We present long-period-grating in a planar optical waveguide that contains a low-index trench in the cladding region. The effect of the trench on transmission spectrum of the grating has been studied. The waveguide structure has been analyzed by the transfer matrix method and the output spectrum of the grating has been calculated by the coupled mode theory. Our numerical results show that position, strength, and width of the trench significantly affect the transmission spectrum of the grating. In particular, we show the appearance of triple resonance between a set of coupled modes and obtain an ultrawide band rejection in the output spectrum. We numerically demonstrate applications of the proposed structure in wideband rejection filters, refractive index sensors, and gain equalization of erbium-doped waveguide amplifiers.