Abstract

This paper presents the elements of the theory and the results of an analysis of the spatial distribution of the field characteristics in the neighborhood of the focus for an input pulse in the form of a harmonic vibration with a Gaussian envelope. The signal parameters are varied from an ultrashort to a quasi-monochromatic pulse. The evolution in time of the input pulse and the edge wave is demonstrated. It is shown that the field structure in the focal plane approaches that for a monochromatic wave when the effective number of vibrations is greater than 3–5.

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  1. O. G. Kozina and G. I. Makarov, “Transient processes in acoustic fields created by a piston membrane of arbitrary shape and with arbitrary character of its surface vibrations,” Akust. Zh. 7, No. 1, 53 (1961). [Soviet Phys.–Acoust. 7, 39 (1961)].
  2. M. K. Lebedev and Yu. A. Tolmachev, “Diffraction of an ultrashort pulse by an aperture,” Opt. Spektrosk. 90, 457 (2001). [Opt. Spectrosc. 90, 398 (2001)].
    [CrossRef]
  3. M. K. Lebedev, Yu. A. Tolmachev, M. V. Frolenkova, and A. V. Kytmanov, “Specific features of the spatiotemporal structure of a broadband signal in the vicinity of the focal point of a converging spherical wave,” Opt. Spektrosk. 100, 129 (2006). [Opt. Spectrosc. 100, 119 (2006)].
    [CrossRef]
  4. M. V. Frolenkova and Yu. A. Tolmachev, “Diffraction of a planar ultrashort pulse at a circular aperture. Oblique incidence,” Vestnik SPbGU Ser. 4 No. 1, 142 (2006).
  5. M. K. Lebedev and Yu. A. Tolmachev, “Pulse method for solving problems of diffraction and interference. I. Diffraction of an ultrashort pulse,” in Laser Research at the St. Petersburg State University, Third ed.eds., V. B. Smirnov and A. A. Petrov(NII Ross. Tsentr Laz. Fiz, St. Petersburg, 2004), pp. 81–153.
  6. M. V. Frolenkova, “Study of a pulse method of solving problems of the diffraction of scalar waves and its application for analyzing the operation of actual optical systems,” in Author’s Abstract of Dissertation for Candidate (St. Petersburg State University, St. Petersburg, 2008).
  7. I. É Suleĭmenov, M. K. Lebedev, and Yu. A. Tolmachev, “Diffraction of an ultrashort pulse by a slit,” Opt. Spektrosk. 88, 104 (2000). [Opt. Spectrosc. 88, 96 (2000)].
  8. P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083 (2010).
    [CrossRef] [PubMed]
  9. J. W. Strutt, The Theory of Sound, Vol. 1 (Macmillan, London, 1877, 1894; Gos. Izd. Tekh. Teor. Lit., Moscow, 1955).

2010 (1)

2006 (2)

M. K. Lebedev, Yu. A. Tolmachev, M. V. Frolenkova, and A. V. Kytmanov, “Specific features of the spatiotemporal structure of a broadband signal in the vicinity of the focal point of a converging spherical wave,” Opt. Spektrosk. 100, 129 (2006). [Opt. Spectrosc. 100, 119 (2006)].
[CrossRef]

M. V. Frolenkova and Yu. A. Tolmachev, “Diffraction of a planar ultrashort pulse at a circular aperture. Oblique incidence,” Vestnik SPbGU Ser. 4 No. 1, 142 (2006).

2001 (1)

M. K. Lebedev and Yu. A. Tolmachev, “Diffraction of an ultrashort pulse by an aperture,” Opt. Spektrosk. 90, 457 (2001). [Opt. Spectrosc. 90, 398 (2001)].
[CrossRef]

2000 (1)

I. É Suleĭmenov, M. K. Lebedev, and Yu. A. Tolmachev, “Diffraction of an ultrashort pulse by a slit,” Opt. Spektrosk. 88, 104 (2000). [Opt. Spectrosc. 88, 96 (2000)].

