An illumination device comprising: a plurality of light-emitting elements (LEEs); a light guide extending in a forward direction from a first end of the light guide to a second end of the light guide, the light guide being positioned to receive at the first end light emitted by the LEEs and configured to guide the light to the second end, wherein divergence of the light received at the first end and divergence of the guided light that reaches the second end are substantially the same; a light divergence modifier (150; 350b; 350f; 350g) optically coupled to the light guide at the second end to receive the guided light, the light divergence modifier configured to modify the divergence of the guided light, such that the light provided by the light divergence modifier has a modified divergence different from the divergence of the guided light; and an optical extractor optically coupled to the light divergence modifier, the optical extractor configured to output into the ambient environment light provided by the light divergence modifier as output light in one or more output angular ranges, characterized in that the light divergence modifier is flared such that the modified divergence of the light provided at the output of the light divergence modifier to the optical extractor is smaller than the divergence of the guided light, or comprises a 3D grating (350-f) extending along a length of the light divergence modifier configured such that the modified divergence of the light provided at the output of the light divergence modifier to the optical extractor is smaller or larger than the divergence of the guided light, or comprises an optical interface configured as a 2D grating (350-g) configured such that the modified divergence of the light provided to the optical extractor is smaller or larger than the divergence of the guided light. a plurality of light-emitting elements (LEEs); a light guide extending in a forward direction from a first end of the light guide to a second end of the light guide, the light guide being positioned to receive at the first end light emitted by the LEEs and configured to guide the light to the second end, wherein divergence of the light received at the first end and divergence of the guided light that reaches the second end are substantially the same; a light divergence modifier (150; 350b; 350f; 350g) optically coupled to the light guide at the second end to receive the guided light, the light divergence modifier configured to modify the divergence of the guided light, such that the light provided by the light divergence modifier has a modified divergence different from the divergence of the guided light; and an optical extractor optically coupled to the light divergence modifier, the optical extractor configured to output into the ambient environment light provided by the light divergence modifier as output light in one or more output angular ranges, characterized in that the light divergence modifier is flared such that the modified divergence of the light provided at the output of the light divergence modifier to the optical extractor is smaller than the divergence of the guided light, or comprises a 3D grating (350-f) extending along a length of the light divergence modifier configured such that the modified divergence of the light provided at the output of the light divergence modifier to the optical extractor is smaller or larger than the divergence of the guided light, or comprises an optical interface configured as a 2D grating (350-g) configured such that the modified divergence of the light provided to the optical extractor is smaller or larger than the divergence of the guided light.