- Open Access
Threshold behavior in quantum-dot nanolasers: Effects of inhomogeneous broadening
Phys. Rev. A 112, 063521 – Published 11 December, 2025
DOI: https://doi.org/10.1103/m9px-p28x
Abstract
We investigate the threshold behavior of lasers under various modeling approaches, considering different numbers of nonlasing cavity modes and analyzing the effects of radiation-matter coupling strength, cavity lifetime, and quantum-dot properties. Thermal and electron-electron decoherence are incorporated as phenomenological relaxation processes, in line with established practices. Both spectrally uniform and polydisperse quantum dots are examined. For the former, we observe strong agreement across modeling approaches: the qualitative behavior remains consistent, with threshold pump values showing quantitative shifts depending on the specific model. In the case of polydisperse quantum dots, leading to inhomogeneous broadening, this picture is reaffirmed—each model type exhibits similar qualitative trends, while threshold variations arise due to the stochastic distribution of emitter transition frequencies. Our results confirm that models that assume homogeneous quantum dots are suitable for comparison with experimental data and that inhomogeneous effects can be directly captured using our framework when required.
Physics Subject Headings (PhySH)
Article Text
References (73)
- A. L. Efros and M. Rosen, The electronic structure of semiconductor nanocrystals, Annu. Rev. Mater. Sci. 30, 475 (2000).
- M. Lorke, F. Jahnke, and W. Chow, Excitation dependences of gain and carrier-induced refractive index change in quantum-dot lasers, Appl. Phys. Lett. 90, 051112 (2007).
- H. Deng, G. L. Lippi, J. Mørk, J. Wiersig, and S. Reitzenstein, Physics and applications of high- micro-and nanolasers, Adv. Opt. Mater. 9, 2100415 (2021).
- D. Bimberg, Semiconductor nanostructures for flying q-bits and green photonics, Nanophotonics 7, 1245 (2018).
- R. Soref, Tutorial: Integrated-photonic switching structures, Apl Photon. 3, 021101 (2018).
- C.-Z. Ning, Semiconductor nanolasers and the size-energy-efficiency challenge: A review, Adv. Photon. 1, 014002 (2019).
- J. R. Orchard, C. Woodhead, S. Shutts, J. Wu, A. Sobiesierski, R. J. Young, R. Beanland, H. Liu, P. M. Smowton, and D. J. Mowbray, Analysing radiative and non-radiative recombination in InAs QDs on Si for integrated laser applications, in Quantum Dots and Nanostructures: Growth, Characterization, and Modeling XIII, SPIE Proceedings Vol. 9758 (SPIE, Bellingham, WA, 2016), pp. 18–24.
- C. R. Fitch, A. Baltušis, I. P. Marko, D. Jung, J. C. Norman, J. E. Bowers, and S. J. Sweeney, Carrier recombination properties of low-threshold quantum dot lasers on silicon, IEEE J. Sel. Top. Quantum Electron. 28, 1 (2021).
- P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoglu, Laser emission from quantum dots in microdisk structures, Appl. Phys. Lett. 77, 184 (2000).
- V. I. Klimov, Semiconductor and Metal Nanocrystals: Synthesis and Electronic and Optical Properties (CRC, Boca Raton, FL, 2003).
- A. F. Phillips, S. J. Sweeney, A. R. Adams, and P. J. Thijs, The temperature dependence of 1.3 and compressively strained inGaAs (P) MQW semiconductor lasers, IEEE J. Sel. Top. Quantum Electron. 5, 401 (1999).
- N. Massé, I. Marko, A. Adams, and S. Sweeney, Temperature insensitive quantum dot lasers: Are we really there yet? J. Mater. Sci.: Mater. Electron. 20, 272 (2009).
- Y. Arakawa and H. Sakaki, Multidimensional quantum well laser and temperature dependence of its threshold current, Appl. Phys. Lett. 40, 939 (1982).
- Q. Gong, R. Nötzel, P. Van Veldhoven, T. Eijkemans, and J. Wolter, Wavelength tuning of InAs quantum dots grown on InP (100) by chemical-beam epitaxy, Appl. Phys. Lett. 84, 275 (2004).
