Abstract

In the diffraction of a supercontinuum source, a redistribution of amplitude and phase at the focal region is incurred by the coupling between the supercontinuum and the spatial phase caused by the lens diffraction, making it extremely difficult to predict the focal behaviour. We show that the coupling between the temporal phase of a SC source and the spatial phase from the diffraction by a low numerical aperture (NA) lens causes dramatic alterations in the spectra and the temporal coherence near the focal region, and that this effect is maximized in points of singularity. Furthermore, we show that such an enhancement in temporal coherence can be controlled by the pulse evolution through the photonic crystal fiber, in which nonlinear and disperive effects such as the soliton fission process provides the key phase evolution necessary for dramatically changing the coherence time of the focused electromagnetic wave.

© 2009 Optical Society of America

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References

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2008 (2)

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer, and K. Dholakia, “Optical micro-manipulation using supercontinuum Laguerre Gaussian and Gaussian beams,” Opt. Express 16, 1011–10129 (2008).
[Crossref]

B. J. Chick, J. W. M. Chon, and M. Gu, “Polarization effects in a highly birefringent nonlinear photonic crystal fiber with two-zero dispersion wavelengths,” Opt. Express 16, 20099–20080 (2008).
[Crossref] [PubMed]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Mod. Phys. Rev. 78, 113–1184 (2006).

2005 (2)

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui, and K. Itoh, “Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source,” Jpn. J. Appl. Phys. 44, L167–L169 (2005).
[Crossref]

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Comm. 248, 59–68 (2005).
[Crossref]

2004 (1)

2003 (3)

H. N. Paulsen, K. M. Hilligsøe, J. Thøgersen, S. R. Keiding, and J. J. Larsen, “Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source,” Opt. Lett. 28, 1123–1125 (2003).
[Crossref] [PubMed]

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windler, “Fundamental noise limitations to supercontinuum generation in microstructured fiber,” Phys. Rev. Lett. 90, 112904 (2003).
[Crossref]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers,” Nature 474, 511–515 (2003).
[Crossref]

2002 (3)

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88, 013901 (2002).
[Crossref] [PubMed]

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

J. M. Dudley and S. Coen, “Coherence properties of supecontinuum sprectra generated in photonic crystal and tapered optical fibers,” Opt. Exp. 27, 1180–1182 (2002).

2001 (2)

2000 (1)

1998 (2)

L. Sereda and M. Bertolotti, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. A 15, 695–705 (1998).
[Crossref]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

1995 (1)

1967 (1)

F. De Martini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-Steepening of light pulses,” Phys. Rev. 164, 312–323 (1967).
[Crossref]

1928 (1)

C.V. Raman, “A change of wave-length in light scattering [8],” Nature 121, 619- (1928).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, “Nonlinear fiber optics,” 3rd ed. (Academic San Diego, Calif., 2002).

Bertolotti, M.

Biancalana, F.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers,” Nature 474, 511–515 (2003).
[Crossref]

Birks, T. A.

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

Born, M.

M. Born and E. Wolf, “Principles of Optics,” 7th ed. (Cambridge University Press, Cambridge, 1999).

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

Carruthers, A. E.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer, and K. Dholakia, “Optical micro-manipulation using supercontinuum Laguerre Gaussian and Gaussian beams,” Opt. Express 16, 1011–10129 (2008).
[Crossref]

Chick, B. J.

Chon, J. W. M.

Chudoba, C.

Cizmar, T.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer, and K. Dholakia, “Optical micro-manipulation using supercontinuum Laguerre Gaussian and Gaussian beams,” Opt. Express 16, 1011–10129 (2008).
[Crossref]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Mod. Phys. Rev. 78, 113–1184 (2006).

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windler, “Fundamental noise limitations to supercontinuum generation in microstructured fiber,” Phys. Rev. Lett. 90, 112904 (2003).
[Crossref]

J. M. Dudley and S. Coen, “Coherence properties of supecontinuum sprectra generated in photonic crystal and tapered optical fibers,” Opt. Exp. 27, 1180–1182 (2002).

Corwin, K. L.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windler, “Fundamental noise limitations to supercontinuum generation in microstructured fiber,” Phys. Rev. Lett. 90, 112904 (2003).
[Crossref]

De Martini, F.

F. De Martini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-Steepening of light pulses,” Phys. Rev. 164, 312–323 (1967).
[Crossref]

Dholakia, K.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer, and K. Dholakia, “Optical micro-manipulation using supercontinuum Laguerre Gaussian and Gaussian beams,” Opt. Express 16, 1011–10129 (2008).
[Crossref]

Diddams, S. A.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windler, “Fundamental noise limitations to supercontinuum generation in microstructured fiber,” Phys. Rev. Lett. 90, 112904 (2003).
[Crossref]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Mod. Phys. Rev. 78, 113–1184 (2006).

