Define "empty string". Consider:

use strict;
use warnings;

for my $str ('', ' ', '\0', "\n", undef) {
    print "matched '$str'\n" if $str =~ /\A\z/;
}
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Prints:

matched ''
Use of uninitialized value $str in pattern match (m//) at C:\Users\Pet
+er\Delme~~\PerlScratch\noname.pl line 8.
matched ''
Use of uninitialized value $str in concatenation (.) or string at C:\U
+sers\Peter\Delme~~\PerlScratch\noname.pl line 8.
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length may be a better test than using a regex, and clearer to the maintenance programmer.