- S. Anantathanasarn, R. Nötzel, P. Van Veldhoven, F. Van Otten, Y. Barbarin, G. Servanton, T. de Vries, E. Smalbrugge, E. Geluk, T. Eijkemans et al., Lasing of wavelength-tunable ( region) InAs/InGa AsP/InP (100) quantum dots grown by metal organic vapor-phase epitaxy, Appl. Phys. Lett. 89, 073115 (2006).
- S. E. White and M. A. Cataluna, Unlocking spectral versatility from broadly-tunable quantum-dot lasers, Photonics 2, 719 (2015).
- S. Strauf and F. Jahnke, Single quantum dot nanolaser, Laser Photon. Rev. 5, 607 (2011).
- K. J. Vahala, Optical microcavities, Nature (London) 424, 839 (2003).
- L. Feng, R. El-Ganainy, and L. Ge, Non-Hermitian photonics based on parity–time symmetry, Nat. Photon. 11, 752 (2017).
- K. Takata and M. Notomi, Photonic topological insulating phase induced solely by gain and loss, Phys. Rev. Lett. 121, 213902 (2018).
- K. Takata, K. Nozaki, E. Kuramochi, S. Matsuo, K. Takeda, T. Fujii, S. Kita, A. Shinya, and M. Notomi, Observing exceptional point degeneracy of radiation with electrically pumped photonic crystal coupled-nanocavity lasers, Optica 8, 184 (2021).
- F. Hentinger, M. Hedir, B. Garbin, M. Marconi, L. Ge, F. Raineri, J. A. Levenson, and A. M. Yacomotti, Direct observation of zero modes in a non-Hermitian optical nanocavity array, Photon. Res. 10, 574 (2022).
- A. Fischer, T. V. Raziman, W. K. Ng, J. Clarysse, D. Saxena, J. Dranczewski, S. Vezzoli, H. Schmid, K. Moselund, and R. Sapienza, Controlling lasing around exceptional points in coupled nanolasers, npj Nanophoton. 1, 6 (2024).
- C. B. Murray, C. R. Kagan, and M. G. Bawendi, Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies, Annu. Rev. Mater. Sci. 30, 545 (2000).
- W. Langbein, J. M. Hvam, M. Umlauff, H. Kalt, B. Jobst, and D. Hommel, Binding-energy distribution and dephasing of localized biexcitons, Phys. Rev. B 55, R7383 (1997).
- W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, Radiatively limited dephasing in InAs quantum dots, Phys. Rev. B 70, 033301 (2004).
- F. Jahnke, C. Gies, M. Aßmann, M. Bayer, H. Leymann, A. Foerster, J. Wiersig, C. Schneider, M. Kamp, and S. Höfling, Giant photon bunching, superradiant pulse emission and excitation trapping in quantum-dot nanolasers, Nat. Commun. 7, 11540 (2016).
- J. Hendrickson, B. C. Richards, J. Sweet, S. Mosor, C. Christenson, D. Lam, G. Khitrova, H. M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, Quantum dot photonic-crystal-slab nanocavities: Quality factors and lasing, Phys. Rev. B 72, 193303 (2005).
- A. P. Alivisatos, Semiconductor clusters, nanocrystals, and quantum dots, Science 271, 933 (1996).
- V. I. Klimov, A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, A. C. Leatherdale, H.-J. Eisler, and M. Bawendi, Optical gain and stimulated emission in nanocrystal quantum dots, Science 290, 314 (2000).
- M. Nirmal and L. Brus, Luminescence photophysics in semiconductor nanocrystals, Acc. Chem. Res. 32, 407 (1999).
- P. Reiss, M. Protiere, and L. Li, Core/shell semiconductor nanocrystals, Small 5, 154 (2009).
- Z. Yang, M. Pelton, I. Fedin, D. V. Talapin, and E. Waks, A room temperature continuous-wave nanolaser using colloidal quantum wells, Nat. Commun. 8, 143 (2017).
- M. Grundmann, The present status of quantum dot lasers, Physica E 5, 167 (1999).
- M. Sugawara, K. Mukai, Y. Nakata, H. Ishikawa, and A. Sakamoto, Effect of homogeneous broadening of optical gain on lasing spectra in self-assembled quantum dot lasers, Phys. Rev. B 61, 7595 (2000).
- M. Sugawara, N. Hatori, H. Ebe, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, Modeling room-temperature lasing spectra of self-assembled InAs/GaAs quantum-dot lasers: Homogeneous broadening of optical gain under current injection, J. Appl. Phys. 97, 043523 (2005).
