Optical element and mach-zehnder optical waveguide element

An optical element comprising an optical waveguide comprising a core formed from:

• a rib part;
• and a first and second slab parts which are located on both sides of the rib part so as to sandwich the rib part and thinner than the rib part, wherein
• the rib part and the first and second slab parts of the core are integrally formed by a semiconductor single crystal,
• the first slab part comprises a P-type region which is doped to be P type,
• the second slab part comprises an N-type region which is doped to be N type,
• the rib part comprises a P-type region which is in contact with the P-type region provided in the first slab part, and an N-type region which is in contact with the N-type region provided in the second slab part,
• the P-type region and the N-type region of the rib part are in contact with each other to constitute a PN junction part,
• the rib part comprises a top portion which is located above the first and second slab parts in a cross section perpendicular to the longitudinal direction of the optical waveguide, and
• the top portion of the rib part comprises an undoped region formed from at least one of an intrinsic region and a low-concentration doping region which is doped at a dopant concentration 1/10 or less of a dopant concentration in at least one of the adjacent P-type region and the adjacent N-type region.