1961 (1)

O. G. Kozina and G. I. Makarov, “Transient processes in acoustic fields created by a piston membrane of arbitrary shape and with arbitrary character of its surface vibrations,” Akust. Zh. 7, No. 1, 53 (1961). [Soviet Phys.–Acoust. 7, 39 (1961)].

Bowlan, P.

Frolenkova, M. V.

M. K. Lebedev, Yu. A. Tolmachev, M. V. Frolenkova, and A. V. Kytmanov, “Specific features of the spatiotemporal structure of a broadband signal in the vicinity of the focal point of a converging spherical wave,” Opt. Spektrosk. 100, 129 (2006). [Opt. Spectrosc. 100, 119 (2006)].
[CrossRef]

M. V. Frolenkova and Yu. A. Tolmachev, “Diffraction of a planar ultrashort pulse at a circular aperture. Oblique incidence,” Vestnik SPbGU Ser. 4 No. 1, 142 (2006).

M. V. Frolenkova, “Study of a pulse method of solving problems of the diffraction of scalar waves and its application for analyzing the operation of actual optical systems,” in Author’s Abstract of Dissertation for Candidate (St. Petersburg State University, St. Petersburg, 2008).

Kozina, O. G.

O. G. Kozina and G. I. Makarov, “Transient processes in acoustic fields created by a piston membrane of arbitrary shape and with arbitrary character of its surface vibrations,” Akust. Zh. 7, No. 1, 53 (1961). [Soviet Phys.–Acoust. 7, 39 (1961)].

Kytmanov, A. V.

M. K. Lebedev, Yu. A. Tolmachev, M. V. Frolenkova, and A. V. Kytmanov, “Specific features of the spatiotemporal structure of a broadband signal in the vicinity of the focal point of a converging spherical wave,” Opt. Spektrosk. 100, 129 (2006). [Opt. Spectrosc. 100, 119 (2006)].
[CrossRef]

Lebedev, M. K.

M. K. Lebedev, Yu. A. Tolmachev, M. V. Frolenkova, and A. V. Kytmanov, “Specific features of the spatiotemporal structure of a broadband signal in the vicinity of the focal point of a converging spherical wave,” Opt. Spektrosk. 100, 129 (2006). [Opt. Spectrosc. 100, 119 (2006)].
[CrossRef]

M. K. Lebedev and Yu. A. Tolmachev, “Diffraction of an ultrashort pulse by an aperture,” Opt. Spektrosk. 90, 457 (2001). [Opt. Spectrosc. 90, 398 (2001)].
[CrossRef]

I. É Suleĭmenov, M. K. Lebedev, and Yu. A. Tolmachev, “Diffraction of an ultrashort pulse by a slit,” Opt. Spektrosk. 88, 104 (2000). [Opt. Spectrosc. 88, 96 (2000)].

M. K. Lebedev and Yu. A. Tolmachev, “Pulse method for solving problems of diffraction and interference. I. Diffraction of an ultrashort pulse,” in Laser Research at the St. Petersburg State University, Third ed.eds., V. B. Smirnov and A. A. Petrov(NII Ross. Tsentr Laz. Fiz, St. Petersburg, 2004), pp. 81–153.

Lõhmus, M.

Makarov, G. I.

O. G. Kozina and G. I. Makarov, “Transient processes in acoustic fields created by a piston membrane of arbitrary shape and with arbitrary character of its surface vibrations,” Akust. Zh. 7, No. 1, 53 (1961). [Soviet Phys.–Acoust. 7, 39 (1961)].

Piksarv, P.

Saari, P.

Strutt, J. W.

J. W. Strutt, The Theory of Sound, Vol. 1 (Macmillan, London, 1877, 1894; Gos. Izd. Tekh. Teor. Lit., Moscow, 1955).

Suleimenov, I. É

I. É Suleĭmenov, M. K. Lebedev, and Yu. A. Tolmachev, “Diffraction of an ultrashort pulse by a slit,” Opt. Spektrosk. 88, 104 (2000). [Opt. Spectrosc. 88, 96 (2000)].

