MetaLayer Pro — joint design of metasurfaces and multilayer coatings

MetaLayer Pro extends the OptiLayer design environment from laterally homogeneous coatings to periodic metasurfaces. A metasurface almost never stands alone: it is patterned on top of a multilayer coating, and the two elements share the same spectral requirements. MetaLayer Pro treats them as a single design problem — the geometry of the patterned layers and the thicknesses of the underlying coating are optimized simultaneously against one merit function, using the synthesis methods already familiar to OptiLayer users.

Design problem

Meta design

A meta design (database item type Meta Design, file extension .mdsg) is composed of two parts: a classical uniform-film design — the deposited stack, to which refinement, monitoring, and reverse engineering remain fully applicable — and a periodic superstructure patterned on top of it. The separation mirrors the fabrication sequence and makes it structurally impossible to hand a patterned design to a classical engine and have the pattern silently ignored.

The superstructure is defined by a two-dimensional Bravais lattice and by one or more patterned layers. The lattice is specified by the two basis-vector lengths and the angle between them: 90° with arbitrary periods gives the rectangular cell, 60° with equal periods the hexagonal close-packed cell, and intermediate values any other Bravais lattice. A patterned layer carries a background material, a height, and a set of shapes standing in that background. A layer without shapes is an ordinary uniform film, so buried gratings and interleaved uniform and patterned layers are expressible without special cases.

Shapes and fabrication features

The following shape primitives are available:

• circle;
• rectangle, with in-plane rotation;
• ellipse, with in-plane rotation;
• arbitrary polygon;
• bitmap, for shapes defined pixel by pixel.

Beyond the ideal vertical extrusion, the geometry description covers the features that distinguish a fabricated structure from a drawn one:

• Sidewall slope — a symmetric taper of the shape cross-section with height, as produced by an etch process;
• Shear — a directional lean of the extrusion, for slanted and blazed profiles such as those used in augmented-reality waveguide couplers;
• Surface relief — a continuous height profile sampled on a grid, for blazed gratings and kinoforms;
• Embedded inclusions — ellipsoidal solids within a layer;
• Uniaxial anisotropy — an ordinary and an extraordinary material with a specified optic axis.

Shape materials are ordinary catalog materials, referenced by abbreviation exactly as layer materials are, so the same dispersion data serve the patterned and the uniform parts of the design.

Meta targets

A meta target (database item type Meta Target, file extension .mtg) is organized in pages. Each page fixes one set of illumination conditions — incidence angle, azimuth, and polarization state — and carries one or more columns of requirements over a wavelength grid. A column addresses an individual diffraction order in reflection or in transmission, so requirements such as “at least 60% into the reflected (−1, 0) order” and “at least 85% into the transmitted (0, 0) order” can be specified in the same target with independent tolerances.

Angular requirements are expressed by spreading the requirement over pages: a field-of-view specification becomes one page per field angle and polarization. Point targets, range targets, and the usual above/below qualifiers are supported, and the tolerance assigned to each column determines its weight in the merit function in the same way as in classical OptiLayer targets.

Synthesis and optimization

Free parameters

The optimization setup (Optimization → Setup) presents the design as a tree of free parameters. Per patterned layer the layer height is refinable; per shape the in-plane parameters of that shape kind are refinable — diameter for circles, width, height, and rotation for rectangles and ellipses, and the centre coordinates for all analytic kinds. Each parameter carries its own bounds.

The film thicknesses of the underlying coating are controlled by a single switch. With it enabled, the classical refinables are optimized together with the geometry; with it disabled, the coating is frozen and the run costs only what the geometry parameters require. Before a run starts, the selected bounds are checked against a worst-case geometry test — overlapping shapes and violations of a minimum fabrication gap are reported, and the bounds can be tightened automatically to the largest range that remains feasible.

Cost of a joint optimization

A laterally homogeneous stack does not couple Floquet harmonics: its reflection operator is diagonal in the harmonic basis. A change of layer thickness therefore does not invalidate the coupled-wave solution of the patterned part — the thickness variables act through a transfer-matrix step, and only a change of grating geometry requires the coupled-wave problem to be solved again.

