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Fiber Bragg gratings and long-period fiber gratings are widely used in optical communication systems and sensing applications. These structures are fabricated by UV-induced index changes along the core of a fiber, with fine control over the grating period and refractive index profile. Further flexibility and control over these structures can be achieved with focused ion beam (FIB) techniques, by fabricating fiber gratings through nano- and micro-machining. These FIB techniques enable the fabrication of gratings with larger index contrast and stronger interaction with environmental samples (ideal for chemical sensing applications). The sub-micron milling of the fibers allows modulating the refractive index with air voids, which can be filled with the sample fluid to be monitored. In this work we explore the design and fabrication of novel fiber grating configurations for sensing applications, inscribed on single-mode fibers using FIB. A single Fabry-Perot cavity is fabricated by milling a hole through the fiber (cladding and core), as well as a long-period grating based on a cascade of partially-etched-through cavities.