We have studied structures where a concentric ring with an index higher than that of the cladding index is added to a conventional fiber core. The structure supports at least one additional symmetric mode with substantial power in the ring, besides the normal mode in the core. Within certain designed parameter regimes, the propagation constants of the lowest two symmetric modes cross at a certain wavelength. This is equivalent to saying that the LP01 mode can change from having more power in core to having more power in ring at a certain wavelength or vice versa. At this resonance, each of the two modes has substantial power in the core and the ring. This resonant nature of the structure creates a strong wavelength dependent mode field for LP01 and LP02 modes near the resonance wavelength. Filters based on this principle are demonstrated for the first time.