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In this work we extend the so called frozen wave method in order to obtain new diffraction resistant light structures that can be shaped on demand, with possible applications in atom guidance. The resulting beams and the corresponding optical dipole potentials exhibit a strong resistance to diffraction effects and their longitudinal and transverse intensity patterns can be chosen a priori. Besides the theoretical development, we also present the experimental confirmation of our approach; specifically, by generating three different beam profiles using a spatial light modulator that is addressed by a computer-generated hologram. In addition to its many potential applications in atom guiding, the method developed here can also lead to many new developments in optics and photonics in general.

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Abstract-Leaky-wave antennas (LWAs) are widely used as single-point-fed linear antenna arrays. The extension of LWAs to 2D implies that they can be used as single-point-fed 2D antenna arrays without requiring a complex feeding network. However, generating a pencil beam from 2D LWAs is not straightforward and due care has to be taken for the design of the LWA. On the other hand, transmission-line (TL) grids have demonstrated interesting behaviors, such as an effective negative refractive index and growing of evanescent waves. In this paper, a singlepoint-fed TL-grid 2D Dirac leaky-wave antenna (DLWA) design is proposed that generates a pencil beam at both broadside and slightly tilted angles. The TL-grid unit cell is analytically treated in light of its scattering and impedance matrices. The optimized TL-grid unit cell is shown to exhibit a closed bandgap in the dispersion relation which is also linearly varying with frequency (hence it is a DLWA). The proposed 2D DLWA design is fabricated and the experimental results are presented.

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