Various embodiments include photonic bandgap fibers (PBGF). Some PBGF embodiments have a hollow core (HC) and may have a square lattice (SQL). In various embodiments, SQL PBGF can have a cladding region including 2-10 layers of air-holes. In various embodiments, an HC SQL PBGF can be configured to provide a relative wavelength transmission window Δλ/λc larger than about 0.35 and a minimum transmission loss in a range from about 70 dB/km to about 0.1 dB/km. In some embodiments, the HC SQL PBGF can be a polarization maintaining fiber. Methods of fabricating PBGF are also disclosed along with some examples of fabricated fibers. Various applications of PBGF are also described.