A B737 FLT CREW DEVIATED FROM THE CHARTED SID WHEN THEY WERE DISTRACTED BY WAKE TURB FROM THE PRECEDING ACFT.

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WE WERE CLRED FOR TAKEOFF BEHIND ANOTHER CARRIER. PASSING 400 FT I SELECTED LNAV AND SUBSEQUENTLY ENCOUNTERED WAKE TURB FROM THE PRECEDING OTHER CARRIER REQUIRING FULL AILERON DEFLECTION TO MAINTAIN WINGS LEVEL. PASSING 1000 FT AGL I ENGAGED THE AUTOPILOT AND DUE TO THE DISTRACTION OF THE CONTINUING WAKE TURB; I DIDN'T NOTICE THE AUTOPILOT WAS IN CWS MODE INSTEAD OF LNAV. I STARTED THE TURN APPROX ONE HALF MILE PAST LEELN AND WHILE WE WERE IN THE TURN; DEP CALLED AND ADVISED US THAT WE NEEDED TO TURN IMMEDIATELY. WE TOLD HIM WE WERE IN THE TURN AND REPORTED THE WAKE TURB. HE REPEATED THAT WE NEEDED TO TURN AND THAT WE SHOULD LET HIM KNOW IF WE NEEDED TO CLB STRAIGHT AHEAD. WE DIDN'T HAVE TIME TO EXPLAIN TO HIM THE DETAILS OF WHAT HAPPENED AND HE PUT US ON A VECTOR AND SWITCHED US TO THE NEXT FREQUENCY. THIS INCIDENT UNDERSCORES THE IMPORTANCE OF CHECKING THE 'SCOREBOARD' TO ENSURE YOU'RE IN THE CORRECT MODE. LAS DEP COULD CONSIDER INCREASING SPACING WHEN WIND CONDITIONS ARE SUCH THAT WAKE TURB ENCOUNTERS ARE LIKELY OR ASSIGNING FAN HEADINGS TO INTERCEPT DEPS. MY BIGGEST ERROR IN THIS SITUATION WAS PROBABLY THAT I DIVERTED ATTENTION FROM OUR FLT PATH WHILE I ATTEMPTED TO ENGAGE THE LNAV MODE OF THE AUTOPILOT.