B777-200 RIGHT ENG FAILED AFTER TKOF. FLT CREW DECLARED EMER; DUMPED FUEL; AND RETURNED TO DEP ARPT.

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RWY DATA OF ACTIVE RWYS GAVE US A CHOICE OF RWYS XY. MAX THRUST FLAPS 5 DEGS WAS USED. RWY LIMIT WAS 540900 LBS; THE LIMITING FACTOR. FINAL WT: ZFW: 393693 TOG: 539393 MAC: 33.5 TRIM: 4.6 PAX: 34/306 LAP 0 CRED 3/9 OMC-1 CJA-NONE SOB 353. FO FLYING; CAPT MADE LNDG. TKOF WAS UNEVENTFUL. FIRST INDICATION OF PROB WAS A LOUD BANG WITH SLIGHT YAW. TAC CORRECTED FOR YAW. REDUCED PITCH TO 10 DEGS CONTINUED TO CLB OUT WITH VERY LITTLE AIRSPD CHANGED. WE HAD STARTED THE TURN TO ASSIGNED HDG OF 330 DEGS THEN STOPPED TURN AND ROLLED BACK TO RWY CTRLINE AND CONTINUED THE ENG FAIL PROFILE. BROUGHT BACK R THROTTLE BACK TO IDLE ENG DID NOT RECOVER BACK TO NORMAL ENG INDICATIONS AND DECLARED AN EMER. ENG INDICATIONS AT THIS POINT: EGT 710 N1 AT 12% OIL QUANTITY; YES SOME OIL PRESSURE NO INDICATION OF ENG FIRE IN THE COCKPIT HOWEVER BY THIS TIME FLT ATTENDANTS FROM 3R CALLED TO SAY THEY SAW FIRE COMING FROM THE R ENG. FIRST WENT TO ENG SEVERE DAMAGE CHKLIST AND RAN THE CHKLIST THEN WENT INTO ECL CHKLIST TO FINISH CHKLIST AND COMPLETED ALL REF ACTIONS. AFTER SECURING ENG N1 ON R ENG WAS 0.0; EGT STILL REMAINED ABOVE 700 DEGS F. ALL INDICATIONS SHOWED THE ENG HAD BEEN SHUT DOWN. FLT ATTENDANTS CALLED AGAIN AT THIS POINT AND TOLD US THAT THE FIRE WAS OUT. WORKED WITH PURSER AND ISSUED A CABIN ADVISORY. AT THIS POINT RELAYED THAT THEY WOULD HAVE 20 MINS TO LNDG. ADVISED ATC WE NEEDED TO DUMP FUEL SO THEY GAVE US A HDG E. CALLED DISPATCH TO RELAY OUR PROB. ASKED INFO ABOUT LNDG PERFORMANCE AND WHAT WE SHOULD DUMP DOWN TO. WAS DECIDED TO DUMP FUEL TO 100000 LBS OF FUEL REMAINING; WHICH PUT OUR LNDG WT AT APPROX 490000 LBS. DISPATCH DETERMINED THE PERFORMANCE LIMIT 530000 LBS FOR LNDG. COMMENCED DUMP WITH ATC APPROVAL AT 6000 FT; TOOK APPROX 5 MINS. WE WERE BEING VECTORED OVER THE LAKE UNTIL WE INFORMED THEM WE WERE READY TO LAND. INTERCEPTED A 10 MI FINAL. FINAL APCH AND LNDG WAS UNEVENTFUL; ROLLED TO THE END OF THE RWY; EXITED AND WAS INSPECTED BY FIELD FIRE DEPT. THEIR INSPECTION FOUND NO SAFETY ISSUE WITH TAXIING BACK TO THE GATE. PROCEEDED BACK TO GATE AND BLOCKED IN. NO HUMAN FACTORS CONTRIBUTED TO THIS EVENT.