Array waveguide lattic type optical multilexer/demultiplexer circuit

An arrayed waveguide grating type optical multiplexer/demultiplexer circuit, comprising on a flat substrate a plurality of first optical waveguides, a first slab waveguide which is connected to the first optical waveguides, an arrayed waveguide, connected to the first slab waveguide, consisting of a plurality of optical waveguides which sequentially become longer with a prescribed waveguide length difference, a second slab waveguide which is connected to the arrayed waveguides, and a plurality of second optical waveguides which are connected to the second slab waveguide;

• further comprising;
• a parabola waveguide in which a width W of the first optical waveguide contacting with the first slab waveguide is defined by the following equation with respect to a propagation axis Z of optical wave,
• Z=A(W2−W02)−Z0
• where, A:
• a coefficient, W0:
• a width of the first optical waveguide, and Z0:
• a length from the first slab waveguide;
• and a taper waveguide in which a width W′ of the second optical waveguide contacting with the second slab waveguide is defined by the following equation with respect to a propagation axis Z of optical wave,
• Z=A′(W′−W0′)−Z0′
• where,
• A′:
• a coefficient, W0′:
• a width of the second optical waveguide, and Z0′:
• a length from the second slab waveguide;
• wherein the length Z0 is set within a range defined by the following condition,
• Za,0≦Z0≦Zp,0
• where
• Za,0:
• a parabola waveguide length for which a ratio of the amplitude absolute value between a main peak and first side peaks in the field distribution of the parabola waveguide far-field has an upper limit of 0.217, and Zp,0:
• a parabola waveguide length for which a relative phase between the main peak and the first side peaks in the field distribution of far-field has a lower limit of 3.14 radians.