# Overlap and Frequency Sweep — Lesson 2

### Overlap and Power Coupling

There are many applications where the coupling of light between devices is required. In this video lesson, we will demonstrate how to calculate the overlap and power coupling of a certain mode with another mode or a beam.

### Frequency Sweep The Frequency Sweep tool allows you to calculate and plot the following results as a function of frequency:

• Effective index $\left ( n_{eff} \right )$ : Effective index of the calculated mode(s)
• Loss: Modal loss (in dB/cm of propagation)
• Gain: Modal gain (in dB/cm of propagation)
• Group index $\left ( n_{g} \right )$: Ratio of the speed of light to the group velocity, $n_{g} = \frac{c}{v_{g}}$
• Group Velocity $\left ( v_{g} \right )$: Rate at which the peak of a temporal pulse will propagate in the absence of non-linearities (in m/s), $v_{g} = \frac{\mathrm{d} \omega }{\mathrm{d} \beta }$
• Group delay (t):  $t = \frac{1}{v_{g}}$ (in ps/km)
• Dispersion: Rate of change of the group delay with respect to the wavelength (in ps/nm/km), $D =\frac{\mathrm{d} t}{\mathrm{d} \lambda }$
• Beta $\left ( \beta \right )$: Propagation constant, where $\lambda _{0}$ is the free-space wavelength (in 1/m), $\beta = \frac{2\pi n_{eff}}{\lambda _{0}}$

When the “track selected mode” option is selected, the solver will use the best overlap to track the modes and not just their effective index.