P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).

[CrossRef]

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett. 37, 1238–1240 (2012).

[CrossRef]

M. Zamboni-Rached, E. Recami, and M. Balma, “A simple and effective method for the analytic description of important optical beams, when truncated by finite apertures,” Appl. Opt. 51, 3370–3379 (2012).

[CrossRef]

M. Zamboni-Rached, K. Z. Nóbrega, and C. A. Dartora, “Analytic description of Airy-type beams when truncated by finite apertures,” Opt. Express 20, 19972–19977 (2012).

[CrossRef]

R. J. Mahon and J. A. Murphy, “Gaussian beam mode analysis of optical pulses,” Proc. SPIE 8171, 81710H (2011).

[CrossRef]

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

E. Cagniot, M. Fromager, and K. Ait-Ameur, “Modeling the propagation of apertured high-order Laguerre–Gaussian beams by a user-friendly version of the mode expansion method,” J. Opt. Soc. Am. A 27, 484–491 (2010).

[CrossRef]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).

[CrossRef]

Y. D. Liu and C. Gao, “Study on the time-varying and propagating characteristics of ultrashort pulse Laguerre–Gaussian beam,” Opt. Express 18, 12104–12110 (2010).

[CrossRef]

M. V. Vasnetsov and V. A. Pas’ko, “Group velocity of Gaussian beams,” Ukr. J. Phys. 54, 50–52 (2009).

M. F. Kling and M. J. J. Vrakking, “Attosecond electron dynamics,” Annu. Rev. Phys. Chem. 59, 463–492 (2008).

[CrossRef]

A. M. Nugrowati, S. F. Pereira, and A. S. van de Nes, “Near and intermediate fields of an ultrashort pulse transmitted through Young’s double-slit experiment,” Phys. Rev. A 77, 053810 (2008).

[CrossRef]

Z. Yang, Z. Yang, and S. Zhang, “Carrier-envelope phase of ultrashort pulsed Laguerre–Gaussian beam,” Chin. Opt. Lett. 6, 189–191 (2008).

[CrossRef]

D. P. Kelly, B. M. Hennelly, A. Grün, and K. Unterrainer, “Numerical sampling rules for paraxial regime pulse diffraction calculations,” J. Opt. Soc. Am. A 25, 2299–2308 (2008).

[CrossRef]

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, M. Fernández-Alonso, and V. Climent, “On-axis diffraction of an ultrashort light pulse by circularly symmetric hard apertures,” Opt. Express 15, 4546–4556 (2007).

[CrossRef]

Q. Zou and B. Lü, “Temporal and spectral properties of ultrashort pulsed Laguerre–Gaussian beams in dispersive media,” Optik 118, 83–87 (2007).

[CrossRef]

D. Deng, H. Guo, D. Han, M. Liu, and C. Li, “Effects of dispersion and longitudinal chromatic aberration on the focusing of isodiffracting pulsed Gaussian light beam,” Phys. Lett. A 334, 73–80 (2005).

[CrossRef]

D. Ding and Y. Zhang, “Notes on the Gaussian beam expansion,” J. Acoust. Soc. Am. 116, 1401–1405 (2004).

[CrossRef]

Z. L. Horváth, J. Klebniczki, G. Kurdi, and A. P. Kovács, “Experimental investigation of the boundary wave pulse,” Opt. Commun. 239, 243–250 (2004).

[CrossRef]

S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26, 485–487 (2001).

[CrossRef]

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63, 026601 (2001).

[CrossRef]

S. Nekkanti, D. Sullivan, and D. S. Citrin, “Simulation of spatiotemporal terahertz pulse shaping in 3-D using conductive apertures of finite thickness,” IEEE J. Quantum Electron. 37, 1226–1231 (2001).

[CrossRef]

S. Feng and H. G. Winful, “Higher-order transverse modes of ultrashort isodiffracting pulses,” Phys. Rev. E 63, 046602 (2001).

[CrossRef]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single cycle terahertz pulses,,” Phys. Rev. Lett. 83, 3410–3413 (1999).

[CrossRef]

Z. L. Horváth and Z. Bor, “Reshaping of femtosecond pulses by the Gouy phase shift,” Phys. Rev. E 60, 2337–2346 (1999).

[CrossRef]

E. Budiarto, N.-W. Pu, S. Jeong, and J. Bokor, “Near-field propagation of terahertz pulses from a large-aperture antenna,” Opt. Lett. 23, 213–215 (1998).

