fix overlap calculations

Author: HelgeGehring

femwell/examples/Aeff.py

@@ -1,23 +1,19 @@
 """Aeff analysis based on https://optics.ansys.com/hc/en-us/articles/15100783091731-Spontaneous-Four-wave-Mixing-SWFM-Microring-Resonator-Photon-Source."""
 from collections import OrderedDict
+
 import numpy as np
+from scipy.constants import c, epsilon_0
 from shapely.geometry import box
 from shapely.ops import clip_by_rect
-from skfem import Basis, ElementTriP0
-from skfem import Functional
+from skfem import Basis, ElementTriP0, Functional
 from skfem.helpers import dot
 from skfem.io.meshio import from_meshio
+
 from femwell.maxwell.waveguide import compute_modes
 from femwell.mesh import mesh_from_OrderedDict
-from scipy.constants import c, epsilon_0
 
-def calculate_sfwm_Aeff(
-        basis: Basis,
-        mode_p, 
-        mode_s, 
-        mode_i
-) -> np.complex64:
-    
+
+def calculate_sfwm_Aeff(basis: Basis, mode_p, mode_s, mode_i) -> np.complex64:
     """
     Calculates the overlap integral for SFWM process by considering the interactions
     between pump, signal, and idler modes in the xy plane.
@@ -30,46 +26,43 @@ def calculate_sfwm_Aeff(
         np.complex64: The Aeff result for the SFWM process(1/overlap integral).
     """
 
-    def normalize_mode(mode):
+    def normalization_factor_mode(mode):
         @Functional
         def E2(w):
             return dot(w["E"][0], np.conj(w["E"][0]))
 
-        E_xy, _ = mode.basis.interpolate(mode.E)  # [0]=xy [1]=z
-        E_squared_integral = E2.assemble(mode.basis, E=E_xy)
+        E = mode.basis.interpolate(mode.E)  # [0]=xy [1]=z
+        E_squared_integral = E2.assemble(mode.basis, E=E)
         normalization_factor = 1 / np.sqrt(E_squared_integral)
         return normalization_factor  # Return the normalization factor instead of modifying the mode
 
-    # Calculate normalization factors for each mode
-    norm_factor_p = normalize_mode(mode_p)
-    norm_factor_s = normalize_mode(mode_s)
-    norm_factor_i = normalize_mode(mode_i)
-
     # Apply normalization factors to the electric fields for the overlap calculation
-    E_p, _ = mode_p.basis.interpolate(mode_p.E * norm_factor_p)
-    E_s, _ = mode_s.basis.interpolate(mode_s.E * norm_factor_s)
-    E_i, _ = mode_i.basis.interpolate(mode_i.E * norm_factor_i)
-
     @Functional(dtype=np.complex64)
     def sfwm_overlap(w):
-        overlap_SFWM = w["E_p"][0] * w["E_p"][0] * np.conj(w["E_s"][0]) * np.conj(w["E_i"][0])
-        return overlap_SFWM
+        return dot(w["E_p"][0], w["E_p"][0]) * dot(np.conj(w["E_s"][0]), np.conj(w["E_i"][0]))
 
-    overlap_result = sfwm_overlap.assemble(basis, E_p=E_p, E_s=E_s, E_i=E_i)
+    overlap_result = sfwm_overlap.assemble(
+        basis,
+        E_p=mode_p.basis.interpolate(mode_p.E * normalization_factor_mode(mode_p)),
+        E_s=mode_s.basis.interpolate(mode_s.E * normalization_factor_mode(mode_s)),
+        E_i=mode_i.basis.interpolate(mode_i.E * normalization_factor_mode(mode_i)),
+    )
 
     return 1 / overlap_result
 
 
-#Dispersion relations of materials
-#Core
+# Dispersion relations of materials
+# Core
 def n_X(wavelength):
     x = wavelength
-    return (1 
-            + 2.19244563 / (1 - (0.20746607 / x) ** 2)
-            + 0.13435116 / (1 - (0.3985835 / x) ** 2)
-            + 2.20997784 / (1 - (0.20747044 / x) ** 2)
+    return (
+        1
+        + 2.19244563 / (1 - (0.20746607 / x) ** 2)
+        + 0.13435116 / (1 - (0.3985835 / x) ** 2)
+        + 2.20997784 / (1 - (0.20747044 / x) ** 2)
     ) ** 0.5
 
