Blend all ingredients in mini processor to coarse puree. Season tapenade to taste with salt and pepper. Transfer to small bowl. DO AHEAD: Can be made 3 days ahead. Cover and chill. Gently mix diced tuna and next 6 ingredients in large bowl. Using moistened hands, shape tuna mixture into six 3/4-inch-thick patties (each about 4 inches in diameter). Place burgers on plate. Cover and refrigerate at least 1 hour and up to 1 day. Spray grill rack with nonstick spray. Prepare barbecue (medium-high heat). Grill burgers until almost cooked through, about 4 minutes per side. Arrange 6 focaccia squares or bottoms of pain rustique on work surface; spread with tapenade. Top each with burger, tomato slice, onion slice, and arugula, then focaccia or bread top. Cut burgers in half and serve.