[CrossRef]

S. Feng, H. G. Winful, and R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23, 385–387 (1998).

[CrossRef]

J. A. Murphy and A. Egan, “Examples of Fresnel diffraction using Gaussian modes,” Eur. J. Phys. 14, 121–127 (1993).

[CrossRef]

R. W. Ziolkowski and J. B. Judkins, “Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams,” J. Opt. Soc. Am. A 9, 2021–2030 (1992).

[CrossRef]

P. M. Goorjian and A. Taflove, “Direct time integration of Maxwell’s equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons,” Opt. Lett. 17, 180–182 (1992).

[CrossRef]

E. Heyman and I. Beracha, “Complex multipole pulsed beams and Hermite pulsed beams: a novel expansion scheme for transient radiation from well-collimated apertures,” J. Opt. Soc. Am. A 9, 1779–1973 (1992).

[CrossRef]

M. Kempe, U. Stamm, B. Wilhelmi, and W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 9, 1158–1165 (1992).

[CrossRef]

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Nondiffracting beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

[CrossRef]

E. Cavanagh and B. D. Cook, “Gaussian–Laguerre description of ultrasonic fields—numerical example: circular piston,” J. Acoust. Soc. Am. 67, 1136–1140 (1980).

[CrossRef]

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63, 026601 (2001).

[CrossRef]

Z. L. Horváth and Z. Bor, “Reshaping of femtosecond pulses by the Gouy phase shift,” Phys. Rev. E 60, 2337–2346 (1999).

[CrossRef]

M. A. Porras, R. Borghi, and M. Santarsiero, “Superluminality in Gaussian beams,” Opt. Commun. 203, 183–189 (2002).

[CrossRef]

R. Borghi, F. Gori, and M. Santarsiero, “Optimization of Laguerre-Gauss truncated series,” Opt. Commun. 125, 197–203(1996).

[CrossRef]

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett. 37, 1238–1240 (2012).

[CrossRef]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).

[CrossRef]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).

[CrossRef]

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2007), pp. 379–380.

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

[CrossRef]

E. Cavanagh and B. D. Cook, “Gaussian–Laguerre description of ultrasonic fields—numerical example: circular piston,” J. Acoust. Soc. Am. 67, 1136–1140 (1980).

[CrossRef]

S. Nekkanti, D. Sullivan, and D. S. Citrin, “Simulation of spatiotemporal terahertz pulse shaping in 3-D using conductive apertures of finite thickness,” IEEE J. Quantum Electron. 37, 1226–1231 (2001).

[CrossRef]

E. Cavanagh and B. D. Cook, “Gaussian–Laguerre description of ultrasonic fields—numerical example: circular piston,” J. Acoust. Soc. Am. 67, 1136–1140 (1980).

[CrossRef]

D. Deng, H. Guo, D. Han, M. Liu, and C. Li, “Effects of dispersion and longitudinal chromatic aberration on the focusing of isodiffracting pulsed Gaussian light beam,” Phys. Lett. A 334, 73–80 (2005).

[CrossRef]

D. Ding and Y. Zhang, “Notes on the Gaussian beam expansion,” J. Acoust. Soc. Am. 116, 1401–1405 (2004).

[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Nondiffracting beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Nondiffracting beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

[CrossRef]

J. A. Murphy and A. Egan, “Examples of Fresnel diffraction using Gaussian modes,” Eur. J. Phys. 14, 121–127 (1993).

[CrossRef]

S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26, 485–487 (2001).

[CrossRef]

S. Feng and H. G. Winful, “Higher-order transverse modes of ultrashort isodiffracting pulses,” Phys. Rev. E 63, 046602 (2001).

[CrossRef]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single cycle terahertz pulses,,” Phys. Rev. Lett. 83, 3410–3413 (1999).

[CrossRef]

S. Feng, H. G. Winful, and R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23, 385–387 (1998).

[CrossRef]

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

R. Borghi, F. Gori, and M. Santarsiero, “Optimization of Laguerre-Gauss truncated series,” Opt. Commun. 125, 197–203(1996).

[CrossRef]

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

I. S. Gradstehyn and I. M. Rhyzik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007), p. 811.

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

D. Deng, H. Guo, D. Han, M. Liu, and C. Li, “Effects of dispersion and longitudinal chromatic aberration on the focusing of isodiffracting pulsed Gaussian light beam,” Phys. Lett. A 334, 73–80 (2005).

