Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Annual Meeting Optical Society of America

Limitations of two-level models in semiconductor gain media

Murray Sargent

Published Jan 1, 1992• 0 citations
Publisher

Abstract

Many papers on semiconductor gain media have presented models for two-level homogeneously and inhomogeneously broadened media. In this paper, we show why and where these models become inadequate. The problems originate from the fact that the two-band semiconductor gain medium is an inhomogeneously broadened four-level medium with rapid cross relaxation due to carrier-carrier scattering, and all four levels have appreciable probability in gain media. The four states are given by |n e n h k s>, where n e (= 0 or 1) and n h (= 0 or 1) are the number of electrons or holes, respectively, for momentum k and spin s. The two-level system is a one-electron system with no states corresponding to the partially excited semiconductor states |0 e 1 h k> and |l e 0 h k>, which involve two electrons. The Pauli exclusion principle never gets a chance to enter the picture. In the absence of many-body effects, semiconductor gain can be fitted in an ad hoc fashion by a two-level model, but problems that involve the level probabilities individually, such as the laser photon statistics, elude a two-level description.

DOI
10.1364/oam.1992.ff5

Related papers

Two-level description of gain and mixing susceptibilities in amplifying semiconductor materials

Bruno J. Thedrez, A. Jones, Robert Frey

Optical-intensity-dependent gain and mixing susceptibilities of amplifying semiconductor materials have been calculated using the density-matrix approach. The model, which takes intraband relaxation and carrier-injection rate into account, allows for numerical computation of these susceptibilities, whatever the medium saturation is. As a simplification, an equivalent two-level system is derived which represents the gain and nearly degenerate four-wave mixing susceptibilities. Such an equivalence, which leads to the same field-induced polarization as the conventional rate equation model, also connects the two-level (or rate equation) parameters to the real characteristics of the semiconductor material.>

IEEE Journal of Quantum Electronics•Aug 1, 1988•18 citations

Steady-state ab initio laser theory for complex gain media

Alexander Cerjan, Y. D. Chong, A. Douglas Stone

We derive and test a generalization of the steady-state ab initio laser theory (SALT) to treat complex gain media. The generalized theory (C-SALT) is able to treat atomic and molecular gain media with diffusion and multiple lasing transitions, and semiconductor gain media in the free carrier approximation including fully the effect of Pauli blocking. The key assumption of the theory is stationarity of the level populations, which leads to coupled self-consistent equations for the populations and the lasing modes that fully include the effects of openness and non-linear spatial hole-burning. These equations can be solved efficiently for the steady-state lasing properties by a similar iteration procedure as in SALT, where a static gain medium with a single transition is assumed. The theory is tested by comparison to much less efficient finite difference time domain (FDTD) methods and excellent agreement is found. Using C-SALT to analyze the effects of varying gain diffusion constant we demonstrate a cross-over between the regime of strong spatial hole burning with multimode lasing to a regime of negligible spatial hole burning, leading to gain-clamping, and single mode lasing. The effect of spatially inhomogeneous pumping combined with diffusion is also studied and a relevant length scale for spatial inhomogeneity to persist under these conditions is determined. For the semiconductor gain model, we demonstrate the frequency shift due to Pauli blocking as the pumping strength changes.

arXiv:1406.6659•Optics Express•Mar 2, 2015•35 citations

Modeling a Bandwidth of a Two-Level Independent Quantum Laser System States

Cliff Orori Mosiori

An electromagnetic radiation is basically considered to be a transverse wave propagating through an accessible media whether it is an optical fibre or a thin film depending on its propagating conditions. In analyzing its propagation, utilized specific cross-section areas have become an important base of understanding its extinction parameters. The term cross-section in this work applies only to boundary conditions within which particles interact within electromagnetic spectra through absorption or scattering. In such small volume contextual framework, nanotechnology reconsiders scattering cross-section coefficients. In this work, two different degenerate states were modeled and analyzed using a developed model of a laser cavity containing a media of length, L, with a gain of, k, per unit length which were mirrored to represent the upper and a lower level manifolds inhomogeneous broadening Stark levels respectively. The model developed created an impression that a laser medium is a coherent ensemble of particles or atoms whose bandwidth depends on how a laser is constructed .

