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nnp:optics:optical_gain [2017/01/13 15:52]
zoltan.jehn [Physics model] 		nnp:optics:optical_gain [2017/02/20 21:21] (current)
stefan.birner
Line 1: Line 1:
 ===== Optical Gain ===== ===== Optical Gain =====
  
-In this tutorial we present how can be calculated ​the generated carriers ​upon optical irradiation. +In this tutorial we calculate ​the optical gain upon optical irradiation. 
-The irradiation parameters are the //poynting vector magnitude//,​ //Mid energy of the irradiation//,  //​Line ​width//. +The irradiation parameters are the 
 +  * photon ​energy of the irradiation ​and the 
 +  * line width.
  
 ==== Physics model ==== ==== Physics model ====
-The transition rate per volume element can be expressed with the following sum:+The transition rate per volume element can be expressed with the following sum,
 \[ \[
-R = R_{ab} - R_{ba} = \frac{2}{V} \sum_{k_a} \sum_{k_b} \frac{2 \pi}{ \hbar} |H_{ba}| ^2 \delta(E_b - E_a -\hbar \omega)(f_a-f_b)+R = R_{ab} - R_{ba} = \frac{2}{V} \sum_{k_a} \sum_{k_b} \frac{2 \pi}{ \hbar} |H_{ba}| ^2 \delta(E_b - E_a -\hbar \omega)(f_a-f_b).
 \] \]
  
