It is shown from basic principles that the core modes of an air-core photonic-bandgap fiber (PBF) exhibit similar qualitative and quantitative behavior as the linearly polarized (LP) modes of an equivalent conventional fiber whose step-index profile is entirely determined by the band edges of the PBF. This analogy leads to the concept of effective numerical aperture (NA), which is used to provide an intuitive interpretation of the qualitative behavior of PBF modes. By using this equivalence, several key properties, including the number of modes, their cutoff, effective index, size, and divergence, and the dependence of these quantities on the PBF core and cladding parameters, can be predicted approximately by simulating the LP modes of the equivalent step-index fiber using standard LP-mode simulators or well-known formula. Besides providing a convenient tool to model the modes of a PBF, this analogy gives new physical insight into the fundamental characteristics of these complex waveguides.
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