content_image/330334.jpg content_image/330341.jpg
<img src='content_image/330334.jpg'>

These become: 

with M$_{s}$ in A/m, α in m $^{2}$/C, f in C $^{2}$/kg m3 and c in cm/s. 

<img src='content_image/330341.jpg'>

Solutions of Eq.(36) and (41) are plotted in Fig.(2(a)) for the case with no applied fields present. There are two gaps in the bulk region which are created by the poles and zeros of Eq.(36). First, as illustrated in Fig.(2(c)), a very narrow gap is located at the frequency ω$_{i}$ around 41 cm − $^{1}$, created by the magneto-electric interaction$^{4}$. This gap is associated with zeros in f ( µ, ϵ ) = µ$_{x}$ϵ$_{y}$ − (4 πχ $^{me}$) $^{2}$. The pole in the bulk modes is due to a zero of the dielectric constant ϵ$_{y}$ . This gap is strongly dependent on the ME susceptibility, χ $^{me}$, and disappears when χ $^{me}$=0. The width of the gap is approximately proportional to ( χ $^{me}$) $^{2}$. Thus the gap becomes wider with larger ME coupling. This increase is illustrated in Fig.(2(d)) where the ME coupling has been increased by a factor of ten. 

A second gap exists near the magnetic frequency ´ ω$_{m}$ ∼ =3 cm -1 , and occurs at zero of f ( µ ) = µ$_{x}$ϵ$_{y}$ − (4 πχ $^{me}$) 2 at the magnetic frequency ´ ω$_{m}$ . The other boundaries for the bulk 

