# Non-Linear Optical Properties of Biexciton in Ellipsoidal Quantum Dot

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## Abstract

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## 1. Introduction

## 2. Exciton and Biexciton States

## 3. Non-Linear Properties

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- Nasilowski, M.; Spinicelli, P.; Patriarche, G.; Dubertret, B. Gradient CdSe/CdS quantum dots with room temperature biexciton unity quantum yield. Nano Lett.
**2015**, 15, 3953–3958. [Google Scholar] [CrossRef] [PubMed] - Chen, G.; Stievater, T.H.; Batteh, E.T.; Li, X.; Steel, D.G.; Gammon, D.; Katzer, D.S.; Park, D.; Sham, L.J. Biexciton quantum coherence in a single quantum dot. Phys. Rev. Lett.
**2002**, 88, 117901. [Google Scholar] [CrossRef] [PubMed] - Bleyan, Y.Y.; Hayrapetyan, D.B. Magnetobiexciton in strongly oblate ellipsoidal quantum dot. Phys. B Cond. Matt.
**2022**, 632, 413725. [Google Scholar] [CrossRef] - Reiter, D.E.; Kuhn, T.; Glässl, M.; Axt, V.M. The role of phonons for exciton and biexciton generation in an optically driven quantum dot. J. Phys. Condens. Matter
**2014**, 26, 423203. [Google Scholar] [CrossRef] [Green Version] - Bacher, G.; Weigand, R.; Seufert, J.; Kulakovskii, V.D.; Gippius, N.A.; Forchel, A.; Leonardi, K.; Hommel, D. Biexciton versus exciton lifetime in a single semiconductor quantum dot. Phys. Rev. Lett.
**1999**, 83, 4417. [Google Scholar] [CrossRef] [Green Version] - Hayrapetyan, D.B.; Bleyan, Y.Y.; Baghdasaryan, D.A.; Sarkisyan, H.A.; Baskoutas, S.; Kazaryan, E.M. Biexciton, negative and positive trions in strongly oblate ellipsoidal quantum dot. Phys. E Low-Dimens. Syst. Nanostruct.
**2019**, 105, 47–55. [Google Scholar] [CrossRef] - Villas-Bôas, J.M.; Ulloa, S.E.; Govorov, A.O. Decoherence of Rabi oscillations in a single quantum dot. Phys. Rev. Lett.
**2005**, 94, 057404. [Google Scholar] [CrossRef] [Green Version] - Le Gall, C.; Brunetti, A.; Boukari, H.; Besombes, L. Optical Stark effect and dressed exciton states in a Mn-doped CdTe quantum dot. Phys. Rev. Lett.
**2011**, 107, 057401. [Google Scholar] [CrossRef] [Green Version] - Baskoutas, S.; Terzis, A.F. Biexciton luminescence in InAs nanorods. J. Appl. Phys.
**2005**, 98, 044309. [Google Scholar] [CrossRef] - Wang, H.; Shah, J.; Damen, T.C.; Pfeiffer, L.N. Polarization-dependent coherent nonlinear optical response in GaAs quantum wells: Dominant effects of two-photon coherence between ground and biexciton states. Solid State Commun.
**1994**, 91, 869–874. [Google Scholar] [CrossRef] - Takagahara, T. Biexciton states in semiconductor quantum dots and their nonlinear optical properties. Phys. Rev. B
**1989**, 39, 10206. [Google Scholar] [CrossRef] [PubMed] - Brunner, K.; Abstreiter, G.; Böhm, G.; Tränkle, G.; Weimann, G. Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure. Phys. Rev. Lett.
**1994**, 73, 1138. [Google Scholar] [CrossRef] [PubMed] - Hawrylak, P.; Narvaez, G.A.; Bayer, M.; Forchel, A. Excitonic absorption in a quantum dot. Phys. Rev. Lett.
**2000**, 85, 389. [Google Scholar] [CrossRef] [PubMed] - Hours, J.; Senellart, P.; Peter, E.; Cavanna, A.; Bloch, J. Exciton radiative lifetime controlled by the lateral confinement energy in a single quantum dot. Phys. Rev. B
**2005**, 71, 161306. [Google Scholar] [CrossRef] - Finley, J.J.; Fry, P.W.; Ashmore, A.D.; Lemaître, A.; Tartakovskii, A.I.; Oulton, R.; Mowbray, D.J.; Skolnick, M.S.; Hopkinson, M.; Buckle, P.D.; et al. Observation of multicharged excitons and biexcitons in a single InGaAs quantum dot. Phys. Rev. B
**2001**, 63, 161305. [Google Scholar] [CrossRef] - Kang, K.I.; Kepner, A.D.; Gaponenko, S.V.; Koch, S.W.; Hu, Y.Z.; Peyghambarian, N. Confinement-enhanced biexciton binding energy in semiconductor quantum dots. Phys. Rev. B
**1993**, 48, 15449. [Google Scholar] [CrossRef] - Smponias, A.; Stefanatos, D.; Paspalakis, E. Efficient biexciton preparation in a quantum dot—metal nanoparticle system using on-off pulses. Nanomaterials
**2021**, 11, 1859. [Google Scholar] [CrossRef] - Renard, J.; Songmuang, R.; Bougerol, C.; Daudin, B.; Gayral, B. Exciton and biexciton luminescence from single GaN/AlN quantum dots in nanowires. Nano Lett.
