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nnp:optics:optical_gain
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nnp:optics:optical_gain [2017/02/03 10:46] stefan.birner [Optical Gain] |
nnp:optics:optical_gain [2017/02/20 21:21] (current) stefan.birner |
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| In this tutorial we calculate the optical gain upon optical irradiation. | In this tutorial we calculate the optical gain upon optical irradiation. | ||
| The irradiation parameters are the | The irradiation parameters are the | ||
| - | * Photon energy of the irradiation | + | * photon energy of the irradiation and the |
| - | * Line width. | + | * 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, |
| \[ | \[ | ||
| - | R(E, w) = C_0(E) \int dE_a dE_b \gamma(E_a-E, w) \cdot H(E_a-E) \cdot [n(E_a) - p(E_b)] | + | R(E, w) = C_0(E) \int \gamma(E_a-E, w) \cdot H(E_a-E) \cdot [n(E_a) - p(E_b)] {\rm d}E_a {\rm d}E_b, |
| \] | \] | ||
| + | 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: | + | Here $C_0(E)$ is an energy dependent constant, |
| \[ | \[ | ||
| - | C_0 = \frac{\pi e^2 \hbar}{n_r c \epsilon_0 m_0^2 E} | + | C_0 = \frac{\pi e^2 \hbar}{n_{\rm r} c \epsilon_0 m_0^2 E}. |
| \] | \] | ||
| ====Input file structure==== | ====Input file structure==== | ||
| - | A new keyword has been introduced to handle an optical device, //opticaldevice{}// | + | A new keyword has been introduced to handle an optical device, ''opticaldevice{}''. |
| <code> | <code> | ||
| opticaldevice{ | opticaldevice{ | ||
| name = "quantum_region_name" | name = "quantum_region_name" | ||
| - | line_broadening = 1 #Line broadening model (1: Lorentzian) | + | line_broadening = 1 # Line broadening model (1: Lorentzian) |
| - | photon_energy = 1 #Photon energy in (eV) | + | photon_energy = 1.0 # Photon energy in (eV) |
| - | line_width = 1 #Line width in (eV) | + | line_width = 1.0 # Line width in (eV) |
| } | } | ||
| </code> | </code> | ||
| - | An in the run paragraph you have to also add //solve_optical_device{}// in order to include it the simulation flow. | + | The ''run'' keyword requires ''solve_optical_device{}'' to be included. |
| ==== Results ==== | ==== Results ==== | ||
| <figure> | <figure> | ||
| ;#; | ;#; | ||
| - | <dataplot xlabel="x(nm)" ylabel="1/s/m^3" ylegends="Gain"> | + | <dataplot xlabel="Position (nm)" ylabel="Gain (1/s/m^3)" ylegends="Gain" title="Optical gain"> |
| -90 0 | -90 0 | ||
| -85 0 | -85 0 | ||
nnp/optics/optical_gain.1486118781.txt.gz · Last modified: 2017/02/03 10:46 by stefan.birner
