I think Holmes’ fascination with Irene Adler is a romantic one and stems from a few different sources. The first being that she seems to be Holmes’ counterpoint; a female version of him. Take into account her own use of disguises, the skulking about, the same observational tendencies, etc and one could see why he would be so drawn to her. The second reason I believe him to be so smitten by her is that he was essentially bested by her as she managed to escape with the photograph and leaving one of herself and a letter to him outlining everything. There was an element of sweetness in the note when she wrote “Yet, with all this, you made me reveal what you wanted to know. Even after I became suspicious, I found it hard to think evil of such a dear, kind old clergyman.” Holmes most likely viewed this as a compliment to his ability and a nod of admiration from her. Lastly, he asks to keep the photograph of her and tells the king of Bohemia that she is “on another level” which is his own admiration for Irene. I have seen the movie and this plays into the cat and mouse exchanges between the two.