Cut cucumber crosswise into three equal pieces.

Peel and chop 2 pieces of the cucumber and put into a blender.

Peel 4 lengthwise strips from the remaining piece of cucumber, leaving stripes of green.

Halve the remaining cucumber piece lengthwise and core it.

Thinly slice the remaining cucumber piece crosswise.

Add water, sugar, fresh ginger, and lemon juice to the blender.

Puree the mixture until smooth.

Pour the puree through a medium-mesh sieve into a pitcher.

Stir in sake and crystallized ginger (if using) into the pitcher.

Add the cucumber slices to the pitcher.

Chill the sangria, covered, for up to 2 hours.

Serve the sangria over ice.