Have you ever played Field Hockey?
I have not ever played field hockey, but I do know it is part of the hockey family
It is a part of the hockey family but played on grass or turf instead of ice like traditional hockey.
You can also play it on an indoor board surface, which is interesting as I've never seen that done
I did not know that. I found it surprising that there are no left handed sticks. 
That is strange. Maybe there is no difference in them? Each stick size is based on players height
Yes after further research it seems the sticks are the same and remain on the right side of the player during games.
Field hockey
Field hockey is a team game of the hockey family. The game can be played on grass, water turf, artificial turf or synthetic field as well as an indoor board surface. Each team plays with eleven players, including the goalie. Players use sticks made out of wood, carbon fibre, fibre glass or a combination of carbon fibre and fibre glass in different quantities (with the higher carbon fibre stick being more expensive and less likely to break) to hit a round, hard, plastic ball.
Field hockey pitch
A hockey pitch is the playing surface for the game of field hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf. The transition onto artificial pitches came during the 1970s and was made mandatory for major competitions in 1976. All the lines, markings and goal specifications are outlined by the International Hockey Federation in "The Rules of Hockey".
All line markings on the pitch form part of the area which they define. For