Searching Multiple Keyword with Text Operator

I want to search two keywords in the collections with text indexes. Let’s say the two words are 1) Girls’ Generation 2) 소녀시대. If I search like this

{
            $match:{
                $text:
                {
                    $search: "Girls' Generation 소녀시대"
                }
            }
        }

This match all documents with consist of “Girls” keyword, not exact to “Girls’ Generation”.So,If I change to this

{
            $match:{
                $text:
                {
                    $search: "\"Girls' Generation\" 소녀시대"
                }
            }
        }

This match only documents with “Girls’ Generation” keyword. korean keyword “소녀시대” are not considered. So I change to this

{
            $match:{
                $text:
                {
                    $search: "\"Girls' Generation\" \"소녀시대\""
                }
            }
        }

This match only documents with both two keywords exists. This doesn’t work if only one keywords exists. Is there any fix which search one of the exact pharases?