Ternary Galois field (GF3) arithmetic can take an important and significant role in future information processing with multi-valued logic (MVL). An all optical circuit for two arithmetical operations (addition and multiplication) in ternary Galois field with OPNLM switch is proposed and discussed. The different states of polarization of light are taken as different logic states. An outline of Ternary Galois field sum of product (TGFSOP) is also discussed. Mathematical simulation has confirmed the result.