When it comes to neighbors, your legal rights are one thing, and the misery of being engaged in open warfare with someone who lives right next door is another.
Did you call the authorities BEFORE talking to him about it, or did you start by explaining about the asthma and asking him nicely to stop (or at least to choose times when the wind blows the smoke away from your house)? If the former, then he's probably angry with you and might not even want to talk to you. I think it would still be worth trying to patch things up, starting with an apology for not talking to him first. It seems to me that you have little to lose beyond your pride, but it's up to you.
In the real world, most people will be nice to you if they like you (and won't if they don't). What do you think this neighbor would do if you were away from home and he noticed that your house was on fire, or that someone was breaking into your house? Wouldn't you rather he tried to help you than that he mutter to himself it serves his nasty neighbor right?
If he burns clean yard waste, would you consider taking it from him and composting it, or trying to find someone else to take it?