Ikarus

High-precision 2-D RCWA simulation for periodic photonic structures.

📖 Read the documentation →

📄 Read the white paper →  ·  Ikarus: High-fidelity RCWA simulation and inverse design for metasurfaces

Ikarus is a rigorous coupled-wave analysis (RCWA / Fourier modal method) solver for 2-D periodic photonic structures — metasurfaces, gratings and photonic crystals. It uses a numerically stable scattering-matrix formulation, supports full vectorial (linear and circular) polarization, arbitrary pixel-map topologies, a built-in dispersive material database, real-space field reconstruction, automatic convergence testing, HDF5 I/O and adjoint + gradient-free inverse design.

import numpy as np
from ikarus import RCWA

rcwa = RCWA(period_x=1e-6, period_y=1e-6, resolution=64, n_orders=15)
rcwa.add_uniform_layer(height=np.inf, material='Air')   # semi-infinite cover
rcwa.add_uniform_layer(height=200e-9, material='Si')
rcwa.add_uniform_layer(height=np.inf, material='SiO2')  # semi-infinite substrate
rcwa.set_source(wavelength=1550e-9, theta=0, polarization='linear')

T, R, result = rcwa.simulate()
print(f"R = {result.R_total:.4f}, T = {result.T_total:.4f}, R+T = {result.energy_balance:.6f}")

Why "high-precision"

Ikarus reproduces the analytic Fresnel/transfer-matrix solution for stratified media to machine precision (~1e-15) at any incidence angle and polarization, and conserves energy to ~1e-9 for diffraction gratings. The patterned-layer machinery is independently validated against a direct mode-matching reference and the effective-medium limit. See ikarus/tests/validation/.

It is also fast and cross-validated: head-to-head against grcwa (an independent RCWA package) it agrees to ~1e-3 on R / T / co- and cross-pol across diverse metaatoms and a full wavelength sweep, while running ~1.5–1.7× faster per solve.

Features

Installation

pip install ikarus-rcwa                # core (numpy, scipy)
pip install "ikarus-rcwa[all]"         # + viz, HDF5, GA inverse design, adjoint (JAX)
pip install "ikarus-rcwa[inverse]"     # + pymoo, for gradient-free inverse design
pip install "ikarus-rcwa[grad]"        # + JAX/optax, for adjoint (gradient) inverse design

The import name is ikarus (the distribution is ikarus-rcwa). From source for development:

git clone https://github.com/CAVITYtechnologies/ikarus.git
cd ikarus && pip install -e ".[dev]"

Usage

Metasurface with a pixel-map topology

import numpy as np
from ikarus import RCWA

rcwa = RCWA(period_x=400e-9, period_y=400e-9, resolution=64, n_orders=10)
topology = rcwa.shapes.ring(center=(0.5, 0.5), inner_radius=0.15,
                            outer_radius=0.3, grid_shape=(64, 64))
rcwa.add_uniform_layer(np.inf, 'Air')
rcwa.add_layer(height=120e-9, topology=topology, materials=['TiO2', 'Air'])
rcwa.add_uniform_layer(np.inf, 'SiO2')
rcwa.set_source(wavelength=532e-9, theta=0, polarization='linear')
T, R, result = rcwa.simulate()

The integer topology array indexes into materials; pixel (i, j) covers period_x/Nx × period_y/Ny of the cell.

Circular polarization (co / cross)

rcwa.set_source(wavelength=1550e-9, theta=30, polarization='RCP')
T, R, result = rcwa.simulate()
print(f"co-pol T:    {abs(T['co']):.4f}")
print(f"cross-pol T: {abs(T['cross']):.4f}")

|T['co']|**2 + |T['cross']|**2 equals the zero-order transmittance.

Order-resolved output and exit angles

T, R, result = rcwa.simulate()
p, q = result.orders
for i in range(len(p)):
    if result.T_orders[i] > 1e-3:
        print(f"order ({p[i]:+d},{q[i]:+d}): T={result.T_orders[i]:.4f} "
              f"at theta_out={result.theta_out_trn[i]:.1f} deg")

Field extraction and visualization

rcwa.simulate()
fields = rcwa.get_fields(z_positions=[50e-9, 100e-9], plane='xy')   # one map per z
xz = rcwa.get_fields(plane='xz')['xz']                              # cross-section

rcwa.visualize_structure(plane='xz', savefig='stack.png')
rcwa.visualize_structure(plane='xy', layer_index=1, savefig='topology.png')
from ikarus.visualization import plot_field
plot_field(xz, component='intensity', savefig='field.png')           # |E|^2
plot_field(xz, component='Ey', savefig='ey_mag.png')                 # |Ey|
plot_field(xz, component='Eyphase', savefig='ey_phase.png')         # arg(Ey)

z = 0 is the cover / first-layer interface, increasing into the stack. Field plots overlay the structure outline semi-transparently by default (the topology for xy slices, the layer interfaces for xz/yz); pass overlay=False to disable.

