I have a collection with the array field. If I want to find all documents with specific tag I use next query:
db.Bookmarks.find({tags : {$regex: \"bbb\"}})
You can use the $all query operator to do this:
db.Bookmarks.find({tags: {$all: ['bbb', 'ccc']}})
You can use regular expressions as well. To include tags that start with c instead:
db.Bookmarks.find({tags: {$all: ['bbb', /^c/]}})