▁following ▁table ▁gives ▁the ▁ 6 ▁common ▁examples ▁of ▁normal ized ▁Jones ▁vectors . ▁ ▁A ▁general ▁vector ▁that ▁points ▁to ▁any ▁place ▁on ▁the ▁surface ▁is ▁written ▁as ▁a ▁k et ▁. ▁When ▁employ ing ▁the ▁Po inc ar é ▁sphere ▁( also ▁known ▁as ▁the ▁Blo ch ▁sphere ), ▁the ▁basis ▁k ets ▁( ▁and ▁) ▁must ▁be ▁assigned ▁to ▁oppos ing ▁( ant ip od al ) ▁pairs ▁of ▁the ▁k ets ▁listed ▁above . ▁ ▁For ▁example , ▁one ▁might ▁assign ▁ ▁= ▁ ▁and ▁ ▁= ▁. ▁ ▁These ▁assign ments ▁are ▁arbitrary . ▁ ▁O pp osing ▁pairs ▁are ▁▁▁ ▁and ▁▁▁ ▁and ▁▁▁ ▁and ▁▁ ▁The ▁polar ization ▁of ▁any ▁point ▁not ▁equal ▁to ▁ ▁or ▁ ▁and ▁not ▁on ▁the ▁circle ▁that ▁passes ▁through ▁ ▁is ▁known ▁as ▁elli pt ical ▁polar ization . ▁ ▁Jones ▁matrices ▁ ▁The ▁Jones ▁matrices ▁are ▁operators ▁that ▁act ▁on ▁the ▁Jones ▁vectors ▁defined ▁above . ▁ ▁These ▁matrices ▁are ▁implemented ▁by ▁various ▁optical ▁elements ▁such ▁as ▁l enses , ▁beam ▁split ters , ▁mirror s , ▁etc . ▁ ▁Each ▁matrix ▁represents ▁projection ▁onto ▁a ▁one - dimensional ▁complex ▁sub space ▁of ▁the ▁Jones ▁vectors . ▁The ▁following ▁table ▁gives ▁examples ▁of ▁Jones ▁matrices ▁for ▁polar izers : ▁ ▁Ph ase ▁ret ard ers ▁ ▁Ph ase ▁ret ard ers ▁introduce ▁a ▁phase ▁shift ▁between ▁the ▁vertical ▁and ▁horizontal ▁component ▁of ▁the ▁field ▁and ▁thus ▁change ▁the ▁polar ization ▁of ▁the ▁beam . ▁Ph ase ▁ret ard ers