# Perovskite Topological Lasers: A Brand New Combination

^{*}

## Abstract

**:**

## 1. Introduction

^{2}[5,6]. Smaller sizes are preferred if the output quality is assured. Based on reference [6], reduced threshold and improved stability in a light source can result in reduced power consumption, faster signalling, faster chip operation and improved parallel computing capability and transmission efficiency. However, the advances in chip technology are still limited by various factors like the quality of the optical cavity in the light source and the operating threshold and mode. The absence of a novel excitation method that fulfils the laser operational requirements for low energy consumption whilst remarkably reducing the device’s size is deemed a major hindrance, as reported in [7].

_{3}, where A is a monovalent cation, such as formamidine (FA

^{+}), methylammonium (MA

^{+}), caesium (Cs

^{+}) or rubidium (Rb

^{+}), and B is a divalent metal cation. Such as tin (Sn

^{2+}), bismuth (Bi

^{3+}) or lead (Pb

^{2+}), and X is a halogen anion, such as chlorine (CI

^{−}), bromine (Br

^{−}), iodine (I

^{−}) or mixtures thereof. Depending on the composition, the usually perovskites can be divided into the following two categories: organic–inorganic hybrid perovskites and pure inorganic perovskites. These materials have attracted attention in the context of gain media due to their distinctive laser gain properties, including high quantum yield, wide bandgap tunability and easy absorption properties [13]. Since 2019, various types of perovskite materials have demonstrated significant potential as laser-active region dielectric materials. Compared to many other active materials, the solution-treated films of these materials have the advantages of large optical absorption cross-section, large exciton binding energy, high photoluminescence quantum yield, high defect tolerance, and device tunability, making their role as a laser gain medium unparalleled [14]. As a result, the combination of topological optics and perovskite is set to lead to new breakthroughs in the research of micro- and nanolasers [15]. Thus, summarizing the topological lasers of low-dimensional perovskites is crucial.

## 2. Fundamental Principles of Topological Lasers

^{2}). In addition, laser emission can be continuously tuned in the gain spectrum range (from λ = 532 to 519 nm) by altering the thickness of the gain medium. This innovation addresses common issues found in thick quantum dot films, such as poor uniformity, aggregation and luminescence quenching [29]. In the two-dimensional structure of perovskite, the nanostructures—known as nanoplates (NPL)—sustain quantum confinement in a singular direction. The electronic properties of these materials are characterised by narrow emission lines at low and room temperatures, with significantly improved exciton binding energy and absorption cross sections (corresponding to the area of NPL) compared to colloidal quantum dots. Additionally, the low threshold for amplified emission and optical gain coefficient provided by simultaneous one-photon and two-photon absorption pumping is approximately four times greater than that offered by the colloidal quantum dots [30]. Although 3D perovskite possesses a high optical gain and a low threshold, it can only achieve high-efficiency laser emission due to its narrow band gap and poor thermal conductivity. This hinders its ability to achieve high-energy laser emission and adversely affects its performance and operational life [31]. After careful consideration and thorough comparison, our recommendation is to utilize a sub-2D low-dimensional perovskite as the gain medium.

Gain Medium | Threshold | Q-Factors | Output Wavelength (nm) | Published Year | Refs. |
---|---|---|---|---|---|

Oregon Green 488 | 0.005 mJ | 14.8 | 531 | 2009 | [38] |

InGaN@GaN | 3.7 kW/cm^{2} | ~17 | 510 | 2012 | [39] |

CH_{3}NH_{3}PbBr_{3} | 59 uJ/cm^{2} | ~855 | ~552 | 2016 | [40] |

PMMA:DCM | 5.6 MW/cm^{2} | 310 | ~643 | 2017 | [41] |

NaYF^{4}:Yb^{3+}/Er^{3+} | 70 W/cm^{2} | >200 | 664 | 2019 | [42] |

InAsP/InP | ~12.5 kW/cm^{2} | ~35,000 | ~1550 | 2019 | [43] |

Ga_{0.05}Al_{0.95}As/Ga_{0.8}Al_{0.2}As | 200 μW | ~72,000 | 754 | 2021 | [27] |

CsPbBr_{3} | 8.95 μJ/cm^{2} | ~5000 | 515 | 2023 | [17] |

^{9}. This precision is a manifestation of the topological nature of ${\sigma}_{xy}$ [46].

_{0.15}Ga

_{0.85}terahertz QCL chip, such as the one used in this work, which is created by the passage of light through the top metal layer and hexagonal air-hole lattice of a terahertz QCL wafer. This structure effectively reduces intracavity reflection and loss, thereby improving the laser’s performance in terms of output and excitation. Due to the high refractive index property of silica, the laser output power and energy can be improved to some extent. However, the excessive refractive index of silica causes the light to be confined, resulting in insufficient oscillation capability, making it difficult to achieve low-threshold operation for topological lasers with silica as the gain medium in new photonic chips that require low energy consumption; therefore, a new material substitution is urgently needed [55].

