (2010).
[Crossref]

Saldin, E. L.

Samoylova, L.

G. Geloni, E. Saldin, L. Samoylova, E. Schneidmiller, H. Sinn, Th. Tschentscher, and M. Yurkov, “Coherence properties of the European XFEL,” N. J. Phys. 12(3), 035021 (2010).
[Crossref]

Sandner, W.

Savoia, A.

Schäfer, B.

B. Schäfer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71(7), 2663–2668 (2000).
[Crossref]

Schlarb, H.

Schmidt, B.

Schmitz, M.

Schmüser, P.

Schneider, R.

Schneidmiller, A.

Schneidmiller, E.

G. Geloni, E. Saldin, L. Samoylova, E. Schneidmiller, H. Sinn, Th. Tschentscher, and M. Yurkov, “Coherence properties of the European XFEL,” N. J. Phys. 12(3), 035021 (2010).
[Crossref]

Schnepp, S.

Schreiber, S.

Schultz, D.

Schwegle, W.

J. Susini, R. Baker, M. Krumrey, W. Schwegle, and I. Kvick, “Adaptive x-ray mirror prototype: first results,” Rev. Sci. Instrum. 66(2), 2048–2052 (1995).
[Crossref]

Seidel, M.

Sertore, D.

Shabunov, V.

Siewert, F.

Simon, C.

Simrock, S.

Sinn, H.

G. Geloni, E. Saldin, L. Samoylova, E. Schneidmiller, H. Sinn, Th. Tschentscher, and M. Yurkov, “Coherence properties of the European XFEL,” N. J. Phys. 12(3), 035021 (2010).
[Crossref]

Smith, T.

Sombrowski, E.

Sorokin, A.

Sostero, G.

Soufli, R.

Spanknebel, P.

Spesyvtsev, R.

Staykov, L.

Stefan, P.

Steffen, B.

Stephan, F.

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Fig. 1

Schematic view of the experimental setup

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Fig. 2

(a) shows residual fluctuations in the wavefront of the test laser beam (3.6nm w_pv ). The thermally induced wavefront distortion of the test laser at the sensor position is shown in (b) for a delay of 82µs (23.9nm w_pv ) and in (c) for a delay of 122µs. (17.7nm w_pv ).

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Fig. 3

(a) shows the reconstructed surface topology from wavefront measurements for a delay of 82µs (peak-to-valley (pv) 17nm) and (b) for a delay of 122µs (pv 8.6nm). The surface profiles correspond to the wavefronts shown in Figs. 2(b) and(c). Figure (c) shows a cross section of the surface profile along the η axis (solid lines) together with the three-dimensional Gaussian fit curve (dash-dotted).

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Fig. 4

Heat bump dynamics from wavefront measurement. The red line is the exponential decay used to fit the experimental points [t₁ = 31.1 µs].

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Fig. 5

Simulated volume with the FEM. The color shows the temperature in K at the end of the x-ray pulse train. The picture corresponds to the Si bare substrate.

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Fig. 6

Height of the surface point at the center of the simulated volume as a function of time resulting from FEM simulations. The blue curve is for the Si substrate and the black on for the Si + Pt coating.

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Tables (1)

Table 1 Thermo-dynamical constants of Si (111) and Pt used in the FEM model

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Equations (9)

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U (ξ, η, 0) = U_{t} (ξ, η, 0) T (ξ, η),

T (ξ, η) = \exp (- 2 i k \cos (α) δ h (ξ, η))

U (x, y, 0) = - \frac{i}{λ} \iint d ξ d η U (ξ, η, 0) \frac{\exp (i k R)}{R} .

R^{2} = {(x_{0} - ξ_{0} \cos α)}^{2} + {(y_{0} - η_{0})}^{2} + {(L + ξ_{0} \sin α)}^{2} .

\begin{array}{l} \hat{U} (ξ, η, 0) = F^{- 1} (U (x, y, 0)) = \frac{i \cos α}{λ L} e^{- i k L} \exp (- \frac{i k}{2 L} (ξ^{2} \cos^{2} α + η^{2})) \times \\ \iint d x d y U (x, y, 0) \exp (- \frac{i k}{2 L} (x^{2} + y^{2})) \exp (\frac{i k}{L} (x ξ \cos α + y η)) \end{array}

T (ξ, η) = \frac{F^{- 1} (U_{d i s t o r t e d} (x, y, 0))}{F^{- 1} (U_{n o n - d i s t o r t e d} (x, y, 0))},

h (ξ, η; h_{0}, h_{1}, β, ξ_{0}, η_{0}) = h_{0} + h_{1} \exp (- \frac{ξ^{'} {(β, ξ_{0})}^{2}}{2 σ_{ξ}^{2}} - \frac{η^{'} {(β, η_{0})}^{2}}{2 σ_{η}^{2}}),

P (W \cdot {cm}^{- 3}) = \frac{p_{0}}{V} \cdot \exp (- \frac{x^{2}}{2 σ_{x}^{2}} - \frac{y^{2}}{2 σ_{y}^{2}}) \cdot \exp (- \frac{z}{l_{abs}}),

\frac{1}{26} * \sum_{n = 0}^{25} 4.2 + 0.5 \cdot n = 10.45 nm,

	Density	Poisson coefficient	Young modulus	Thermal expansion	Thermal conductivity	Specific heat
Material	g/cm3		GPa	10⁻⁶/°C	W/m°C	J/g.°C
Si (111)	2.34	0.26	187	2.56 10⁻⁶	163.3	0.703
Pt	21.4	0.36	275	9.0 10⁻⁶	71.6	0.133