Based on Rayleigh-Sommerfeld scalar diffraction formula, analyzed is the diffraction field distribution of the restricted output end surface of multiple quantum wells planar waveguide by slit. Obtained is its analytical expression of field distribution, which permits accurate and effective study on the characteristic of diffraction field from the restricted output end surface of the waveguide by slit. Then, the variation curve of the beam propagation factor M2 versus the slit width is computed by the second moment method. It is useful for understanding the restricted diffraction properties of the multiple quantum wells planar waveguide. When the slit half width is bigger than the core layer's half width, the beam propagation factor M2 value tends to a constant 1.108. Therefore, the corresponding field amplitude distribution is approximated by Gaussian function, and the far field divergence half angle(θ0,G=0.091 8) is calculated by matching efficiency method.
HU Lin-shun GUO Fu-yuan LI Lian-huang GAO Rui PENG Yu-jia
As for single mode symmetric step refractive index structure dielectric planar optical waveguide, when its output end is restricted, the diffractive field distribution is derived. It can be expressed as the convolution between the Dirac function and the Sinc and Lorenz functions. It is helpful to deepen the recognition of the restricted diffraction. The characteristic of the diffractive field is discussed. The variational curve of the full angle width at half maximum intensity of central bright fringe versus the half width of slit is presented by numerical calculation, and the fitting curve with the exponential function is close to it.
The diffractive beam parameters of LP01 mode of fiber are analyzed in detail. Based on solving linear equations, two formulas for two kinds of mode-field radii as functions of normalized frequency are presented, and relations between angular radius of far-field divergence, beam propagation factor, and normalized frequency are given. Numerical calculation indicates that the maximal relative error is smaller than 1% within a reasonable parameter range.