[CrossRef]

W. Hu and H. Guo, “Ultrashort pulsed Bessel beams and spatially induced group-velocity dispersion,” J. Opt. Soc. Am. A 19, 49–53 (2002).

[CrossRef]

D. Deng, H. Guo, D. Han, M. Liu, and C. Li, “Effects of dispersion and longitudinal chromatic aberration on the focusing of isodiffracting pulsed Gaussian light beam,” Phys. Lett. A 334, 73–80 (2005).

[CrossRef]

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

Z. L. Horváth, J. Klebniczki, G. Kurdi, and A. P. Kovács, “Experimental investigation of the boundary wave pulse,” Opt. Commun. 239, 243–250 (2004).

[CrossRef]

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63, 026601 (2001).

[CrossRef]

Z. L. Horváth and Z. Bor, “Reshaping of femtosecond pulses by the Gouy phase shift,” Phys. Rev. E 60, 2337–2346 (1999).

[CrossRef]

Z. L. Horváth, J. Klebniczki, G. Kurdi, and A. P. Kovács, “Experimental investigation of the boundary wave pulse,” Opt. Commun. 239, 243–250 (2004).

[CrossRef]

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

M. F. Kling and M. J. J. Vrakking, “Attosecond electron dynamics,” Annu. Rev. Phys. Chem. 59, 463–492 (2008).

[CrossRef]

Z. L. Horváth, J. Klebniczki, G. Kurdi, and A. P. Kovács, “Experimental investigation of the boundary wave pulse,” Opt. Commun. 239, 243–250 (2004).

[CrossRef]

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

Z. L. Horváth, J. Klebniczki, G. Kurdi, and A. P. Kovács, “Experimental investigation of the boundary wave pulse,” Opt. Commun. 239, 243–250 (2004).

[CrossRef]

D. Deng, H. Guo, D. Han, M. Liu, and C. Li, “Effects of dispersion and longitudinal chromatic aberration on the focusing of isodiffracting pulsed Gaussian light beam,” Phys. Lett. A 334, 73–80 (2005).

[CrossRef]

D. Deng, H. Guo, D. Han, M. Liu, and C. Li, “Effects of dispersion and longitudinal chromatic aberration on the focusing of isodiffracting pulsed Gaussian light beam,” Phys. Lett. A 334, 73–80 (2005).

[CrossRef]

Y. Liu and B. Lü, “Truncated Hermite–Gauss series expansion and its application,” Optik 117, 437–442 (2006).

[CrossRef]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).

[CrossRef]

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett. 37, 1238–1240 (2012).

[CrossRef]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).

[CrossRef]

Q. Zou and B. Lü, “Temporal and spectral properties of ultrashort pulsed Laguerre–Gaussian beams in dispersive media,” Optik 118, 83–87 (2007).

[CrossRef]

Q. Zou and B. Lü, “Anomalous spectral behaviour near phase singularities in diffraction of pulsed Laguerre–Gaussian beams,” J. Opt. A 8, 531–536 (2006).

Y. Liu and B. Lü, “Truncated Hermite–Gauss series expansion and its application,” Optik 117, 437–442 (2006).

[CrossRef]

R. J. Mahon and J. A. Murphy, “Gaussian beam mode analysis of optical pulses,” Proc. SPIE 8171, 81710H (2011).

[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Nondiffracting beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

[CrossRef]

R. J. Mahon and J. A. Murphy, “Gaussian beam mode analysis of optical pulses,” Proc. SPIE 8171, 81710H (2011).

[CrossRef]

N. Trappe, J. A. Murphy, and S. Withington, “The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems,” Eur. J. Phys. 24, 403–412 (2003).

[CrossRef]

J. A. Murphy and A. Egan, “Examples of Fresnel diffraction using Gaussian modes,” Eur. J. Phys. 14, 121–127 (1993).

[CrossRef]

S. Nekkanti, D. Sullivan, and D. S. Citrin, “Simulation of spatiotemporal terahertz pulse shaping in 3-D using conductive apertures of finite thickness,” IEEE J. Quantum Electron. 37, 1226–1231 (2001).

[CrossRef]

A. M. Nugrowati, S. F. Pereira, and A. S. van de Nes, “Near and intermediate fields of an ultrashort pulse transmitted through Young’s double-slit experiment,” Phys. Rev. A 77, 053810 (2008).

[CrossRef]

M. V. Vasnetsov and V. A. Pas’ko, “Group velocity of Gaussian beams,” Ukr. J. Phys. 54, 50–52 (2009).

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett. 37, 1238–1240 (2012).