**2008**, 8, 2092–2096. [Google Scholar] [CrossRef] - Muller, A.; Fang, W.; Lawall, J.; Solomon, G.S. Emission spectrum of a dressed exciton-biexciton complex in a semiconductor quantum dot. Phys. Rev. Lett.
**2008**, 101, 027401. [Google Scholar] [CrossRef] [Green Version] - Kamada, H.; Ando, H.; Temmyo, J.; Tamamura, T. Excited-state optical transitions of excitons and biexcitons in a single In x Ga 1− x As quantum disk. Phys. Rev. B
**1998**, 58, 16243. [Google Scholar] [CrossRef] - Hanamura, E. Giant two-photon absorption due to excitonic molecule. Solid State Commun.
**1993**, 88, 1073–1075. [Google Scholar] [CrossRef] - Abram, I. Nonlinear-optical properties of biexcitons: Single-beam propagation. Phys. Rev. B
**1983**, 28, 4433. [Google Scholar] [CrossRef] - Lenihan, A.S.; Dutt, M.G.; Steel, D.G.; Ghosh, S.; Bhattacharya, P. Biexcitonic resonance in the nonlinear optical response of an InAs quantum dot ensemble. Phys. Rev. B
**2004**, 69, 045306. [Google Scholar] [CrossRef] - Shojaei, S.; Asgari, A.; Kalafi, M. Nonlinear optical properties of biexciton states in GaN quantum disks. Eur. Phys. J. B
**2009**, 72, 211–216. [Google Scholar] [CrossRef] - Xie, W. Optical absorptions of a biexciton quantum dot. Phys. B Condens. Matter
**2012**, 407, 2329–2333. [Google Scholar] [CrossRef] - Shojaei, S. Biexciton induced refractive index changes in a semiconductor quantum dot. Superlattices Microstruct.
**2015**, 82, 357–367. [Google Scholar] [CrossRef] - Sarkisyan, H.A. Direct optical absorption in cylindrical quantum dot. Mod. Phys. Lett. B
**2004**, 18, 443–452. [Google Scholar] [CrossRef] - Niculescu, E.C.; Bejan, D. Nonlinear optical properties of GaAs pyramidal quantum dots: Effects of elliptically polarized radiation, impurity, and magnetic applied fields. Phys. E Low-Dimens. Syst. Nanostructures
**2015**, 74, 51–58. [Google Scholar] [CrossRef] - Dvoyan, K.G.; Hayrapetyan, D.B.; Kazaryan, E.M.; Tshantshapanyan, A.A. Electron states and light absorption in strongly oblate and strongly prolate ellipsoidal quantum dots in presence of electrical and magnetic fields. Nanoscale Res. Lett.
**2007**, 2, 601–608. [Google Scholar] [CrossRef] [Green Version] - Hayrapetyan, D.B.; Dvoyan, K.G.; Kazaryan, E.M. Direct interband light absorption in a strongly oblated ellipsoidal quantum dot. J. Contemp. Phys.
**2007**, 42, 151–157. [Google Scholar] [CrossRef] - Hayrapetyan, D.B.; Kazaryan, E.M.; Sarkisyan, H.A. Implementation of Kohn’s theorem for the ellipsoidal quantum dot in the presence of external magnetic field. Phys. E Low-Dimens. Syst. Nanostructures
**2016**, 75, 353–357. [Google Scholar] [CrossRef] - Sarkisyan, H.A.; Hayrapetyan, D.B.; Petrosyan, L.S.; Kazaryan, E.M.; Sofronov, A.N.; Balagula, R.M.; Firsov, D.A.; Vorobjev, L.E.; Tonkikh, A.A. Realization of the Kohn’s theorem in Ge/Si quantum dots with hole gas: Theory and experiment. Nanomaterials
**2019**, 9, 56. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Griffiths, D.J.; Schroeter, D.F. Introduction to Quantum Mechanics; Cambridge University Press: Cambridge, UK, 2018. [Google Scholar]
- Glushkov, A.V.; Ivanov, L.N. Radiation decay of atomic states: Atomic residue polarization and gauge noninvariant contributions. Phys. Lett. A
**1992**, 170, 33–36. [Google Scholar] [CrossRef] - Akimoto, O.; Hanamura, E. Excitonic molecule. I. Calculation of the binding energy. J. Phys. Soc. Jpn.
**1972**, 33, 1537–1544. [Google Scholar] [CrossRef] - Masumoto, Y.; Takagahara, T. Semiconductor Quantum Dots; Springer: Berlin/Heidelberg, Germany, 2002. [Google Scholar]
- Boyd, R.W. Nonlinear Optics, 3rd ed.; Academic Press, Inc.: New York, NY, USA, 2008. [Google Scholar]
- Rosencher, E.; Vinter, B. Optoelectronics; Cambridge University Press: Cambridge, UK, 2002. [Google Scholar]

