A lighting device comprising: one or more light-emitting elements (LEEs) configured to provide pump light; a cylinder-shaped scattering element comprising a matrix of phosphor embedded in dielectric material, wherein the phosphor is configured to absorb at least a portion of the pump light and to emit converted light with converted light wavelengths longer than pump light wavelengths, and the dielectric material is transparent to the pump light and the converted light, the scattering element forming an immersion-coupled input interface with the LEEs, such that the pump light emitted by the LEEs is input into the scattering element through the input interface, wherein the input interface has a first dimension (2R d) corresponding to a characteristic dimension of the LEEs representing a length of the LED die or LED package that forms the LEE, and wherein the scattering element has a second dimension representing a thickness orthogonal to and 1-10 times larger than the first dimension, and a spherical dome-shaped optical extractor forming an extraction interface with the scattering element that is located outside the optical extractor, such that mixed light from the scattering element is input into the optical extractor through the extraction interface, wherein the extraction interface has a third dimension (2R E) being along, and 3-30 times larger than, the first dimension, wherein an output surface of the optical extractor is arranged and shaped relative to the extraction interface such that the mixed light received by the optical extractor through the extraction interface impinges on the output surface at incident angles smaller than or equal to a Brewster angle θ B = arctan(n E /n 0), wherein n E is a refractive index of the optical extractor and n 0 is a refraction index of an environment surrounding the optical extractor. one or more light-emitting elements (LEEs) configured to provide pump light; a cylinder-shaped scattering element comprising a matrix of phosphor embedded in dielectric material, wherein the phosphor is configured to absorb at least a portion of the pump light and to emit converted light with converted light wavelengths longer than pump light wavelengths, and the dielectric material is transparent to the pump light and the converted light, the scattering element forming an immersion-coupled input interface with the LEEs, such that the pump light emitted by the LEEs is input into the scattering element through the input interface, wherein the input interface has a first dimension (2R d) corresponding to a characteristic dimension of the LEEs representing a length of the LED die or LED package that forms the LEE, and wherein the scattering element has a second dimension representing a thickness orthogonal to and 1-10 times larger than the first dimension, and a spherical dome-shaped optical extractor forming an extraction interface with the scattering element that is located outside the optical extractor, such that mixed light from the scattering element is input into the optical extractor through the extraction interface, wherein the extraction interface has a third dimension (2R E) being along, and 3-30 times larger than, the first dimension, wherein an output surface of the optical extractor is arranged and shaped relative to the extraction interface such that the mixed light received by the optical extractor through the extraction interface impinges on the output surface at incident angles smaller than or equal to a Brewster angle θ B = arctan(n E /n 0), wherein n E is a refractive index of the optical extractor and n 0 is a refraction index of an environment surrounding the optical extractor.