If you invited your participants via Doodle, go ahead and click the 'invite' button at the top of the page to invite more people. Click 'email' and then add the new email addresses. Only the new participants will receive an invitation. No mail will be sent to the previous invited participants.
If you invited your participants manually (via your email or Facebook) you can send out another email. You can click 'invite' at the top of the page and then 'link.' You can copy the link and send it out as you like.