^{2}area. This study demonstrates compact spin-valley-locked perovskite emissive surfaces that assign spin-dependent geometrical phases to bound states in the continuum via Brillouin zone folding and process photons with different spins selectively to opposite valleys. This topology of spin-valley-locked perovskites is believed to create possibilities for tunable laser emission. This approach can generate entangled photon pairs on-chip for use as a light source for topological lasers and is also expected to contribute to the realization of chiral light-emitting diodes [58].

_{3}waveguide (width: 150 nm; height: 300 nm), which are shown in the upper right section. The use of these resistors can lead to a significant improvement in the optical field quality factor and uniformity, which, according to the physical analysis, favours high-power and high-brightness laser applications. To achieve a higher optical field quality factor, it is necessary to optimise the resonator’s physical structure and material selection. In addition, the optical field uniformity can be improved by precisely controlling the resonator’s vibration modes. This study extends the research directions for non-Hermitian photonics in terms of nonlinear optics and topological photonics [61].

## 3. The Structure of Topological Lasers

_{Zak}), determined from the integration of the Berry connection within the first Brillouin zone. By suitably tuning the gap distance between the trivial and nontrivial parts of the PhC slab, a higher Q factor can be achieved. In addition, Figure 7b depicts the electric field distribution of the corresponding angular state, showing significant confinement in the nanoscale and resulting in strong light-matter interactions. This characteristic has promising applications like developing topological nanolasers. Figure 7c illustrates a one-dimensional SSH structure [42]. The structure consists of linear chains of dimer unit cells comprising of identical resonators (with resonance frequency ω

_{0}) having staggered nearest-neighbour coupling strengths. The capacitances used are C

_{1}= C

_{3}= ----- = C

_{odd}= C

_{A}and C

_{2}= C

_{4}= ----- = C

_{even}= C

_{B}(with C

_{A}being greater than C

_{B}). Figure 7d displays a one-dimensional non-Hermitian photonic lattice. It consists of 17 InGaAsP microrings (shown in red). Each microring consists of three microrings, exhibiting optical loss and gain, respectively [64]. The gain cavity comprises of an InGaAsP quantum well on an InP substrate, whereas the loss is realized by a layer of metal (Cr + Au) at the corresponding position.

_{3}lead halide perovskite nanocrystals (IPNCs). These lasers are characterised by a low excitation threshold of 9 µJ/cm

^{2}, a directional output with a beam dispersion of approximately 3.6 degrees, and exhibit good stability. In the same year, Huang’s group [7] at the University of Washington in the United States reported an ultra-low lasing threshold of 0.39 µJ/cm

^{2}. The research team created a VCSELs laser incorporating CSB-bBr

_{3}QDs in a thin film and two high-reflection distributed Bragg reflectors (DBRs). In 2023, Tian et al. from Nanyang Technological University in Singapore demonstrated a low-threshold single-mode laser emission with vertical emission. Their lithography-free, solution-processed and fully inorganic monolayer of lead halide perovskite quantum dots acted as an ultrathin gain medium. This experiment demonstrated the resilience of topological lasers to localised perturbations in multilayer structures. The cavity, as illustrated in Figure 8a, comprises an interface between two semi-infinite, one-dimensional binary photonic crystals, referred to as PC1 and PC2, where PC2 has inversion symmetry along the z-direction. The LI and HI present near the inversion centre display different Zak phases in the lowest optical band because of their varied positions (Figure 8b). The one-dimensional topological cavity consists of two 10-unit half-cavities positioned at the centre of the first optical bandgap. At approximately 515 nanometres, it exhibits a high-quality interface state with a Q-value above 5000. The transmission spectrum calculated is illustrated in Figure 8c, with the electric field heavily confined to the interface of the two photonic crystals (PCs). Moreover, the asymmetrical distribution reaches its peak within the first Hole-Injection (HI) layer of PC1, which is depicted in Figure 8d.

## 4. Applications and Prospects of Topological Lasers

^{6}. The topology cavity consists of a VPC waveguide closed loop (see Figure 10) with a Q of 0.2 × 10

^{6}, which is the first experimental proof of achieving ultra-high Q resonance at terahertz frequencies. In Figure 10a, the black and grey highlighted regions indicate the topologically distinct VPC domains formed by Type A and Type B unit cells, respectively. It is not difficult to see from Figure 10b,c that the peak frequencies of the two types of transmission intensities under low-power laser excitation are in good agreement.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Recent process summarizes in topological lasers. Schematic of the CsPbBr

_{3}Perovskite Quantum Dot Vertical Cavity Lasers, reproduced with permission from [7], copyright 2017, ACS Photonics. Laser mode in a topological cavity, reproduced with permission from [8], copyright 2018, Science. Schematic of the photonic crystal-based topological insulator, reproduced with permission from [9], copyright 2019, Nature Nanotechnology. Topological laser in a directional outcoupling configuration, reproduced with permission from [10], copyright 2020 Nature. Topological-cavity surface-emitting laser structure with the vertical-mode profile in green, reproduced with permission from [11], copyright 2022, Nature photonics. Illustration of the 2D perovskite lattice embedded between distributed Bragg reflectors (DBRs), reproduced with permission from [12], copyright 2023, Science Advances.

