a semiconductor light-emitting diode structure having front and back surfaces and one or more light-emitting active layers arranged to emit output light at a nominal vacuum wavelength λ₀ to propagate within the semiconductor diode structure, the front surface being characterized by a critical angle Θc at the nominal vacuum wavelength λ₀;

an anti-reflection coating on the front surface that is arranged so that the front surface exhibits reflectivity, for a range of internal incidence angles on the front surface less than Θc and at the nominal vacuum wavelength λ₀, that is less than corresponding Fresnel reflectivity of the front surface without the anti-reflection coating; and

a redirection layer on the back surface that includes an array of nano-antennae that include one or more antenna materials, are shaped, sized, and spaced relative to the nominal vacuum wavelength λ₀, and arranged along the redirection layer, so as to reradiate, upon irradiation by the output light at internal incidence angles on the back surface greater than Θc and at the nominal vacuum wavelength λ₀, at least a portion of the output light to result collectively in redirection thereof to propagate toward the front surface within the range of internal incidence angles on the front surface less than Θc,

the semiconductor light-emitting device exhibiting a mean number of redirections per photon emitted by the active layer, by the redirection layer before exiting through the front surface, that is less than 30.