from Eq. (44) at the frequency ω = ω$_{p}$ for a surface mode solution to exist. The requirement that f ( µ ) vanish means that For BaMnF$_{4}$, the requirement in Eq. (43) is never satisfied as shown in Fig. 4(a), hence there is no surface modes at k >> ω $_{c}$. The condition Eq. (45) can be satisfied by changing, for example, the parameters so that λ/α = 1 . 5. An example is shown in Fig. 4(b) , and the associated dispersion relation is presented in Fig.4(c). In this case a surface mode is able to exist at the top of the middle bulk band, for arbitrarily small wavelengths. FIG. 5. The influence of magnetic field. In (a)influence on canting angle. In (b), the application of a magnetic external field of 15 T increases and allows the negative surface branch to enter the magnetostatic region, where k >> ω $_{c}$. In principle, application of an external field can be used to modify the surface mode frequencies by changing the canting angle. However, as mention above that the electric part is uncoupled from the magnetic part, and application of an electric field has negligible effect on the polariton frequencies. The application of an external static magnetic field changes directly the canting angle and thereby affect the frequencies. The canting angle as a function of applied magnetic field shown in Fig. 5(a). In fact, for sufficiently strong magnetic field, the condition of Eq. (43) can be satisfied and a surface modes branch extend to k = −∞ . This occurs through an increase in ω$_{r}$ via the field dependence of Ω$_{o}$(see Eq. (22)). 13 0 5 10 15 4 8 12  H  (T) $_{ }$θ  (10 −2  rad) (a)canting angle versus H −700 −500 −300 −100 15.22 15.24 15.26  k  (cm −1 ) /2  c  (cm −1 ) −A −L SP (b)Surface modes at H = 15T ω$_{p}$ ≤ ω$_{a}$ cos 2 θ + 2 ω$_{me}$ sin 2 θ (45)