- K. M. Cha, I. Horiuchi, K. Shibata, and K. Hirakawa, Size-limiting effect of site-controlled InAs quantum dots grown at high temperatures by molecular beam epitaxy, Appl. Phys. Express 5, 085501 (2012).
- H. Lan and Y. Ding, Ordering, positioning and uniformity of quantum dot arrays, Nano Today 7, 94 (2012).
- M. Felici, P. Gallo, A. Mohan, B. Dwir, A. Rudra, and E. Kapon, Site-controlled inGaAs quantum dots with tunable emission energy, Small 5, 938 (2009).
- C. Schneider, S. Höfling, and M. Kamp, In(Ga)As/GaAs site-controlled quantum dots with tailored morphology and high optical quality, Phys. Status Solidi A 209, 2379 (2012).
- A. Kaganskiy, F. Gericke, T. Heuser, T. Heindel, X. Porte, and S. Reitzenstein, Micropillars with a controlled number of site-controlled quantum dots, Appl. Phys. Lett. 112, 071101 (2018).
- J. Große, M. von Helversen, A. Koulas-Simos, M. Hermann, and S. Reitzenstein, Development of site-controlled quantum dot arrays acting as scalable sources of indistinguishable photons, APL Photon. 5, 096107 (2020).
- X. Zhao, W. Liu, Y. Bao, X. Chen, C. Ji, G. Yang, B. Wei, F. Yang, and X. Wang, Site-controlled growth of In(Ga)As/GaAs quantum dots on patterned substrate, Nanotechnology 36, 052001 (2025).
- M. Podhorský, M. Klonz, I. Limame, S. Tripathi, K. Gaur, C. C. Palekar, P. Mudi, P. Klenovský, S. Rodt, and S. Reitzenstein, Site-controlled growth of inGaAs quantum dots based on buried stressors for the development of microlasers and quantum light sources, J. Phys.: Conf. Ser. 2931, 012016 (2024).
- C.-W. Shih, I. Limame, C. C. Palekar, A. Koulas-Simos, A. Kaganskiy, P. Klenovský, and S. Reitzenstein, Self-aligned photonic defect microcavity lasers with site-controlled quantum dots, Laser Photon. Rev. 18, 2301242 (2024).
- V. Khatri, V. Sichkovskyi, L. Popilevsky, Y. Kauffmann, G. Eisenstein, and J. P. Reithmaier, Increased modal gain in quantum dot lasers based on improved size homogeneity obtained by comprehensive growth optimization, ACS Photon. 12, 3687 (2025).
- C. Shen, W. Zhan, K. Xin, M. Li, Z. Sun, H. Cong, C. Xu, J. Tang, Z. Wu, B. Xu et al., Machine-learning-assisted and real-time-feedback-controlled growth of InAs/GaAs quantum dots, Nat. Commun. 15, 2724 (2024).
- A. Kaganskiy, S. Kreinberg, X. Porte, and S. Reitzenstein, Micropillar lasers with site-controlled quantum dots as active medium, Optica 6, 404 (2019).
- A. Abdollahinia, S. Banyoudeh, A. Rippien, F. Schnabel, O. Eyal, I. Cestier, I. Kalifa, E. Mentovich, G. Eisenstein, and J. Reithmaier, Temperature stability of static and dynamic properties of quantum dot lasers, Opt. Express 26, 6056 (2018).
- M. Bayer, F. Weidner, A. Larionov, A. McDonald, A. Forchel, and T. L. Reinecke, Inhibition and enhancement of the spontaneous emission of quantum dots in structured microresonators, Phys. Rev. Lett. 86, 3168 (2001).
- M. Lodde, R. P. van Veldhoven, E. Verhagen, and A. Fiore, The effect of In(Ga)As/GaAs quantum dots on the optical loss of photonic crystal cavities, J. Appl. Phys. 135, 063103 (2024).
- P. Harrison and A. Valavanis, Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures (Wiley, New York, 2016).
- S. Sapra and D. D. Sarma, Evolution of the electronic structure with size in II-VI semiconductor nanocrystals, Phys. Rev. B 69, 125304 (2004).
- I. E. Protsenko and A. V. Uskov, Perturbation approach in Heisenberg equations for lasers, Phys. Rev. A 105, 053713 (2022).
