\text{cosh}(r_{\omega})\text{sinh}(r_{\omega})(0-\text{cos}\,\theta_{\omega}) {\hat{c}_{0\omega}^{\dag} \choose \hat{c}_{0\omega}} +[\text{cosh}^0(r_{\omega})-\text{sinh}^0(r_{\omega})\text{cos}\,\theta_{\omega}]{\hat{d}_{0\omega} \choose \hat{d}_{0\omega}^{\dag}} 