**Figure 3.**(

**a**) Electro-pump quantum cascade laser (QCL) based on photonic Majorana zero-mode (MZM), reproduced with permission from [54], copyright 2023, Nature Communications. (

**b**) Schematic representation of perovskite metasurfaces supporting spin-valley locking emission, reproduced with permission from [56], copyright 2023, Nature Materials.

**Figure 4.**(

**a**) Schematic representation of the laser formed by the pump mirror (PM) and the reflection type spatial light modulator (SLM). (

**b**) Phase modulation provided by SLM and combining with limited helical and concave phases. (

**c**) Phase modulation is provided by SLM and combines limited helical and concave phases, reproduced with permission from [59] copyright 2022, IEEE Photonics Journal.

**Figure 5.**On-chip integrated visible light micro-nano laser, reproduced with permission from [60], copyright 2023, Science Advances: (

**a**) Schematic of excitation of 400 nm optical pumped laser. (

**b**) Top view and 52° tilt scanning electron microscope (SEM) images of CsPbBr

_{3}microcavity coupling system (inset). (

**c**) The electric field distribution of the intrinsic mode of a topological laser system is obtained by simulating the intrinsic frequency (the radius of the microcavity is 1.5 μm).

**Figure 6.**Schematic structure diagram of the topological laser: (

**a**) A topological cavity of an arbitrary shape and an integration, reproduced with permission from [24], copyright 2017, Science. (

**b**) Geometry and laser patterns of topological insulator lasers based on the Haldane model, (

**A**) Cavity geometry (same for topological and trivial), (

**B**) The steady state topological lasing mode of the topological cavity, reproduced with permission from [8], copyright 2018, Science.

**Figure 7.**Structural diagram of the topological laser (The scale bar is 1µm): (

**a**) SEM image of a square two-dimensional topological PhC cavity. (

**b**) Topological angular electric field distribution, reproduced with permission from [63]. Copyright 2020, Light:Science & Applications. (

**c**) One-dimensional SSH structure consisting of linear chains of dimeric unit cells, reproduced with permission from [42], copyright 2019, Light:Science & Applications. (

**d**) A one-dimensional non-Hermitian photonic lattice composed of 17 InGaAsP microloops, reproduced with permission from [64], copyright 2023, Physical Review Letters.

**Figure 8.**Design principle of a 1D topological microcavity, reproduced with permission from 17, copyright 2023, Nature Communications: (

**a**) A 1D topological microcavity formed by two photonic crystals (PC1 and PC2) composed of high refractive index (HI) and low refractive index (LI) layers. (

**b**) Normalized electric field distribution of the first two optical bands along the z-axis within the respective cell. (

**c**)The high Q interface state appearing within the optical band gap; (

**d**) Spatial distribution of the electric field in the microcavity.

**Figure 9.**Application scenario of the topological laser: (

**a**) A schematic representation of the formation of a petal-shaped condensed pattern, reproduced with permission from [67], copyright 2023, ACS Photonic. (

**b**) Normalized electric field distribution of the first two optical bands along the z-axis within the respective cell, reproduced with permission from [68], copyright 2009, Nature. (

**c**) Integrated of resonant second-order nonlinear optical devices, reproduced with permission from [69], copyright 2022, Nature Communications.

**Figure 10.**All-optical control of a THz topological cavity-waveguide chip, reproduced with permission from [70], copyright 2022, Advanced Materials: (

**a**) Artistic illustration of a valley photonic crystal (VPC) cavity-waveguide chip on an all-silicon (Si) platform. A continuous laser with wavelength 532 nm (energy 2.33 eV) photoexcites the Si above the bandgap (1.1 eV). The inset shows the unit cell of the VPC, where a denotes the periodicity and h represents the height equal to 200 μm. The unit cell contains two triangular air holes of side lengths I

_{1}and I

_{2}. δ = I

_{2}− I

_{1}denotes the degree of asymmetry, with δ > 0 and δ < 0 corresponding to Type A and Type B VPCs (shaded in black and grey in the schematic). (

**b**) Schematic illustration of THz intensity modulation caused by photoexciting the domain wall of VPC cavity (The black, red and blue lines represent the transmission intensity when δ > 0, δ < 0 and δ = 0, respectively). (

**c**) Schematic representation of frequency agility of the topological cavity resonance upon high-power photoexcitation.

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## Share and Cite

**MDPI and ACS Style**

Wang, L.; Wu, L.; Pan, Y.
Perovskite Topological Lasers: A Brand New Combination. *Nanomaterials* **2024**, *14*, 28.
https://doi.org/10.3390/nano14010028

**AMA Style**

Wang L, Wu L, Pan Y.
Perovskite Topological Lasers: A Brand New Combination. *Nanomaterials*. 2024; 14(1):28.
https://doi.org/10.3390/nano14010028

**Chicago/Turabian Style**

Wang, Liangshen, Lijie Wu, and Yong Pan.
2024. "Perovskite Topological Lasers: A Brand New Combination" *Nanomaterials* 14, no. 1: 28.
https://doi.org/10.3390/nano14010028