We demonstrated an arrayed-waveguide-grating (AWG) demultiplexer using Si photonic wire waveguides, for the first time. We designed and fabricated an AWG of 110 Â 93 mm 2 size on a silicon-on-insulator substrate. The demultiplexing function was observed in the wavelength range of 1.50-1.57 mm with a channel spacing of $6 nm and a free spectral range of >90 nm. A narrower channel spacing of 1 nm is possible in an area of $(500 mm) 2 , using an optimization of arrayed waveguides and slab waveguides.

We use Monte Carlo methods to investigate the asymptotic behaviour of the number and mean-square radius of gyration of polygons in the simple cubic lattice with fixed knot type. Let p n (τ ) be the number of n-edge polygons of a fixed knot type τ in the cubic lattice, and let R 2 n (τ ) be the mean square radius of gyration of all the polygons counted by p n (τ ). If we assume that p n (τ ) ∼ n α(τ )−3 µ(τ ) n , where µ(τ ) is the growth constant of polygons of knot type τ , and α(τ ) is the entropic exponent of polygons of knot type τ , then our numerical data are consistent with the relation α(τ ) = α(∅) + N f , where ∅ is the unknot and N f is the number of prime factors of the knot τ . If we assume that R 2 n (τ ) ∼ A ν (τ )n 2ν(τ ) , then our data are consistent with both A ν (τ ) and ν(τ ) being independent of τ . These results support the claims made

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We fabricated an ultra small H-tree-type optical signal distribution circuit on a silicon-on-insulator substrate. We used a micronsize bent-waveguide-type optical branch in a Si photonic wire waveguide and observed clear light output from eight output ports for laser light of 1.5 µm wavelength. The fluctuation of distributed light intensity was 2-5 dB. It was caused by a nonuniform branching ratio, and can be reduced by improving asymmetric corner shapes of each branch.