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We report on ground state properties of a one-dimensional, weakly-interactingBose gas constrained by an infinite multi-rods periodic structure at zerotemperature. We solve the stationary Gross-Pitaevskii equation (GPE) to obtainthe Bloch wave functions from which we give a semi-analytical solution for thedensity profile, as well as for the phase of the wave function in terms of theJacobi elliptic functions, and the incomplete elliptic integrals of the first,second and third kind. Then, we determine numerically the energy of the groundstate, the chemical potential and the compressibility of the condensate andshow their dependence on the potential height, as well as on the interactionbetween the bosons. We show the appearance of loops in the energy band spectrumof the system for strong enough interactions, which appear at the edges of thefirst Brillouin zone for odd bands and at the center for even bands. We applyour model to predict the energy band structure of the Bose gas in an opticallattice with subwavelength spatial structure. To discuss the density range ofthe validity of the GPE predictions, we calculate the ground state energies ofthe free Bose gas using the GPE, which we compare with the Lieb-Liniger exactenergies.

Periodic Ultranarrow Rods as 1D Subwavelength Optical Lattices