If your intervals are potentially long, then I'd suggest the array of array approach because it avoids constructing long lists of elements. You can produce that array of arrays with:

my @interval_arrays = map [$a[$_], $b[$_]], 0..$#a;
[download]

And then you can intersect with your interval and get a result in the same format with:

my @intersected_arrays = map {
    my $min = $s1 < $_->[0] ? $_->[0] : $s1;
    my $max = $s2 > $_->[1] ? $_->[1] : $s2;
    $min <= $max ? [$min, $max] : ();
} @interval_arrays;
[download]