# Fresnel equations and transmission line analogues for diffraction gratings

## Abstract

A simple and intuitive formalism is presented to describe diffraction in multi-layered periodic structures. We use the well known results from scalar analysis (wave propagation in homogeneous layered media) and show that they can be generalized rather readily to vector problems such as diffraction analysis. Specifically, we derive: (1) generalized Fresnel equations appropriate for reflection and transmission from an infinitely thick grating, (2) a generalized Airy formula for thin-film to describe reflection and transmission of light through a lamellar grating and (3) a matrix propagation method akin to that used for multi-layer thin film analysis. The results developed here complement the recent work on R-matrix and S-matrix propagation algorithms that have been used in connection with modal and differential grating theories. These algorithms have proven to be numerically stable for calculating diffraction efficiencies from deep groove gratings. The formalism developed here expands upon the earlier literature by providing important details that are hitherto unavailable.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Labs., Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 100032

- Report Number(s):
- SAND-95-1891C; CONF-950793-23

ON: DE95016739

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Conference

- Resource Relation:
- Conference: 40. annual meeting of the Society of Photo-Optical Instrumentation Engineers, San Diego, CA (United States), 9-14 Jul 1995; Other Information: PBD: [1995]

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; 44 INSTRUMENTATION, INCLUDING NUCLEAR AND PARTICLE DETECTORS; DIFFRACTION; MATHEMATICAL MODELS; OPTICAL SYSTEMS; DIFFRACTION GRATINGS; OPTICS; AIRY FUNCTIONS; LIGHT TRANSMISSION; REFLECTION; INTERFACES

### Citation Formats

```
Kaushik, S.
```*Fresnel equations and transmission line analogues for diffraction gratings*. United States: N. p., 1995.
Web.

```
Kaushik, S.
```*Fresnel equations and transmission line analogues for diffraction gratings*. United States.

```
Kaushik, S. Tue .
"Fresnel equations and transmission line analogues for diffraction gratings". United States. https://www.osti.gov/servlets/purl/100032.
```

```
@article{osti_100032,
```

title = {Fresnel equations and transmission line analogues for diffraction gratings},

author = {Kaushik, S},

abstractNote = {A simple and intuitive formalism is presented to describe diffraction in multi-layered periodic structures. We use the well known results from scalar analysis (wave propagation in homogeneous layered media) and show that they can be generalized rather readily to vector problems such as diffraction analysis. Specifically, we derive: (1) generalized Fresnel equations appropriate for reflection and transmission from an infinitely thick grating, (2) a generalized Airy formula for thin-film to describe reflection and transmission of light through a lamellar grating and (3) a matrix propagation method akin to that used for multi-layer thin film analysis. The results developed here complement the recent work on R-matrix and S-matrix propagation algorithms that have been used in connection with modal and differential grating theories. These algorithms have proven to be numerically stable for calculating diffraction efficiencies from deep groove gratings. The formalism developed here expands upon the earlier literature by providing important details that are hitherto unavailable.},

doi = {},

url = {https://www.osti.gov/biblio/100032},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1995},

month = {8}

}