Evidence of X-Shaped Propagation-Invariant Localized Light Waves

Ten years ago Durnin, Miceli, and Eberly [1] reported on the startling first experimental investigation of the socalled nondiffracting Bessel beam, which was formed from a cw laser light by an annular slit and a collimating lens. The beam was found to maintain its sharply peaked radial profile over large distances outclassing the Rayleigh range. During the decade monochromatic Bessel beams have been further extensively studied and applied in both optics and acoustics (see, e.g., Refs. [2–10], and references therein). On the other hand, there have been discovered several classes of nonspreading wideband wave-packet solutions to the linear wave equations of mathematical physics (“focus wave modes,” “Bessel-Gauss pulses,” “directed energy pulse trains,” “electromagnetic bullets,” “slingshot pulses,” “X waves,” etc. [10–18]), which maintain their spatiotemporal localization in the course of propagation in free space. The feasibility of experimental launching has been tested in acoustics for the directed energy pulse train [13] and for the X wave [17]. The acoustical X-type waves are attracting growing interest, particularly, due to the outlook of application in medical ultrasonic imaging [10]. Unfortunately, difficulties with meeting the requirement of ultrawideband spectral content in the case of light field, have obstructed the study of these particlelike solutions in optics. However, recently an optical version of the X wave, named the Bessel-X pulse, was treated theoretically and its propagation-invariant high localization s,1023 mmd as well as an ability to carry arbitrary images diffraction freely over large distances was shown by computer simulations [19,20]. Specially designed femtosecond-duration Bessel-X pulses not only maintain their lateral localization but also the longitudinal one in a dispersive propagation media [21,20]. Such a possibility to suppress the temporal spread caused by the group velocity dispersion has been experimentally verified [22] on subpicosecond laser pulses. To our best knowledge, Ref. [22] gives so far the only experimental test of the feasibility of the optical X waves. In this Letter we report on experimental measurements of the whole three-dimensional distribution of the field of optical X waves in free space. In order to make the idea of the experiment better comprehensible, we first discuss different mathematical