Abstract

The design of aperiodic reflecting multilayer (ML) structures for attosecond physics in the extreme ultraviolet spectral region is presented. An optimization procedure based on “evolutive strategy” has been developed in order to get coating structures reflecting high photon fluxes in ultrashort duration pulses. The MLs are designed for a specific (75105  eV) spectral interval with suitable reflectance and phase characteristics, in particular high total spectral reflectivity coupled with very wide bandwidth, spectral phase compensation, and amplitude reshaping. Furthermore, to take into account manufacturing tolerances, solutions stable with respect to random layer thickness variations are selected. To test the reliability of the proposed design procedure, examples of Mo∕Si ML structures designed to reflect ultrashort pulses with different amplitude profiles and phase behavior are considered. The performances of the various structures are analyzed.

© 2007 Optical Society of America

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2006 (3)

2005 (2)

A.-S. Morlens, P. Balcou, P. Zeitoun, C. Valentin, V. Laude, and S. Kazamias, "Compression of attosecond harmonic pulses by extreme-ultraviolet chirped mirrors," Opt. Lett. 30, 1554-1556 (2005).
[CrossRef] [PubMed]

R. Lopez-Martens, K. Varju, P. Johnsson, J. Mauritsson, Y. Mairesse, P. Salieres, M. B. Gaarde, K. J. Schafer, A. Persson, S. Svanberg, C.-G. Wahlstrom, and A. L'Huillier, "Amplitude and phase control of attosecond light pulses," Phys. Rev. Lett. 94, 033001 (2005).
[CrossRef] [PubMed]

2004 (2)

A. Wonisch, Th. Westerwalbesloh, W. Hachmann, and N. Kabachnik, "Aperiodic nanometer multilayer systems as optical key components for attosecond electron spectroscopy," Thin Solid Films 464-465, 473-477 (2004).
[CrossRef]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, T. Auguste, B. Carré, H. G. Muller, P. Agostini, and P. Salières, "Optimization of attosecond pulse generation," Phys. Rev. Lett. 93, 163901 (2004).
[CrossRef] [PubMed]

2002 (3)

I. L. Beigman, A. S. Pirozhkov, and E. N. Ragozin, "Reflection of few-cycle x-ray pulses by aperiodic multilayer structures," J. Opt. A 4, 433-439 (2002).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419, 803-807 (2002).
[CrossRef] [PubMed]

R. Kienberger, M. Hentschel, M. Uiberacker, C. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Steering attosecond electron wave packets with light," Science 297, 1144-1148 (2002).
[CrossRef] [PubMed]

2001 (3)

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, "X-ray pulses approaching the attosecond frontier," Science 291, 1923-1927 (2001).
[CrossRef] [PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug, P. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from High Harmonic Generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

1999 (1)

N. A. Papadogiannis, B. Witzel, C. Kalpouzos, and D. Charalambidis, "Observation of attosecond light localization in higher order harmonic generation," Phys. Rev. Lett. 83, 4289-4292 (1999).
[CrossRef]

1996 (1)

P. Antoine, A. L'Huillier, and M. Lewenstein, "Attosecond pulse trains using High-Order Harmonics," Phys. Rev. Lett. 77, 1234-1237 (1996).
[CrossRef] [PubMed]

1994 (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L'Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

1993 (1)

P. B. Corkum, "Plasma perspective on strong field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Opt. A (1)

I. L. Beigman, A. S. Pirozhkov, and E. N. Ragozin, "Reflection of few-cycle x-ray pulses by aperiodic multilayer structures," J. Opt. A 4, 433-439 (2002).
[CrossRef]

Nature (2)

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419, 803-807 (2002).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L'Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

N. A. Papadogiannis, B. Witzel, C. Kalpouzos, and D. Charalambidis, "Observation of attosecond light localization in higher order harmonic generation," Phys. Rev. Lett. 83, 4289-4292 (1999).
[CrossRef]

P. Antoine, A. L'Huillier, and M. Lewenstein, "Attosecond pulse trains using High-Order Harmonics," Phys. Rev. Lett. 77, 1234-1237 (1996).
[CrossRef] [PubMed]

P. B. Corkum, "Plasma perspective on strong field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
[CrossRef] [PubMed]

R. Lopez-Martens, K. Varju, P. Johnsson, J. Mauritsson, Y. Mairesse, P. Salieres, M. B. Gaarde, K. J. Schafer, A. Persson, S. Svanberg, C.-G. Wahlstrom, and A. L'Huillier, "Amplitude and phase control of attosecond light pulses," Phys. Rev. Lett. 94, 033001 (2005).
[CrossRef] [PubMed]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, T. Auguste, B. Carré, H. G. Muller, P. Agostini, and P. Salières, "Optimization of attosecond pulse generation," Phys. Rev. Lett. 93, 163901 (2004).
[CrossRef] [PubMed]

Science (3)

R. Kienberger, M. Hentschel, M. Uiberacker, C. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Steering attosecond electron wave packets with light," Science 297, 1144-1148 (2002).
[CrossRef] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, "X-ray pulses approaching the attosecond frontier," Science 291, 1923-1927 (2001).
[CrossRef] [PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug, P. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from High Harmonic Generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Thin Solid Films (1)

A. Wonisch, Th. Westerwalbesloh, W. Hachmann, and N. Kabachnik, "Aperiodic nanometer multilayer systems as optical key components for attosecond electron spectroscopy," Thin Solid Films 464-465, 473-477 (2004).
[CrossRef]

Other (3)

E. A. Spiller, Soft X-Ray Optics (SPIE, 1994).
[CrossRef]

"Center for X-ray Optics,"http://www.cxro.lbl.gov/.