[CrossRef]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).

[CrossRef]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).

[CrossRef]

M. A. Porras, R. Borghi, and M. Santarsiero, “Superluminality in Gaussian beams,” Opt. Commun. 203, 183–189 (2002).

[CrossRef]

I. S. Gradstehyn and I. M. Rhyzik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007), p. 811.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single cycle terahertz pulses,,” Phys. Rev. Lett. 83, 3410–3413 (1999).

[CrossRef]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single cycle terahertz pulses,,” Phys. Rev. Lett. 83, 3410–3413 (1999).

[CrossRef]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).

[CrossRef]

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett. 37, 1238–1240 (2012).

[CrossRef]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).

[CrossRef]

P. Saari and H. Sõnajalg, “Pulsed Bessel beams,” Laser Phys. 7, 32–39 (1997).

M. A. Porras, R. Borghi, and M. Santarsiero, “Superluminality in Gaussian beams,” Opt. Commun. 203, 183–189 (2002).

[CrossRef]

R. Borghi, F. Gori, and M. Santarsiero, “Optimization of Laguerre-Gauss truncated series,” Opt. Commun. 125, 197–203(1996).

[CrossRef]

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

A. E. Siegman, Lasers (University Science, 1986).

P. Saari and H. Sõnajalg, “Pulsed Bessel beams,” Laser Phys. 7, 32–39 (1997).

S. Nekkanti, D. Sullivan, and D. S. Citrin, “Simulation of spatiotemporal terahertz pulse shaping in 3-D using conductive apertures of finite thickness,” IEEE J. Quantum Electron. 37, 1226–1231 (2001).

[CrossRef]

N. Trappe, J. A. Murphy, and S. Withington, “The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems,” Eur. J. Phys. 24, 403–412 (2003).

[CrossRef]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).

[CrossRef]

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett. 37, 1238–1240 (2012).

[CrossRef]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).

[CrossRef]

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).

[CrossRef]

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett. 37, 1238–1240 (2012).

[CrossRef]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).

[CrossRef]

A. M. Nugrowati, S. F. Pereira, and A. S. van de Nes, “Near and intermediate fields of an ultrashort pulse transmitted through Young’s double-slit experiment,” Phys. Rev. A 77, 053810 (2008).

[CrossRef]

M. V. Vasnetsov and V. A. Pas’ko, “Group velocity of Gaussian beams,” Ukr. J. Phys. 54, 50–52 (2009).

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

M. F. Kling and M. J. J. Vrakking, “Attosecond electron dynamics,” Annu. Rev. Phys. Chem. 59, 463–492 (2008).

[CrossRef]

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

[CrossRef]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single cycle terahertz pulses,,” Phys. Rev. Lett. 83, 3410–3413 (1999).

[CrossRef]

S. Feng and H. G. Winful, “Higher-order transverse modes of ultrashort isodiffracting pulses,” Phys. Rev. E 63, 046602 (2001).

[CrossRef]

S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26, 485–487 (2001).

[CrossRef]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single cycle terahertz pulses,,” Phys. Rev. Lett. 83, 3410–3413 (1999).

[CrossRef]

S. Feng, H. G. Winful, and R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23, 385–387 (1998).

[CrossRef]

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

N. Trappe, J. A. Murphy, and S. Withington, “The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems,” Eur. J. Phys. 24, 403–412 (2003).

[CrossRef]

Z. Yang, Z. Yang, and S. Zhang, “Carrier-envelope phase of ultrashort pulsed Laguerre–Gaussian beam,” Chin. Opt. Lett. 6, 189–191 (2008).

[CrossRef]

Z. Yang, Z. Yang, and S. Zhang, “Carrier-envelope phase of ultrashort pulsed Laguerre–Gaussian beam,” Chin. Opt. Lett. 6, 189–191 (2008).

[CrossRef]

M. Zamboni-Rached, K. Z. Nóbrega, and C. A. Dartora, “Analytic description of Airy-type beams when truncated by finite apertures,” Opt. Express 20, 19972–19977 (2012).

[CrossRef]

M. Zamboni-Rached, E. Recami, and M. Balma, “A simple and effective method for the analytic description of important optical beams, when truncated by finite apertures,” Appl. Opt. 51, 3370–3379 (2012).

[CrossRef]

D. Ding and Y. Zhang, “Notes on the Gaussian beam expansion,” J. Acoust. Soc. Am. 116, 1401–1405 (2004).

[CrossRef]

Q. Zou and B. Lü, “Temporal and spectral properties of ultrashort pulsed Laguerre–Gaussian beams in dispersive media,” Optik 118, 83–87 (2007).

