Abstract
From a model of focusing with lenses that includes the effects of the lens variable thickness, material dispersion, aperture, spherical and chromatic aberrations, we characterize the conditions under which a lens can focus to few-cycle, transform-limited pulses propagating without distortion along the focal region. A lens also allows to control the carrier–envelope phase shift along the focus. The carrier–envelope phase shift is drastically reduced by focusing with specific focal lengths and input spot sizes, which are of the same order as those typically used in experiments involving focusing for phase-sensitive, light-matter interactions.
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See, for example, [27], or http://refractiveindex.info.
See footnote 1.
References
C.A. Haworth, L.E. Chipperfield, J.S. Robinson, P.L. Knight, J.P. Marangos, J.W.G. Tisch, Nat. Phys. 3, 52 (2007)
M. Schnn̈urer, Z. Cheng, M. Hentschel, F. Krausz, T. Wilhein, D. Hambach, G. Schmahl, M. Drescher, Y. Lim, U. Heinzmann, Appl. Phys. B 70, S227 (2000)
F. Krausz, M.Yu. Ivanov, Rev. Mod. Phys. 81, 161 (2009)
M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, Nature 414, 509 (2001)
A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, F. Krausz, Phys. Rev. Lett. 92, 073902 (2004)
S.E. Irvine, P. Dombi, G. Farkas, A.Y. Elezzabi, Phys. Rev. Lett. 97, 146801 (2006)
T. Tritschler, K.D. Hof, M.W. Klein, M. Wegener, Opt. Lett. 30, 753 (2005)
T.M. Fortier, P.A. Ross, D.J. Jones, S.T. Cundiff, R.D.R. Bhat, J.E. Sipe, Phys. Rev. Lett. 92, 147403 (2004)
T. Wittmann, B. Horvath, W. Helml, M.G. Schätzel, X. Gu, A.L. Cavalieri, G.G. Paulus, R. Kienberger, Nat. Phys. 5, 357 (2009)
G.G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, F. Krausz, Phys. Rev. Lett. 91, 253004 (2003)
F. Lindner, G.G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, F. Krausz, Phys. Rev. Lett. 92, 113001 (2004)
S.A. Trushin, K. Kosma, W. Fuss, W.E. Schmid, Opt. Lett. 32, 2432 (2007)
C.P. Hauri, W. Kornelis, F.W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, U. Keller, Appl. Phys. B 79, 673 (2004)
P. Salieres, A. L’Huillier, M. Lewenstein, Phys. Rev. Lett. 74, 3776 (1995)
M.A. Porras, Opt. Lett. 34, 1546 (2009)
M.A. Porras, P. Dombi, Opt. Express 17, 19424 (2009)
Zs. Bor, J. Mod. Opt. 35, 1907 (1988)
Zs. Bor, Z.L. Horváth, Opt. Commun. 94, 249 (1992)
Z.L. Horváth, Zs. Bor, Opt. Commun. 108, 333 (1994)
M. Kempe, W. Rudolph, Phys. Rev. A 48, 4721 (1993)
M. Kempe, U. Stamm, B. Wilhelmi, W. Rudolph, J. Opt. Soc. Am. B 9, 1158 (1992)
M. Kempe, W. Rudolph, Opt. Lett. 18, 137 (1993)
J.J. Stamnes, Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves (Hilger, Bristol, 1986)
M. Born, E. Wolf, Principles of Optics (Oxford, Pergamon Press, 1987)
E. Hecht, Optics (Addison-Wesley, Reading, 2002)
I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products (Academic Press, San Diego, 1994)
Optical Society of America, Handbook of Optics, vol. II (1994), M. Bass (ed.)
A.E. Siegman, Lasers (University Science Books, Mill Valley, 1986)
Edmund Optics and Optical Instruments Catalog, 2011
M.A. Porras, Phys. Rev. E 65, 026606 (2002)
S. Feng, H.G. Winful, Phys. Rev. E 61, 862 (2000)
M.A. Porras, Phys. Rev. E 58, 1086 (1998)
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Porras, M.A., Horvath, Z.L. & Major, B. On the use of lenses to focus few-cycle pulses with controlled carrier–envelope phase. Appl. Phys. B 108, 521–531 (2012). https://doi.org/10.1007/s00340-012-5073-y
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DOI: https://doi.org/10.1007/s00340-012-5073-y