A method of exact analysis for the cylindrical fiber with an arbitrary but azimuthally symmetric refractive-index distribution is given. The index distribution is simulated by a multilayer structure and the analysis is formulated exactly by using iterative multiplication of four by four matrices. Then the four by four matrices are approximately separated into two systems of two by two matrices with a good accuracy for the fiber with small index difference. In this way, the computing time is reduced almost 1/6 times compared with the former method. As an example of the application, the propagation modes of a focusing fiber are identified which previously were not exactly known. It is revealed that the group-velocity differences between the modes which are degenerate in the scalar analysis can be larger than those of the non-degenerate modes.

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.

Silicon avalanche photodiode with the Nπ₁Pπ₂P structure is fabricated, using the technology of epitaxitial growth after boron ion-implantation to bury a P layer. The diode with the excess noise factor of F5 is obtained at the multiplication factor of M100 for λµm.