+
 # Box
 def n_silicon_dioxide(wavelength):
     x = wavelength
@@ -80,35 +73,43 @@ def n_silicon_dioxide(wavelength):
         + 0.8974794 / (1 - (9.896161 / x) ** 2)
     ) ** 0.5
 
-Clad=1
+
+Clad = 1
 
 
-core = box(0, 0, 0.5, 0.39) #500x390nm
+core = box(0, 0, 1.05, 0.5)  # 1050x500nm
+# core = box(0, 0, .5, 0.39)  # 500x390nm
 polygons = OrderedDict(
     core=core,
     box=clip_by_rect(core.buffer(1.5, resolution=4), -np.inf, -np.inf, np.inf, 0),
     clad=clip_by_rect(core.buffer(1.5, resolution=4), -np.inf, 0, np.inf, np.inf),
 )
 
-resolutions = {"core": {"resolution": 0.025, "distance": 2.}}
+resolutions = {"core": {"resolution": 0.025, "distance": 2.0}}
 
-mesh = from_meshio(mesh_from_OrderedDict(polygons, resolutions, default_resolution_max=0.6))
+mesh = from_meshio(mesh_from_OrderedDict(polygons, resolutions, default_resolution_max=0.2))
 
 num_modes = 2
 
-#For SFWM we have energy conservation and momemtum(k) conservation for 2pumps and signal+idler
+# For SFWM we have energy conservation and momemtum(k) conservation for 2pumps and signal+idler
 lambda_p0 = 1.4
 lambda_s0 = 1.097
 lambda_i0 = 1.686
 
+# lambda_p0 = 1.55
+# lambda_s0 = 1.55
+# lambda_i0 = 1.55
+
 basis0 = Basis(mesh, ElementTriP0())
 
 epsilon_p = basis0.zeros()
 epsilon_s = basis0.zeros()
 epsilon_i = basis0.zeros()
 
 
-for wavelength, epsilon in zip([lambda_p0, lambda_s0, lambda_i0], [epsilon_p, epsilon_s, epsilon_i]):
+for wavelength, epsilon in zip(
+    [lambda_p0, lambda_s0, lambda_i0], [epsilon_p, epsilon_s, epsilon_i]
+):
     for subdomain, n_func in {
         "core": n_X,
         "box": n_silicon_dioxide,
@@ -122,6 +123,7 @@ def n_silicon_dioxide(wavelength):
 modes_s = compute_modes(basis0, epsilon_s, wavelength=lambda_s0, num_modes=num_modes, order=1)
 modes_i = compute_modes(basis0, epsilon_i, wavelength=lambda_i0, num_modes=num_modes, order=1)
 
+# modes_p[0].show(modes_p[0].E.real)
 
 mode_p = max(modes_p, key=lambda mode: mode.te_fraction)
 mode_s = max(modes_s, key=lambda mode: mode.te_fraction)
@@ -130,14 +132,15 @@ def n_silicon_dioxide(wavelength):
 A_eff = calculate_sfwm_Aeff(basis0, mode_p, mode_s, mode_i)
 print("Aeff in um2:", A_eff)
 
-#Calculation for non-linear coef
+# Calculation for non-linear coef
 chi_3 = 5e-21  # m^2/V^2  #7e-20?
-lambda_p0_m = lambda_p0 * 1e-6  #to m
+chi_3 = 7e-20  # ?
+lambda_p0_m = lambda_p0 * 1e-6  # to m
 n_p0 = np.real(mode_p.n_eff)
-A_eff_m2 = A_eff * 1e-12  #to m^2
+A_eff_m2 = A_eff * 1e-12  # to m^2
 
 omega_p0 = 2 * np.pi * c / lambda_p0_m
 
 gamma = (3 * chi_3 * omega_p0) / (4 * epsilon_0 * c**2 * n_p0**2 * A_eff_m2)
 
-print("gamma:",gamma)
+print("gamma:", gamma)