To characterize and represent an electromagnetic field exactly, only electric field intensity is not sufficient. The physical parameters of a nano-optical field at least include amplitude, phase, polarization state and the corresponding magnetic field, etc. Phase and amplitude information in near field are crucial not only for understanding of near-field physical mechanism, but also for design and optimization of nanophotonics devices based on phase-modulation principles, such as plasmonic-focusing devices [
29], focusing-control devices [
30-
33], directional-beaming control devices [
3], etc. The basic method to measure amplitude and phase is by means of SNOM tip and heterodyne interferometry (THI) [
34-
36]. Phase and amplitude measurements and mappings in the nanoscale have been realized, which verify experimentally the basic principles and mechanisms of light-matter interaction, and benefit design and optimization of nanophotonics devices. THI systems have been developed in several leading laboratories on the world. A typical system generally consists of a highly stable laser source, a delicate and reliable heterodyne interferometer, a SNOM tip, phase- and amplitude-detecting unit, scanning and mapping unit and so on. The data of optical intensity, phase, amplitude, topography and position can be acquired simultaneously. Using such a system, some beautiful and exciting experimental results of several types of nano-optical fields have been presented. Figure 3(a) shows the topography, amplitude mapping, phase mapping and the real field composed by amplitude and phase of an optical waveguide [
37]. White arrow expresses the weak directional leakage. Besides, the characterization results of other nano-structures such as nano-rod, nano-particle, nano-triangle [
36] and bowtie [
38] are reported (see Fig. 3(b)). Also, the information on topography, amplitude and phase of the nano-optical fields are given.