-In order to make evaluate the sum much faster we calculate the $H_{ba}$ matrix element at $k_a = 0; k_b = 0$(Remark: $k_a = k_b$), and we neglect the k dependence of it.  +In order to evaluate the sum much faster we calculate the $H_{ba}$ matrix element at $k_a = 0; k_b = 0$ (Remark: $k_a = k_b$), and we neglect the $k$ dependence of it.  
-Then we can simplify the sum in the following form, if the irradiation has the $\gamma(E, w)$ broadening function, where $E$ is the irradiation energy, and $w$ is the line width.  +Then we can simplify the sum as follows, 
 \[ \[
-R(E, w) = C $\abs(S)$ \int dE_a dE_b \gamma(E_a-E,​ w) \cdot  H(E_a-E) \cdot  [n(E_a) - p(E_b)]+R(E, w) = C_0(E)   ​\int \gamma(E_a-E,​ w) \cdot  H(E_a-E) \cdot  [n(E_a) - p(E_b)] ​ {\rm d}E_a {\rm d}E_b,
 \] \]
 +where $E$ is the irradiation energy, $w$ is the line width and we assume that the irradiation has the $\gamma(E, w)$ broadening function.
 +
 +Here $C_0(E)$ is an energy dependent constant,
 +\[
 +C_0 = \frac{\pi e^2 \hbar}{n_{\rm r} c \epsilon_0 m_0^2 E}.
 +\] 
 +
 +====Input file structure====
 +
 +A new keyword has been introduced to handle an optical device, ''​opticaldevice{}''​.
 +
 +<​code>​
 +opticaldevice{
 + name = "​quantum_region_name"​
 + line_broadening = 1            # Line broadening model (1: Lorentzian)
 + photon_energy ​  = 1.0          # Photon energy in (eV)
 + line_width ​     = 1.0          # Line width in (eV)
 +}
 +</​code>​
 +
 +The ''​run''​ keyword requires ''​solve_optical_device{}''​ to be included.
 +
 +==== Results ====
 +<​figure>​
 +;#;
 +<​dataplot xlabel="​Position (nm)" ylabel="​Gain (1/​s/​m^3)"​ ylegends="​Gain"​ title="​Optical gain">​
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 +18.6 -3.5003561751546e+19
 +18.8 -3.0300488588568e+19
 +19 -2.6223807117976e+19
 +19.2 -2.2690544089663e+19
 +19.4 -1.9628659487142e+19
 +19.6 -1.6961955102625e+19
 +19.8 -1.4656114287649e+19
 +20 -1.2658397369305e+19
 +20.2 -1.0927282739712e+19
 +20.4 -9.427031756854e+18
 +20.6 -8.1267083787815e+18
 +20.8 -6.9994908302834e+18
 +21 -6.0221157590868e+18
 +21.2 -5.1744001865334e+18
 +21.4 -4.4388309649028e+18
 +21.6 -3.8002096783317e+18
 +21.8 -3.2453448999777e+18
 +22 -2.7627852351459e+18
 +22.2 -2.3425876263364e+18
 +22.4 -1.9761162018976e+18
 +22.6 -1.6558676068944e+18
 +22.8 -1.3753193061654e+18
 +23 -1.1287978193544e+18
 +23.2 -9.113642512659e+17
 +23.4 -7.1871482913277e+17
 +23.6 -5.4709445964235e+17
 +23.8 -3.9322157958407e+17
 +24 -2.5422280031622e+17
 +24.2 -1.2757604260063e+17
 +24.4 -1.1061028709922e+16
 +24.6 9.7283853509352e+16
 +24.8 1.9919917181501e+17
 +25 2.9623730223796e+17
 +25.2 3.8979116362588e+17
 +25.4 4.8111940197526e+17
 +25.6 5.7136852213701e+17
 +25.8 6.6159240563072e+17
 +26 7.5276960619019e+17
 +26.2 8.4581878128761e+17
 +26.4 9.4161260395087e+17
 +26.6 1.0409905192217e+18
 +26.8 1.144770801328e+18
 +27 1.2537626372951e+18
 +27.2 1.3687797494775e+18
 +27.4 1.4906596701e+18
 +27.6 1.6203036970485e+18
 +27.8 1.7588245451379e+18
 +28 1.9097926805291e+18
 +28.2 2.0636970928785e+18
 +28.4 2.2290417373803e+18
 +28.6 2.4067177327278e+18
 +28.8 2.5976767637574e+18
 +29 2.8029360983978e+18
 +29.2 3.0235838842453e+18
 +29.4 3.2607847549977e+18
 +29.6 3.5157857777756e+18
 +29.8 3.7899227733835e+18
 +30 4.0846270428074e+18
 +30.2 4.4014325347038e+18
 +30.4 4.7419834903108e+18
 +30.6 5.108042604099e+18
 +30.8 5.5014997405852e+18
 +31 5.9243812500567e+18
 +31.2 6.3788599285036e+18
 +31.4 6.8672656698409e+18
 +31.6 7.3920968615231e+18
 +31.8 7.9560325779303e+18
 +32 8.5619456294403e+18
 +32.2 9.2129165289105e+18
 +32.4 9.9122484413969e+18
 +32.6 1.0663483187338e+19
 +32.8 1.1470418374159e+19
 +33 1.2337125736316e+19
 +33.2 1.3267970769228e+19
 +33.4 1.4267633748348e+19
