Ultra-thin backlight

A liquid crystal display device, comprising:

• a liquid crystal display module;
• and
• a backlight structure, including:
• a light source,
• a wave guide, including two faces,
• a foconic coupler disposed between the light source and a face of the wave guide, and
• a reflector disposed proximate to one of the faces of the wave guide;

An apparatus for use with a radiation- or lighting device comprising:

• a radiation source with a refraction index Nem;
• a plurality of dielectric materials with successively decreasing Nex,n (Nem>Nex1>Nex,2>. . . Nex,n≧1), first material being in optical contact with said radiation source and each subsequent material being in direct optical contact, without an air interface, with materials adjacent thereto, wherein said source and materials have a progressively increasing minimal projected surface area, scaled according to an Extraction Invariant, which is expressed as:
• Sex,n≧Sex,n-1*(Nn-1/Nn)2
• and
• Sex,n≧Sem*(Nem/Nex,n)2.