In a semiconductor light emitting device, a semiconductor light emitting
element has a light extracted surface on which a plurality of convex
structures is formed. The convex structures each have a conical mesa
portion constituting a refractive index gradient structure, a cylindrical
portion constituting a diffraction grating structure, and a conical
portion constituting a refractive index gradient structure. The mesa
portion, cylindrical portion, and conical portion are arranged in this
order from the light extracted surface. The period between the convex
structures is longer than 1/(the refractive index of an external
medium+the refractive index of the convex structures) of an emission
wavelength and equal to or shorter than the emission wavelength. The
circle-equivalent average diameter of the cylindrical portion is 1/3 to
9/10 of that of the bottom of the mesa portion.