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windler, “Fundamental noise limitations to supercontinuum generation in microstructured fiber,” Phys. Rev. Lett. 90, 112904 (2003).
[Crossref]

J. M. Dudley and S. Coen, “Coherence properties of supecontinuum sprectra generated in photonic crystal and tapered optical fibers,” Opt. Exp. 27, 1180–1182 (2002).

Efimov, A.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers,” Nature 474, 511–515 (2003).
[Crossref]

Ferrari, A.

Fischer, P.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer, and K. Dholakia, “Optical micro-manipulation using supercontinuum Laguerre Gaussian and Gaussian beams,” Opt. Express 16, 1011–10129 (2008).
[Crossref]

Fujimoto, J. G.

Fukui, K.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui, and K. Itoh, “Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source,” Jpn. J. Appl. Phys. 44, L167–L169 (2005).
[Crossref]

Gbur, G.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88, 013901 (2002).
[Crossref] [PubMed]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Mod. Phys. Rev. 78, 113–1184 (2006).

Ghanta, R. K.

Gu, M.

Gustafson, T. K.

F. De Martini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-Steepening of light pulses,” Phys. Rev. 164, 312–323 (1967).
[Crossref]

Hänsch, T. W.

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

Hanson, S. G.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Comm. 248, 59–68 (2005).
[Crossref]

Hartl, I.

Herrmann, J.

A. V. Husakou and J. Herrmann, “Supercontinuum generation higher-order solutions by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Higashi, T.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui, and K. Itoh, “Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source,” Jpn. J. Appl. Phys. 44, L167–L169 (2005).
[Crossref]

Hilligsøe, K. M.

Holzwarth, R.

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

Husakou, A. V.

A. V. Husakou and J. Herrmann, “Supercontinuum generation higher-order solutions by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Ishii, N.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Comm. 248, 59–68 (2005).
[Crossref]

Isobe, K.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui, and K. Itoh, “Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source,” Jpn. J. Appl. Phys. 44, L167–L169 (2005).
[Crossref]

Itoh, K.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui, and K. Itoh, “Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source,” Jpn. J. Appl. Phys. 44, L167–L169 (2005).
[Crossref]

Keiding, S. R.

Kelley, P. L.

F. De Martini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-Steepening of light pulses,” Phys. Rev. 164, 312–323 (1967).
[Crossref]

Knight, J. C.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers,” Nature 474, 511–515 (2003).
[Crossref]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

Ko, T. H.

Larsen, J. J.

Li, P.

Li, X. D.

Liu, Z. W.

Loudon, R.

R. Loudon, “The quantum theory of light,” 2nd ed. (Oxford University Press, 1983).

Matsunaga, S.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui, and K. Itoh, “Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source,” Jpn. J. Appl. Phys. 44, L167–L169 (2005).
[Crossref]

Mazilu, M.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer, and K. Dholakia, “Optical micro-manipulation using supercontinuum Laguerre Gaussian and Gaussian beams,” Opt. Express 16, 1011–10129 (2008).
[Crossref]

Miyamoto, Y.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Comm. 248, 59–68 (2005).
[Crossref]

Morris, J. E.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer, and K. Dholakia, “Optical micro-manipulation using supercontinuum Laguerre Gaussian and Gaussian beams,” Opt. Express 16, 1011–10129 (2008).
[Crossref]

Newbury, N. R.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windler, “Fundamental noise limitations to supercontinuum generation in microstructured fiber,” Phys. Rev. Lett. 90, 112904 (2003).
[Crossref]

Omenetto, F. G.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers,” Nature 474, 511–515 (2003).
[Crossref]

Paulsen, H. N.

Raman, C.V.

C.V. Raman, “A change of wave-length in light scattering [8],” Nature 121, 619- (1928).
[Crossref]

Ranka, J. K.

Reece, P. J.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer, and K. Dholakia, “Optical micro-manipulation using supercontinuum Laguerre Gaussian and Gaussian beams,” Opt. Express 16, 1011–10129 (2008).
[Crossref]

Reeves, W. H.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers,” Nature 474, 511–515 (2003).
[Crossref]

Reid, G. T.

D. W. Robinson and G. T. Reid, “Phase unwrapping methods,” Interferogram Analysis, 194–229 (1993).

Robinson, D. W.

