Turning a whole side of fish on the grill is easier if you use a fish-shaped grilling basket. Fire Roasted Vidalia Onion Halves make an ideal dinner accompaniment during the late spring and summer for this salmon.
Combine all seeds in a skillet over medium heat; toast, shaking pan, until aromatic, 4 to 6 minutes. Grind seeds coarsely in a spice grinder or with a mortar and pestle. Transfer to a bowl; add salt, pepper, and sugar.
Rub spice mixture into flesh side of salmon. Let stand 30 minutes; if not grilling right away, refrigerate, wrapped in plastic, for up to 2 days. Let salmon come to room temperature before grilling.
Heat grill to hot; coals should be glowing red, and rack should be very hot. Brush both sides of salmon and hot rack with oil. Grill salmon (if using a gas grill, close lid while cooking), flesh side down, until firm and slightly charred, 4 to 8 minutes. Carefully turn salmon using 2 large spatulas. Cook 4 to 6 minutes more, or until mostly opaque but slightly translucent and cooked through. Serve with cucumber salsa.