The fundamental sync tool is the ubiquitous unix rsync, and you want it on windows. It can find the missing files and copy them over. It can do a lot more than that but it seems this will satisfy your needs.
cwRsync is basically rsync for windows that even comes with a client GUI for ease of use: https://www.itefix.net/cwrsync
Rsync uses the Rsync algorithm which provides a very fast method for bringing remote files into sync. It does this by sending just the differences in the files across the link, without requiring that both sets of files are present at one of the ends of the link beforehand. At first glance this may seem impossible because the calculation of diffs between two files normally requires local access to both files.
DeltaCopy is an alternative, you may find the GUI less intimidating perhaps, open source as well: http://www.aboutmyip.com/AboutMyXApp/DeltaCopy.jsp
In general terms, DeltaCopy is an open source, fast incremental backup program. Let's say you have to backup one file that is 500 MB every night. A normal file copy would copy the entire file even if a few bytes have changed. DeltaCopy, on the other hand, would only copy the part of file that has actually been modified. This reduces the data transfer to just a small fraction of 500 MB saving time and network bandwidth.
In technical terms, DeltaCopy is a "Windows Friendly" wrapper around the Rsync program, currently maintained by Wayne Davison. "rsync" is primarily designed for Unix/Linux/BSD systems. Although ports are available for Windows, they typically require downloading Cygwin libraries and manual configuration.