Figure 1

Geometrical interpretation of diffraction of waves propagating along the $z$ axis: (a) positive, or normal diffraction in propagation through homogeneous materials; (b) negative, or anomalous diffraction; (c) zero diffraction. The area of negligible diffraction (for evaluation of the minimum size of the nondiffractive beam) is indicated.Reuse & Permissions

Figure 2

Band structure for steel cylinders in water, for $r=1\mathrm{mm}$ and $a=5.25\mathrm{mm}$, as calculated by the expansion into Bloch modes (4, 5, 6, 7). The solid squares mark the nondiffractive points (see Fig. 3).Reuse & Permissions

Figure 3

Isofrequency lines, evaluated for $a=5.25\mathrm{mm}$ and $r=1\mathrm{mm}$, for the first (a) and second (b) bands, centered at the $\Gamma$ point, as calculated by the expansion into Bloch modes (4, 5, 6, 7).Reuse & Permissions

Figure 4

Numerical FDTD simulation of the nondiffractive beam, for the first two bands. Upper row corresponds to the field radiated by the source without crystal, lower row to the nondiffractive propagation in the [1,1] (left) and [1,0] (right) directions, at the frequencies equal to $\nu =154\mathrm{kHz}$ and $\nu =217\mathrm{kHz}$ as predicted by the theory. Gray levels are in decibel scale and the coordinates in meters. The other parameters are as in Figs. 2, 3; i.e., steel cylinders in water are simulated with $r=1\mathrm{mm}$ and $a=5.25\mathrm{mm}$.Reuse & Permissions

Figure 5

Schematic picture showing the nondiffractive region (shadowed area) resulting from the interaction of three modes. The square represents the limits of the first Brillouin zone. The inset illustrates the lift of the degenerancy at the cross sections of the dispersion curves and the formation of the Bloch modes. The upper Bloch mode can develop flat segments depending on the interaction strength, as the degree of the lift of degenerancy is proportional to the interaction strength.Reuse & Permissions

Figure 6

Schematic picture showing the nondiffractive region (shadowed area) in the second propagation band. Everything as in Fig. 5. Here the most relevant modes are $\mathbf{k}+{\mathbf{G}}_1$ and $\mathbf{k}\pm {\mathbf{G}}_2$.Reuse & Permissions

Figure 7

Dependence of the frequency (a) and wave number of nondiffractive beam, measured with respect to the band gap values, as results from numerical calculation (symbols) and the analytical expressions given in Eqs. (14, 15). The open circles and squares correspond to the parameter values used for FDTD calculation of nondiffractive propagation (Fig. 4) in the first and second bands, respectively.Reuse & Permissions