# 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

- Yablonovitch, E. Photonic band-gap structures. J. Opt. Soc. Am. B
**1993**, 10, 283–295. [Google Scholar] [CrossRef] - Kossel, D. Analogies between thin-film optics and electron band theory of solids. J. Opt. Soc. Am.
**1966**, 56, 1434. [Google Scholar] - Arnaud, J.A.; Saleh, A.A.M. Guidance of surface waves by multilayer coatings. Appl. Opt.
**1974**, 13, 2343–2345. [Google Scholar] [CrossRef] [PubMed] - Yeh, P.; Yariv, A.; Hong, C.S. Electromagnetic propagation in periodic stratified media. I. General theory. J. Opt. Soc. Am.
**1977**, 67, 423–438. [Google Scholar] [CrossRef][Green Version] - Yeh, P.; Yariv, A.; Cho, A.Y. Optical surface waves in periodic layered media. Appl. Phys. Lett.
**1978**, 32, 104–105. [Google Scholar] [CrossRef][Green Version] - Robertson, W.M.; May, M.S. Surface electromagnetic waves on one-dimensional photonic band gap arrays. Appl. Phys. Lett.
**1999**, 74, 1800–1802. [Google Scholar] [CrossRef] - Shinn, A.; Robertson, W. Surface plasmon-like sensor based on surface electromagnetic waves in a photonic band-gap material. Sens. Actuator B-Chem.
**2005**, 105, 360–364. [Google Scholar] [CrossRef] - Konopsky, V.N.; Alieva, E.V. Long-range plasmons in lossy metal films on photonic crystal surfaces. Opt. Lett.
**2009**, 34, 479–481. [Google Scholar] [CrossRef][Green Version] - Hamidi, S.; Ramezani, R.; Bananej, A. Hydrogen gas sensor based on long-range surface plasmons in lossy palladium film placed on photonic crystal stack. Opt. Mater.
**2016**, 53, 201–208. [Google Scholar] [CrossRef] - Konopsky, V.N.; Basmanov, D.V.; Alieva, E.V.; Sekatskii, S.K.; Dietler, G. Size-dependent hydrogen uptake behavior of Pd nanoparticles revealed by photonic crystal surface waves. Appl. Phys. Lett.
**2012**, 100, 083108. [Google Scholar] [CrossRef] - Ignatyeva, D.O.; Knyazev, G.A.; Kapralov, P.O.; Dietler, G.; Sekatskii, S.K.; Belotelov, V.I. Magneto-optical plasmonic heterostructure with ultranarrow resonance for sensing applications. Sci. Rep.
**2016**, 6, 28077. [Google Scholar] [CrossRef][Green Version] - Alieva, E.; Konopsky, V.; Basmanov, D.; Sekatskii, S.; Dietler, G. Blue surface plasmon propagation along thin gold film–gas interface and its use for sensitive nitrogen dioxide detection. Opt. Commun.
**2013**, 309, 148–152. [Google Scholar] [CrossRef] - Li, J.; Tang, T.; Zhang, Y.; Luo, L.; Sun, P. Magneto-plasmonic sensor with one dimensional photonic crystal for methane detection. Optik
**2018**, 155, 74–80. [Google Scholar] [CrossRef] - Ignatyeva, D.; Kapralov, P.; Golovko, P.; Shilina, P.; Khramova, A.; Sekatskii, S.; Nur-E-Alam, M.; Alameh, K.; Vasiliev, M.; Kalish, A.; et al. Sensing of surface and bulk refractive index using magnetophotonic crystal with hybrid magneto-optical response. Sensors
**2021**, 21, 1984. [Google Scholar] [CrossRef] - Konopsky, V.N.; Alieva, E.V. Photonic crystal surface waves for optical biosensors. Anal. Chem.
**2007**, 79, 4729–4735. [Google Scholar] [CrossRef] - Guo, Y.; Ye, J.Y.; Divin, C.; Huang, B.; Thomas, T.P.; Baker, J.R., Jr.; Norris, T.B. Real-time biomolecular binding detection using a sensitive photonic crystal biosensor. Anal. Chem.