Reflection / transmission phase

The complex zero-order coefficients carry phase (key for phase-gradient metasurface design):

T, R, result = rcwa.simulate()
print(result.T_phase, result.R_phase)   # radians; dict {'co','cross'} for circular pol

Convergence control

T, R, result = rcwa.simulate(auto_converge='once', converge_tol=1e-4, max_orders=80)
print("converged n_orders:", rcwa.n_orders)

'once' finds and caches the optimal order count (reused across a sweep); 'always' re-converges every call; 'never' (default) uses the current n_orders.

Materials

from ikarus.core.materials import default_library as lib
lib.get('Si', wavelength=1550e-9)          # -> (3.479+0j)
lib.available()                            # list built-in materials
lib.add_from_file('my_nk.csv', name='MyMat', persist=True)

Or from the command line:

python -m ikarus.tools.add_material my_nk.csv --name MyMaterial

CSV columns are wavelength_nm n [k] (k optional, # comments ignored).

Saving results

rcwa.save_results('run.h5', include=['T', 'R', 'fields', 'metadata'], result=result)
data = RCWA.load_results('run.h5')

Inverse design

Define a metaatom with free degrees of freedom, declare what you want, optimize — gradient-free (genetic algorithm / NSGA-III via pymoo). Install the extra: pip install "ikarus-rcwa[inverse]".

import numpy as np
from ikarus.inverse import MetaAtom, free, pixels, Target, optimize

# Si-on-SiO2 metaatom: free binary pixel map (c4v-symmetric) + free layer height
atom = MetaAtom(period=700e-9, cover='Air', substrate='SiO2')
atom.add_pattern(topology=pixels(12, 12, symmetry='c4v'),
                 materials=['Air', 'Si'], height=free(300e-9, 900e-9))

# maximize reflection into the 0th order at 1550 nm  ->  a metamirror, in one line
best = optimize(atom, Target.maximize('R', order=(0, 0), at=1550e-9))
print(best.report())
mirror = best.metaatom          # the optimized, ready-to-simulate RCWA structure

Degrees of freedom. free(lo, hi) marks a continuous parameter (height, period); pixels(nx, ny, symmetry=...) a binary pixel map (bit-flip mutation, with optional 'c4v' / 'mirror_x' / 'c2' … symmetry that both cuts the DOF count and enforces the structural symmetry — e.g. c4v reduces a 12×12 map from 144 to 21 free bits).

Targets declare the figure of merit, over one or many wavelengths:

Target.maximize('R', order=(1, 0), at=1550e-9)        # anomalous reflection (+1 order)
Target.match('r_co', 1, at=[1064e-9, 1550e-9])        # bispectral mirror
Target.minimize('R', band=(1064e-9, 1550e-9))         # broadband AR coating
Target.match('t_phase', np.pi/2, at=1550e-9)          # transmission-phase target

Metrics: R/T (per diffraction order), r_co/t_co (complex), r_phase / t_phase. Wavelengths via at= (scalar or list) or band=(lo, hi[, n]), aggregated by mean or worst_case=True. Pass a list of targets for multi-objective (NSGA-III) optimization — best.X / best.F then hold the Pareto set.

Conventions

• Time convention exp(-i ω t): absorbing materials have k > 0, Im(ε) > 0; materials.get returns n + i k.
• theta is measured from the +z axis (0 = normal incidence); phi is the azimuth from +x.
• Wavevectors are normalized by the vacuum wavenumber internally.
• The two outermost layers must be uniform and semi-infinite (height=inf).

Architecture

ikarus/
├── core/            rcwa, layer, source, materials, fourier, solver, fields, polarization
├── shapes/          topology primitives (circle, ring, rectangle, polygon, …)
├── materials/       JSON dispersion database
├── tools/           add_material (CLI), convergence, io (HDF5)
├── visualization/   structure & field plotting
├── inverse/         gradient-free inverse design (MetaAtom, Target, optimize via pymoo)
├── tests/           unit + validation (Fresnel, gratings, fields, …)
└── examples/        runnable scripts

The solver (core/solver.py) is a stateless scattering-matrix engine: per-layer eigenmodes → layer S-matrices referenced to a vacuum gap → Redheffer cascade → diffraction efficiencies and field amplitudes.

Testing and examples

pytest ikarus/tests/                              # full suite (~1.4s)
python -m ikarus.examples.feature_tour            # guided tour: structure/field plots, spectrum, HDF5
python -m ikarus.examples.validation_fresnel      # machine-precision Fresnel check
python -m ikarus.examples.grating_diffraction     # order-resolved grating
python -m ikarus.examples.metasurface_spectrum    # resonant metasurface sweep
python -m ikarus.examples.inverse_metamirror      # one-line metamirror inverse design ([inverse])

feature_tour is the best starting point — it exercises the material database, structure/topology visualization, field reconstruction, a wavelength sweep, circular polarization and HDF5 export, saving figures to ikarus_tour_output/.

License

MIT — Copyright © 2026 CAVITY technologies GmbH. See LICENSE. Created by Liam Shelling Neto.