[CrossRef]

Q. Zou and B. Lü, “Anomalous spectral behaviour near phase singularities in diffraction of pulsed Laguerre–Gaussian beams,” J. Opt. A 8, 531–536 (2006).

M. F. Kling and M. J. J. Vrakking, “Attosecond electron dynamics,” Annu. Rev. Phys. Chem. 59, 463–492 (2008).

[CrossRef]

R. L. Phillips and L. C. Andrews, “Spot size and divergence for Laguerre Gaussian beams of any order,” Appl. Opt. 22, 643–644 (1983).

[CrossRef]

Z. Jiang, R. Jacquemin, and W. Eberhardt, “Time dependence of Fresnel diffraction of ultrashort laser pulses by a circular aperture,” Appl. Opt. 36, 4358–4361 (1997).

[CrossRef]

M. Zamboni-Rached, E. Recami, and M. Balma, “A simple and effective method for the analytic description of important optical beams, when truncated by finite apertures,” Appl. Opt. 51, 3370–3379 (2012).

[CrossRef]

J. A. Murphy and A. Egan, “Examples of Fresnel diffraction using Gaussian modes,” Eur. J. Phys. 14, 121–127 (1993).

[CrossRef]

N. Trappe, J. A. Murphy, and S. Withington, “The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems,” Eur. J. Phys. 24, 403–412 (2003).

[CrossRef]

S. Nekkanti, D. Sullivan, and D. S. Citrin, “Simulation of spatiotemporal terahertz pulse shaping in 3-D using conductive apertures of finite thickness,” IEEE J. Quantum Electron. 37, 1226–1231 (2001).

[CrossRef]

E. Cavanagh and B. D. Cook, “Gaussian–Laguerre description of ultrasonic fields—numerical example: circular piston,” J. Acoust. Soc. Am. 67, 1136–1140 (1980).

[CrossRef]

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

[CrossRef]

D. Ding and Y. Zhang, “Notes on the Gaussian beam expansion,” J. Acoust. Soc. Am. 116, 1401–1405 (2004).

[CrossRef]

M. Schultze, A. Wirth, I. Grguras, M. Uiberacker, T. Uphues, A. J. Verhoef, J. Gagnon, M. Hofstetter, U. Kleineberg, E. Goulielmakis, and F. Krausz, “State-of-the-art attosecond metrology,” J. Electron Spectrosc. Relat. Phenom. 184, 68–77 (2011).

[CrossRef]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).

[CrossRef]

Q. Zou and B. Lü, “Anomalous spectral behaviour near phase singularities in diffraction of pulsed Laguerre–Gaussian beams,” J. Opt. A 8, 531–536 (2006).

A. Gürtler, C. Winnewisser, H. Helm, and P. U. Jepsen, “Terahertz pulse propagation in the near field and the far field,” J. Opt. Soc. Am. A 17, 74–83 (2000).

[CrossRef]

E. Heyman and I. Beracha, “Complex multipole pulsed beams and Hermite pulsed beams: a novel expansion scheme for transient radiation from well-collimated apertures,” J. Opt. Soc. Am. A 9, 1779–1973 (1992).

[CrossRef]

D. P. Kelly, B. M. Hennelly, A. Grün, and K. Unterrainer, “Numerical sampling rules for paraxial regime pulse diffraction calculations,” J. Opt. Soc. Am. A 25, 2299–2308 (2008).

[CrossRef]

E. Cagniot, M. Fromager, and K. Ait-Ameur, “Modeling the propagation of apertured high-order Laguerre–Gaussian beams by a user-friendly version of the mode expansion method,” J. Opt. Soc. Am. A 27, 484–491 (2010).

[CrossRef]

R. W. Ziolkowski and J. B. Judkins, “Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams,” J. Opt. Soc. Am. A 9, 2021–2030 (1992).

[CrossRef]

W. Hu and H. Guo, “Ultrashort pulsed Bessel beams and spatially induced group-velocity dispersion,” J. Opt. Soc. Am. A 19, 49–53 (2002).

[CrossRef]

C. J. Zapata-Rodríguez, “Temporal effects in ultrashort pulsed beams focused by planar diffracting elements,” J. Opt. Soc. Am. A 23, 2335–2341 (2006).

