Question: I would like your advice about what I should bid in the following situation. Partner opens 1C, I answer 1H, he bids 2H. My hand is:

S : none  

H : K Q J x x x  

D : A K Q x x x  

C : J 

What should I bid now?

Answer: 
The things your partner need most to know about are your spade void and strong diamonds. So I would bid three diamonds [changed from spades], to show my stopper in that suit. 

If partner has "nothing" to say, he'll bid hearts, but more likely, he'll bid four clubs to show his ace in that suit. Then you can bid four spades [changed from diamonds] to show your void [changed from ace].

You have the material for a small, or even grand slam. All you need are the ace of clubs and the ace of hearts for the latter. Since partner opened, he will have one or both of those unless he has a lot of wasted honors in spades. (Hopefully he has the two good aces, eight high card points, plus a few, but not "many" spade honors for his opener).

Edit: Based on the comments of others, I believe I got the original order of suits wrong. That is, I now believe that you should bid three diamonds first to show the stopper, then spades to show the void. That is, lower-ranking suit, then higher.
From my comment to Thanos' answer:

Logically speaking, 3S splinter followed by 4NT over the expected 4H by partner should be keycard ask, without counting the Spade Ace (otherwise why not bid 4NT directly?). If partner bids 4D (likely singleton), you can still continue with a 4S bid and partner will know to take you further with the heart or club Ace.

So I would suggest bidding 3S, followed by 4NT over 4H.