Tutorial 6d - Dichroic Mirror Optimization for Polarization Separation
We optimize a thin-film stack to create a dichroic mirror that separates s and p polarizations near 600 nm.
This version demonstrates the operand-centric architecture in ThinFilmOptimizer with a single API entry point: - standard spectral operands with add_operand(…) - a custom user-defined operand registered with register_operand(…) and used through add_operand(…)
[1]:
from optiland.thin_film.optimization import ThinFilmOptimizer
import optiland.backend as be
from optiland.thin_film import ThinFilmStack, SpectralAnalyzer
from optiland.materials import Material, IdealMaterial
SiO2 = Material("SiO2", reference="Gao")
TiO2 = Material("TiO2", reference="Zhukovsky")
BK7 = Material("N-BK7", reference="SCHOTT")
air = IdealMaterial(n=1.0)
dichroic_stack = ThinFilmStack(
incident_material=air,
substrate_material=BK7,
reference_wl_um=0.6,
reference_AOI_deg=45.0,
)
for i in range(10): # 10 pairs = 20 layers
dichroic_stack.add_layer_qwot(material=TiO2, qwot_thickness=1.0, name=f"$TiO_2$")
dichroic_stack.add_layer_qwot(material=SiO2, qwot_thickness=1.0, name=f"$SiO_2$")
[2]:
optimizer = ThinFilmOptimizer(dichroic_stack)
# Add all thicknesses as optimization variables
for i in range(len(dichroic_stack.layers)):
optimizer.add_variable(
layer_index=i,
min_nm=30,
max_nm=300
)
# we want to maximize the polarization contrast (Rs-Rp) at 600 nm and 45° AOI, so we
# minimize the negative contrast, averaged over a wavelength range to make it more
# robust to fabrication variations. The contrast is normalized to be between 0 and 1,
# where 1 corresponds to Rs=1 and Rp=0
wl_nm = be.linspace(595, 605, 11)
# Register and add a custom operand through add_operand
def polarization_contrast(stack: ThinFilmStack, wavelength_nm: be.ndarray, aoi_deg:float):
"""Calculate the polarization contrast (Rs-Rp) averaged over a wavelength range.
The contrast is normalized to be between 0 and 1, where 1 corresponds to Rs=1 and Rp=0."""
rs = stack.reflectance_nm_deg(wavelength_nm, aoi_deg, "s")
rp = stack.reflectance_nm_deg(wavelength_nm, aoi_deg, "p")
return (1 + be.mean(rs - rp))/2
ThinFilmOptimizer.register_operand(
"polarization_contrast", polarization_contrast, overwrite=True
)
optimizer.add_operand(
property="polarization_contrast",
min_val=0.99,
input_data={"wavelength_nm": wl_nm, "aoi_deg": 45.0},
label="Rs-Rp @ 595-605nm, 45deg",
)
# Display optimization information
optimizer.info()
contrast_initial=optimizer.rss()
print(f"Initial RSS: {contrast_initial:.6e}")
ThinFilm Optimizer Information
==================================================
+--------------+---------+
| Property | Count |
+==============+=========+
| Stack layers | 20 |
+--------------+---------+
| Variables | 20 |
+--------------+---------+
| Targets | 1 |
+--------------+---------+
Variables:
+------+---------+------------------+------------+------------+
| ID | Layer | Thickness (nm) | Min (nm) | Max (nm) |
+======+=========+==================+============+============+
| 0 | 0 | 88.2 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 1 | 1 | 143.6 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 2 | 2 | 88.2 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 3 | 3 | 143.6 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 4 | 4 | 88.2 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 5 | 5 | 143.6 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 6 | 6 | 88.2 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 7 | 7 | 143.6 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 8 | 8 | 88.2 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 9 | 9 | 143.6 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 10 | 10 | 88.2 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 11 | 11 | 143.6 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 12 | 12 | 88.2 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 13 | 13 | 143.6 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 14 | 14 | 88.2 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 15 | 15 | 143.6 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 16 | 16 | 88.2 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 17 | 17 | 143.6 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 18 | 18 | 88.2 | 30 | 300 |
+------+---------+------------------+------------+------------+
| 19 | 19 | 143.6 | 30 | 300 |