- A. M. Yacomotti, Z. Denis, A. Biella, and C. Ciuti, Quantum density matrix theory for a laser without adiabatic elimination of the population inversion: Transition to lasing in the class-b limit, Laser Photon. Rev. 17, 2200377 (2023).
- A. A. Vyshnevyy, Gain-dependent Purcell enhancement, breakdown of Einstein's relations, and superradiance in nanolasers, Phys. Rev. B 105, 085116 (2022).
- J. Fricke, Transport equations including many-particle correlations for an arbitrary quantum system: A general formalism, Ann. Phys. (NY) 252, 479 (1996).
- W. Chow and F. Jahnke, On the physics of semiconductor quantum dots for applications in lasers and quantum optics, Prog. Quantum Electron. 37, 109 (2013).
- W. Chow, F. Jahnke, and C. Gies, Emission properties of nanolasers during the transition to lasing, Light Sci. Appl. 3, e201 (2014).
- S. Kreinberg, W. W. Chow, J. Wolters, C. Schneider, C. Gies, F. Jahnke, S. Höfling, M. Kamp, and S. Reitzenstein, Emission from quantum-dot high-ß microcavities: Transition from spontaneous emission to lasing and the effects of superradiant emitter coupling, Light Sci. Appl. 6, e17030 (2017).
- C. Gies, J. Wiersig, M. Lorke, and F. Jahnke, Semiconductor model for quantum-dot-based microcavity lasers, Phys. Rev. A 75, 013803 (2007).
- M. A. Carroll, G. D'Alessandro, G. L. Lippi, G.-L. Oppo, and F. Papoff, Thermal, quantum antibunching and lasing thresholds from single emitters to macroscopic devices, Phys. Rev. Lett. 126, 063902 (2021).
- M. Carroll, G. D'Alessandro, G. Lippi, G.-L. Oppo, and F. Papoff, Photon-number squeezing in nano- and microlasers, Appl. Phys. Lett. 119, 101102 (2021).
- J.-S. Tempel, I. Akimov, M. Aßmann, C. Schneider, S. Höfling, C. Kistner, S. Reitzenstein, L. Worschech, A. Forchel, and M. Bayer, Extrapolation of the intensity autocorrelation function of a quantum-dot micropillar laser into the thermal emission regime, J. Opt. Soc. Am. B 28, 1404 (2011).
- M. A. Carroll, G. D'Alessandro, G. L. Lippi, G.-L. Oppo, and F. Papoff, Coherence buildup and laser thresholds from nanolasers to macroscopic lasers, Phys. Rev. A 107, 063710 (2023).
- F. Papoff, M. A. Carroll, G. L. Lippi, G.-L. Oppo, and G. D'Alessandro, Quantum correlations, mixed states, and bistability at the onset of lasing, Phys. Rev. A 111, L011501 (2025).
- M. A. Carroll, G. D'Alessandro, G. L. Lippi, G.-L. Oppo, and F. Papoff, Carroll reply: Thermal, quantum antibunching and lasing thresholds from single emitters to macroscopic devices, Phys. Rev. Lett. 128, 029402 (2022).
- N. Baer, C. Gies, J. Wiersig, and F. Jahnke, Luminescence of a semiconductor quantum dot system, Eur. Phys. J. B 50, 411 (2006).
- M. Kira and S.W. Koch, Semiconductor Quantum Optics (Cambridge University, New York, 2011).
- M. Florian, C. Gies, F. Jahnke, H. A. M. Leymann, and J. Wiersig, Equation-of-motion technique for finite-size quantum-dot systems: Cluster expansion method, Phys. Rev. B 87, 165306 (2013).
- M. Schwab, H. Kurtze, T. Auer, T. Berstermann, M. Bayer, J. Wiersig, N. Baer, C. Gies, F. Jahnke, J. P. Reithmaier, A. Forchel, M. Benyoucef, and P. Michler, Radiative emission dynamics of quantum dots in a single cavity micropillar, Phys. Rev. B 74, 045323 (2006).
- M. Saldutti, Y. Yu, and J. Mørk, The onset of lasing in semiconductor nanolasers, Laser Photon. Rev. 18, 2300840 (2024).
- G. D'Alessandro, G.L. Lippi, and F. Papoff, QD lasers GitHub site, https://github.com/giampaolo314/QD_laser_models.