两个集合之间的MongoDb内部联接？

Question

提供了两个mongo集合

collection - bacteria (id)
       Coccus
       Spirochete
       Spirillum
       Vibrio
       Bacillus

collection - bacteria_relations (left_type, right_type, relation_type)
       Coccus, Spirillum, can_cause
       Coccus, Vibrio, can_cause
       Coccus, Vibrio, infect
       Bacillus, Spirillum, can_cause

如何获取与关联类型相关的所有细菌？
例如，所有与细菌有关的球菌，关联类型都可能是can_cause：

 Spirillum  
 Vibrio  

使用sql会很容易（伪代码）

select bacteria_relations.right_type from bacteria
               left join bacteria_relations on bacteria.id=bacteria_relations.left_type
                           and relation_type='can_cause'
                           and bacteria.id ='Coccus'

我知道我需要使用LookupOperation和AggregationResults 这是我开始的伪代码：

    LookupOperation lookupOperation = LookupOperation.newLookup()
            .from("bacteria_relations")
            .localField("left_type")
            .foreignField("right_type").as("?");

            AggregationResults<Object> entities =
                    mongoTemplate.aggregate(
                    Aggregation.newAggregation(lookupOperation,
                        Aggregation.match(Criteria.where("id").in(ids))), 
                        Bacteria.class, Bacteria.class);