This function analytically calculates the dipole emission properties of an unpatterned multilayer stack. For structures that can be reduced to 1D this is technique is much more efficient than running fully vectorial simulations with FDTD.
For more information on the theory behind this approach, see Stack dipole half-space example. The radiance is calculated via the equation. Results returned are the luminescence \( (cd/m^2) \) and radiance \( (W/steradian/m^2) \) as a function of emission angle, as well as the corresponding X, Y, Z tri-stimulus values, assuming current density of 1 \( A/m^2\). The CIE 1931 color functions [1] are used for calculating X, Y, Z.
$$
\text {stackdipole}(\theta)=\int_{\lambda}(j \times e f \times st) \left(\frac{r d \times F_{r a d}(\theta, \lambda)}{r d \times F(\lambda)+(1-r d)}\right) \left(\text {photon probability}(\lambda) \times E_{ph}(\lambda)\right) d \lambda
$$
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NOTE: Stackdipole is a component of the STACK product, and requires a STACK license. To run the command, you will also need access to any of Lumerical's products that have a GUI. STACK is most frequently used with FDTD, but this command can also be called from Lumerical's other products. In 2021R1.1 the length of the results from stack dipole may have changed. Previously singleton dimensions were reduced before output. If you have updated and run into problems you may need to pinch the results yourself. |
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Syntax |
Description |
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dipole_emission = stackdipole(n,d,f,z,dipole_spec, orientation,res,direction, ef,st,rd); |
Analytically calculates the dipole emission properties of a multi-layer stack
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dipole_emission = stackdipole(n,d,f,z,dipole_spec, options); |
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Parameter |
Default value |
Type |
Description |
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|---|---|---|---|---|
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n |
required |
vector |
n: Refractive index of each layer. Size can be
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d |
required |
vector |
Thickness of each layer. Size is N_layers. |
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f |
required |
vector |
Frequency vector with a length of Nfreq. |
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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. |
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dipole_spec |
required |
vector |
Dipole spectrum. This is treated as a power intensity distribution, integrated by midpoint rule in wavelength. The photon probability distribution is calculated by normalizing dipole_spec/f. Size is N_dipoles x length(f). |
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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. |
|
direction |
optional |
1 |
number |
Choice of far-field half-space, this can be +1 (top) or -1 (bottom). |
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ef |
optional |
1 |
vector |
The exciton fraction. The default value is 1, which means that every carrier results in an exciton. Size is N_dipoles. |
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st |
optional |
0.25 |
vector |
The singlet exciton fraction. The default value is 0.25, which means that there are 3 spin triplets per spin-singlet. Size is N_dipoles. |
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rd |
optional |
1 |
vector |
The relative decay rate. The default value is 1, which means that every singlet exciton results in a photon and there is no contribution from non-radiative decay processes. Size is N_dipoles. |
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options |
optional |
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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
Calculate the radiated power of a dipole source in a dielectric half-space.
# geometry: halfspace of material n1 and n2 n1 = 1.5; # lower halfspace n2 = 1.0; # upper halfspace
# source: monochrome 500nm dipole wavelength = 500e-9; delta = 80e-9; # position: in material n2 delta nm from interface
angular_res = 173; # resolution for emission angle (farfield angle)
# set-up for STACK command n = [n1; n2]; #STACK optical properties d = [0, 2*delta]; #STACK geometric properties f = [c/wavelength]; #STACK frequency points z = [delta]; #STACK dipole position spectrum = [1.0]; #STACK dipole spectrum
result_unpol = stackdipole(n,d,f,z,spectrum,"rand",angular_res); result_Vert = stackdipole(n,d,f,z,spectrum,"vert",angular_res); result_Horz = stackdipole(n,d,f,z,spectrum,"horz",angular_res); plot(result_unpol.theta,result_unpol.radiance,"emission angle (degrees)","power/steradian (W/steradian/m^2)","unpolarized"); plot(result_Vert.theta,result_Vert.radiance,"emission angle (degrees)","power/steradian (W/steradian/m^2)","vertical P orientation"); plot(result_Horz.theta,result_Horz.radiance,"emission angle (degrees)","power/steradian (W/steradian/m^2)","horizontal P orientation");
# calculate power sin_theta = sin(pi/180*pinch(result_unpol.theta)); #integrate power theta 0-pi/2 and phi 0-2pi ?total_power_pVert_upward = (0.5*pi)*(2*pi)*integrate(sin_theta*result_Vert.radiance,1,linspace(0,1,angular_res));
# In 2020R1.3
options={ "res": 173, "orientation": 'rand', "incoherent_propagation": incoherent_propagation};
result = stackdipole(n,d,f,z,spectrum,options);
options={ "theta": linspace(0,30,100), "orientation": 'rand', "incoherent_propagation": incoherent_propagation};
result = stackdipole(n,d,f,z,spectrum,options);
Related publications
- CIE Proceedings (1932), 1931. Cambridge: Cambridge University Press.
See also
Stack optical solver overview, stackrt, stackfield, stackpurcell, Stack dipole half-space, OLED slab mode analysis