The phenomena of the wave propagation in a nonlinear transmission line are analyzed theoretically by the derivative expansion method. Each section of this line is constructed with a series inductor L₁ and the shunt circuit consisting of a seriesed L₂ - C₂ element and a nonlinear capacitor C (V) in which V is a line voltage. There exist two modes; L.F. mode propagating in the frequency range 0ωω_t and H.F. mode in the range ω_pω, where (L₂ C₂)¹ and (1C₂/C(0)). In the strongly dispersive region the asymptotic behavior of the nonlinear waves is described by the nonlinear Schrödinger equation and by the Korteweg-de Vries equation in the weakly dispersive region. Critical frequencies ω₁₀ and ω₂₀ (ω_pω₂₀ω₁₀) decompose the H.F. mode into three regions (1) ω_pωω₂₀, (2) ω₂₀ωω₁₀ and (3) ω₁₀ω. The resonant interaction between the L.F. mode and the H.F. mode occurs in the frequency ω₁₀, while the lowest order nonlinear interaction disappears in the frequency ω₂₀. In the regions (1), (3) and the L.F. mode the plane wave is stable under the wave modulation, while the plane wave is unstable in the region (2). We derive the basic equations describing the three wave interactions and find that the plane wave with a large amplitude becomes unstable through the parametric decay instability. The wave number and maximum growth rate of the excited waves are determined.

A new type of 1:1 optical branch for optical fiber with low insertion loss was fabricated using three graded-index rods. Two pieces of the graded-index rods were cut in parallel to their own optical axes and cemented together with the cut surfaces, and then the third rod is butt-joined to the combined rods. The experimental results were that the insertion loss was 1.1 dB and the distribution ratio was 1:0.98 at 6328 wavelength. Minor modification of this structure enables us to get distribution rations other than 1:1.

The proportional relationship between the adaptive array under directional constraint and the adaptive array under least-mean-square-error criterion is proved for narrow-banded signal under the condition that the incident direction of the desired signal is identical with the constraint direction.