An optical wavelength multi/demultiplexer (1700, 2600, 3700), comprising: an arrayed waveguide grating, and a two-stage lattice circuit connected to the arrayed waveguide grating, wherein the arrayed waveguide grating includes: an arrayed waveguide (1702, 2602; 3702A, 3702B); first and second slab waveguides (1701, 1703; 2601, 2603; 3701A, 3701B, 3703A, 3703B) connected to both ends of the arrayed-waveguide (1702, 2602; 3702A, 3702B); and an output waveguide (1704, 2604; 3704A, 3704B) connected to the second slab waveguide (1703, 2603, 3703), and the two-stage lattice circuit includes: a first optical coupler (1706, 2606; 3706A, 3706B) connected to another end of the first slab waveguide (1701, 2601; 3701A, 3701B) which is not connected to the arrayed-waveguide (1702, 2602; 3702A, 3702B) with an interface where the first optical coupler (1706, 2606; 3706A, 3706B) is joined to the first slab waveguide (1701, 2601; 3701A, 3701B); first and second arm waveguides (1707, 1708; 2607, 2608; 3707A, 3707B, 3708A, 3708B) connected to the first optical coupler (1706, 2606; 3706A, 3706B); a second optical coupler (1709, 2609; 3709A, 3709B) connected to other ends of the first and second arm waveguides (1707, 1708; 2607, 2608; 3707A, 3707B, 3708A, 3708B) which are not connected to the first optical coupler (1706, 2606; 3706A, 3706B); third and fourth arm waveguides (1710, 1711; 2610, 2611; 3710A, 3710B, 3711A, 3711B) connected to the second optical coupler (1709; 2609; 3709A, 3709B); a third optical coupler (1712, 2612; 3712A, 3712B) connected to other ends of the third and fourth arm waveguides (1710, 1711; 2610, 2611; 3710A, 3710B, 3711A, 3711B) which are not connected to the second optical coupler (1709, 2609; 3709A, 3709B); and an input waveguide (1705, 2605; 3705A, 3705B) connected to the third optical coupler (1712, 2612; 3712A, 3712B), wherein the first optical coupler, the first and second arm waveguides, and the second optical coupler form a first Mach-Zehnder-interferometer; and the second optical coupler, the third and fourth arm waveguides, and the third optical coupler form a second Mach-Zehnder-interferometer; and wherein an optical frequency period of the two-stage lattice circuit includes an optical frequency channel spacing of the arrayed waveguide grating and a period half the optical frequency channel spacing; a first optical frequency period defined by an optical path length difference between the first and second arm waveguides (1707,1708; 2607, 2608; 3707A, 3707B, 3708A, 3708B) is equal to the optical frequency channel spacing of the arrayed waveguide grating; and a second optical frequency period defined by an optical path length difference between the third and fourth arm waveguides (1710, 1711; 2610, 2611; 3710A, 3710B, 3711A, 3711B) is half the optical frequency period of the arrayed waveguide grating. an arrayed waveguide grating, and a two-stage lattice circuit connected to the arrayed waveguide grating, wherein the arrayed waveguide grating includes: an arrayed waveguide (1702, 2602; 3702A, 3702B); first and second slab waveguides (1701, 1703; 2601, 2603; 3701A, 3701B, 3703A, 3703B) connected to both ends of the arrayed-waveguide (1702, 2602; 3702A, 3702B); and an output waveguide (1704, 2604; 3704A, 3704B) connected to the second slab waveguide (1703, 2603, 3703), and the two-stage lattice circuit includes: a first optical coupler (1706, 2606; 3706A, 3706B) connected to another end of the first slab waveguide (1701, 2601; 3701A, 3701B) which is not connected to the arrayed-waveguide (1702, 2602; 3702A, 3702B) with an interface where the first optical coupler (1706, 2606; 3706A, 3706B) is joined to the first slab waveguide (1701, 2601; 3701A, 3701B); first and second arm waveguides (1707, 1708; 2607, 2608; 3707A, 3707B, 3708A, 3708B) connected to the first optical coupler (1706, 2606; 3706A, 3706B); a second optical coupler (1709, 2609; 3709A, 3709B) connected to other ends of the first and second arm waveguides (1707, 1708; 2607, 2608; 3707A, 3707B, 3708A, 3708B) which are not connected to the first optical coupler (1706, 2606; 3706A, 3706B); third and fourth arm waveguides (1710, 1711; 2610, 2611; 3710A, 3710B, 3711A, 3711B) connected to the second optical coupler (1709; 2609; 3709A, 3709B); a third optical coupler (1712, 2612; 3712A, 3712B) connected to other ends of the third and fourth arm waveguides (1710, 1711; 2610, 2611; 3710A, 3710B, 3711A, 3711B) which are not connected to the second optical coupler (1709, 2609; 3709A, 3709B); and an input waveguide (1705, 2605; 3705A, 3705B) connected to the third optical coupler (1712, 2612; 3712A, 3712B), wherein the first optical coupler, the first and second arm waveguides, and the second optical coupler form a first Mach-Zehnder-interferometer; and the second optical coupler, the third and fourth arm waveguides, and the third optical coupler form a second Mach-Zehnder-interferometer; and wherein an optical frequency period of the two-stage lattice circuit includes an optical frequency channel spacing of the arrayed waveguide grating and a period half the optical frequency channel spacing; a first optical frequency period defined by an optical path length difference between the first and second arm waveguides (1707,1708; 2607, 2608; 3707A, 3707B, 3708A, 3708B) is equal to the optical frequency channel spacing of the arrayed waveguide grating; and a second optical frequency period defined by an optical path length difference between the third and fourth arm waveguides (1710, 1711; 2610, 2611; 3710A, 3710B, 3711A, 3711B) is half the optical frequency period of the arrayed waveguide grating.