The two-dimensional spatial image transmission characteristics of the optical graded-index fiber with a refractive index distribution including fourth and sixth order terms in the core region are investigated. Since the GRIN fiber for image transmission has a large core radius, the most field is tightly confined to the center of the core. The effect of the core-clad interface on the image transmission characteristics is approximately evaluated. Therefore the GRIN fiber is assumed to have an infinitely-extended index profile. The propagation constants and the electric field distributions in the core region are strongly affected by the coefficient of the fourth order term, D4, but, are only slightly affected by the sixth order term. The optimum value of D4 is found to be 0.8, because the deviation of the difference between the propagation constants of the two consecutive modes becomes minimum. For the graded-index fiber with D40.8, the on-axis and off-axis transmission characteristics show that the two dimensional image can be transmitted for a length of more than 50 m and the beam waist of the output image becomes 1.3 times of that of the input for spatial impulse image signal.

The purpose of the present note is to provide a necessary and sufficient condition in order that strongly connected group-matrix type automata, whose orders are prime, may be regular. Further, as an applications, a problem concerning factor automata of a strongly connected automaton will be discussed.

In the present paper, we introduce a new type of automata, called generalized group-matrix type automata, for representing general automata in connection with their automorphism groups. A family of subgroups of a given finite group, satisfying a certain condition, called the separation condition, will play a fundamental role.