Path of Science•Dec 18, 2017•0 citations

Collisional-cross-relaxation effects in amplified-spontaneous-emission lasers

G. J. Pert

The role of collisional cross relaxation in saturated laser amplification is considered by using a simple strong-collisional model. Expressions for the particle-state density distribution and gain are derived for a four-level system. These are reduced to a simple analytic form, subject to an approximation of wide applicability. The role of collisions in changing an inhomogeneous-broadened line to homogeneous, with a change from rebroadening to narrowing on saturation, is demonstrated. The results are shown to be consistent with the existing limited experimental data.

Physical Review A•Nov 1, 1994•12 citations

On correctness of the two-level model for description of active medium in quantum plasmonics

Eugeny D. Chubchev, E S Andrianov, A A Pukhov +2 more

Abstract In order to simplify the theoretical description of spasers, a gain medium is commonly represented by a two-level system (TLS). A realistic model, however, should have four levels. By using the Lindblad equations we develop a description of such a system and show that depending on ratios of the Rabi frequency and the rate of relaxation of the polarization, a four-level system (FLS) may be reduced to one of two effective TLSs that reproduce the key properties of a FLS.

arXiv:1612.01231•Journal of Physics B Atomic Molecular and Optical Physics•Aug 2, 2017•6 citations

Pump-scheme dependence of few-emitter lasers: exact multilevel correlations and photon statistics

Stephan Hartmann

Few-emitter laser models usually replace the excitation cycle of the gain medium by a single Markovian pump jump of a two-level emitter. We test this replacement with the cavity and laser-transition parameters held fixed and the two-level pump rate fitted to the same mean photon number, using an exact damping-basis continued-fraction solution of the cavity--emitter master equation for $N$ identical $d$-level emitters with arbitrary independent incoherent transitions and one cavity-coupled transition, in the known reduced space of level populations and lasing coherences. First, a pump-quantum filtration shows that the inter-emitter coherence of $Λ$ and ladder media starts at second rather than first order in the pump; we evaluate its leading coefficient from the exact finite-system series and map the recycling rate at which its sign changes. Second, at matched photon number, rate-limited steps in the pump cycle push the long-time output-counting Fano factor of two and three emitters well below one: for two emitters it reaches 0.66 at a mean cavity occupation of 0.3 and is still 0.74 at an occupation of one, where $g^{(2)}(0)$ is within 3% of unity, because the anticorrelation sits at delays of about half a cavity lifetime rather than at zero delay. For two and three emitters the fitted two-level model gets both statistics wrong and places the output above the shot-noise level. Against independent single-emitter lasers at the same output, the common cavity erodes rather than enhances this single-emitter effect.

