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qcl:photon-assisted_transport_and_gain_clamping [2020/11/19 15:56]
thomas.grange
qcl:photon-assisted_transport_and_gain_clamping [2020/11/20 14:14] (current)
thomas.grange
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 ==== 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.
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 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>​
 +</​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 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 gain surpasses the cavity losses, lasing starts and the gain is clamped to the cavity losses. 
 + 
 +To simulate gain clamping, the following command should be used: 
 +<​code>​ 
 +    <​Gain>​ 
 +       ... 
 +       <​Cavity_Losses unit="​cm^{-1}">​2.76</​Cavity_Losses>​ 
 +       <​GainClamping>​yes</​GainClamping>​ 
 +    </​Gain>​ 
 +</​code>​  
 +Note that in this case, the EM electric field should be set to zero: 
 +<​code>​ 
 +<​EMfield>​ 
 +<​EMmode>​ 
 +<​PhotonEnergy unit="​mV">​253.0</​PhotonEnergy>​ 
 +<​ElectricField unit="​V.m^-1">​0.0</​ElectricField>​ 
 +</​EMmode>​ 
 +</​code>​ 
 + 
 +In this case, the electric field in the cavity is adjusted self-consistently so that the gain for this photon energy matchs the specified cavity 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