# Modes

Modes — MC Grating documentation for Modal Crossed. This page provides the user with the possibility to calculate the Fourier modes and scattering matrix…

Canonical: https://mcgrating.com/docs/modal-crossed/modes.html


Written by Nikolay M. LyndinLast revised 2017-12-30

This documentation was written for releases up to 2018 and is being revised. Some dialogs have changed since. If something does not match what you see, write to [mc@mcgrating.com](mailto:mc@mcgrating.com).

This page provides the user with the possibility to calculate the Fourier modes and scattering matrix parameters of a grating structure, and to analyze their values as well as to draw the eigenmode field distributions. Most of the controls of this page have an obvious meaning; only a few deserve an explanation:

- The ***Incidence Layer*** edit window provides the possibility to select a layer of the structure where from an incident mode propagates towards one of the layer interfaces, and the ***Mode N*** edit windows provide the possibility to select the order of an incident mode whose effective index/permittivity is displayed under ***Mode Propagation ***control.
- The ***Output Layer*** edit window provides the possibility to choose which one of the adjacent layers or the layer itself contains the scattered mode and the ***Mode M*** edit window provides the possibility to select the order of this mode.
- The ***Output*** control informs which part (up or down) of the ***N to M ******Mode*** ***Scattering Coefficient* **is displayed. If the ***Incidence Layer*** and the ***Output Layer*** is the same, the ***Up*** choice means the scattering from a bottom interface the ***Down*** choice corresponds to the scattering from a top interface.
- The ***Polarization*** control (is applicable only to the diffraction orders of layers without a grating) provides the possibility to select a mode polarization type. In this case, the mode polarization is defined as Hs for H component of the Es mode electric field and as Hp for H component of the Ep mode electric field. In the general case, the concept of a definite polarization is not applicable to the modes of the grating layer, however, only two Eigen functions with conditional polarization identification of Hs and Hp correspond to each grating mode.
- The ***Save Modes*** button provides the possibility to save in a text or data file an effective index and permittivity table of all modes for the selected ***Incidence Layer*** and optionally to save an ***N to M Mode*** ***Scattering Coefficient* **table.

**Note 1 **If the layer index is *0* or *N+1* (where *N* is the number of layers), this index corresponds to the cover or substrate media respectively.

**Note 2** Only zero X and Y orders of a simple (without grating) layer are available.

From the in-application help of Modal Crossed, documented through 2018. If you publish results computed with MC Grating, see [how to cite it](https://mcgrating.com/references.html#cite).