Preheat oven to 400 degrees.
Trim ends of fennel bulb. Trim outer layer if it is blemished. Cut vertically down the center. Remove the core in a V shape at the bottom of the bulb. Slice the bulb halves thinly, horizontally.
Wash and zest the limes.
Lay or roll out the puff pastry in a rectangle large enough to wrap the fillet and seal.
Center salmon fillet on the puff pastry. Sprinkle zest from first lime over salmon. Top with ¾ of the fennel slices. Squeeze juice of first lime over the fennel.
Close up the puff pastry edges. Wet the edges if you need to to make it seal.
Cover baking sheet with parchment paper. Place pastry on the pan, sealed side down.
Bake at 400 degrees about 40 minutes.
While salmon is baking, heat the remaining fennel in a non stick frying pan over medium low heat about 12 minutes till it is soft.
Put sour cream, fennel, zest of 2nd lime and juice of 2nd lime in a blender and blend til smooth. Reserve to serve on the side.
When salmon is done slice the puff pastry package into 4 equal portions and serve.