D. W. Robinson and G. T. Reid, “Phase unwrapping methods,” Interferogram Analysis, 194–229 (1993).

Russell, P. St. J.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers,” Nature 474, 511–515 (2003).
[Crossref]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

Sereda, L.

Shi, K. B.

Skryabin, D. V.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers,” Nature 474, 511–515 (2003).
[Crossref]

Stentz, A. J.

Takeda, M.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Comm. 248, 59–68 (2005).
[Crossref]

Taylor, A.J.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers,” Nature 474, 511–515 (2003).
[Crossref]

Thøgersen, J.

Townes, C. H.

F. De Martini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-Steepening of light pulses,” Phys. Rev. 164, 312–323 (1967).
[Crossref]

Udem, Th.

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

Visser, T. D.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88, 013901 (2002).
[Crossref] [PubMed]

Wang, W.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Comm. 248, 59–68 (2005).
[Crossref]

Watanabe, W.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui, and K. Itoh, “Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source,” Jpn. J. Appl. Phys. 44, L167–L169 (2005).
[Crossref]

Weber, K.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windler, “Fundamental noise limitations to supercontinuum generation in microstructured fiber,” Phys. Rev. Lett. 90, 112904 (2003).
[Crossref]

Windeler, R. S.

Windler, R. S.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windler, “Fundamental noise limitations to supercontinuum generation in microstructured fiber,” Phys. Rev. Lett. 90, 112904 (2003).
[Crossref]

Wolf, E.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88, 013901 (2002).
[Crossref] [PubMed]

M. Born and E. Wolf, “Principles of Optics,” 7th ed. (Cambridge University Press, Cambridge, 1999).

Yin, S. Z.

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui, and K. Itoh, “Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source,” Jpn. J. Appl. Phys. 44, L167–L169 (2005).
[Crossref]

Mod. Phys. Rev. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Mod. Phys. Rev. 78, 113–1184 (2006).

Nature (3)

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers,” Nature 474, 511–515 (2003).
[Crossref]

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

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Supplementary Material (2)

» Media 1: MOV (1635 KB)     
» Media 2: MOV (2948 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

An illustration of pulse diffraction by a low NA lens. (a) shows how the path length and the NA affect the pulse distribution as the temporal envelope passes through the focus. (b) shows the observation frames of the intensity profile in the focus.

Fig. 2.
Fig. 2.

The temporal effects of a SC propagating through the focus of a low NA (0.1) objective. (a) On axis diffraction centered at the focal point (the full temporal evolution of the SC on the axis can be viewed from the supplementary Media 1). (b) On axis diffraction centered at u 0=5π. (c) Radial and axial diffraction pattern centered at the focal point (the full temporal evolution of the SC in the radial and axial direction can be viewed from the supplementary Media 2). (d) Complete axial and temporal diffraction field. The SC field was calculated with a peak power of 2500W and a pulse width of 0.1ps with the dispersion and nonlinear parameters as described by Chick et. al. [19].

Fig. 3.
Fig. 3.

The coherence time within a focused SC for the stationary and the non-stationary cases. (a) Axial and radial distribution of the coherence time for the 0.1 NA lens for the stationary case; (b) Axial and radial distribution of the coherence time for the 0.1 NA lens for the non-stationary case; (c) Effect of NA on the coherence time on the axis for the stationary case; and (d) Effect of NA on the coherence time on the axis for the non-stationary case.

Fig. 4.
Fig. 4.

Propagation of an ultrashort hyperbolic secant pulse through a nonlinear photonic crystal fiber. (a) field propagation as a function of fiber length (b) coherence time in the focal region for different length fiber. The peak input power to the photonic crystal fiber is 2500W with a pulse duration of 100fs. (1) represents the cross section used for Fig. 3d (blue).

Fig. 5.
Fig. 5.

Mean frequency distribution of the focused SC in the axial and radial plane of a 0.1 NA lens for stationary (a) and non-stationary (b) cases.

Equations (6)

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U1(u,v,ω)=iωNA2ceiuNA2baU(ω)J0(vρ)e12iuρ2ρdρ
U1(u,v,ω)=ωNA2ucU(ω)eiuNA2(e12ib2ue12ia2u)
g1(z1,t1:z2,t2)=U*(z1,t1)U(z2,t2)[U(z1,t1)2U(z2,t2)2]12
g1(u0,v0,τ)=U1*(u0,v0,t),U1(u0,v0,t+τ)U1(u0,v0,t),U1(u0,v0,t)
g1(u0,v0,τ)=U1*(u,v0,t)U1(u+u0,v0,t+τ)[U1(u,v0,t)2U1(u+u0,v0,t+τ)2]12
τc(u0,v0)=g1(u0,v0,τ)2dτ

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