Miguel A. Bandres, B. M. Rodríguez-Lara
Diffraction is one of the universal phenomena of physics, and a way to overcome it has always represented a challenge for physicists. In order to control diffraction, the study of structured waves has become decisive. Here, we present nondiffracting spatially accelerating solutions of the Maxwell equations: the Weber waves. These nonparaxial waves propagate along a parabolic trajectory while preserving its shape to a good approximation. They are expressed in analytic closed form and naturally separate in forward and backward propagation. We show that the Weber waves are self-healing, can form periodic breather waves, and have a well-defined conserved quantity: the parabolic momentum. We find that our Weber waves for moderate to large values of the parabolic momenta can be described by a modulated Airy function. Because the Weber waves are exact time-harmonic solution of the wave equation, they have implications to many linear wave systems in nature, ranging from acoustic and elastic waves to surface waves in fluids and membranes.
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http://arxiv.org/abs/1209.4680
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