Identification of zero density of states domains in band gap fibers using a single binary function

Here we introduce a new calculation method to find the domains of zero density of states for photonic band gap guiding fibers consisting of arrays of high refractive index strands in a low refractive index cladding. We find an analytic expression that associates any combination of geometric parameter, effective index, material and wavelength with a single binary value which allows direct determination whether the density of cladding states is zero or not. The method does not require the typically used root finding procedure, making mode tracking or defining starting values obsolete. We verify the validity of our approach on well-established results and reveal as example that band gap regions are mainly determined by the two lowest order Bessel function orders. Our method allows for extensive parameter scans and evaluation of photonic band gap structures against structural and material inaccuracies with substantially reduced simulation effort.