 +33.6 1.5341132230841e+19
 +33.8 1.6493845143954e+19
 +34 1.7731538571306e+19
 +34.2 2.6102791190001e+19
 +34.4 3.3680495518877e+19
 +34.6 4.024204778331e+19
 +34.8 4.6696724981377e+19
 +35 5.33136060908e+19
 +35.2 6.0229591063294e+19
 +35.4 6.7535868495545e+19
 +35.6 7.5304381313219e+19
 +35.8 8.3598455211246e+19
 +36 9.2477871435918e+19
 +36.2 1.0200162143131e+20
 +36.4 1.1222957371972e+20
 +36.6 1.2322358640242e+20
 +36.8 1.3504832055503e+20
 +37 1.4777188663989e+20
 +37.2 1.6146639690226e+20
 +37.4 1.7620846638476e+20
 +37.6 1.9207968878743e+20
 +37.8 2.0916710412647e+20
 +38 2.2756366970928e+20
 +38.2 2.4736874266337e+20
 +38.4 2.6868858023301e+20
 +38.6 2.9163686279086e+20
 +38.8 3.1633524371456e+20
 +39 3.4291392978122e+20
 +39.2 3.7151229543081e+20
 +39.4 4.0227953407972e+20
 +39.6 4.353753495855e+20
 +39.8 4.7097069094669e+20
 +40 5.0924853334973e+20
 +40.2 5.5040470873577e+20
 +40.4 5.9464878914527e+20
 +40.6 6.422050262013e+20
 +40.8 6.9331335020914e+20
 +41 7.4823043247572e+20
 +41.2 8.072308145859e+20
 +41.4 8.7060810850942e+20
 +41.6 9.3867627155149e+20
 +41.8 1.0117709602979e+21
 +42 1.090250967841e+21
 +42.2 1.1744997487008e+21
 +42.4 1.2649270359773e+21
 +42.6 1.3619705553773e+21
 +42.8 1.4660978408522e+21
 +43 1.5778081566558e+21
 +43.2 1.6976345306828e+21
 +43.4 1.8261459039646e+21
 +43.6 1.9639494011887e+21
 +43.8 2.1116927270492e+21
 +44 2.2700666931334e+21
 +44.2 2.4398078798886e+21
 +44.4 2.6217014379889e+21
 +44.6 2.8165840331219e+21
 +44.8 3.0253469378291e+21
 +45 3.2489392735562e+21
 +45.2 3.4883714054732e+21
 +45.4 3.7447184919127e+21
 +45.6 4.0191241894243e+21
 +45.8 4.3128045134315e+21
 +46 4.627051853305e+21
 +46.2 4.9632391393008e+21
 +46.4 5.3228241572359e+21
 +46.6 5.7073540049833e+21
 +46.8 6.1184696828197e+21
 +47 6.5579108073587e+21
 +47.2 7.0275204362099e+21
 +47.4 7.5292499876199e+21
 +47.6 8.0651642361429e+21
 +47.8 8.6374463618553e+21
 +48 9.2484030267551e+21
 +48.2 9.900469447759e+21
 +48.4 1.0596214431143e+22
 +48.6 1.1338345328351e+22
 +48.8 1.2129712867856e+22
 +49 1.2973315812189e+22
 +49.2 1.3872305383423e+22
 +49.4 1.4829989394338e+22
 +49.6 1.5849836016214e+22
 +49.8 1.6935477107901e+22
 +50 9.0503277327804e+21
 +50.2 0
 +50.4 0
 +50.6 0
 +50.8 0
 +51 0
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 +51.6 0
 +51.8 0
 +52 0
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 +52.8 0
 +53 0
 +53.2 0
 +53.4 0
 +53.6 0
 +53.8 0
 +54 0
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 +54.8 0
 +55 0
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 +56 0
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 +57 0
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 +58 0
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 +59 0
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 +59.4 0
 +59.6 0
 +59.8 0
 +60 0
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 +61 0
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 +62 0
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 +63 0
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 +64 0
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 +64.6 0
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 +65 0
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 +65.6 0
 +65.8 0
 +66 0
 +66.2 0
 +66.4 0
 +66.6 0
 +66.8 0
 +67 0
 +67.2 0
 +67.4 0
 +67.6 0
 +67.8 0
 +68 0
 +68.2 0
 +68.4 0
 +68.6 0
 +68.8 0
 +69 0
 +69.2 0
 +69.4 0
 +69.6 0
 +69.8 0
 +70 0
 +75 0
 +80 0
 +85 0
 +90 0
 +
 +</​dataplot>​
 +;#;
 +</​figure>​
  
-Here C is an energy independent constant. and $S$ is the magnitude of the Poynting vector. ​ 
nnp/optics/optical_gain.1484322727.txt.gz · Last modified: 2017/01/13 15:52 by zoltan.jehn

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