Light emitting element, method for manufacturing light emitting element, and method for designing phase modulation layer

A light-emitting element, comprising:

• a substrate having a main surface;
• a light-emitting unit configured to output light for forming an optical image along a normal direction of the main surface or a tilt direction intersecting the normal direction, or both the normal direction and the tilt direction;
• and
• a bonding layer provided between the substrate and the light-emitting unit, and bonding the main surface of the substrate and the light-emitting unit, wherein
• the light-emitting unit has:
• a semiconductor stack having a back surface and a front surface positioned on an opposite side of the bonding layer with respect to the back surface, the semiconductor stack including a first cladding layer of a first conductivity type provided between the back surface and the front surface, a second cladding layer of a second conductivity type provided between the first cladding layer and the front surface, an active layer provided between the first cladding layer and the second cladding layer, and a phase modulation layer provided between the first cladding layer and the second cladding layer;
• a first electrode in contact with the back surface of the semiconductor stack;
• and
• a second electrode in contact with the front surface of the semiconductor stack, and wherein
• the phase modulation layer includes a base layer and a plurality of modified refractive index regions each having a refractive index different from a refractive index of the base layer, and includes:
• a first region having been set to have a size including an entire part positioned in an effective area of the second electrode when viewed from a thickness direction from the front surface toward the back surface of the semiconductor stack, the effective area defined as an area where the light for forming the optical image is outputted;
• and
• a second region other than the first region,
• on a virtual square lattice set on a reference plane of the phase modulation layer orthogonal to the thickness direction, each of the plurality of modified refractive index regions is associated with any one of lattice points of the virtual square lattice, and a center of gravity of each specific modified refractive index region included in the plurality of modified refractive index regions and positioned in the second region is arranged on the reference plane according to a first array condition or a second array condition,
• the first array condition is defined in such a manner that the center of gravity of each specific modified refractive index region is separated from the associated lattice point, and a rotation angle around the associated lattice point, which is defined by an angle formed by a line segment extending from the associated lattice point to the center of gravity and the virtual square lattice, is individually set according to a phase distribution for forming the optical image,
• the second array condition is defined in such a manner that the center of gravity of each specific modified refractive index region is positioned on a straight line passing through the associated lattice point in a tilting state with respect to the virtual square lattice, and a distance from the associated lattice point to the center of gravity is individually set according to the phase distribution,
• the light for forming the optical image is outputted from the front surface of the semiconductor stack, and the optical image is completed as a single beam pattern including only light components having passed through the second electrode from the second region, and
• in a specific region on the main surface of the substrate overlapping the effective area when viewed along the thickness direction, a first variation amount of a first distance from the main surface to the front surface of the semiconductor stack at a plurality of first points aligned along a first straight line on the main surface, and a second variation amount of a second distance from the main surface to the back surface of the semiconductor stack at the plurality of first points satisfy a relationship:
• (first variation amount)<(second variation amount), and a third variation amount of the first distance at a plurality of second points aligned along a second straight line on the main surface intersecting the first straight line, and a fourth variation amount of the second distance at the plurality of second points satisfy a relationship:
• (third variation amount)<(fourth variation amount).