Dr. Vadym Zayets

The expression, which described optical loss in the case of transverse MO, effect will be derived. Utilizing a few very general facts, the important properties of the effect are derived. Expression (14) can be applied to calculate and estimate the transverse MO effect for a variety of possible structure. It can be applied to plasmons, hybrids waveguides, slab and rib waveguides and more. Eqn.(14) is main result. This method may be used for calculations of the transverse MO effect in devices with complex shape. For the devices with less complex shape the usage of simple rigorous method is preferable.

In the following we will calculate the magnetization-dependent loss for a very general structure, which contains a ferromagnetic metals and a transparent dielectric. The metals absorb the light and there is MO effect in the metal. The light along z direction. Let us to put as less  limitations on the structure as possible. Only we assume that the light is confined inside the structure, so

Because there is a metal inside the structure, light experience an optical loss, so there is a loss of energy, when the light propagates along z direction. The electrical and magnetic field of light can be described as

where A(x,y,z) is the slowly-varied function along z. nz is the effective refractive index and kz is the absorption coefficient.

Since the wave is absorbed, the energy flow is decreasing along z axis and Poynting vector is

The optical loss can be calculated as

Poynting theorem reads

where U is the energy density of the electromagnetic wave. Integrating Exp.(4) we obtain

Since there is no flux when