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We developed a highly birefringent micro-structured optical fiber that, in combination with a fiber Bragg grating sensor, allows measuring transverse strains in reinforced composites. The first generation of this dedicated fiber sensor featured a hydrostatic pressure sensitivity of -15 pm/MPa and yielded a transverse strain sensitivity of -0.16 pm/με when embedded in a carbon fiber reinforced polymer. The second generation of this sensor has now been fabricated and hydrostatic pressure experiments and FEM simulations show that this generation returns a sensitivity of more than twice that of the first generation. FEM simulations additionally show an increased sensitivity when this sensor is embedded in a reinforced composite, achieving an unprecedented transverse strain sensitivity of 0.29 pm/με. We explain how the optimized micro-structure yields this record-high sensitivity. In addition we demonstrate the selectivity of the bare fiber sensor, which remains insensitive to temperature changes or axial strain. This sensor can therefore play an important role in the domain of structural health monitoring.