# Symmetry-Induced Light Confinement in a Photonic Quasicrystal-Based Mirrorless Cavity

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## Abstract

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## 1. Introduction

## 2. Results

#### 2.1. Octagonal-Based Holographic Tiling

#### 2.2. Methods

#### 2.3. Mirrorless Cavity

## 3. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

PQC | Photonic quasi-crystal |

PBG | Photonic band gap |

DFLM | Defect-free localized mode |

HT | Holographic tiling |

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**Figure 1.**(

**a**) Holographic-tiling binary irradiance: black points correspond to high intensity levels; the inset shows the Fourier diffraction spectrum of the pattern with pseudo-octagonal symmetry. (

**b**) 2D Photonic Quasicrystal (PQC) finite pattern: open black circles correspond to the higher index pillars with $r=240$ nm; the positions of the sources and field monitors is indicated in the scheme (please note that monitors in different positions along the pattern detect different propagation direction of scattered field). (

**c**) Same as in (b) for a structure in which an air channel is open along the vertical y-axis; extended monitors are used for integral power measurements. (

**d**,

**e**) local density of states (LDOS) of the finite holographic tiling (HT)-PQC for excitation pulse in different positions (red and grey source) in accordance with the scheme in (b). The spectra were calculated from several field monitors: the line color corresponds to the field monitor color depicted in (b) (red open circle monitors are not shown:); in (e), a different spectral range is used to better visualize the defect-free localized mode (DFLM) resonances in the wide PBG around 2.8 $\mathsf{\mu}$m. (

**f**) LDOS for the channel-PQC pattern shown in (c) for low refractive index. The star indicates a representative resonance (2.01 $\mathsf{\mu}$m, DFLM) at which light propagation is forbidden above the symmetry center x = 0, y = 0 along the channel (crossed lines are a guide to the eye). The spectra line colors correspond to the field monitor colors in (c).

**Figure 2.**(

**a**) Contour map of the normalized field amplitude ${E}_{z}$ at the DFLM wavelength of 2.01 $\mathsf{\mu}$m in the channel-PQC ($\mathrm{\Delta}n=0.8$): light cannot efficiently cross the pattern center. (

**b**) Normalized contour map of ${E}_{z}$ at 2.01 $\mathsf{\mu}$m in the channel-PQC with a central pillar ($\mathrm{\Delta}n=0.8$): light couples efficiently to the top half channel thanks to the central pillar. The field around the source is due to the sum of input and back-scattering fields, and takes into account also back-scattering from the pillars around the channel (due to the source injection).

**Figure 3.**(

**a**) Contour map of the normalized field amplitude ${E}_{z}$ at the DFLM wavelength of 2.01 $\mathsf{\mu}$m in the doubled channel-PQC ($\mathrm{\Delta}n=0.8$): light cannot efficiently cross the top and bottom DFLMs, respectively at coordinates ($x=0$, $y=0$) and ($x=0$, $y=-L$), acting as virtual mirrors that confine the electromagnetic field inside a mirrorless cavity. (

**b**) Power monitored by the detectors placed as represented in the scheme in (a). The color of the solid lines corresponds to the field monitor colors in (a), i.e., blue for the input power, red for top transmitted power (T), yellow for the bottom transmitted power (B) and green for power detected just above the top virtual mirror ($x=0$, $y=0$). The field reaches a steady state with only ∼ 10% of loss through the open waveguide despite the relative low refractive index contrast of the photonic PQC. The input field has unitary power. The blue line indicates total power integrated in the blue-box area around the center where input source is launched.

**Figure 4.**(

**a**) Contour map of ${E}_{z}$ at the DFLM wavelength of 2.01μm in the three-port channel-PQC ($\mathrm{\Delta}n=0.8$). (

**b**) Contour map of ${E}_{z}$ at the DFLM wavelength of 2.01μm in the four-port channel-PQC ($\mathrm{\Delta}n=0.8$).

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zito, G.; Rusciano, G.; Sasso, A.; De Nicola, S.
Symmetry-Induced Light Confinement in a Photonic Quasicrystal-Based Mirrorless Cavity. *Crystals* **2016**, *6*, 111.
https://doi.org/10.3390/cryst6090111

**AMA Style**

Zito G, Rusciano G, Sasso A, De Nicola S.
Symmetry-Induced Light Confinement in a Photonic Quasicrystal-Based Mirrorless Cavity. *Crystals*. 2016; 6(9):111.
https://doi.org/10.3390/cryst6090111

**Chicago/Turabian Style**

Zito, Gianluigi, Giulia Rusciano, Antonio Sasso, and Sergio De Nicola.
2016. "Symmetry-Induced Light Confinement in a Photonic Quasicrystal-Based Mirrorless Cavity" *Crystals* 6, no. 9: 111.
https://doi.org/10.3390/cryst6090111