**Figure 1.**The energy diagram for the biexciton of ground and excited states for different sets of geometrical parameters.

**Figure 2.**The transition diagram for the biexciton, exciton, and ground states. The geometrical parameters of the ellipsoidal QD have been chosen as follows: $c=5\mathrm{nm}$ and $a=50\mathrm{nm}$.

**Figure 3.**The real and imaginary parts of the susceptibility of ground and excited levels (

**a**) around one-photon resonance at $\omega ={\omega}_{eg}$, (

**b**) around one-photon resonance at $\omega ={\omega}_{be}$, and (

**c**) around two-photon resonance at $\omega ={\omega}_{bg}$; (

**d**) the dependence of the real and imaginary parts of the total susceptibility on the photon energy.

**Figure 4.**The real and imaginary parts of the susceptibility for ground levels for different small semiaxis (

**a**) around one-photon resonance at $\omega ={\omega}_{eg}$, (

**b**) around one-photon resonance at $\omega ={\omega}_{be}$, and (

**c**) around two-photon resonance at $\omega ={\omega}_{bg}$; (

**d**) the dependence of the real and imaginary parts of the total susceptibility on the photon energy.

**Figure 5.**The absorption of ground and excited levels (

**a**) around one-photon resonance at $\omega ={\omega}_{eg}$, (

**b**) around one-photon resonance at, $\omega ={\omega}_{be}$, and (

**c**) around two-photon resonance at $\omega ={\omega}_{bg}$; (

**d**) the dependence of the total absorption on the photon energy.

**Figure 6.**The absorption coefficient for ground levels for different small semiaxis (

**a**) around one-photon resonance at $\omega ={\omega}_{eg}$, (

**b**) around one-photon resonance at, $\omega ={\omega}_{be}$, and (

**c**) around two-photon resonance at $\omega ={\omega}_{bg}$; (

**d**) the dependence of the total absorption on the photon energy.

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**MDPI and ACS Style**

Bleyan, Y.Y.; Mantashyan, P.A.; Kazaryan, E.M.; Sarkisyan, H.A.; Accorsi, G.; Baskoutas, S.; Hayrapetyan, D.B.
Non-Linear Optical Properties of Biexciton in Ellipsoidal Quantum Dot. *Nanomaterials* **2022**, *12*, 1412.
https://doi.org/10.3390/nano12091412

**AMA Style**

Bleyan YY, Mantashyan PA, Kazaryan EM, Sarkisyan HA, Accorsi G, Baskoutas S, Hayrapetyan DB.
Non-Linear Optical Properties of Biexciton in Ellipsoidal Quantum Dot. *Nanomaterials*. 2022; 12(9):1412.
https://doi.org/10.3390/nano12091412

**Chicago/Turabian Style**

Bleyan, Yuri Y., Paytsar A. Mantashyan, Eduard M. Kazaryan, Hayk A. Sarkisyan, Gianluca Accorsi, Sotirios Baskoutas, and David B. Hayrapetyan.
2022. "Non-Linear Optical Properties of Biexciton in Ellipsoidal Quantum Dot" *Nanomaterials* 12, no. 9: 1412.
https://doi.org/10.3390/nano12091412