The concept of photonic bandgap fiber-based surface plasmon resonance sensor operating with low refractive index analytes is developed. Plasmon wave on the surface of a thin metal film embedded into a fiber microstructure is excited by a leaky Gaussian-like core mode of a fiber. We demonstrate that by judicious design of the photonic crystal reflector, the effective refractive index of the core mode can be made considerably smaller than that of the core material, thus enabling efficient phase matching with a plasmon, high sensitivity, and high coupling efficiency from an external Gaussian source, at any wavelength of choice from the visible to near-IR. To our knowledge, this is not achievable by any other traditional sensor design. Moreover, unlike the case of total internal reflection waveguide-based sensors, there is no limitation on the upper value of the waveguide core refractive index, therefore, any optical materials can be used in fabrication of photonic bandgap fiber-based sensors. Based on numerical simulations, we finally present designs using various types of photonic bandgap fibers, including solid and hollow core Bragg fibers, as well as honeycomb photonic crystal fibers. Amplitude and spectrum based methodologies for the detection of changes in the analyte refractive index are discussed. Furthermore, sensitivity enhancement of a degenerate double plasmon peak excitation is demonstrated for the case of a honeycomb fiber. Sensor resolutions in the range 7 * 10(-6) -5 * 10(-5) RIU were demonstrated for an aqueous analyte.