quant-pharXiv:2611.01205•Nov 3, 2026
Many papers on semiconductor gain media have presented models for two-level homogeneously and inhomogeneously broadened media. In this paper, we show why and where these models become inadequate. The problems originate from the fact that the two-band semiconductor gain medium is an inhomogeneously broadened four-level medium with rapid cross relaxation due to carrier-carrier scattering, and all four levels have appreciable probability in gain media. The four states are given by |n e n h k s>, where n e (= 0 or 1) and n h (= 0 or 1) are the number of electrons or holes, respectively, for momentum k and spin s. The two-level system is a one-electron system with no states corresponding to the partially excited semiconductor states |0 e 1 h k> and |l e 0 h k>, which involve two electrons. The Pauli exclusion principle never gets a chance to enter the picture. In the absence of many-body effects, semiconductor gain can be fitted in an ad hoc fashion by a two-level model, but problems that involve the level probabilities individually, such as the laser photon statistics, elude a two-level description.
Optical-intensity-dependent gain and mixing susceptibilities of amplifying semiconductor materials have been calculated using the density-matrix approach. The model, which takes intraband relaxation and carrier-injection rate into account, allows for numerical computation of these susceptibilities, whatever the medium saturation is. As a simplification, an equivalent two-level system is derived which represents the gain and nearly degenerate four-wave mixing susceptibilities. Such an equivalence, which leads to the same field-induced polarization as the conventional rate equation model, also connects the two-level (or rate equation) parameters to the real characteristics of the semiconductor material.>
We derive and test a generalization of the steady-state ab initio laser theory (SALT) to treat complex gain media. The generalized theory (C-SALT) is able to treat atomic and molecular gain media with diffusion and multiple lasing transitions, and semiconductor gain media in the free carrier approximation including fully the effect of Pauli blocking. The key assumption of the theory is stationarity of the level populations, which leads to coupled self-consistent equations for the populations and the lasing modes that fully include the effects of openness and non-linear spatial hole-burning. These equations can be solved efficiently for the steady-state lasing properties by a similar iteration procedure as in SALT, where a static gain medium with a single transition is assumed. The theory is tested by comparison to much less efficient finite difference time domain (FDTD) methods and excellent agreement is found. Using C-SALT to analyze the effects of varying gain diffusion constant we demonstrate a cross-over between the regime of strong spatial hole burning with multimode lasing to a regime of negligible spatial hole burning, leading to gain-clamping, and single mode lasing. The effect of spatially inhomogeneous pumping combined with diffusion is also studied and a relevant length scale for spatial inhomogeneity to persist under these conditions is determined. For the semiconductor gain model, we demonstrate the frequency shift due to Pauli blocking as the pumping strength changes.
An electromagnetic radiation is basically considered to be a transverse wave propagating through an accessible media whether it is an optical fibre or a thin film depending on its propagating conditions. In analyzing its propagation, utilized specific cross-section areas have become an important base of understanding its extinction parameters. The term cross-section in this work applies only to boundary conditions within which particles interact within electromagnetic spectra through absorption or scattering. In such small volume contextual framework, nanotechnology reconsiders scattering cross-section coefficients. In this work, two different degenerate states were modeled and analyzed using a developed model of a laser cavity containing a media of length, L, with a gain of, k, per unit length which were mirrored to represent the upper and a lower level manifolds inhomogeneous broadening Stark levels respectively. The model developed created an impression that a laser medium is a coherent ensemble of particles or atoms whose bandwidth depends on how a laser is constructed .
The role of collisional cross relaxation in saturated laser amplification is considered by using a simple strong-collisional model. Expressions for the particle-state density distribution and gain are derived for a four-level system. These are reduced to a simple analytic form, subject to an approximation of wide applicability. The role of collisions in changing an inhomogeneous-broadened line to homogeneous, with a change from rebroadening to narrowing on saturation, is demonstrated. The results are shown to be consistent with the existing limited experimental data.
Few-emitter laser models usually replace the excitation cycle of the gain medium by a single Markovian pump jump of a two-level emitter. We test this replacement with the cavity and laser-transition parameters held fixed and the two-level pump rate fitted to the same mean photon number, using an exact damping-basis continued-fraction solution of the cavity--emitter master equation for NNN identical ddd-level emitters with arbitrary independent incoherent transitions and one cavity-coupled transition, in the known reduced space of level populations and lasing coherences. First, a pump-quantum filtration shows that the inter-emitter coherence of ΛΛΛ and ladder media starts at second rather than first order in the pump; we evaluate its leading coefficient from the exact finite-system series and map the recycling rate at which its sign changes. Second, at matched photon number, rate-limited steps in the pump cycle push the long-time output-counting Fano factor of two and three emitters well below one: for two emitters it reaches 0.66 at a mean cavity occupation of 0.3 and is still 0.74 at an occupation of one, where g(2)(0)g^{(2)}(0)g(2)(0) is within 3% of unity, because the anticorrelation sits at delays of about half a cavity lifetime rather than at zero delay. For two and three emitters the fitted two-level model gets both statistics wrong and places the output above the shot-noise level. Against independent single-emitter lasers at the same output, the common cavity erodes rather than enhances this single-emitter effect.