An haifi Arthur Ashkin a Brooklyn, New York, a 1922, zuwa dangin Yahudawa na Ukraine. Iyayensa sun kasance Isadore da Anna Ashkin. Yana da 'yan'uwa biyu, ɗan'uwa, Julius, kuma masanin kimiyyar lissafi, da' yar'uwa, Ruth. Ɗaya daga cikin 'yan uwansa, Gertrude, ya mutu yayin da yake matashi. Gidan iyali yana cikin Brooklyn, New York, a 983 E 27 Street. Isadore (né Ashkinazi) ya yi hijira zuwa Amurka daga Odessa (sa'an nan kuma Daular Rasha, yanzu Ukraine), yana da shekaru 18. Anna, shekaru biyar da suka fi ƙanƙanta, ya fito ne daga Ukraine na yau, sa'an nan Galicia, Daular Austro-Hungarian. A cikin shekaru goma da ya sauka a New York, Isadore ya zama dan ƙasar Amurka kuma yana gudanar da dakin gwaje-gwaje a 139 Dely Street a Manhattan. Ashkin ya sadu da matarsa, Aline Cornell, a Jami'ar Cornell, da kuma kakarsa, Gertrude, ya mutu yayin da suke ƙuruciya.
Ƙaunar Isadore