# Design and Modelling of a Novel Integrated Photonic Device for Nano-Scale Magnetic Memory Reading
## 2 Materials and Methods
### Optical Simulation and Device Concept  
Before describing the optical simulation method to quantify the MOKE in waveguides, a brief overview is given on MOKE and its impact on the light confined in waveguides. Following this, the devcie concept is introduced.  
MOKE is a type of magneto-optic interaction that takes place when the light reflects from a magnetized material. In polar configuration, the effect causes a change in the light's polarization state which is quantified by Kerr rotation and ellipticity (in angles). Typically, in the literature, MOKE is reported for single reflections. Comparing a single reflection case with our work, more interaction, thus a larger MOKE are expected in waveguides with magnetized top claddings. To our best knowledge, there is no prior work that quantifies the Kerr rotation in a waveguide setting. Therefore, finite-difference time-domain (FDTD) simulations [24] of the waveguides with top-claddings are conducted to estimate the MOKE in the guided modes. In the simulation, multi-layer cladding material is defined by using the magneto-optic constant obtained from the literature [25]. It is seen that the Kerr effect causes conversion between \(TE\) and \(TM\) modes in the waveguide, comparable to the polarization rotation in free-space optics. The resulting Kerr rotation (\(\theta\)), ellipticity (\(\phi\)) and optical loss (\(Loss_{\textit{clad.}}\)) values obtained for a single memory bit are listed in Table 2. These values are used as inputs for the mathematical model explained in Section 2.2.  
The device design is done by considering the key enabler of the magnetic memory reading functionality: a change in the sign of the Kerr rotation upon flipping of the magnetization direction of the memory bit (memory bit \"1\" and \"0\"). Assuming the confined light is initially in \(TE\) mode, the Kerr rotation \(\pm\theta\) (\(\theta\ll 1\)) leads to an emergent \(TM\) mode whose field amplitude is proportional to \(\theta\) for bit 1 and \(-\theta\) for bit 0. Therefore, devices which can probe the phase of the emergent \(TM\) mode are explored. Mach-Zehnder Interferometers (MZI) are chosen due their ability to convert the phase difference (between the interfering branches) into intensity difference. Balanced and unbalanced MZI are considered as two candidates for the final design. An unbalanced MZI, which has a defined path length difference between the two branches is chosen due to the noise related issues that cannot be addressed in a balanced MZI. This is further elaborated when the presented results are discussed in Section 3. Since at an initial stage, a device is designed for research and exploration purposes, on-chip light source or detector are not considered. To couple an off-chip laser source and an off-chip detector to the device, mode-selective grating couplers are added to the design.  
The device design is shown in Figure 1. In this device, \(TE\) mode-selective grating coupler is used to couple the light in. Later, a multi-mode interferometer (MMI) is used to split the light equally into two branches. On the upper branch, the \(TE\) mode is converted into \(TM\) via the polarization converter. The propagation continued (in \(TM\) mode) and a delay line is crossed. On the lower branch, the memory bit (magnetic cladding section) caused the \(TE\) mode to partially convert into \(TM\) mode due to Kerr rotation (\(\theta\)). The light from the two branches are merged via another MMI. After interference took place, the resulting intensity is picked up via a \(TM\)-selective grating coupler.