+------+---------+------------------+------------+------------+
Targets:
+------+--------------------------+--------+---------+--------------+-------+----------+-------+
| ID | Prop | Type | Value | Wavelength | AOI | Weight | Pol |
+======+==========================+========+=========+==============+=======+==========+=======+
| 0 | Rs-Rp @ 595-605nm, 45deg | custom | | - | - | 1 | - |
+------+--------------------------+--------+---------+--------------+-------+----------+-------+
Initial RSS: 3.058333e-01
[3]:
# Launch optimization
result = optimizer.optimize(
method="L-BFGS-B",
max_iterations=1000,
)
print(f"Merit: {result['initial_merit']:.15f} -> {result['final_merit']:.15f} in {result['iterations']} iterations")
print(f"Improvement: {result['improvement']:.15f}")
Merit: 0.093534002618582 -> 0.000329856133348 in 46 iterations
Improvement: 0.093204146485235
[4]:
from optiland.thin_film.optimization import ThinFilmReport
report = ThinFilmReport(optimizer, result)
report.summary_table()
[4]:
| Variable | Initial | Final | Change | Unit | |
|---|---|---|---|---|---|
| 0 | Layer 0 thickness | 88.2 | 71.4 | -16.8 (-19.1%) | nm |
| 1 | Layer 1 thickness | 143.6 | 145.8 | +2.2 (+1.5%) | nm |
| 2 | Layer 2 thickness | 88.2 | 78.3 | -9.9 (-11.2%) | nm |
| 3 | Layer 3 thickness | 143.6 | 153.6 | +10.0 (+7.0%) | nm |
| 4 | Layer 4 thickness | 88.2 | 199.6 | +111.4 (+126.3%) | nm |
| 5 | Layer 5 thickness | 143.6 | 146.2 | +2.6 (+1.8%) | nm |
| 6 | Layer 6 thickness | 88.2 | 74.2 | -14.1 (-16.0%) | nm |
| 7 | Layer 7 thickness | 143.6 | 135.6 | -8.0 (-5.6%) | nm |
| 8 | Layer 8 thickness | 88.2 | 72.0 | -16.2 (-18.4%) | nm |
| 9 | Layer 9 thickness | 143.6 | 132.5 | -11.1 (-7.7%) | nm |
| 10 | Layer 10 thickness | 88.2 | 70.8 | -17.4 (-19.8%) | nm |
| 11 | Layer 11 thickness | 143.6 | 132.5 | -11.1 (-7.7%) | nm |
| 12 | Layer 12 thickness | 88.2 | 67.3 | -20.9 (-23.7%) | nm |
| 13 | Layer 13 thickness | 143.6 | 161.4 | +17.8 (+12.4%) | nm |
| 14 | Layer 14 thickness | 88.2 | 196.0 | +107.7 (+122.1%) | nm |
| 15 | Layer 15 thickness | 143.6 | 161.7 | +18.1 (+12.6%) | nm |
| 16 | Layer 16 thickness | 88.2 | 77.6 | -10.7 (-12.1%) | nm |
| 17 | Layer 17 thickness | 143.6 | 137.2 | -6.4 (-4.5%) | nm |
| 18 | Layer 18 thickness | 88.2 | 71.3 | -16.9 (-19.1%) | nm |
| 19 | Layer 19 thickness | 143.6 | 140.0 | -3.6 (-2.5%) | nm |
[5]:
import matplotlib.pyplot as plt
analyzer = SpectralAnalyzer(dichroic_stack)
fig, axes = plt.subplots(1, 3, figsize=(12, 4))
wl_range = be.linspace(500, 700, 201) # Around 600 nm
# Calculate before optimization (reset and recalculate)
optimizer.reset()
Rs_before = dichroic_stack.reflectance_nm_deg(wl_range, 45, 's')
Rp_before = dichroic_stack.reflectance_nm_deg(wl_range, 45, 'p')
# Restore optimized state
for i, var_info in enumerate(optimizer.variables):
final_thickness = result['thickness_changes'][i]['final_nm'] / 1000 # nm → μm
dichroic_stack.layers[i].update_thickness(final_thickness)
Rs_after = dichroic_stack.reflectance_nm_deg(wl_range, 45, 's')
Rp_after = dichroic_stack.reflectance_nm_deg(wl_range, 45, 'p')
axes[0].plot(wl_range, Rs_before, 'b:', label='$R_s$ before', alpha=0.7)
axes[0].plot(wl_range, Rp_before, 'g:', label='$P_p$ before', alpha=0.7)
axes[0].plot(wl_range, Rs_after, 'b-', label='$R_s$ after', linewidth=2)
axes[0].plot(wl_range, Rp_after, 'g-', label='$P_p$ after', linewidth=2)
axes[0].set_xlabel('$\lambda$ (nm)')
axes[0].set_ylabel('Reflectance')
axes[0].set_title('Spectral Performance (AOI=45°)')
axes[0].legend()
axes[0].grid(True, alpha=0.3)
axes[0].fill_betweenx([0, 1], 595, 605, color='gray', alpha=0.2, label='Optimization Range')
# 2. Polarization contrast (Rs - Rp)
contrast_before = Rs_before - Rp_before
contrast_after = Rs_after - Rp_after
axes[1].plot(wl_range, contrast_before, 'g--', label='Before', alpha=0.7)
axes[1].plot(wl_range, contrast_after, 'g-', label='After', linewidth=2)
axes[1].set_xlabel('$\lambda$ (nm)')
axes[1].set_ylabel('Contrast ($R_s - R_p$)')
axes[1].set_title('Polarization Contrast')
axes[1].legend()
axes[1].grid(True, alpha=0.3)
# 3. Optimized stack structure
dichroic_stack.plot_structure_thickness(axes[2])
axes[2].set_title('Optimized Stack Structure')
fig.tight_layout()
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axes[0].set_xlabel('$\lambda$ (nm)')
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axes[1].set_xlabel('$\lambda$ (nm)')
