Semiconductor laser element

A semiconductor laser element comprising:

• a substrate having a main surface;
• and
• a light-emitting layer and a photonic crystal layer provided on the substrate in a state of being laminated along a normal direction of the main surface, wherein
• the photonic crystal 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 arranged in a two-dimensional shape on a reference surface orthogonal to the normal direction,
• in a virtual square lattice set on the reference surface, each of the plurality of modified refractive index regions is arranged such that a center of gravity is located on a corresponding lattice point out of lattice points of the virtual square lattice,
• a lattice spacing a of the virtual square lattice and a light emission wavelength λ of the light-emitting layer satisfy a condition for T-point oscillation,
• each of the plurality of modified refractive index regions has an annular shape or a circular shape with the corresponding lattice point as a center, a (m1, n1)-order Fourier coefficient of the annular shape or the circular shape depending on a size of the annular shape or the circular shape includes (−2,0)-order, (+2,0)-order, (0,−2)-order, and (0,+2)-order four Fourier coefficients, and
• a position of the center of gravity of each of the plurality of modified refractive index regions is set to make an absolute value of the (m1, n1)-order Fourier coefficient of the annular shape or the circular shape 0.01 or less, or 20% or less of a maximum peak value the (m1, n1)-order Fourier coefficient of the circular shape is able to take.

A semiconductor laser element comprising:

• a substrate having a main surface;
• and
• a light-emitting layer and a phase modulation layer provided on the substrate in a state of being laminated along a normal direction of the main surface, 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 arranged in a two-dimensional shape on a reference surface orthogonal to the normal direction,
• in a virtual square lattice set on the reference surface, the plurality of modified refractive index regions is associated one-to-one with lattice points of the virtual square lattice,
• each of the plurality of modified refractive index regions is arranged in a state where a center of gravity is physically separated from a corresponding lattice point out of the lattice points of the virtual square lattice, and an angle of a vector connecting the corresponding lattice point to the center of gravity with respect to the virtual square lattice is set individually for each of the plurality of modified refractive index regions,
• a lattice spacing a of the virtual square lattice and a light emission wavelength λ of the light-emitting layer satisfy a condition for M-point oscillation,
• a (m2, n2)-order Fourier coefficient of an annular shape or a circular shape depending on a size of the annular shape or the circular shape obtained by virtually rotating each of the plurality of modified refractive index regions by one lap with the corresponding lattice point as a rotation center includes (−1,−1)-order, (+1,−1)-order, (−1,+1)-order, and (+1,+1)-order four Fourier coefficients, and
• a position of the center of gravity of each of the plurality of modified refractive index regions is set to make an absolute value of the (m2, n2)-order Fourier coefficient of the annular shape or the circular shape 0.01 or less, or 10% or less of a maximum peak value the (m2, n2)-order Fourier coefficient of the circular shape is able to take.

A semiconductor laser element comprising:

• a substrate having a main surface;
• and
• a light-emitting layer and a photonic crystal layer provided on the substrate in a state of being laminated along a normal direction of the main surface, wherein
• the photonic crystal 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 arranged in a two-dimensional shape on a reference surface orthogonal to the normal direction,
• in a virtual square lattice set on the reference surface, each of the plurality of modified refractive index regions is arranged such that a center of gravity is placed on a corresponding lattice point out of lattice points of the virtual square lattice,
• a lattice spacing a of the virtual square lattice and a light emission wavelength λ of the light-emitting layer satisfy a condition for M-point oscillation,
• each of the plurality of modified refractive index regions has an annular shape or a circular shape with the corresponding lattice point as a center, a (m2, n2)-order Fourier coefficient of the annular shape or the circular shape depending on a size of the annular shape or the circular shape includes (−1,−1)-order, (+1,−1)-order, (−1,+1)-order, and (+1,+1)-order four Fourier coefficients, and
• a position of the center of gravity of each of the plurality of modified refractive index regions is set to make an absolute value of the (m2, n2)-order Fourier coefficient of the annular shape or the circular shape is 0.01 or less, or 10% or less of a maximum peak value the (m2, n2)-order Fourier coefficient of the circular shape is able to take.