Design and global optimization of dielectric coatings

Description

Thin film coating design, optimization, and analysis tools based on G. Venugopalan et. al.

Install

From within your favorite python environment (e.g. conda) run:

python -m pip install OptimalBragg

Examples

Quarter-wave high-reflectivity (HR) coating

import numpy as np
import matplotlib.pyplot as plt
from physunits import um, nm, ppm

from OptimalBragg.materials import *
from OptimalBragg import qw_stack, Material
from OptimalBragg.layers import *
from OptimalBragg.plot import plot_layers, plot_spectral

lam_ref = 1064 * nm
silica = Material(SiO2)
tantala = Material(Ta2O5)
Nlayers = 11

# Makes arbitrary quarter-wave stack
stack = qw_stack(
    lam_ref,
    substrate=silica,
    superstrate=Material(air),
    thin_films={"A": silica, "B": tantala},
    pattern="BA" * Nlayers,
)

# Results
T_ref = trans(lam_ref, stack)
print(Rf"T = {T_ref/ppm:.1f} ppm at {lam_ref/um:.2f} um.")

# Show layer structure and spectral refl/trans
plot_layers(stack)

rel_lambdas = np.linspace(0.75 * lam_ref, 1.25 * lam_ref, 2**10)

# Let's pretend I have custom dispersion data for these thin films
lam_disp = np.array([0.532, 0.633, 0.780, 0.852, 1.064, 1.083, 1.550]) * um
nSiO2 = np.interp(
    rel_lambdas,
    lam_disp,
    [1.4607, 1.4570, 1.4537, 1.4525, 1.4496, 1.4494, 1.444],
)
nTa2O5 = np.interp(
    rel_lambdas,
    lam_disp,
    [2.24, 2.1979, 2.1628, 2.1515, 2.1297, 2.1282, 2.1046],
)

plot_spectral(rel_lambdas, stack)
plot_spectral(rel_lambdas, stack, dispersion={"A": nSiO2, "B": nTa2O5})
plt.show()

Optimize an existing anti-reflective (AR) coating

import time
import h5py
import numpy as np
import matplotlib.pyplot as plt
from physunits import um, nm, ppm, Hz

from OptimalBragg.materials import *
from OptimalBragg import qw_stack, h5write, Material
from OptimalBragg.layers import *
from OptimalBragg.plot import plot_layers, plot_spectral
from OptimalBragg.optimizer import diff_evo

lam_ref = 1550 * nm

# Initialize QW stack but override with user defined pre-designed stack
stack = qw_stack(
    lam_ref=lam_ref,
    substrate=Material(SiO2),
    superstrate=Material(air),
    thin_films={"L": Material(SiO2), "H": Material(Ta2O5)},
    pattern="LH" * 4,
    hwcap="H",
)
# stack["ns"] = np.array([1.0, 2.1, 1.45, 2.1, 1.45, 2.1, 1.45])
# stack["Ls"] = np.array([0.8548, 268.4, 204.2, 90.18, 61.42]) * nm
T_ref = trans(lam_ref, stack)
stack["T_ref"] = T_ref
print(Rf"R < {(1 - T_ref)*100:.8f} % at {lam_ref/um:.2f} um.")

# Optimization over multiple wavelength AR and absorption
lam_m = 1545 * nm
lam_p = 1564 * nm
T_p = trans(lam_p, stack)
T_m = trans(lam_m, stack)

# Reference (initial) stack
stack["init"] = {"ns": stack["ns"], "Ls": stack["Ls"], "T_ref": T_ref}
multi_target = {
    "R": {
        "target": {
            lam_ref: 10 * ppm,
            lam_p: 10 * ppm,
            lam_m: 10 * ppm,
        },
        "weight": {lam_ref: 1, lam_p: 1, lam_m: 1},
    },
    "abs": {"target": 25 * ppm, "weight": 1e-2},
}
optimization_result = diff_evo(stack, multi_target)
stack["optimized"] = True

# Update thicknesses and other optimized attributes
stack["Ls"] = optimization_result["Ls"]
T_ref = trans(lam_ref, stack)
_, Enorm = field_zmag(
    stack["ns"], stack["Ls"], n_pts=2**8, lam=stack["lam_ref"]
)
intAbs = calc_abs(Enorm, stack["Ls"], stack["alphas"])
stack["Absorption"] = intAbs
stack["T_ref"] = T_ref

# Results
plot_layers(stack)
plt.show()

wavelengths = np.linspace(0.95 * lam_m, 1.05 * lam_p, 2**12)
plot_spectral(wavelengths, stack, markers={"R": [lam_p, lam_m, lam_ref]})
plt.show()

# Save to hdf5
time_tag = time.strftime("%Y%m%d-%H%M%S")
h5write(
    Rf"./AR1550_R_{(1-T_ref)/ppm:.0f}_A_{intAbs/ppm:.0f}_ppm_{time_tag}.h5",
    stack,
)