Dirac cone dispensions in various periodic systems can lead to intriguing transport properties, such as Klein tunneling, Zitterbewegung, antilocalization, abnormal quantum Hall effect. From an effective medium perspective photonic crystals (PhCs) with the k = 0 Dirac-like point at the BZ center also can be regarded as the effective zero-refractive index materials with ε _eff = λ _eff = 0, which provide quasi-infinite phase velocity and infinite wavelength for the light propagating inside. Compared with the high intrinsic losses of the conventional zero-refractive index metamaterials comprising metallic components, photonic crystals can be made of dielectric or semiconductor materials with low loss. Some interesting wave propagation behaviors have be realized in the dielectric PhCs with k = 0 Dirac-like point at the BZ center, such as cloaking, focusing lens and unidirectional transmission. Near the Dirac point, the PhCs can be regard as quasi-effective-zero-index mediums with some characteristics greatly different from that of the original component materials. In this work, we systematically investigate the transmission properties of PhCs near the Dirac-like point and try to explore the applications of PhCs near Dirac point to design some interesting optical devices, which can be used to realize the precision measurements of wavelength, frequency and phase. By optimizing the geometry of artificially engineered PhCs to give a specific electric and magnetic response to incident electromagnetic waves, and enable optical devices with entirely new physical properties, optical functions. We believe this investigation of the low-loss PhC near Dirac-like point paves the way to more advanced PhC-enabled devices that require a range of low-index values.