Properties of nanolasers based on few discrete emitters

Anders Mølbjerg Lund, Per Kær Nielsen, Michael Lorke, Bjarne Tromborg, Jesper Mørk

Research output: Chapter in Book/Report/Conference proceedingConference abstract in proceedingsResearchpeer-review

Abstract

The laser has evolved from table size apparatuses to truly nano sized devices, in much the same way that computer chips have been continuously minimized. The few-emitter nanolaser represents an extreme in terms of size. The emitters can be either atoms or quantum dots, and they are coupled to a high-Q optical cavity. This system has previously been studied for the one and two emitters case, see e.g. [1, 2]. The emitters and cavity are modelled as two-level systems and a harmonic oscillator, respectively. The coupled system is modelled using the Jaynes-Cummings Hamiltonian and the two-level systems are pumped incoherently by a rate P. Solutions are found using the corresponding master equation. However, with cavity populations exceeding 100 and several emitters, the dimension of the Hilbert space of the system becomes too large to handle efficiently on a conventional computer. E.g. for four emitters and 100 photon states the density matrix has more than 2.5 × 106 elements.
We have been able to simplify the problem significantly by adiabatically eliminating the photon-assisted polarizations and the correlations between emitters and cavity [3]. This results in a set of rate equations for the population of the cavity, na, and the occupation of the emitters. Fig. 1a) shows na for up to 4 emitters coupled to a cavity, as a function of the pumping rate P. The figure also shows results from a full master equation solution, and the correspondence is very good for large values of P. In Fig. 1b) the second order correlation functions g(2)(0) are shown, as obtained using the full model. The second order correlation functions become 1 for sufficiently large values of P signifying the onset of lasing. However, for larger values of P the laser quenches and the emission becomes chaotic (g(2)(0) = 2). This quenching effect is well-known in two-level models [3], but might not be realistic for semiconductor quantum dots.
A proposed application for these nanolasers is in on-chip optical interconnects. In this application the modulation bandwidth is important. We have calculated the modulation bandwidth using a small-signal analysis of the rate equations, which has the advantage compared the full model of yielding a semianalytical result. The results are shown in Fig. 1c). The nanolaser has a high bandwidth, which is mostly limited by the cavity lifetime (/ 1/), but shows a prominent drop during the lasing regime. The modulation bandwidth again becomes limited by as the output becomes chaotic.
Original languageEnglish
Title of host publication11th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors
Number of pages1
Publication date2012
Pages89
Publication statusPublished - 2012
Event11th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors (NOEKS) - University of Stuttgart, Stuttgart, Germany
Duration: 23 Sep 201227 Sep 2012
http://www.uni-stuttgart.de/noeks11

Conference

Conference11th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors (NOEKS)
LocationUniversity of Stuttgart
CountryGermany
CityStuttgart
Period23/09/201227/09/2012
Internet address

Bibliographical note

Poster presentation P35.

Cite this

Lund, A. M., Nielsen, P. K., Lorke, M., Tromborg, B., & Mørk, J. (2012). Properties of nanolasers based on few discrete emitters. In 11th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors (pp. 89)
Lund, Anders Mølbjerg ; Nielsen, Per Kær ; Lorke, Michael ; Tromborg, Bjarne ; Mørk, Jesper. / Properties of nanolasers based on few discrete emitters. 11th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors. 2012. pp. 89
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Lund, AM, Nielsen, PK, Lorke, M, Tromborg, B & Mørk, J 2012, Properties of nanolasers based on few discrete emitters. in 11th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors. pp. 89, 11th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors (NOEKS), Stuttgart, Germany, 23/09/2012.

Properties of nanolasers based on few discrete emitters. / Lund, Anders Mølbjerg; Nielsen, Per Kær; Lorke, Michael; Tromborg, Bjarne; Mørk, Jesper.

11th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors. 2012. p. 89.

Research output: Chapter in Book/Report/Conference proceedingConference abstract in proceedingsResearchpeer-review

TY - ABST

T1 - Properties of nanolasers based on few discrete emitters

AU - Lund, Anders Mølbjerg

AU - Nielsen, Per Kær

AU - Lorke, Michael

AU - Tromborg, Bjarne

AU - Mørk, Jesper

N1 - Poster presentation P35.

