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

A miniature arrayed waveguide grating of 70 Â 60 mm 2 size consisting of Si photonic wire waveguides was designed using complete modelling in the finite-difference time-domain simulation. The device was fabricated onto a silicon-on-insulator substrate and evaluated in the wavelength range around 1.55 mm. The clear demultiplexing characteristics were observed with a channel spacing of 11 nm and a loss of less than 1 dB.

We fabricated compact Mach-Zehnder interferometers consisting of-branches and/or-couplers in a Si photonic wire waveguide. Clear interference spectra with a maximum extinction ratio of more than 20 dB and an alternating light output between two output ports were observed. A high diffraction order of 300 was also demonstrated within a small foot space of 30 Â 20 mm 2 .

We designed and fabricated 70 × 75 μm 2 arrayed waveguide grating demultiplexer consisting of Si slab and wire waveguides on a silicon-on-insulator substrate. By optimizing the connection between components and the layout of arrayed waveguides, internal light scattering and the increase in phase error were suppressed. As a result, clear demultiplexing characteristics were observed with a channel spacing of 8 nm and a sidelobe level of −22 dB in the wavelength range from 1.5 to 1.6 μm.