**2010**, 82, 5211–5218. [Google Scholar] [CrossRef][Green Version] - Konopsky, V.N.; Karakouz, T.; Alieva, E.V.; Vicario, C.; Sekatskii, S.K.; Dietler, G. Photonic crystal biosensor based on optical surface waves. Sensors
**2013**, 13, 2566–2578. [Google Scholar] [CrossRef][Green Version] - Rivolo, P.; Michelotti, F.; Frascella, F.; Digregorio, G.; Mandracci, P.; Dominici, L.; Giorgis, F.; Descrovi, E. Real time secondary antibody detection by means of silicon-based multilayers sustaining Bloch surface waves. Sens. Actuators B Chem.
**2012**, 161, 1046–1052. [Google Scholar] [CrossRef] - Konopsky, V.; Mitko, T.; Aldarov, K.; Alieva, E.; Basmanov, D.; Moskalets, A.; Matveeva, A.; Morozova, O.; Klinov, D. Photonic crystal surface mode imaging for multiplexed and high-throughput label-free biosensing. Biosens. Bioelectron.
**2020**, 168, 112575. [Google Scholar] [CrossRef] - Khodami, M.; Hirbodvash, Z.; Krupin, O.; Wong, W.R.; Lisicka-Skrzek, E.; Northfield, H.; Hahn, C.; Berini, P. Fabrication of Bloch Long Range Surface Plasmon Waveguides Integrating Counter Electrodes and Microfluidic Channels for Multimodal Biosensing. J. Microelectromechanical Syst.
**2021**, 30, 686–695. [Google Scholar] [CrossRef] - Sizova, S.; Shakurov, R.; Mitko, T.; Shirshikov, F.; Solovyeva, D.; Konopsky, V.; Alieva, E.; Klinov, D.; Bespyatykh, J.; Basmanov, D. The Elaboration of Effective Coatings for Photonic Crystal Chips in Optical Biosensors. Polymers
**2021**, 14, 152. [Google Scholar] [CrossRef] - Kalas, B.; Ferencz, K.; Saftics, A.; Czigany, Z.; Fried, M.; Petrik, P. Bloch surface waves biosensing in the ultraviolet wavelength range—Bragg structure design for investigating protein adsorption by in situ Kretschmann-Raether ellipsometry. Appl. Surf. Sci.
**2021**, 536, 147869. [Google Scholar] [CrossRef] - Petrova, I.; Konopsky, V.; Nabiev, I.; Sukhanova, A. Label-Free Flow Multiplex Biosensing via Photonic Crystal Surface Mode Detection. Sci. Rep.
**2019**, 9, 8745. [Google Scholar] [CrossRef][Green Version] - Delfan, A.; Liscidini, M.; Sipe, J.E. Surface enhanced Raman scattering in the presence of multilayer dielectric structures. JOSA B
**2012**, 29, 1863–1874. [Google Scholar] [CrossRef][Green Version] - Konopsky, V.N.; Alieva, E.V.; Alyatkin, S.Y.; Melnikov, A.A.; Chekalin, S.V.; Agranovich, V.M. Phase-matched third-harmonic generation via doubly resonant optical surface modes in 1D photonic crystals. Light. Sci. Appl.
**2016**, 5, e16168. [Google Scholar] [CrossRef][Green Version] - Fong, N.R.; Menotti, M.; Lisicka-Skrzek, E.; Northfield, H.; Olivieri, A.; Tait, N.; Liscidini, M.; Berini, P. Bloch long-range surface plasmon polaritons on metal stripe waveguides on a multilayer substrate. ACS Photonics
**2017**, 4, 593–599. [Google Scholar] [CrossRef] - Konopsky, V. Long-range surface plasmon amplification with current injection on a one-dimensional photonic crystal surface. Opt. Lett.
**2015**, 40, 2261–2264. [Google Scholar] [CrossRef] - Degli-Eredi, I.; Sipe, J.; Vermeulen, N. TE-polarized graphene modes sustained by photonic crystal structures. Opt. Lett.
**2015**, 40, 2076–2079. [Google Scholar] [CrossRef] [PubMed] - Konopsky, V.; Prokhorov, V.; Lypenko, D.; Dmitriev, A.; Alieva, E.; Dietler, G.; Sekatskii, S. Electrical excitation of long-range surface plasmons in PC/OLED structure with two metal nanolayers. Nano-Micro Lett.