Tolmachev, Yu. A.

M. V. Frolenkova and Yu. A. Tolmachev, “Diffraction of a planar ultrashort pulse at a circular aperture. Oblique incidence,” Vestnik SPbGU Ser. 4 No. 1, 142 (2006).

M. K. Lebedev, Yu. A. Tolmachev, M. V. Frolenkova, and A. V. Kytmanov, “Specific features of the spatiotemporal structure of a broadband signal in the vicinity of the focal point of a converging spherical wave,” Opt. Spektrosk. 100, 129 (2006). [Opt. Spectrosc. 100, 119 (2006)].
[CrossRef]

M. K. Lebedev and Yu. A. Tolmachev, “Diffraction of an ultrashort pulse by an aperture,” Opt. Spektrosk. 90, 457 (2001). [Opt. Spectrosc. 90, 398 (2001)].
[CrossRef]

I. É Suleĭmenov, M. K. Lebedev, and Yu. A. Tolmachev, “Diffraction of an ultrashort pulse by a slit,” Opt. Spektrosk. 88, 104 (2000). [Opt. Spectrosc. 88, 96 (2000)].

M. K. Lebedev and Yu. A. Tolmachev, “Pulse method for solving problems of diffraction and interference. I. Diffraction of an ultrashort pulse,” in Laser Research at the St. Petersburg State University, Third ed.eds., V. B. Smirnov and A. A. Petrov(NII Ross. Tsentr Laz. Fiz, St. Petersburg, 2004), pp. 81–153.

Trebino, R.

Valtna-Lukner, H.

Akust. Zh. (1)

O. G. Kozina and G. I. Makarov, “Transient processes in acoustic fields created by a piston membrane of arbitrary shape and with arbitrary character of its surface vibrations,” Akust. Zh. 7, No. 1, 53 (1961). [Soviet Phys.–Acoust. 7, 39 (1961)].

Opt. Express (1)

Opt. Spektrosk. (3)

I. É Suleĭmenov, M. K. Lebedev, and Yu. A. Tolmachev, “Diffraction of an ultrashort pulse by a slit,” Opt. Spektrosk. 88, 104 (2000). [Opt. Spectrosc. 88, 96 (2000)].

M. K. Lebedev and Yu. A. Tolmachev, “Diffraction of an ultrashort pulse by an aperture,” Opt. Spektrosk. 90, 457 (2001). [Opt. Spectrosc. 90, 398 (2001)].
[CrossRef]

M. K. Lebedev, Yu. A. Tolmachev, M. V. Frolenkova, and A. V. Kytmanov, “Specific features of the spatiotemporal structure of a broadband signal in the vicinity of the focal point of a converging spherical wave,” Opt. Spektrosk. 100, 129 (2006). [Opt. Spectrosc. 100, 119 (2006)].
[CrossRef]

Vestnik SPbGU Ser. 4 (1)

M. V. Frolenkova and Yu. A. Tolmachev, “Diffraction of a planar ultrashort pulse at a circular aperture. Oblique incidence,” Vestnik SPbGU Ser. 4 No. 1, 142 (2006).

Other (3)

M. K. Lebedev and Yu. A. Tolmachev, “Pulse method for solving problems of diffraction and interference. I. Diffraction of an ultrashort pulse,” in Laser Research at the St. Petersburg State University, Third ed.eds., V. B. Smirnov and A. A. Petrov(NII Ross. Tsentr Laz. Fiz, St. Petersburg, 2004), pp. 81–153.

M. V. Frolenkova, “Study of a pulse method of solving problems of the diffraction of scalar waves and its application for analyzing the operation of actual optical systems,” in Author’s Abstract of Dissertation for Candidate (St. Petersburg State University, St. Petersburg, 2008).

J. W. Strutt, The Theory of Sound, Vol. 1 (Macmillan, London, 1877, 1894; Gos. Izd. Tekh. Teor. Lit., Moscow, 1955).

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