Optical Properties Metals for Optical Isolators

Optical isolators fabricated in semiconductor and polymer optical waveguides, must employ anisotropic materials such as iron, nickel or cobalt [1, 2, 3]. In anisotropic media the susceptibility turns out to be a susceptibility tensor with non-zero off-diagonal elements under the effect of an applied magnetic bias. Analysis of the susceptibility tensor requires an appropriate model of band structure for magnetic materials. There are various models which depict the behavior of optical constants depending on electronic band structure [4, 5, 6, 7, 8]. One of the earlier studies on optical constants of Silver and Copper has been provided by Ehrenheich et al. [4]. They analyzed experimental data from 1 to 25 eV by the help of three mechanisms which are free electron effects, interband transitions, and plasma oscillations. In order to distinguish plasma transitions from interband ones, the real <f"g and imaginary parts =f"g of the dielectric constant as well as the loss function =f" g was plotted as a function of photon energy. They acquire average optical mass value for the free electron effect region by comparing the theoretical and experimental values of the dielectric constant. In 1987, Adachi has reconciled the harmonic oscillator (HO) model with critical pointparabolic band (CPPB) model to have optical constants as a function of alloy composition for Zinc-Blende structured semiconductors [5]. In this study, he associated Lorentzian broadening in their model by including a temperature dependent term to the line width. The main pronounced feature of Adachi et al. is to obtain large contributions from indirect transitions [5]. In earlier studies, the Lorentz-Drude (LD) model was used in order to describe the behavior of optical constants in various regions of electromagnetic spectrum. Unlike free electron Drude model, the LD model incorporates the effects of bound electrons; the model is based on the damped harmonic oscillator approximation, it is well-behaved in the near-IR and visible ranges of the spectrum in contrast to Drude case [9]. In 1991, Brendel and Bormann [6] (BB) proposed a new model in order to describe behavior of dielectric constants for the IR range. They used the Voigt profile by convoluting Gaussian and Lorentzian types of broadening to model optical constants, especially at critical points. The main reason of compensating pure Lorentzian profile to the nearly Gaussian one is to provide a reliable model for optical constants at room temperatures as the LD model is incorrect at room temperatures [7]. Also, Kim et al. explained the failure of Lorentzian model for elements and compounds at room temperatures [7, 8]. The superiority of Gaussian approach over Lorentzian has been explained in terms of broadening approximation.invariability condition of oscillator strength and full width at half maximum (FWHM), the Lorentzian approach has wider wings compared to Gaussian [9]. The studies that have been mentioned so far are related with diagonal elements of the permittivity tensor. However, one needs to account for off-diagonal elements when the material is ferromagnetic and there is an external magnetic bias producing the anisotropic medium. The off-diagonal elements entered to the picture by the contribution of Magneto-Optic Kerr Effect which includes the Kerr rotation angle and ellipticity [10]. The investigation of the off-diagonal elements has been done by Krinchik et al., [11, 12, 13] by introducing the equatorial Kerr effect (T-MOKE) to the experimental setup.