| The characteristic of diffraction in a cylindrical waveguide is the basic of analysing mode field and the theories of optical apparatus and fiber coupling, so it is significative to investigate the characteristic of diffraction in a cylindrical waveguide. Mode field diameter is used to describe the size of fundamental modes facula in single mode fiber, so nowadays measurement of MFD is regarded highly in fiber researching..According to the Rayleigh-Sommerfeld diffraction scalar integral formula, the calculable formula and the equation of spatial frequency at half maximum intensity of central bright spot of far-field diffraction of cylindrical waveguide in LPoi mode are deduced. The relationship between the full width at half maximum intensity of central bright spot and the value of normalized frequency of cylindrical waveguide is plotted. The scale of the full spatial frequency width at half maximum intensity of central bright spot of far-field diffraction in LPoi mode is also calculated. Synchronously, the relationship between the full angle width at half maximum intensity of central bright spot versus wavelength, width of cylindrical waveguide and relative refractive index of waveguide are also presented.According to the Rayleigh-Sommerfeld diffraction scalar integral formula, through mode distributions of cylindrical inhomogeneous waveguide calculated from the improved WKB methods, we get mode distributions of far-field diffraction. Far-field diffraction distributions of far field diffraction of the parabola and Epstein cylindrical inhomogeneous waveguide are also presented, as numerical analysis is developed.MFD of single mode fiber has several definitions and measurements. Studying a new way to measuring MFD, we scan far-field intensitydistributions of fiber. With Fourier-Bessel transformation and the far-field intensity distributions, we can get the near-field mode distributions of fiber, and ultimately compute MFD.
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