**2020**, 12, 35. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kovalevich, T.; Belharet, D.; Robert, L.; Ulliac, G.; Kim, M.S.; Herzig, H.P.; Grosjean, T.; Bernal, M.P. Bloch surface waves at the telecommunication wavelength with lithium niobate as the top layer for integrated optics. Appl. Opt.
**2019**, 58, 1757–1762. [Google Scholar] [CrossRef] [PubMed][Green Version] - Rizzo, R.; Danz, N.; Michelotti, F.; Maillart, E.; Anopchenko, A.; Wächter, C. Optimization of angularly resolved Bloch surface wave biosensors. Opt. Express
**2014**, 22, 23202–23214. [Google Scholar] [CrossRef] - Delfan, A.; Degli-Eredi, I.; Sipe, J. Long-range surface plasmons in multilayer structures. JOSA B
**2015**, 32, 1615–1623. [Google Scholar] [CrossRef][Green Version] - Fong, N.; Menotti, M.; Lisicka-Skrzek, E.; Northfield, H.; Olivieri, A.; Tait, N.; Liscidini, M.; Berini, P. Guided Bloch long-range surface plasmon polaritons. In Proceedings of the 2017 19th International Conference on Transparent Optical Networks (ICTON), IEEE, Girona, Spain, 2–6 July 2017; pp. 1–4. [Google Scholar]
- Degli-Eredi, I.; Sipe, J.; Vermeulen, N. Power-flow-based design strategy for Bloch surface wave biosensors. Opt. Lett.
**2018**, 43, 1095–1098. [Google Scholar] [CrossRef] - Konopsky, V. Version 1.0.8134.15784. 2022. Available online: https://www.pcbiosensors.com/1DPC4all.htm (accessed on 1 October 2022).
- Konopsky, V.N. Plasmon-polariton waves in nanofilms on one-dimensional photonic crystal surfaces. New J. Phys.
**2010**, 12, 093006. [Google Scholar] [CrossRef][Green Version] - Konopsky, V.N. Long-range surface plasmons on duplex metal nanolayers. Photonics Nanostruct.–Fundam. Appl.
**2020**, 39, 100788. [Google Scholar] [CrossRef] - Brekhovskikh, L. Waves in Layered Media; Academic: New York, NY, USA, 1980. [Google Scholar]
- Delano, E.; Pegis, R. Chapter 2: Methods of syntesis for dielectric multilayer filters. In Progress in Optics; Wolf, E., Ed.; North-Holland: Amsterdam, The Netherlands, 1969; Volume VII, pp. 77, 130. [Google Scholar]
- Yuffa, A.J.; Scales, J.A. Object-oriented electrodynamic S-matrix code with modern applications. J. Comput. Phys.
**2012**, 231, 4823–4835. [Google Scholar] [CrossRef] - Reiser, P. Calculation of lossy dielectric multilayer filter response. J. Sci. Comput.
**2005**, 25, 499–513. [Google Scholar] [CrossRef] - Konopsky, V.N.; Alieva, E.V. Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface. Phys. Rev. Lett.
**2006**, 97, 253904. [Google Scholar] [CrossRef] - Bohren, C.; Huffman, D. Absorption and Scattering of Light by Small Particles; Wiley & Sons: New York, NY, USA, 1983. [Google Scholar]
- Konopsky, V.N.; Alieva, E.V. Observation of fine interference structures at total internal reflection of focused light beams. Phys. Rev. A
**2012**, 86, 063807. [Google Scholar] [CrossRef] - Yang, H.; Alexopoulos, N. Gain enhancement methods for printed circuit antennas through multiple superstrates. IEEE Trans. Antennas Propag.
**1987**, 35, 860–863. [Google Scholar] [CrossRef] - Wu, X.H.; Kishk, A.A.; Glisson, A.W. A transmission line method to compute the far-field radiation of arbitrarily directed Hertzian dipoles in a multilayer dielectric structure: Theory and applications. IEEE Trans. Antennas Propag.
**2006**, 54, 2731–2741. [Google Scholar] [CrossRef]

**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