G. Lambert, B. Carré, M.-E. Couprie, A. Doria, D. Garzella, L. Giannessi, H. Hara, H. Kitamura, Y. Mairesse, P. Salières, and T. Shintake, "Seeding high gain harmonic generation with laser harmonics produced in gases," in Proceedings of the 26th International Free Electron Laser Conference and 11th FEL Users Workshop (Comitato Conference Elettra, 2004), pp. 155-158.
[PubMed]

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Figures (18)

Fig. 1
Fig. 1

Representative flow chart of the evolutive strategy implemented in the described algorithm. The zeroth subdomain represents the initial ML structures ensemble.

Fig. 2
Fig. 2

Case (a): characteristics of an optimized ML used to reflect, minimizing deformation, an ideal Gaussian pulse with linear phase. Continuous curve, spectral reflectivity curve; Dashed–dotted curve, phase behavior.

Fig. 3
Fig. 3

Case (a): (a) incident pulse, (b) reflected pulse.

Fig. 4
Fig. 4

Case (b): characteristics of an optimized ML designed to compress an ideal Gaussian pulse, with constant second-order positive GDD. Continuous curve, spectral reflectivity curve; dashed–dotted curve, phase behavior.

Fig. 5
Fig. 5

Phase compensation referred to in case (b): continuous dark curve; pulse phase; dashed–dotted curve; ML phase; continuous gray curve, phase of the reflected pulse.

Fig. 6
Fig. 6

Case (b): dashed–dotted curve, incident pulse; continuous curve, reflected pulse.

Fig. 7
Fig. 7

Case (c): characteristics of an optimized ML used to reflect, minimizing deformation, an ideal pulse with rectangular spectrum and linear phase. Continuous curve, spectral reflectivity curve; dashed–dotted curve, phase behavior.

Fig. 8
Fig. 8

Case (c): continuous gray curve, incident pulse; continuous dark curve, normalized reflected pulse; dashed–dotted curve, Gaussian spectrum (for comparison, see text).

Fig. 9
Fig. 9

Case (c): (a) incident pulse, (b) reflected pulse.

Fig. 10
Fig. 10

Case (d): characteristics of an optimized ML used to compress an ideal pulse presenting rectangular spectral feature and second order chirping. Continuous curve, spectral reflectivity curve; dashed–dotted curve, phase behavior.

Fig. 11
Fig. 11

Case (d): continuous gray curve, incident pulse spectrum and continuous dark curve, normalized reflected one, are compared to a dashed–dotted curve, Gaussian spectrum.

Fig. 12
Fig. 12

Case (d): continuous dark curve; pulse phase; dashed–dotted curve, ML phase correction; continuous gray curve, phase of the reflected pulse.

Fig. 13
Fig. 13

Case (d): (dashed–dotted curve) incident and (continuous curve) reflected pulses in time domain.

Fig. 14
Fig. 14

Case (e): (a) continuous curves, incident spectrum and ML reflectivity; dotted curve, phase behavior of incident spectrum; and dashed–dotted curve, ML phase. (b) Continuous curve, spectrum; and dashed–dotted curve, phase of the reflected pulse.

Fig. 15
Fig. 15

Case (e): (dashed–dotted curve) incident and (continuous curve) reflected pulse in time domain.

Fig. 16
Fig. 16

Cases (a)–(e) stability analysis. The plots in the left column report the P values corresponding to different perturbed versions of the nominal structures. The right column shows the same results with histogram plots. Each row refers to one of the five considered cases.

Fig. 17
Fig. 17

Cases (a)–(e) stability analysis. The plots in the left column report the T values corresponding to different perturbed versions of the nominal structures. The right column shows the same results with histogram plots. Each row refers to one of the five considered cases.

Fig. 18
Fig. 18

Case (a): Thickness of MLs layers, starting from the top, are presented for cases (a)–(e). The abscissa represent the progressive index period number starting from the top of the structure. For sake of clarity points are joined with straight segments. The gray curve represents the spacer thickness while the dark curve represents the absorber one.

Tables (2)

Tables Icon

Table 1 Test Cases Description: Input Refers to the Characteristics of the Incident Radiation in Terms of Intensity and Phase Behavior; the Output Requirements Are Those Optimized in the S∕W Evaluation Process

Tables Icon

Table 2 Summarization of the Obtained Results for All the Considered Cases

Equations (7)

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I i ( f ) = E i ( f ) E i ( f ) * ,
E i ( f ) = T E i ( t ) ,
E r ( f ) = E i ( f ) r ML ( f ) ,
E r ( t ) = T 1 E r ( f ) ,
I r ( t ) = E r ( t ) E r ( t ) * ,
E i ( f ) = e - 2 σ 2 π 2 ( f - f 0 ) 2 e j l ( f - f 0 ) 2 ,
T := I r ( t ) d t M a x [ I r ( t ) ] .

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