This is what makes joint design practical. The expensive part of the calculation has a handful of parameters; the inexpensive part has as many as the coating needs. A joint synthesis cycle therefore costs approximately what a coating-only synthesis costs, even for stacks of several tens of layers. Each optimization iteration evaluates a finite-difference Jacobian, requiring two rigorous solutions per free geometry parameter, so meta iterations are measured in minutes rather than in the microseconds of classical thin-film refinement; the number of iterations is limited by a user-specified cap, and a run also terminates on stagnation.

Needle optimization for metasurfaces

The needle synthesis method underlying OptiLayer is extended to the patterned part of the design in two respects.

First, the needle criterion is applied to lateral geometry: instead of indicating the depth at which a new layer should be inserted into a stack, it indicates the position within the period at which a new feature should be introduced. Unlike a layer, a lateral feature cannot be inserted with vanishing width, since a feature of zero width would require an unbounded number of harmonics to represent; the width of the trial feature is therefore determined by the number of harmonics retained in the calculation, which keeps the insertion consistent with the basis in which it is evaluated.

Second, the same insertion machinery serves phase-derivative requirements. Group delay and group delay dispersion are the first and second derivatives of the phase with respect to circular frequency, taken with a minus sign; the derivative of the phase with respect to a trial insertion is already formed by the needle procedure, so targets on GD and GDD require no separate apparatus. Dispersive mirrors consequently join the class of problems that needle synthesis can address with a metasurface as an additional degree of freedom.

Solvers

Rigorous coupled-wave analysis

Periodic structures are solved by rigorous coupled-wave analysis. The truncation order along each lattice direction is specified in the diffraction-order settings, which are the single point of control for the solver accuracy. Evanescent orders are retained in the calculation: although they carry no power to the far field, they determine the field at the interface between the patterned layer and the coating beneath it, and therefore affect the reflected phase and its frequency derivatives.

Finite-difference time domain

Structures that cannot be treated as periodic — finite apertures, aperiodic arrangements, locally periodic elements such as metalenses — are handled in the time domain, which also provides near-field distributions and the time-domain response of the structure.

Transfer-matrix method

The uniform part of the design is computed by the transfer-matrix method, at the full speed of classical OptiLayer. Designs without a lattice follow the classical computational path unchanged, so the addition of metasurface capability does not affect the performance of ordinary coating work.

Analysis

Diffraction Orders

The Diffraction Orders window displays order-resolved spectral characteristics. Reflected and transmitted efficiencies are shown for a selected order, for the total over all orders, or per polarization, with the exit angle of each propagating order given by the grating equation. The merit function is recalculated automatically when a target is loaded, so the effect of a design change on the specified requirements is visible immediately.

Angular Map

The Angular Map window shows the response as a function of incidence angle at a fixed wavelength, or as a map over angle and wavelength — the natural presentation for field-of-view requirements, where the behaviour between the specified field angles matters as much as the behaviour at them.

Unit Cell 3D

The Unit Cell 3D window renders the unit cell as it is passed to the solver: the patterned layers with their shapes, slopes, and reliefs, standing on the layers of the coating. It is the direct check that the structure being computed is the structure that was intended.

Interoperability

Complete problems — geometry, materials, illumination, and targets — can be exported to external full-wave software and the results of an external calculation imported back (File → Import). Independent verification of a MetaLayer Pro result with a third-party time-domain solver is therefore a matter of exporting the design rather than of rebuilding it, and the comparison is made on the same materials, the same conventions, and the same spectral grid.

Application examples

Deflectors and waveguide couplers

Beam-steering elements for waveguide displays, in which the working near-infrared order must be deflected with high efficiency while the visible band passes through the element undisturbed. The two requirements act on different diffraction orders and different spectral ranges, and they are specified in a single target.

Broadband antireflection

A tapered surface relief acts as a gradual transition of the effective refractive index and is limited by the achievable aspect ratio; an interference coating acts through the interference of reflections and is limited by the available materials. Synthesized together, the two mechanisms cover spectral ranges that neither reaches alone.

Dispersive mirrors

Chirped mirrors must combine high reflectance with a specified group delay dispersion. The residual reflection at the front interface forms a weak Gires–Tournois resonator with the turning point of the chirped structure, and the resulting oscillations of the group delay dispersion are an intrinsic property of the high-reflection region. A subwavelength structure on the front surface acts directly on that interface, adding a degree of freedom that additional layers do not provide.