# Training Videos

## Polarization of Light

This part continues from the linear optical susceptibility tutorial. Consider a monochromatic plane optical wave that has a complex field where is a constant independent of r and t, and is its unit vector. The polarization of the optical field is characterized by the unit vector . The wave is linearly polarized, also called plane polarized, if 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 direction so that and assume that both...

## Linear Optical Susceptibility

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)....

## Harmonic Fields

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): E(r, t) = E(r, t) + E*(r, t) = E(r, t) + c.c., (39) where c.c. means the complex conjugate. In our convention, E(r, t) contains the complex field...

## Optical Fields and Maxwell's Equations

## Probabilistic Approaches to System Optimization