Variable wavelength filter

A variable wavelength filter comprising:

• on a substrate,
• an input light waveguide;
• an arrayed-waveguide grating including a first slab waveguide, two or more array waveguides, and a second slab waveguide;
• and
• at least one output light waveguide,
• wherein at least one of the first slab waveguide and the second slab waveguide includes a groove and a resin inserted into the groove,
• wherein the groove is formed:
• such that, on condition that the groove intersects with a plurality of line segments A joining a place of connection between the input light waveguide and the first slab waveguide to places of connection between the respective array waveguides and the first slab waveguide, a total length LA of an intersection of the groove and each of the line segments A monotonously increases or decreases between the adjacent line segments A with a difference in the total length LA between the adjacent line segments A being constant, or
• such that, on condition that the groove intersects with a plurality of line segments B joining a place of connection between the at least one output light waveguide and the second slab waveguide to places of connection between the respective array waveguides and the second slab waveguide, a total length LB of an intersection of the groove and each of the line segments B monotonously increases or decreases between the adjacent line segments B with a difference in the total length LB between the adjacent line segments B being constant, and
• wherein the variable wavelength filter includes temperature control means to heat or cool or heat and cool the substrate and temperature detection means to detect a temperature of the substrate.