I'm trying to find a way to find a value(s) of $\omega$ which minimise
$$\mathbb{R} = 1 - \frac{1+R_0^4-2R_0^2}{1+R_0^4 -2R_0^2\cos(2\omega\beta_1 L)}.$$
The terms in the equation depend on $\omega$, namely
$$R_0 = \frac{\bar\rho_0\sqrt{\frac{\bar \rho_1}{c_{44}}}+\bar\rho_1 \sqrt{\frac{\bar\rho_1}{\mu_0}}}{\bar \rho_1 \sqrt{\frac{\bar \rho_0}{\mu_0}}-\bar \rho_0 \sqrt{\frac{\bar \rho_1}{c_{44}}}}$$
where
$$\beta_1 = \sqrt{\frac{\bar \rho_1}{c_{44}}},$$
$$\bar \rho_0 = \rho_0 - \frac{k_1^2\mu_0}{\omega^2},$$
$$\bar \rho_1 = \rho_1 - \frac{k_1^2c_{66}}{\omega^2}-\frac{k_1^2c_{64}^2}{\omega^2 c_{44}},$$
$$\bar \rho_2 = \rho_2 - \frac{k_1^2\mu_2}{\omega^2}.$$
The constants in this equation are
$$\mu_{0,2}, \rho_{0,1,2}, c_{44}, c_{64},c_{66},k_1,L$$
Am I in over my head here? Is there anything I could do to make analytical headway?