How to query lucene for empty fields?

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I want in 2nd part of my query to have a list of result for while data not null. I find how do it in solr but not in lucene. Anyone have a idea Thanks

String :

( field_one:search AND field_two:3000) OR (field_three:search AND field_two:3000 AND NOT NULL field_one )

Query:

+field_one:search +field_two:3000 +field_three:search +field_two:3000 -field_one:null

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