Anisotropic waveguides

Diao, Z., Huang, W., Peng, Z., Mu, Q., liu, Y., Ma, J., Xuan, L. Anisotropic waveguide theory fta electrically mnable distributed feedback laser from dye-doped holographic polymer dispersed liquid crystal. liq. Cryst. 41, 239-246 (2014)... 

In the previous sections we assumed the waveguides were constructed from isotropic material. We now consider waveguides constructed from anisotropic material. For perspective, we first treat plane-wave propagation in an unbounded, uniform anisotropic medium. Then we discuss the modes of anisotropic waveguides. 

The values of the core and cladding refractive indices of the anisotropic waveguide depend on the direction, or polarization, of the electric field E. Assuming the principal axes are parallel to the waveguide axes, we have... 

When the anisotropic waveguide is weakly guiding, all six values of the refractive index in Eq. (12-38) are approximately equal, and thus = 1... 

Modes of anisotropic waveguides 13-13 Single-mode single-polarization fibers... 

If the principal axes of the anisotropic material are parallel to the optical axes of a fiber of noncircular cross-section, it is intuitive that the two fundamental modes must also be polarized along these axes. We then have a situation identical to the circular cross-section, discussed above, except that (r) in Eq. (13-20) is replaced by P,(x,y) and P,(r) by P,(x,y). Thus, all results for weakly guiding isotropic waveguides apply to weakly guiding anisotropic waveguides by following the simple substitution discussed above. 

The principal refractive indices of a uniaxial anisotropic waveguide satisfy riy = riy riy, and, if the z-direction is parallel to the waveguide axis, the vector wave equations can be simplified. The longitudinal components of Eq. (30-31) are readily shown to be... 

---