The geometry origin of frequency-sensitive super-collimation phenomenon for two-dimensional photonic crystals

Frequency-sensitive super-collimation (FSSC) is a novel dispersion phenomenon of photonic crystals (PhCs) that can realize the beam collimating propagation with very high frequency sensitivity. In order to deeply investigate the origin and the stability of FSSC phenomenon in a wide parameter space, we study the geometry of dispersion surface in detail. Four features for the special geometry of dispersion surface with FSSC are found for rectangular PhCs. The special geometry supports the stability of FSSC in a wide range of parameter space. Two-parameter modulation (TPM) method, in which the aspect ratio β and the dielectric constant of rods ɛr of rectangular lattice are chosen as the key parameters, is used to analyze the geometry of dispersion surface from the frequency changes at the high-symmetry points. Step by step, the origin of such geometry is revealed and the evolving process can be explained by the field distribution changes of Bloch modes at the high-symmetry points. Furthermore, we show that the geometry not only can be used to explain the origin and the stability of FSSC, but also can help us to find other FSSC phenomenons. Theoretically, we believe the geometry of dispersion surface and the TPM can be widely used on the studies of complex dispersion properties of PhCs. The FSSCs found in this work with higher sensitivity or higher stability can help us to design new on-chip PhC devices.