User Tools

Site Tools


qcl:photon-assisted_transport_and_gain_clamping

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
qcl:photon-assisted_transport_and_gain_clamping [2020/11/19 15:56]
thomas.grange
qcl:photon-assisted_transport_and_gain_clamping [2022/03/30 17:19] (current)
thomas.grange
Line 2: Line 2:
  
 ==== Photon-assisted transport ==== ==== Photon-assisted transport ====
- 
-Photon-assisted transport can be considered 
  
 Photon-assisted transport can be modeled by considering electromagnetic (EM) modes at specific energies. Photon-assisted transport can be modeled by considering electromagnetic (EM) modes at specific energies.
Line 14: Line 12:
 </​code>​ </​code>​
  
-Note that in the current version (2020-11-16), only a single EM mode is supported at a time.+Note that in the current version (2022-03-30), only a single EM mode is supported at a time (i.e. multi-mode lasing operation is not supported).
  
 The electric field in this EM mode can be either imposed (detection mode) or calculated self-consistently (gain clamping). The electric field in this EM mode can be either imposed (detection mode) or calculated self-consistently (gain clamping).
Line 22: Line 20:
  
 The electric field can be set in the following way: The electric field can be set in the following way:
 +<​code>​
 <​EMfield>​ <​EMfield>​
 <​EMmode>​ <​EMmode>​
Line 27: Line 26:
 <​ElectricField unit="​V.m^-1">​1.0e6</​ElectricField>​ <​ElectricField unit="​V.m^-1">​1.0e6</​ElectricField>​
 </​EMmode>​ </​EMmode>​
 +</​EMfield>​
 +</​code>​
  
 === Relation to gain calculation === === Relation to gain calculation ===
 The gain feature calculates the linear response to an a.c. incoming field. In this case, the d.c. current is not modified. ​ The gain feature calculates the linear response to an a.c. incoming field. In this case, the d.c. current is not modified. ​
-On the other hand, the photon-assisted transport is modeled through the use of a self-energy to describe ​the influence of absorption and stimulated emission on d.c. transport. ​+On the other hand, the photon-assisted transport is modeled through the use of a self-energy ​(self-consistent Born approximation) ​to describe ​both absorption and stimulated emission ​processes, and has an influence ​on the d.c. transport. ​ 
 +In the case of the electron-photon self-energy,​ a gain is also calculated at the specified EM mode energy. However, the calculated gain slightly differ from the one calculated using linear response, even for small intensities,​ as broadening effects are not treated within the same level of approximations in the two cases. This is all the more the case when going to small photon energy (i.e. long wavelengths). Hence this method can produce unreliable results in terahertz devices where broadening effects are comparable to the photon energy. 
 + 
 +==== Gain clamping ==== 
 +Gain clamping is relevant to the simulation of quantum cascade lasers above threshold. Indeed, when the modal gain $g_c$ reaches the cavity losses, lasing starts and the gain is clamped to the cavity losses, that is  
 +$$ g_c = \alpha$$ 
 +The modal gain (or cross-section gain), is defined as 
 +$$ g_c = \Gamma g$$ 
 +where $g$ is the material gain in the active region and $\Gamma$ the overlap factor between the cavity mode and the active region. 
 + 
 +To simulate gain clamping, the following command should be used: 
 +<​code>​ 
 +    <​Gain>​ 
 +       ... 
 +       <​Cavity_Losses unit="​cm^{-1}">​2.76</​Cavity_Losses>​ 
 +       <​GainClamping>​yes</​GainClamping>​ 
 +       <​OverlapFactor>​0.9</​OverlapFactor>​ 
 +    </​Gain>​ 
 +</​code>​  
 +If not specified, the default value for the overlap factor $Gamma$ is assumed to be 1.0 (i.e. perfect overlap between the active region and the cavity mode). 
 + 
 +Note that in the case of gain clamping, the EM electric field value should be either not specified or set to zero: 
 +<​code>​ 
 +<​EMfield>​ 
 +<​EMmode>​ 
 +<​PhotonEnergy unit="​mV">​253.0</​PhotonEnergy>​ 
 +<​ElectricField unit="​V.m^-1">​0.0</​ElectricField>​ 
 +</​EMmode>​ 
 +</​code>​ 
 + 
 +Indeed, for gain clamping, ​ the electric field in the cavity is adjusted self-consistently so that the modal gain $g_c$ for this photon energy matches the specified cavity losses $\alpha$.  
 + 
 +=== Wall plug efficiency === 
 + 
 +The internal wall plug efficiency (WPE)  is calculated when gain clamping occurs. It is defined as 
 +$$ \eta_{\text{WPE}}^{internal} = \frac{P_{\text{stimulated emission}} - P_{\text{absorption}}}{UI} $$ 
 + 
 +If the front mirror losses are specified, the external WPE is output as 
 + 
 +$$ \eta_{\text{WPE}}^{external} = \eta_{\text{WPE}}^{internal} \frac{\alpha_{\text{fm}}}{\alpha_{\text{cavity}}}$$ 
 +where $\alpha_{\text{fm}}$ is the front mirror losses, which can be defined using the command: 
 +<​code>​ 
 +    <​Gain>​ 
 +       ... 
 +       <​Cavity_Losses unit="​cm^{-1}">​2.76</​Cavity_Losses>​ 
 +       <​FrontMirror_Losses unit="​cm^{-1}">​2.26</​FrontMirror_Losses>​ 
 +       ... 
 +    </​Gain>​ 
 +</​code>​ 
 + 
 +Note that the relation between the specified cavity losses and the front mirror one reads  
 +$$ \alpha_{\text{cavity}} =  \alpha_{\text{fm}} + \alpha_{\text{bm}} + \alpha_{\text{waveguide}} $$ 
 +where $\alpha_{\text{bm}}$ are the losses due to the back mirror and  $\alpha_{\text{waveguide}}$ are the waveguide losses. 
  
-=== Gain clamping ​=== +=== Example: Mid-infrared QCL  ​===
-Gain clamping is relevant to +
  
 +The following animated gifs show the electron density, current density and output as the voltage is swept. Above the threshold bias (around 300 meV), the clamping of the gain to the cavity losses results a rapid increase in the internal electric field in the cavity. The photon-assisted transport results in a discontinuity in the slope of the current-voltage characteristics at the threshold bias/​current:​ above threshold, the current increases much faster as stimulated emission reduces the upper laser level lifetime.
 +{{:​negf:​bai2011_electrondensity.gif?​direct&​600|}}
 +{{:​negf:​bai2011_current.gif?​direct&​600|}}
 +{{:​negf:​bai2011_emission.gif?​direct&​600|}}
qcl/photon-assisted_transport_and_gain_clamping.1605801393.txt.gz · Last modified: 2020/11/19 15:56 by thomas.grange