# Design of 1D Photonic Crystals Sustaining Optical Surface Modes

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Theoretical Background: Impedance Approach

#### 2.2. Reflection and Transmission for a Multilayer with N Layers

#### 2.3. Input Impedance of a SEMI-Infinite 1D PC

#### 2.4. Band Gap Maximum Extinction Per Length

#### 2.5. Dispersion Relation for PC SM and Its Solution for the Truncated Layer Thickness

## 3. Results

#### 3.1. Practical Implementation in the Program

`1DPC4all.exe`can be run on any 64-bit Windows above Windows 7. The user of the program is not required to download and install any versions of .NET.

#### 3.2. Refractive Indices Data

#### 3.2.1. Sellmeier Formula

`.slmr`in subfolder ‘

`\1DPC4all\Resources\calcRI\`’. These coefficients (${c}_{i}$) will be substituted into the Sellmeier formula in the following form:

`\1DPC4all\Resources\calcRI\BK7.slmr`’ (which can be changed by users, if desired).

#### 3.2.2. Drude Formula

`\1DPC4all\Resources\calcRI\`’ as an ASCII file with the extension

`.drd`. These nine coefficients (${c}_{i}$) will be substituted into the Drude formula in the following form:

`\1DPC4all\Resources\calcRI\Ag.drd`’ (users can change it, if desired).

#### 3.2.3. Experimental n-k Dataset

`.nk`and added to the zip file ‘

`\1DPC4all\Resources\allRI.zip`’, where 188

`.nk`files (representing various materials) are already stored. The values of n and k between the wavelengths presented in the table will be found by linear interpolation.

#### 3.2.4. Maxwell Garnett Approximation for Mixed Layers

`.gnt`in the subfolder ‘

`\1DPC4all\Resources\calcRI\`’. Each line in the file must represent the matrix medium and one (or two) inclusion(s) followed by their volume percentage. For example, a file with lines: ‘

`SiO2.nk 97 Au.drd 2 air.slmr 1`’ will provide an effective RI for a layer consisting of 97% $Si{O}_{2}$ as a matrix material (given as

`.nk`dataset ‘$\lambda $ n k’), 2% Au inclusion (represented by the Drude formula) and 1% of air bubbles (represented by Sellmeier formula). Such file can also be automatically created from two or three selected layers in Step 2 of the program, where the volume percentage will be given by the thicknesses of the layers (hints in the program will provide all the details).

#### 3.3. Step 1: Selection of Double Layer Materials, Wavelength and Angle

#### 3.4. Step 2: Choosing the Number of Layers and Final Adjustment of the Structure

#### 3.5. Step 3: Presentation and Analysis

#### 3.6. Additional Features

#### 3.6.1. 1D PC Structures with Two Metal Nanolayers

`\1DPC4all\savedResults\NanoMicroLetters2020\`’ subfolder of the program.

#### 3.6.2. Luminescence from 1D PC structures

#### 3.7. A Practical Example of Designing a 1D PC Structure Sustaining Long-Range Surface Plasmons

## 4. Discussion

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Step 2 program’s window for choosing the number of layers and final adjustment of the structure.

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**MDPI and ACS Style**

Konopsky, V.
Design of 1D Photonic Crystals Sustaining Optical Surface Modes. *Coatings* **2022**, *12*, 1489.
https://doi.org/10.3390/coatings12101489

**AMA Style**

Konopsky V.
Design of 1D Photonic Crystals Sustaining Optical Surface Modes. *Coatings*. 2022; 12(10):1489.
https://doi.org/10.3390/coatings12101489

**Chicago/Turabian Style**

Konopsky, Valery.
2022. "Design of 1D Photonic Crystals Sustaining Optical Surface Modes" *Coatings* 12, no. 10: 1489.
https://doi.org/10.3390/coatings12101489