B767 Captain reports L OIL FILTER EICAS message at FL360. Filter light did not extinguish at low power setting and engine was shut down in compliance with procedures. An emergency was declared and flight diverted to the nearest suitable airport.

Narrative

We were cruising at FL360 when 'L Oil Filter' EICAS message appeared. We referred to the QRH and accomplished the procedure. We began retarding the throttle to see if the light would go out; to no avail. As we knew we could not maintain altitude; we notified ATC that we were doing a procedure for a maintenance problem and we needed a lower altitude. We were cleared to a lower altitude and we advised them we would get back to them. When it was apparent that we had to shutdown the affected engine; we declared an emergency and asked for vectors to descend and divert. During that time I asked the jumpseater (very familiar with the airplane and route) to get a frequency for Dispatch and advised them of our problem and that we were diverting. He was also able to tell the Flight Attendants that we were diverting and to prepare the cabin for landing. Continuing our vectors for descent and approach to airport; we went through the appropriate checklists for engine shutdown and our single engine approach. I made a PA to advise the passengers about our mechanical issues and our diversion; and TESTed the Flight Attendants. On approach we advised ATC that we would like a 15 mile final to the longest runway into the wind. We were overweight (287;000 LBS) on landing; but touched down at less than 300 FPM; with no side loads. We requested Airport Rescue and Fire Fighting to check for any abnormalities before we proceeded to the gate.