Recently, the nested Mach–Zehnder interferometer [Phys. Rev. Lett. 111, 240402 (2013)] was modified by adding Dove prisms in a paper [Quantum Stud.: Math. Found. 2, 255 (2015)], and an interesting result is that, after the Dove prisms were inserted, a signal at the first mirror of the nested interferometer was obtained. But, according to the former original paper, the photons have never been present near that mirror. In this work, we interpret this result naturally by resorting to the three-path interference method. Moreover, we find that even though the photons have been somewhere, they can hide the trace of being there.

We investigate the reflected field for few-cycle ultra-short laser pulses propagating through resonant media embedded within wavelength-scale structures. Full-wave Maxwell–Bloch equations are solved numerically by using the finite-difference time-domain method. The results show that the spectral feature of the reflected spectrum is determined by the Bragg reflection condition, and that the periodic structure of a dense atomic system can be regarded as a one-dimensional photonic crystal and even as a highly reflective multilayer film. Our study explains the suppression of the frequency shifts in the reflected spectrum based on the Bragg reflection theory and provides a method to control the frequency and frequency intervals of the spectral spikes in the reflected spectrum.