Results
Analytically calculates the Purcell factor and far-field emission power density for a multilayer stack. For more information on the theory behind this approach, see Stack dipole half-space example. The usage for this command is very similar to stackdipole, but the result returned in this case is a struct that contains the following datasets. The power_density is functions of the emission angle \( \theta \) measured from the surface normal (see above image).
| Result | Description |
|---|---|
| power |
Power [normalized] Attribute: purcell_factor. This is the total power of a monochromatic dipole at the specified position and emission frequency divided by the power that it would radiate in a homogeneous medium. Parameters: dipole/z, f/lambda |
| density |
Power [normalized/steradian] Attributes: upward, downward, upward_into_air, downward_into_air. This is the power density per unit solid angle, as function of far field emission angle, also normalized to the power that would radiate in a homogeneous medium. Parameters: theta, dipole/z, f/lambda |
For more information on the theory behind this approach, see Stack dipole half-space example. Additional discussion on the results can be found at STACK GUI - OLED Device Introduction.
Usage
|
Syntax |
Description |
|---|---|
|
result = stackpurcell(n,d,f,z,orientation,res) |
Analytically calculates the Purcell factor and far-field emission power density of a multi-layer stack
|
|
result = stackpurcell(n,d,f,z,options) |
|
Parameter |
Default value |
Type |
Description |
|
|---|---|---|---|---|
|
n |
required |
vector |
n: Refractive index of each layer. Size can be
|
|
|
d |
required |
vector |
Thickness of each layer. Size is N_layers. |
|
|
f |
required |
vector |
Frequency vector. |
|
|
z |
required |
vector |
Position of the dipoles (0 is the bottom of the stack). Size is N_dipoles, and dipoles must be located within boundaries. |
|
|
orientation |
optional |
"rand" |
cell of strings |
Orientation of the dipoles. Accepts string or cell array as 'orientation' argument with values:
Size is N_dipoles. |
|
res |
optional |
1000 |
number |
The resolution for far-field emission angle. |
|
options |
optional |
|
struct |
In 2021R1.1 and later: This struct can be used to pass optional arguments. Passing this struct allows users to specify the following parameters: "orientation": defines orientation of the dipole. "res"/"theta": defines the output angles explicitly, instead of simply resolution. To specify the angles pass them as a vector "theta" in degrees [0,90). "incoherent_propagation": a vector argument defines the coherent and incoherent layers of the stack with 0 = coherent propagation and 1 = incoherent propagation. The dipole cannot be located in an incoherent layer. If using options then all optional arguments, must be passed through the struct. |
Example
Explore the effect of the dipole position on the angular distribution of the far-field emission:
### Use stackpurcell to explore the position of dipole in a multilayer stack
# frequency range
N_freq = 101;
lambda = linspace(380e-9,780e-9,N_freq); # 380nm to 780nm
f = c/lambda;
# Intialize multilayer geometry
n = matrix(5,N_freq);
d = matrix(5,1);
#Define optical and geometric layer propertie
n(1,1:N_freq) = getfdtdindex("Al (Aluminium) - Palik",f,f(1),f(N_freq)); d(1) = 0; # bottom substrate
# Note: this reads the material properties from FDTD material database. If you are using another product, please enter (n,k) explicitly
n(2,1:N_freq) = 1.85; d(2) = 60e-9;
n(3,1:N_freq) = 1.9; d(3) = 220e-9;
n(4,1:N_freq) = 1.8; d(4) = 120e-9;
n(5,1:N_freq) = 1.53; d(5) = 0; # top substrate (glass)
# dipole positions/orientations
N_dipole= 51; # number of dipoles
z = linspace( d(2)+1e-10, d(2)+d(3)+1e-10, N_dipole ); # consider positions only within middle dielectric layer
orientation = cell(N_dipole); # consider only randomly oriented dipoles
for(ii = 1:N_dipole){
orientation{ii} = "rand";}
# angular_res: resolution for emission angle (farfield angle)
res = 198;
result = stackpurcell(n,d,f,z,orientation,res); # result is a struct
# plot Purcell factor for dipole located at the middle of the layer
purcell = pinch(result.power.purcell_factor); # size is Ndipole by Nfreqs
plot(lambda*1e9, pinch(purcell,1,round(N_dipole/2)),'wavelength (nm)','Purcell factor');
# plot far field power density at center frequency
theta = pinch(result.density.theta);
density = pinch(result.density.upward_into_air); # size is res by Ndipole by Nfreqs
image(theta, z*1e+9, pinch(density,3,round(N_freq/2)), "far-field angle (degrees)", "dipole position (nm)", num2str(f(round(N_freq/2))*1e-12)+"THz into Air");
# In 2020R1.2
incoherent_propagation = [0, 0, 1, 0, 0];
options={ "res": 1000, "orientation": 'rand',"incoherent_propagation":incoherent_propagation};
stackpurcell(n,d,f,z,options);
#or
options={ "theta": linspace(0,45,100) , "orientation": 'vert', "incoherent_propagation":incoherent_propagation};
stackpurcell(n,d,f,z,options);
See Also
Stack optical solver overview, stackrt, stackfield, stackdipole, Stack dipole half-space, OLED slab mode analysis