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We investigate vortex structure and melting transition in very anisotropiclayered superconductors at fields tilted with respect to the c-axis. We showthat even a small in-plane field does not homogeneously tilt the vortex latticebut, instead, penetrates inside the superconductor in the form of Josephsonvortices (JVs) similar to the Meissner state. At high c-axis magnetic field thephase field of the JV is built up from the phase perturbations created bydisplacements of pancake vortices. The crossing-lattices ground state leads tolinear dependencies of the melting field and melting temperature on thein-plane field, in agreement with recent experimental observations. At smallfields stacks of JVs accumulate additional pancake strings creating vortex rowswith enhanced density. This mechanism explains the mixed chains-lattice stateobserved by Bitter decorations.Comment: 4 Pages, 2 Postscript figure

Crossing Lattices, Vortex Chains, and Angular Dependence of Melting Line in Layered Superconductors