PY - 2012

Y1 - 2012

N2 - The laser has evolved from table size apparatuses to truly nano sized devices, in much the same way that computer chips have been continuously minimized. The few-emitter nanolaser represents an extreme in terms of size. The emitters can be either atoms or quantum dots, and they are coupled to a high-Q optical cavity. This system has previously been studied for the one and two emitters case, see e.g. [1, 2]. The emitters and cavity are modelled as two-level systems and a harmonic oscillator, respectively. The coupled system is modelled using the Jaynes-Cummings Hamiltonian and the two-level systems are pumped incoherently by a rate P. Solutions are found using the corresponding master equation. However, with cavity populations exceeding 100 and several emitters, the dimension of the Hilbert space of the system becomes too large to handle efficiently on a conventional computer. E.g. for four emitters and 100 photon states the density matrix has more than 2.5 × 106 elements.We have been able to simplify the problem significantly by adiabatically eliminating the photon-assisted polarizations and the correlations between emitters and cavity [3]. This results in a set of rate equations for the population of the cavity, na, and the occupation of the emitters. Fig. 1a) shows na for up to 4 emitters coupled to a cavity, as a function of the pumping rate P. The figure also shows results from a full master equation solution, and the correspondence is very good for large values of P. In Fig. 1b) the second order correlation functions g(2)(0) are shown, as obtained using the full model. The second order correlation functions become 1 for sufficiently large values of P signifying the onset of lasing. However, for larger values of P the laser quenches and the emission becomes chaotic (g(2)(0) = 2). This quenching effect is well-known in two-level models [3], but might not be realistic for semiconductor quantum dots.A proposed application for these nanolasers is in on-chip optical interconnects. In this application the modulation bandwidth is important. We have calculated the modulation bandwidth using a small-signal analysis of the rate equations, which has the advantage compared the full model of yielding a semianalytical result. The results are shown in Fig. 1c). The nanolaser has a high bandwidth, which is mostly limited by the cavity lifetime (/ 1/), but shows a prominent drop during the lasing regime. The modulation bandwidth again becomes limited by as the output becomes chaotic.

AB - The laser has evolved from table size apparatuses to truly nano sized devices, in much the same way that computer chips have been continuously minimized. The few-emitter nanolaser represents an extreme in terms of size. The emitters can be either atoms or quantum dots, and they are coupled to a high-Q optical cavity. This system has previously been studied for the one and two emitters case, see e.g. [1, 2]. The emitters and cavity are modelled as two-level systems and a harmonic oscillator, respectively. The coupled system is modelled using the Jaynes-Cummings Hamiltonian and the two-level systems are pumped incoherently by a rate P. Solutions are found using the corresponding master equation. However, with cavity populations exceeding 100 and several emitters, the dimension of the Hilbert space of the system becomes too large to handle efficiently on a conventional computer. E.g. for four emitters and 100 photon states the density matrix has more than 2.5 × 106 elements.We have been able to simplify the problem significantly by adiabatically eliminating the photon-assisted polarizations and the correlations between emitters and cavity [3]. This results in a set of rate equations for the population of the cavity, na, and the occupation of the emitters. Fig. 1a) shows na for up to 4 emitters coupled to a cavity, as a function of the pumping rate P. The figure also shows results from a full master equation solution, and the correspondence is very good for large values of P. In Fig. 1b) the second order correlation functions g(2)(0) are shown, as obtained using the full model. The second order correlation functions become 1 for sufficiently large values of P signifying the onset of lasing. However, for larger values of P the laser quenches and the emission becomes chaotic (g(2)(0) = 2). This quenching effect is well-known in two-level models [3], but might not be realistic for semiconductor quantum dots.A proposed application for these nanolasers is in on-chip optical interconnects. In this application the modulation bandwidth is important. We have calculated the modulation bandwidth using a small-signal analysis of the rate equations, which has the advantage compared the full model of yielding a semianalytical result. The results are shown in Fig. 1c). The nanolaser has a high bandwidth, which is mostly limited by the cavity lifetime (/ 1/), but shows a prominent drop during the lasing regime. The modulation bandwidth again becomes limited by as the output becomes chaotic.

M3 - Conference abstract in proceedings

SP - 89

BT - 11th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors

ER -

Lund AM, Nielsen PK, Lorke M, Tromborg B, Mørk J. Properties of nanolasers based on few discrete emitters. In 11th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors. 2012. p. 89