Split waveguide

The split waveguide is a square waveguide that after a propagation distance $l_1$ splits in two square waveguides separated by an angle $\alpha$.



In [1]:

    
from pypropagate import *
%matplotlib inline

Setting up the propagators

We create a settings object to store the propagator settings.



In [2]:

    
settings = presets.settings.create_paraxial_wave_equation_settings()

We create a settings category that stores the paramters of the split waveguide. This allows a more flexible simulation routines we may change the paramter values at any point before initializing a propagator.



In [3]:

    
sw = settings.create_category('split_waveguide',short_name='SW')
sw.create_symbol('l_1',info='propagation length before split')
sw.create_symbol('alpha',info='separation angle')
sw.create_symbol('d',info='waveguide profile edge length')
sw.create_symbol('n_core',info='refractive index in the guiding core')
sw.create_symbol('n_cladding',info='refractive index in the cladding');

Using these paramters we define the position depenent index of refraction.



In [4]:

    
s = settings.symbols

settings.wave_equation.n = pc.piecewise(
    (sw.n_core,(abs(s.x)<sw.d/2) & (abs(s.y)<sw.d/2) & (s.z <= sw.l_1)), # initial channel
    (sw.n_core,(abs(s.x - pc.tan(sw.alpha) * (s.z - sw.l_1) ) < sw.d/2) & (abs(s.y)<sw.d/2) & (s.z > sw.l_1)), # upper channel
    (sw.n_core,(abs(s.x + pc.tan(sw.alpha) * (s.z - sw.l_1) ) < sw.d/2) & (abs(s.y)<sw.d/2) & (s.z > sw.l_1)), # lower channel
    (sw.n_cladding,True) # cladding
)

settings.get(settings.wave_equation.n)









    Out[4]:





$$\begin{cases} {n}_{{\text{core} }_{\text{SW} } }  & \text{if } \left( \left| \left( z-{l}_{{1}_{\text{SW} } }  \right) \, \text{tan}  \mathopen{} \left({\alpha }_{\text{SW} }  \right) \mathclose{} +x \right| < \frac{{d}_{\text{SW} } }{2} \,  \land \left| y \right| < \frac{{d}_{\text{SW} } }{2} \,  \land {l}_{{1}_{\text{SW} } }  < z \right) \lor \left( \left| x \right| < \frac{{d}_{\text{SW} } }{2} \,  \land \left| y \right| < \frac{{d}_{\text{SW} } }{2} \,  \land z\le {l}_{{1}_{\text{SW} } }  \right) \lor \left( \left| x-\left( z-{l}_{{1}_{\text{SW} } }  \right) \, \text{tan}  \mathopen{} \left({\alpha }_{\text{SW} }  \right) \mathclose{}  \right| < \frac{{d}_{\text{SW} } }{2} \,  \land \left| y \right| < \frac{{d}_{\text{SW} } }{2} \,  \land {l}_{{1}_{\text{SW} } }  < z \right)  \\ {n}_{{\text{cladding} }_{\text{SW} } }  & \text{otherwise }  \end{cases}$$

Numerical values

We now set all numerical paramter values for the simulation, including the simulation box size, boundary conditions and photon energy.



In [5]:

    
settings.wave_equation.set_energy(12*units.keV)
presets.boundaries.set_plane_wave_initial_conditions(settings)



In [6]:

    
sw.n_core = 1
sw.n_cladding = presets.medium.create_material('Ti',settings)
sw.l_1 = 0.2 * units.mm
sw.d = 70 * units.nm
sw.alpha = 0.01 * units.degrees

Set a simulation box size to plot the index of refraction.



In [7]:

    
settings.simulation_box.set((0.5*units.um,0.3*units.um,1*units.mm),(1000,500,1000))
plot(s.n.subs(s.y,0),settings,figsize=(10,4))
plot(s.n.subs(s.z,s.zmax),settings,figsize=(3,4));

Calculating the stationary field

We use the 2D Finite Difference Prpagator to get the full stationary solution. We plot a slice of the field in the $y = 0$ slice.



In [8]:

    
settings.simulation_box.set((0.5*units.um,0.3*units.um,1*units.mm),(1000,500,5000))



In [9]:

    
propagator = propagators.FiniteDifferences3D(settings)
plot(propagator.run_slice()[-0.2*units.um:0.2*units.um,0,::1*units.um],figsize=(16,5));









    



propagating:|█████████████████████| 999/999 [253.0s < 0(0)s]]

Plotting the exit field



In [10]:

    
plot(propagator.get_field(),figsize=(5,7));