A lot of times after asking a question I can think of some people on Stack Exchange who may be interested in my question, or even able to answer my question. It would be very convenient if on the some page of my question, there is a button to message those people about my question.
There is already a thread on meta dedicated to something like this: Opt-in to be always pingable to answer questions. If a person has opted in there, feel free to place a comment under their post to let them know about a question they might be interested in.
Note that this is definitely opt-in -- there is not, nor will there ever be, a feature to allow arbitrary pinging of users who haven't even participated in a thread. Remember, this is a question and answer site, not a social network, and the experts are already giving precious time to answer questions as it is. If the site allowed anyone to initiate conversations with anyone else requesting assistance, all of the experts would quickly abandon it.
Also, note there is a tendency for inexperienced members to single out certain high-rep individuals as being the only people capable of answering questions. You should avoid this tendency. For the vast majority of questions asked on this site, many people can give equally satisfactory answers.