help with references

[dw_perlmonks]

Hi there esteemed Monks,
I have a very noob-ish question here regarding refs, though still confounding to me at the very least...
In the code example below, i'm trying to create a hash of arrays:

#!/usr/bin/perl

use strict;
use warnings;
use 5.010;
use Data::Dumper;

$Data::Dumper::Sortkeys = 1;
$Data::Dumper::Terse = 1;
$Data::Dumper::Quotekeys = 0;

my @a1 = ( 'a1', 1, 1, 1 );
my @a2 = ( 'a2', 2, 2, 2 );

my $a1_ref = \@a1;
my $a2_ref = \@a2;

my @a = ( $a1_ref, $a2_ref );

my %h = ();

for my $i ( 1 .. 2 ) {
        $h{"$i"} = \@a;
}

say Dumper \%h;

The Dumper output is

{
          '1' => [
                   [
                     'a1',
                     1,
                     1,
                     1
                   ],
                   [
                     'a2',
                     2,
                     2,
                     2
                   ]
                 ],
          '2' => $VAR1->{'1'}
        }

The question here is:
why is $h{'2'} a reference to $h{'1'}? I'm trying to create a hash %h with identical key-values made of the @a array-of-arrays. I want each key-value of the hash to have it's own AoA based on @a, but i'm getting references to $h{'1'} instead. What am i doing wrong??
The Dumper output i'm trying to achieve is:

{
          '1' => [
                   [   
                     'a1',
                     1,  
                     1,  
                     1   
                   ],  
                   [   
                     'a2',
                     2,  
                     2,  
                     2   
                   ]   
                 ],  
          '2' => [
                   [   
                     'a1',
                     1,  
                     1,  
                     1   
                   ],  
                   [   
                     'a2',
                     2,  
                     2,  
                     2   
                   ]   
                 ]   
        }

Any help appreciated. thanks in advance!
-dan