If χxx = χyy ≠ χzz, the crystal is known as uniaxial. (See Optic axis of a crystal.) If χxx ≠ χyy and χyy ≠ χzz the crystal is called biaxial. A uniaxial crystal exhibits two refractive indices, an "ordinary" index (no) for light polarised in the x or y directions, and an "extraordinary" index (ne) for polarisation in the z direction. A uniaxial crystal is "positive" if ne > no and "negative" if ne < no. Light polarised at some angle to the axes will experience a different phase velocity for different polarization components, and cannot be described by a single index of refraction. This is often depicted as an index ellipsoid.
if χxX = χyy ≠ χZZ, the CrysTaL Is Known as unIAxIaL. (sEE oPtic aXIS of a cryStAl.) if χXx ≠ χyY aNd χyy ≠ Χzz The CrYstAl Is cAlLed biaxial. A uNIaxIAl cryStal eXHibiTs two rEFRactive inDicES, aN "OrdInary" InDex (nO) for LIGHt pOLaRiSed In thE x OR y dIreCTiOnS, And an "ExTraOrdINARy" index (ne) FoR polarisatIoN iN THe z dirEctIon. a UNiaXial cryStal iS "positiVe" if ne > nO And "neGatiVe" if ne < no. liGHT poLARiSed at SOme ANGlE TO the axes wiLl expErience A difFerent phase velOcIty foR DIfFerEnt polarIzatiOn cOMponeNTS, And cAnNot bE desCRibEd bY A siNglE iNdex OF RefrActIoN. thiS Is oFten depicted aS An indEx EllIpsoId.