Fiber Optic Tutorials

This is a continuation from the previous tutorial - Step-Index Planar Waveguides. In a symmetric slab waveguide, n3 = n2 and aE = aM = 0. In addition, we also have γ3 = γ2. Then, it can be seen from (57) and (62) [refer to the step-index planar waveguides tutorial] that \(\tan2\psi=0\) and \[\tag{83}\psi=\frac{m\pi}{2}, \qquad m = 0, 1, 2, ...,\] for both TE and TM modes. Therefore, the mode field patterns of a symmetric waveguide given by (55) and (60) are either even functions of x with cos(h1x) in the region -d/2 < x < d/2 for even values of...

This part is a continuation from the previous tutorial - Wave Equations for Optical Waveguides. A step-index planar waveguide is also called a slab waveguide. We have used it in the waveguide modes tutorial with the approach of ray optics to illustrate an intuitive picture and some basic characteristics of the wave behavior in a waveguide. In this tutorial, the important characteristics of a slab waveguide are discussed, beginning with solution of the wave equations developed in the wave equations for optical waveguide tutorial. The structure and parameters of the three-layer slab waveguide under discussion are shown in figure 4...

This is a continuation from the Optical Waveguide Field Equations tutorial. The field equations obtained in the optical waveguide field equations tutorial establish the relations among the field components. In general, it is only necessary to find \(\mathcal{E}_z\) and \(\mathcal{H}_z\). Then all other components can be calculated by simply using (16) - (19). The common approach to finding \(\mathcal{E}_z\) and \(\mathcal{H}_z\) is to solve the wave equations together with boundary conditions. In this tutorial, we examine the form of the wave equations for waveguides. To obtain the wave equations, we need the other two Maxwell's equations in addition to (8) and (9). For the case of...

This is a continuation from the previous tutorial - Waveguide Modes. For a linear, isotropic dielectric waveguide characterized by a spatial permittivity distribution of ε(x, y), Maxwell's equations in (40) and (41) [refer to the Harmonic Fields tutorial] can be written as \[\tag{8}\pmb{\nabla}\times\mathbf{E}=-\mu_0\frac{\partial{\mathbf{H}}}{\partial{t}}\] \[\tag{9}\pmb{\nabla}\times\mathbf{H}=\epsilon\frac{\partial{\mathbf{E}}}{\partial{t}}\] Because the optical fields in the waveguide have the form of (1) and (2) [refer to the waveguide modes tutorial], these two Maxwell's equations can be written in the following form: \[\tag{10}\frac{\partial{\mathcal{E}_z}}{\partial{y}}-\text{i}\beta\mathcal{E}_y=\text{i}\omega\mu_0\mathcal{H}_x\] \[\tag{11}\text{i}\beta\mathcal{E}_x-\frac{\partial{\mathcal{E}_z}}{\partial{x}}=\text{i}\omega\mu_0\mathcal{H}_y\] \[\tag{12}\frac{\partial{\mathcal{E}_y}}{\partial{x}}-\frac{\partial{\mathcal{E}_x}}{\partial{y}}=\text{i}\omega\mu_0\mathcal{H}_z\] and \[\tag{13}\frac{\partial{\mathcal{H}_z}}{\partial{y}}-\text{i}\beta\mathcal{H}_y=-\text{i}\omega\epsilon\mathcal{E}_x\] \[\tag{14}\text{i}\beta\mathcal{H}_x-\frac{\partial{\mathcal{H}_z}}{\partial{x}}=-\text{i}\omega\epsilon\mathcal{E}_y\] \[\tag{15}\frac{\partial{\mathcal{H}_y}}{\partial{x}}-\frac{\partial{\mathcal{H}_x}}{\partial{y}}=-\text{i}\omega\epsilon\mathcal{E}_z\] From these equations, the transverse components of the electric and magnetic fields can be expressed in terms of the...

This is a continuation from the previous tutorial - Material Dispersion. Optical waveguides are the basic elements for confinement and transmission of light over various distances, ranging from tens or hundreds of micrometers in integrated photonics to hundreds or thousands of kilometers in long-distance fiber-optic transmission. They are used to connect various photonic devices. In many devices, they form important parts or key structures, such as the waveguides providing optical confinement in semiconductor lasers. Furthermore, they form important active or passive photonic devices by themselves, such as waveguide couplers and modulators. In this part, we consider the basic characteristics of...