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public class Teacher
{
        public string Id{ get; set; }
        public string Name{ get; set; }
        public string TeacherFilter{ get; set; }
        ...
}

public class Student
{
        public string Id{ get; set; }
        public string Name{ get; set; }
        public string StudentFilter{ get; set; }
        public string TeacherId{ get; set; }
        ...
}

public class TeacherStudents
{
        public string Id{ get; set; } -- from teacher
        public string Name{ get; set; } -- from teacher
        public IEnumerable<Student> Students{get;set;}
}

public class TeacherStudents
{
        public string Id{ get; set; } -- from teacher
        public string Name{ get; set; } -- from teacher
        public IEnumerable<Student> Student{get;set;}
}

public class TeacherStudent
{
        public string Id{ get; set; } -- from teacher
        public string Name{ get; set; } -- from teacher
        ...
        public Student Student{get;set;}
}

Get(string TeacherFilter,string StudentFilter).

var query = teacherCollection.Aggregate().Match(x => x.TeacherFilter== TeacherFilter); //filter teach
var query1 = query
.Lookup<Teacher, Student, TeacherStudent>(studentCollection, t => t.Id, s => s.TeacherId, l => l.Student)
.Unwind(x => x.Student, new AggregateUnwindOptions<TeacherStudent>())
.Match(x => x.StudentFilter== StudentFilter) //filter student