[CrossRef]

M. Gu and X. S. Gan, “Fresnel diffraction by circular and serrated apertures illuminated with an ultrashort pulsed-laser beam,” J. Opt. Soc. Am. A 13, 771–778 (1996).

[CrossRef]

P. Saari and H. Sõnajalg, “Pulsed Bessel beams,” Laser Phys. 7, 32–39 (1997).

M. A. Porras, R. Borghi, and M. Santarsiero, “Superluminality in Gaussian beams,” Opt. Commun. 203, 183–189 (2002).

[CrossRef]

R. Borghi, F. Gori, and M. Santarsiero, “Optimization of Laguerre-Gauss truncated series,” Opt. Commun. 125, 197–203(1996).

[CrossRef]

Z. L. Horváth, J. Klebniczki, G. Kurdi, and A. P. Kovács, “Experimental investigation of the boundary wave pulse,” Opt. Commun. 239, 243–250 (2004).

[CrossRef]

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, M. Fernández-Alonso, and V. Climent, “On-axis diffraction of an ultrashort light pulse by circularly symmetric hard apertures,” Opt. Express 15, 4546–4556 (2007).

[CrossRef]

M. Zamboni-Rached, K. Z. Nóbrega, and C. A. Dartora, “Analytic description of Airy-type beams when truncated by finite apertures,” Opt. Express 20, 19972–19977 (2012).

[CrossRef]

M. Lefrançois and S. F. Pereira, “Time evolution of the diffraction pattern of an ultrashort laser pulse,” Opt. Express 11, 1114–1122 (2003).

[CrossRef]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).

[CrossRef]

Y. D. Liu and C. Gao, “Study on the time-varying and propagating characteristics of ultrashort pulse Laguerre–Gaussian beam,” Opt. Express 18, 12104–12110 (2010).

[CrossRef]

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett. 37, 1238–1240 (2012).

[CrossRef]

S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26, 485–487 (2001).

[CrossRef]

R. M. Joseph, S. C. Hagness, and A. Taflove, “Direct time integration of Maxwell’s equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses,” Opt. Lett. 16, 1412–1414 (1991).

[CrossRef]

P. M. Goorjian and A. Taflove, “Direct time integration of Maxwell’s equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons,” Opt. Lett. 17, 180–182 (1992).

[CrossRef]

E. Budiarto, N.-W. Pu, S. Jeong, and J. Bokor, “Near-field propagation of terahertz pulses from a large-aperture antenna,” Opt. Lett. 23, 213–215 (1998).

[CrossRef]

S. Feng, H. G. Winful, and R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23, 385–387 (1998).

[CrossRef]

Q. Zou and B. Lü, “Temporal and spectral properties of ultrashort pulsed Laguerre–Gaussian beams in dispersive media,” Optik 118, 83–87 (2007).

[CrossRef]

Y. Liu and B. Lü, “Truncated Hermite–Gauss series expansion and its application,” Optik 117, 437–442 (2006).

[CrossRef]

D. Deng, H. Guo, D. Han, M. Liu, and C. Li, “Effects of dispersion and longitudinal chromatic aberration on the focusing of isodiffracting pulsed Gaussian light beam,” Phys. Lett. A 334, 73–80 (2005).

[CrossRef]

A. M. Nugrowati, S. F. Pereira, and A. S. van de Nes, “Near and intermediate fields of an ultrashort pulse transmitted through Young’s double-slit experiment,” Phys. Rev. A 77, 053810 (2008).

[CrossRef]

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63, 026601 (2001).

[CrossRef]

S. Feng and H. G. Winful, “Higher-order transverse modes of ultrashort isodiffracting pulses,” Phys. Rev. E 63, 046602 (2001).

[CrossRef]

Z. L. Horváth and Z. Bor, “Reshaping of femtosecond pulses by the Gouy phase shift,” Phys. Rev. E 60, 2337–2346 (1999).

[CrossRef]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single cycle terahertz pulses,,” Phys. Rev. Lett. 83, 3410–3413 (1999).

[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Nondiffracting beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

[CrossRef]

R. J. Mahon and J. A. Murphy, “Gaussian beam mode analysis of optical pulses,” Proc. SPIE 8171, 81710H (2011).

[CrossRef]

M. V. Vasnetsov and V. A. Pas’ko, “Group velocity of Gaussian beams,” Ukr. J. Phys. 54, 50–52 (2009).

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2007), pp. 379–380.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

I. S. Gradstehyn and I. M. Rhyzik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007), p. 811.

A. E. Siegman, Lasers (University Science, 1986).