How can I measure the interferometric autocorrelation of an electric field

I am trying to evaluate the interferometric autocorrelation of an electric pulse. This means to evaluate

IAC(tau) = \int( (E(t) +E(t+tau))^2)^2 dt

where E is my electric field. I am trying to do that straightforward just by integrating my function E and its copy shifted in time. Has anyone an idea of how to that in a clever manner?

What I do is here:

if true
  n = length(E);
n_tau = 2*n;                                            % 2* length vector 
E_tau_app = zeros(1,n_tau);                             % temporary variable
E_long = [zeros(1,round(n/2)), E, zeros(1,round(n/2))];
IAC = zeros(n,1);                                       % Interferometric Autocorrelation
for i=1:n; 

    E_tau = E_tau_app;   % The Delay tau is the independent variable
    E_tau(i:n+i-1) = E;

    IAC(i) = sum(((E_tau(2:n_tau-1)+E_long(2:n_tau-1)).^2).^2)*dt + ...
        0.5*((E_tau(1)+E_long(1))^4+(E_tau(n_tau)+E_long(n_tau))^4)*dt; % integral with trapezoidal method
end

Thank you in advance!

L.