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The phase cloak works more or less like a normal cloaking device, but the matter which is cloaked goes through a molecular rotation, allowing it to pass through normal matter.
The phase cloak was initially developed illicitly by a group from Starfleet Intelligence. They began conducting experiments on board the USS Peagusus, ending in disaster. 12 years later, the USS Enterprise-D managed to salvage the phase cloak from the Peagusus and use it to escape from an asteroid. Starfleet HQ was contacted, the phase cloak destroyed, and those responsible were courtmarshalled for violation of the Treaty of Algoran. The Romulans, who witnessed the Enterprise de-cloaking after escaping the asteroid, were contacted by Starfleet HQ and relations were patched up.
Naturally, the Romulans (and possibly Klingons, Worf was on board the Enterprise at the time) were intrigued by the possibility of a phase cloak and began to attempt to re-create it.
It is suggested that the phase cloak be introduced as a piece of Romulan technology, probably which they are more than a little reluctant to share with the Federation. I would strongly recommend against supplying the 7th Fleet ships with their own phase cloaks, although a single spy ship could be introduced which could be equipped with a phase cloak. It is of the utmost importance that the phase cloak not fall into widespread use, as it would upset the Star Trek universe considerably.
~Jeremy Lennert, Simon Dark of the 7th Fleet