▁be ▁treated ▁using ▁Mu eller ▁calculus . ▁ ▁The ▁Jones ▁vector ▁ ▁The ▁Jones ▁vector ▁describes ▁the ▁polar ization ▁of ▁light ▁in ▁free ▁space ▁or ▁another ▁hom ogeneous ▁is otrop ic ▁non - atten u ating ▁medium , ▁where ▁the ▁light ▁can ▁be ▁properly ▁described ▁as ▁trans verse ▁waves . ▁Suppose ▁that ▁a ▁mon och rom atic ▁plane ▁wave ▁of ▁light ▁is ▁trav elling ▁in ▁the ▁positive ▁z - direction , ▁with ▁angular ▁frequency ▁ ω ▁and ▁wave vector ▁k ▁= ▁( 0 , 0 , k ), ▁where ▁the ▁w aven umber ▁k ▁= ▁ ω / c . ▁Then ▁the ▁electric ▁and ▁magnetic ▁fields ▁E ▁and ▁H ▁are ▁orthogonal ▁to ▁k ▁at ▁each ▁point ; ▁they ▁both ▁lie ▁in ▁the ▁plane ▁" trans verse " ▁to ▁the ▁direction ▁of ▁motion . ▁Furthermore , ▁H ▁is ▁determined ▁from ▁E ▁by ▁ 9 0 - deg ree ▁rotation ▁and ▁a ▁fixed ▁multip lier ▁depending ▁on ▁the ▁wave ▁imped ance ▁of ▁the ▁medium . ▁So ▁the ▁polar ization ▁of ▁the ▁light ▁can ▁be ▁determined ▁by ▁studying ▁E . ▁The ▁complex ▁amplitude ▁of ▁E ▁is ▁written ▁▁ ▁Note ▁that ▁the ▁physical ▁E ▁field ▁is ▁the ▁real ▁part ▁of ▁this ▁vector ; ▁the ▁complex ▁multip lier ▁serves ▁up ▁the ▁phase ▁information . ▁Here ▁ ▁is ▁the ▁imag inary ▁unit ▁with ▁. ▁ ▁The ▁Jones ▁vector ▁is ▁then ▁ ▁Thus , ▁the ▁Jones ▁vector ▁represents ▁the ▁amplitude ▁and ▁phase ▁of ▁the ▁electric ▁field ▁in ▁the ▁x ▁and ▁y ▁ ▁directions . ▁ ▁The ▁sum ▁of ▁the ▁squares