Grant Jones, 24, almost blinded the aircraft's crew when he flashed a bright green light into the aircraft's cockpit on October 1 last year.
Edinburgh's sheriff court heard how the pilot was forced to turn the aircraft away from the laser in order to avoid his sight being affected by the intense ray.
Colleagues sitting beside him used heat-seeking cameras to track Jones, who fled into a house in Silverknowes Crescent, Edinburgh.
They alerted officers on the ground who tracked Jones down and found a laser pen in his possession and arrested him.
The story emerged after Jones, of Silverknowes Crescent, Edinburgh, pleaded guilty to breaching the Civil Aviation Act before Sheriff Nigel Ross. He pleaded guilty to directing a light so as to dazzle or distract the pilot of an aircraft in flight.
Depute procurator fiscal Isabel Clark told the court the helicopter was helping officers search for a stolen vehicle when Jones put the crew's lives at risk.
Ms Clark added: "The pilot of the helicopter had to take immediate action in order to avoid danger to his sight or to the sight of the other people on board the helicopter."
Ms Clark told the court that the helicopter pilot had to turn his aircraft to avoid the bright glare of the laser.
The Police Scotland helicopter was based in Finnieston, Glasgow. It crashed into the Clutha Bar on Friday November 29 2013. 10 people died. Sheriff Ross deferred sentence on Jones until June 2 to await reports .