Combine sugar and 1/4 cup water in a small saucepan; bring to a boil. Reduce heat, and simmer 2 minutes or just until sugar dissolves. Remove from heat; cool.
Combine sugar syrup, club soda, pomegranate juice, vodka, and lime juice. Place crushed ice in a martini shaker; add about 3/4 cup pomegranate mixture. Cover and shake. Strain into a glass. Garnish with lime slice, if desired. Repeat procedure with remaining pomegranate mixture.