Fiber Optic Tutorials

This part continues from the Polarization of Light tutorial. The propagation of an optical wave is governed by the wave equation. It depends on the optical property and physical structure of the medium. It also depends on the makeup of the optical wave, such as its frequency contents and its temporal characteristics. In this part, we consider the basic characteristics of the propagation of a monochromatic plane optical wave in an infinite homogeneous medium. For such a monochromatic wave, there is only one value of k and one value of ω. Its complex electric field is that given by (58) in...

This part continues from the linear optical susceptibility tutorial. Consider a monochromatic plane optical wave that has a complex field \[\tag{58}\mathbf{E}(\mathbf{r},t)=\pmb{\mathcal{E}}\exp(\text{i}\mathbf{k}\cdot\mathbf{r}-\text{i}\omega t)=\hat{e}\mathcal{E}\exp(\text{i}\mathbf{k}\cdot\mathbf{r}-\text{i}\omega t)\] where \(\pmb{\mathcal{E}}\) is a constant independent of r and t, and \(\hat{e}\) is its unit vector. The polarization of the optical field is characterized by the unit vector \(\hat{e}\). The wave is linearly polarized, also called plane polarized, if \(\hat{e}\) can be expressed as a constant, real vector. Otherwise, the wave is elliptically polarized in general, and is circularly polarized in some special cases. For the convenience of discussion, we take the direction of the wave propagation to be the z...

This part continues from the harmonic fields tutorial. The susceptibility tensor χ(r, t) and the permittivity tensor ε(r, t) of space and time are always real quantities although all field quantities, including both E(r, t) and E(k, ω), can be defined in a complex form. This is true even in the presence of an optical loss or gain in the medium. However, the susceptibility and permittivity tensors in the momentum space and frequency domain, χ(k, ω) and ε(k, ω), can be complex. If an eigenvalue, χi, of χ is complex, the corresponding eigenvalue, εi, of ε is also complex, and their imaginary parts have the same sign because ε = ε0(1 + χ)....

This continues from the optical fields and Maxwell's equations tutorial. Optical fields are harmonic fields that vary sinusoidally with time. The field vectors defined in the preceding tutorials are all real quantities. For harmonic fields, it is always convenient to use complex fields. We define the space- and time-dependent complex electric field, E(r, t), through its relation to the real electric field, E(r, t): \[\tag{39}\pmb{E}(\mathbf{r},t)=\mathbf{E}(\mathbf{r},t)+\mathbf{E}^*(\mathbf{r},t)=\mathbf{E}(\mathbf{r},t)+\text{c.c.}\] where c.c. means the complex conjugate. In our convention, E(r, t)  contains the complex field components that vary with time as exp(-iωt) with positive values of ω, while E*(r, t) contains those varying with time as...