Unexpected to you. Variable interpolation happens before the regular expression is parsed and compiled so there is no difference between

$a=1;
print "Match\n" if "aa1" =~ /^(a)\1$a$/; # not match!
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and

print "Match\n" if "aa1" =~ /^(a)\11$/; # not match!
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or

$a='\11';
print "Match\n" if "aa1" =~ /^(a)$a$/; # not match!
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If it did not work like this you could not build regular expressions out of parts stored in variables.