The energy band structure and the surface wave local electric field distribution of the left-handed and right-handed photonic crystals materials, were studied based on parameter matching by using the transmission matrix theory of plane wave and Bloch theorem in order to study and design novel optical waveguide and optical sensor. The results show that there are semi closed and closed band gap structures in the energy band of the left-handed and right-handed materials with zero mean refractive index, and the energy level curve in the transmission band attenuates from high frequency to low frequency with oscillation. After the surface coating medium is added, the discrete energy level of forward and reverse waves appear in the partially semi-closed and closed band gap of the photonic crystal, the discrete energy level moves to lower wave vector with the increase of the coating thickness, and the discrete energy level in the semi-closed band gap splits when the coating thickness is at a certain value. In the band gap, the maximum value of the local electric field of the forward surface wave and the highest light intensity are near the junction of the coating and the surface of the photonic crystal, and decay with the coating thickness increasing or away from the junction. The response sensitivity of the maximum value of the local electric field corresponding to the closed band gap to the coating thickness is weaker than that of the semi closed band gap. In the band gap, the local electric field, the maximum value of the local electric field of the reverse surface wave and the highest light intensity are in the the photonic crystal, and increase with the coating thickness. The local restriction of the closed band gap on the reverse surface wave, the coupling effect of the surface wave and the incident light, and the response sensitivity of the local electric field to the coating thickness are stronger than those of the semi-closed band gap.