Space-frequency analysis of nondiffracting pulses

• Published in: Optics communications Vol. 136; no. 3; pp. 207 - 212
• Main Authors: Friberg, Ari T, Fagerholm, Juha, Salomaa, Martti M
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.03.1997
• Subjects: Angular-spectrum representation; Localized fields; Nondiffracting beams; Space-frequency analysis; X pulses; X waves; Localized fields; 62.30.+d; X pulses; 02.90.+p; X waves; Nondiffracting beams; 03.40.Kf; 43.20.+g; Angular-spectrum representation; Space-frequency analysis
• ISSN: 0030-4018; 1873-0310
• DOI: 10.1016/S0030-4018(96)00703-1

A recently introduced method of producing nondiffracting space-time fields from ordinary diffracting solutions is here examined in the space-frequency domain. It is shown that in a 3D space the method leads to localized wavefields whose Fourier components are nondiffracting beams. Hence the nondiffracting pulses are spectral generalizations of the monochromatic conical waves, a property which provides novel insight into the physical analysis and the actual preparation of such localized space-time fields. In 2D, the resulting temporally varying wavefields are nonlocalized. The nondiffracting pulses obtained via the space-frequency synthesis of conical waves are illustrated with the help of broadband X waves and their temporal derivatives for which explicit expressions are derived. The relation of these fields to the previously known localized solutions is established.