AN MDT CREW ON APCH TO HOMER; AK (PAHO) FLEW THROUGH THE BACK COURSE LOC WHILE FLYING THE ARC TO INTERCEPT.

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THE EVENT IN QUESTION OCCURRED DURING A PART 121 SCHEDULED FLT WHICH DEPARTED ANC AT APPROX XA45. AFTER DEPARTING RWY 6L ON THE ANC 3 SID; WE WERE INSTRUCTED BY DEP CTL TO FLY HDG 180 DEGS UNTIL RECEIVING HOMER VOR; THEN PROCEED DIRECT. UPON RECEIVING HOM VOR; WE PROCEEDED DIRECT; INBOUND ON THE APPROX 360 DEG RADIAL; AT A CRUISE ALT OF 11000 FT MSL. ENRTE INDICATIONS WERE NORMAL AND THE FLT PATH CROSSED SEVERAL PROMINENT LANDMARKS AT THE APPROX CORRECT POS (E/W RELATIVE TO COURSE). EXAMPLE: TUSTMENA LAKE. THE LOC DME (BACK COURSE) APCH TO RWY 21 WAS BRIEFED AND INITIAL DSCNT TO 5000 FT MSL WAS COMMENCED AT BOUT 35 DME; WITH THE APPROPRIATE CHKLIST. ALL NAV INDICATIONS WERE NORMAL THROUGH THIS POINT IN THE FLT. DEST WX WAS 9-10 MI VISIBILITY 12000 SCATTERED 4400 BROKEN TO OVCST; LIGHT WINDS. AT 15-18 DME; WE HAD NOT RECEIVED APCH CLRNC AND THE FO QUESTIONED THE CTLR. HIS COMMENTS WERE SOMEWHAT AMBIGUOUS. AT THAT POINT I INSTRUCTED THE FO TO TELL THE CTLR THAT WE WERE JOINING THE 11 DME ARC; AND THE CTLR THEN CLRED US FOR THE APCH. I THEN COMMENCED DSCNT TO 3800 FT MSL FOR THAT SEGMENT OF THE ARC. I COMMENTED THAT I WOULD CONTINUE TO 3600 FT; AS WE WOULD CROSS THE STEPDOWN RADIAL PRIOR TO 3800 FT. AT THIS POINT THE FO STATED THAT WE HAD ALREADY CROSSED THE STEPDOWN AND WERE IN FACT AT/NEAR THE LEAD-IN RADIAL. ABOUT THE SAME TIME; I OBSERVED THAT WE HAD CROSSED THE W SHORELINE OF KACHEMACK BAY (AFTER BREAKING OUT OF THE OVCST LAYER). AT THIS POINT WE REALIZED THERE WAS A PROB AND I IMMEDIATELY COMMENCED A R TURN TO A WSW DIRECTION AND SELECTED THE LOC FREQ. WE HAD PASSED THROUGH THE LOC COURSE AND WERE HEADED TOWARD HIGH TERRAIN TO THE E; PRIOR TO TURNING. AT THIS POINT; WE WERE IN VISUAL CONDITIONS; WITH THE ARPT IN SIGHT (APPROX 8 DME ON THE LOC FREQ) AND CANCELED IFR WITH HOMER FSS. WE CONDUCTED A NORMAL LNDG AND POSTFLT CHKLISTS. WE THEN REVIEWED THE EVENT IN DETAIL BUT WERE UNABLE TO DETERMINE A CAUSE. ADDITIONALLY; WE VERIFIED THE OP OF THE NAV RADIOS PRIOR TO THE NEXT LEG; THEN CONFIRMED THIS WITH ATC RADAR. A CLR STATEMENT FROM THE CTR CTLR WOULD HAVE BEEN HELPFUL IN AVOIDING THIS SIT.