  In this paper, an analytical formula for the sensitivity of optical sensors
based on one-dimensional photonic crystals (PCs) with a defect was derived for
the first time. Based on this formula, a comparative analysis of the
sensitivity of defected PCs with and without mirror symmetry was carried out.
In addition, the exact values of sensitivity in the limit of an infinite PC
with a quarter-wave unit cell were obtained. It was shown that the sensitivity
of a defective PC with an infinitely thick defect layer is equal to that of a
perfectly reflecting Fabry-Perot resonator and does not depend on the specific
structure of the PC. The results of this work provide a significant
simplification of the analysis and optimization of optical sensors based on
defective PCs, as well as a better understanding of the numerous numerical
results obtained previously.
