What is claimed is:1. A light emitting diode (LED) device comprising:a transparent substrate;an n-type layer disposed on or above the transparent substrate;an electroluminescent (EL) quantum well (QW) formed on the n-type layer and configured to emit a first light;a photoluminescent (PL) QW formed in the n-type layer and configured to absorb at least a portion of the first light and in response emit a second light having a longer wavelength than the first light, the EL QW and the PL QW separated from one another by a portion of the n-type layer;a p-type layer formed on the EL QW; anda dichroic reflector having a greater reflectivity for the first light than for the second light, the dichroic reflector arranged to transmit the second light out of the LED device and to reflect back to the PL QW a portion of the first light transmitted through the PL QW and incident on the dichroic reflector.2. The LED device of claim 1, wherein the PL QW comprises multiple QWs emitting a same wavelength of light.3. The LED device of claim 1, wherein the EL QW comprises multiple QWs emitting a same wavelength of light.4. The LED device of claim 1, wherein the PL QW is adjacent to a depletion region of a p-n junction between the n-type layer and the p-type layer.5. The LED device of claim 1, wherein the thickness of the p-type layer is optimized to exploit self-interference of the EL QW.6. The LED device of claim 1, wherein the EL QW and the p-type electrode are separated by a distance equivalent to approximately 0.25 to approximately 0.45 times a peak wavelength of an emission of the EL QW in the p-type layer.7. The LED device of claim 1, wherein the dichroic reflector is disposed on a surface of the transparent substrate opposite from the n-type layer.8. The LED device of claim 7, wherein the dichroic reflector extends along one or more sidewalls of the transparent substrate, n-type layer, EL QW, and p-type layer.9. The LED device of claim 7, wherein the dichroic reflector comprises a stack of dielectric layers having different refractive indices.10. The LED device of claim 1, wherein the dichroic reflector has a thickness of approximately one quarter of a peak wavelength of light emitted by the EL QW.11. The LED device of claim 1, wherein EL QW is located within a depletion region of a p-n junction between the n-type layer and the p-type layer.12. The LED device of claim 7, further comprisingtrenches formed through at least an entire thickness of the p-type layer and an entire thickness of the EL QW to expose the n-type layer, the trenches defining an emitting area;a passivation material formed on sidewalls of the trenches and an upper surface of the p-type layer;n-type contacts formed in the trenches; anda p-type contact formed on the upper surface of the p-type layer in the emitting area.13. The LED device of claim 1, wherein the dichroic reflector is disposed between the transparent substrate and the n-type layer.14. The LED device of claim 13, wherein the dichroic reflector comprises multiple layers of Group III-V semiconductor materials having different compositions.15. The LED device of claim 14, wherein one or more of the multiple layers of Group III-V semiconductor materials are oxidized such that they have a lower refractive index than as-grown material.16. The LED device of claim 14, wherein one or more of the multiple layers of Group III-V semiconductor materials comprise dopants of one or more of Si and Ge and are processed to include voids such that they have a lower refractive index than as-grown material.17. The LED device of claim 14, further comprising:a first epitaxial layer formed on the substrate between the substrate and the dichroic reflector; anda second epitaxial layer formed between the dichroic reflector and the n-type layer.18. The LED device of claim 1 wherein the PL QW is configured to emit green light.19. The LED device of claim 1 comprising a second PL QW formed in the n-type layer and configured to absorb at least a portion of the first light and in response emit a third light having a longer wavelength than the first light, the PL QW and the second PL QW separated from one another by a portion of the n-type layer.20. The LED device of claim 19 wherein the second PL QW is configured to emit red light.21. The LED device of claim 20 wherein the PL QW is configured to emit green light.