# Two Types of Localized States in a Photonic Crystal Bounded by an Epsilon near Zero Nanocomposite

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## Abstract

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## 1. Introduction

## 2. Model Description and Determining the Transmittance

## 3. Results and Discussion

#### 3.1. Fresnel Reflection from a Nanocomposite Film

#### 3.2. Coupled Mode Theory

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Dependences of the imaginary $\Im {\epsilon}_{\mathit{eff}}\left(\omega \right)$ (dashed red line) and real $\Re {\epsilon}_{\mathit{eff}}$($\omega $) (solid black line) parts of the effective permittivity ${\epsilon}_{\mathit{eff}}\left(\omega \right)$ on normalized frequency $\omega /{\omega}_{p}$ (on the top) and transmittance (dashed blue line), reflectance (solid red line) and absorbance (dash-and-dot black line) spectra of the PhC/nanocomposite structure at the normal incidence of light onto it (Figure 1). The nanocomposite layer thickness is ${d}_{\mathit{eff}}=300$ nm and $f=0.11$.

**Figure 3.**Schematic of a one-dimensional PhC (yellow - SiO${}_{2}$, grey - ZiO${}_{2}$) conjugated with the nanocomposite layer (red) and field intensity distribution (solid black line) at the frequencies of (

**a**) TPP ($\omega =0.3377{\omega}_{p}$) and (

**b**) defect mode ($\omega =0.3470{\omega}_{p}$) normalized to the input intensity. The nanocomposite layer thickness is ${d}_{\mathit{eff}}=300$ nm and $f=0.11$.

**Figure 4.**Reflectance spectra of the PhC/nanocomposite structure at the normal incidence of light onto the sample at different nanocomposite filling factors. The nanocomposite layer thickness is ${d}_{\mathit{eff}}=300$ nm.

**Figure 5.**Reflectance spectra of the PhC/nanocomposite structure at the normal incidence of light onto the sample with nanocomposite film thicknesses in the ranges of: (

**a**) 50 nm $<{d}_{\mathit{eff}}<350$ nm; and (

**b**) 350 nm $<{d}_{\mathit{eff}}<700$ nm. The filling factor is $f=0.11$.

**Figure 6.**Reflectance spectra of the PhC/nanocomposite structure at the normal incidence of light onto the sample at different PhC first-layer thicknesses. The filling factor is $f=0.11$ and ${d}_{\mathit{eff}}=300$ nm.

**Figure 7.**Angular and frequency dependences of the reflectance spectra (red line) of the PhC/nanocomposite structure for the TE and TM modes. The filling factor is $f=0.11$ and ${d}_{\mathit{eff}}=300$ nm. Purple and green fillings denote the $\Re {\epsilon}_{\mathit{eff}}<0$ and photonic band gap, respectively.

**Figure 8.**Schematic of a one-dimensional PhC (yellow - SiO${}_{2}$, grey - ZiO${}_{2}$) conjugated with the nanocomposite layer (red) and field intensity distribution at oblique light incidence on the structure at the frequencies of TPP (black line) and defect mode (red line) normalized to the input intensity for the TM (

**a**) and TE (

**b**) waves. The nanocomposite layer thickness is ${d}_{\mathit{eff}}=300$ nm and $f=0.11$.

**Figure 9.**Fresnel reflectance at the nanocomposite/silicon dioxide interface in the photonic band gap region (

**a**) and TPP region (

**b**). The nanocomposite filling factor is $f=0.11$.

**Figure 11.**Graphic solution of the critical coupling condition in Equation (10) at a nanocomposite layer thickness of 341 nm (

**a**) and 576 nm (

**b**). The nanocomposite filling factor is $f=0.25$.

**Figure 12.**Reflectance spectra of the structure for the radiation incident from the nanocomposite layer side. ${d}_{\mathit{eff}}=341$ nm and $f=0.25$.

Method | Reflectance |
---|---|

Transfer martix | 0.9694 |

CMT | 0.9693 |

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**MDPI and ACS Style**

Bikbaev, R.G.; Vetrov, S.Y.; Timofeev, I.V.
Two Types of Localized States in a Photonic Crystal Bounded by an Epsilon near Zero Nanocomposite. *Photonics* **2018**, *5*, 22.
https://doi.org/10.3390/photonics5030022

**AMA Style**

Bikbaev RG, Vetrov SY, Timofeev IV.
Two Types of Localized States in a Photonic Crystal Bounded by an Epsilon near Zero Nanocomposite. *Photonics*. 2018; 5(3):22.
https://doi.org/10.3390/photonics5030022

**Chicago/Turabian Style**

Bikbaev, Rashid G., Stepan Ya. Vetrov, and Ivan V. Timofeev.
2018. "Two Types of Localized States in a Photonic Crystal Bounded by an Epsilon near Zero Nanocomposite" *Photonics* 5, no. 3: 22.
https://doi.org/10.3390/photonics5030022