Light emitting systems are disclosed. The light emitting system includes an LED that emits light at a first wave-length. A primary portion of the emitted first wavelength light exits the LED from a top surface of the LED that has a minimum lateral dimension Wmin. The remaining portion of the emitted first wavelength light exits the LED from one or more sides of the LED that has a maximum edge thickness Tmax (122, 124). The ratio Wmin/Tmax is at least 30. The light emitting system further includes a re-emitting semiconductor construction that includes a semiconductor potential well. The re-emitting semiconductor construction receives the first wavelength light that exits the LED from the top surface and converts at least a portion of the received light to light of a second wavelength. The integrated emission intensity of all light at the second wavelength that exit the light emitting system is at least 4 times the integrated emission intensity of all light at the first wavelength that exit the light emitting system.