# Tiling Photonic Topological Insulator for Laser Applications

^{1}

^{2}

^{*}

## Abstract

**:**

## Featured Application

**A new class of active topological photonic devices and laser arrays.**

## Abstract

## 1. Introduction

## 2. Materials and Methods

^{3}were ensured by the Maksutov method [23] with 10 um accuracy. To avoid accuracy problems with the half-wavelength gap and multilayer covering, we chose the zero gap. The immersion liquid infiltrated the unintentional air gaps between the prism resonators to suppress the parasitic reflection and to ensure the lossless beam penetration between the resonators. Therefore, a liquid with a refractive index close to the refractive index of quartz glass was selected.

^{2}in size. A rectangular triangular prism was used as a coupler to lead the light beam into and out of the quartz glass at the angle of total internal reflection. The angle of total internal reflection is 44.37° according to Snell’s law. The resonators were fixed on an adhesive composition of a mixture of vinyl acetate (30%) and acetone (70%) copolymers. The immersion liquid was an aqueous solution of glycerin with a density of 1.228 g per cubic centimeter. The refractive index of the immersion liquid was 1.45. No more than 0.01 mL of immersion liquid covered each face to avoid a meniscus on adjacent vertical faces, producing scattering and deviation of the beam. Before applying the immersion liquid, each prism was cleaned of dust and stains using crepe paper impregnated with a solution of water (80%), isopropanol (10%), metaxypropanol (5%), and nonionic surfactant (5%). Then, rectangular quartz prisms were connected, strictly in the order of numbering, as denoted in Figure 1b. After connecting each new segment, the operability of the tiling was checked using violet (405 nm) and red (650 nm) lasers (Figure 1c). Each prism was adjusted according to three degrees of freedom, namely one rotation and two translations along the axes X and Y (Figure 1a). The glass platform with assembled tiling and a triangular coupler was fixed on an optical bench next to the laser source.

## 3. Results

^{3}(Figure 4a). Their linear dimensions were ensured by the Maksutov method [23] with 10 um accuracy. The second set was manufactured from Chinese crown glass K9 with a refractive index of 1.517 and linear dimensions 30 × 30 × 30 mm

^{3}, with 30 um accuracy (Figure 4b).

## 4. Discussion

- Propagation of the light beam at the angle of total internal reflection; the intensity of the beam weakens with small deviations of the angle of incidence of the beam through a triangular coupler.
- The presence of dust particles, air bubbles in the immersion liquid layer between the prism resonators, or remnants of immersion liquid on the side faces of prism resonators scatters the light beam. Violation of the parallelism of the faces when connecting prism resonators and inaccuracies in the manufacturing of prism resonators deflect the direction of the light beam, as well as changing its aperture and cross-section shape. With a strong deviation, splitting of the light beam on the vertical edges of the prism resonators is possible.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The prism resonator made of quartz glass with a refractive index of 1.43. (

**b**) A model of the tiling photonic topological insulator (TPhTI) composed of 28 prism resonators. (

**c**) The TPhTI, composed of seven prism resonators.

**Figure 2.**(

**a**) The beam trajectory inside a smooth TPhTI model. (

**b**) The corrected trajectory inside the TPhTI without prism resonator #3, as denoted in (

**b**). The model shows that the light beam successfully bends around the defect of TPhTI.

**Figure 3.**Beam trajectory photographs. The trajectory for smooth TPhTI (

**a**,

**c**) is robust against a defect obtained by removing prism resonator #3 (

**b**,

**d**) or attaching a new prism resonator below resonator #28 (

**e**). Light beams for both a violet laser of 405 nm wavelength (

**a**,

**b**) and green laser of 532 nm (

**c**–

**e**) act in the same manner, proving the wavelength independence of the TPhTI principle.

**Figure 4.**Scalability of the TPhTI is manifested by comparing two resonator sizes: (

**a**) 12 × 12 × 8 mm

^{3}. (

**b**) 30 × 30 × 30 mm

^{3}. Both trajectories are homothetic and proportional to prism linear dimensions.

**Figure 5.**Wavelength-independent beam trajectory. Laser beams of RGB-colors pass the same trajectory through a TPhTI made of seven prism resonators: (

**a**) red 650 nm, (

**b**) green 532 nm, and (

**c**) blue 405 nm.

Color | Red, 650 nm | Green, 532 nm | Blue, 405 nm |
---|---|---|---|

28 resonator TPhTI | 51% | 78% | 68% |

27 resonator TPhTI | 43% | 65% | 48% |

Name | Value | Value | Affects (+)/Does Not Affect (−) Stability |
---|---|---|---|

Linear dimensions of the prism resonator | 12 × 12 × 8 mm^{3} | 30 × 30 × 30 mm^{3} | - (see Figure 4) |

Refractive index of the immersion liquid | 1.45 | 1.45 | ± |

Refractive index of quartz glass | 1.43 | 1.517 | ± |

Angle of total internal reflection | >44.37° | >41.24° | ± |

Angle of beam incidence | ~45° | ~45° | + |

Laser wavelength | 405/532/650 nm | 405/532/650 nm | ± (see Figure 5) |

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**MDPI and ACS Style**

Kim, P.N.; Fedchenko, D.P.; Rudakova, N.V.; Timofeev, I.V.
Tiling Photonic Topological Insulator for Laser Applications. *Appl. Sci.* **2023**, *13*, 4004.
https://doi.org/10.3390/app13064004

**AMA Style**

Kim PN, Fedchenko DP, Rudakova NV, Timofeev IV.
Tiling Photonic Topological Insulator for Laser Applications. *Applied Sciences*. 2023; 13(6):4004.
https://doi.org/10.3390/app13064004

**Chicago/Turabian Style**

Kim, Petr N., Dmitry P. Fedchenko, Natalya V. Rudakova, and Ivan V. Timofeev.
2023. "Tiling Photonic Topological Insulator for Laser Applications" *Applied Sciences* 13, no. 6: 4004.
https://doi.org/10.3390/app13064004