Two worlds: geometrical and wave optics
A first approximation when choosing a method comes from the question: how large are the elements of the system relative to the wavelength of light? That is a good engineering rule of thumb, but not a complete physical criterion.
- When the elements are much larger than the wavelength (lenses, reflectors, objectives), it is usually enough to treat light as geometric rays — the domain of ray tracing. Even then, wave effects can be significant: diffraction at apertures, resolution limited by the pupil, periodic structures. In those places ray tracing is supplemented with approximate models or, locally, with a diffraction method.
- When the sizes are on the order of the wavelength (waveguides, gratings, metasurfaces, nanostructures), a wave method is needed — amplitude, phase, polarisation, diffraction and interference become important. This does not always mean a full solution of Maxwell's equations by FDTD: for many such tasks BPM, EME, RCWA, mode solvers, or physical-optics methods are more appropriate and cheaper.
- Between these extremes lies physical / diffraction optics — scalar diffraction on the macro scale (laser-beam propagation, apertures, the Airy spot, coupling to a fiber).
- When the elements are much larger than the wavelength (lenses, reflectors, objectives), it is usually enough to treat light as geometric rays — the domain of ray tracing. Even then, wave effects can be significant: diffraction at apertures, resolution limited by the pupil, periodic structures. In those places ray tracing is supplemented with approximate models or, locally, with a diffraction method.
- When the sizes are on the order of the wavelength (waveguides, gratings, metasurfaces, nanostructures), a wave method is needed — amplitude, phase, polarisation, diffraction and interference become important. This does not always mean a full solution of Maxwell's equations by FDTD: for many such tasks BPM, EME, RCWA, mode solvers, or physical-optics methods are more appropriate and cheaper.
- Between these extremes lies physical / diffraction optics — scalar diffraction on the macro scale (laser-beam propagation, apertures, the Airy spot, coupling to a fiber).
A safer rule than the size-to-wavelength ratio alone: the more significant the wave effects are relative to the geometric scale of the problem, the more a wave or diffraction method is needed — and the choice of a specific wave method depends on the geometry, the directionality of propagation, and whether back-reflections matter.
We cover the fundamentals of ray tracing separately → What is ray tracing?. Here we focus on the map of methods.
We cover the fundamentals of ray tracing separately → What is ray tracing?. Here we focus on the map of methods.
Ray tracing (geometrical optics)
Tracing millions of rays through a 3D model. Two modes:
- Sequential — rays pass through surfaces in a fixed order. For imaging systems: aberrations, MTF, diffraction PSF analysis. Tool: OSLO; sequential ray tracing (Sequence Editor) is now also offered by TracePro.
- Non-sequential — rays hit any surfaces in any order, reflecting and scattering multiple times; the Monte Carlo method. For illumination, stray light, and optical efficiency. Tool: TracePro.
When: macro-optics, illumination, imaging systems, stray light analysis. Ray tracing is not a full-wave solution of Maxwell's equations — phenomena that require amplitude and phase information need appropriate models or wave methods. TracePro does, however, provide selected models and functions that let you account for specific diffraction effects (e.g. Aperture Diffraction), as well as ray splitting, reverse ray tracing, importance sampling, and scattering and fluorescence models.
- Sequential — rays pass through surfaces in a fixed order. For imaging systems: aberrations, MTF, diffraction PSF analysis. Tool: OSLO; sequential ray tracing (Sequence Editor) is now also offered by TracePro.
- Non-sequential — rays hit any surfaces in any order, reflecting and scattering multiple times; the Monte Carlo method. For illumination, stray light, and optical efficiency. Tool: TracePro.
When: macro-optics, illumination, imaging systems, stray light analysis. Ray tracing is not a full-wave solution of Maxwell's equations — phenomena that require amplitude and phase information need appropriate models or wave methods. TracePro does, however, provide selected models and functions that let you account for specific diffraction effects (e.g. Aperture Diffraction), as well as ray splitting, reverse ray tracing, importance sampling, and scattering and fluorescence models.
FDTD — the full Maxwell's equations
The Finite-Difference Time-Domain method discretises space onto a Yee grid and propagates the E and H fields step by step in time. It solves Maxwell's equations directly and handles very complex geometries and materials — dispersive and nonlinear; a single run covers a broad band (the Fourier transform of the impulse response).
Cost: the grid resolution must faithfully reproduce the wavelength in the medium (on the order of ten to a few tens of points per wave), and the time step is limited by a stability condition (CFL). In three-dimensional FDTD the computational effort can grow very quickly as the grid is refined — with the spatial and time steps reduced together, the scaling can be roughly fourth-order. The actual size of the region you can compute depends on the resolution, the dimensionality (2D/3D), the materials, the number of time steps, and the available memory and hardware (CPU/GPU).
When: nanostructures, photonic crystals, metasurfaces, plasmonics, 2D/3D gratings, strong back-scattering, resonators. Tool: OptiFDTD; OptiOmega is a GPU-accelerated 3D FDTD solver with a mode solver, intended for larger tasks.
How it works and when exactly to use it — full description → How does the FDTD method work, and when should you use it?.
Cost: the grid resolution must faithfully reproduce the wavelength in the medium (on the order of ten to a few tens of points per wave), and the time step is limited by a stability condition (CFL). In three-dimensional FDTD the computational effort can grow very quickly as the grid is refined — with the spatial and time steps reduced together, the scaling can be roughly fourth-order. The actual size of the region you can compute depends on the resolution, the dimensionality (2D/3D), the materials, the number of time steps, and the available memory and hardware (CPU/GPU).
When: nanostructures, photonic crystals, metasurfaces, plasmonics, 2D/3D gratings, strong back-scattering, resonators. Tool: OptiFDTD; OptiOmega is a GPU-accelerated 3D FDTD solver with a mode solver, intended for larger tasks.
How it works and when exactly to use it — full description → How does the FDTD method work, and when should you use it?.
BPM — the Beam Propagation Method
Solves an approximate (paraxial or wide-angle) wave equation, propagating the beam step by step along one axis. It assumes that propagation is mainly in one direction and that the refractive-index contrast is small.
Advantage: orders of magnitude faster than FDTD for long structures. Limitation: it captures back-reflections, large angles, and strong contrast poorly or not at all.
When: long waveguides, directional couplers, Y-branches, tapers, MMI structures, mode analysis in fibers. Tool: OptiBPM.
Advantage: orders of magnitude faster than FDTD for long structures. Limitation: it captures back-reflections, large angles, and strong contrast poorly or not at all.
When: long waveguides, directional couplers, Y-branches, tapers, MMI structures, mode analysis in fibers. Tool: OptiBPM.
EME — eigenmode expansion
EME (eigenmode expansion) splits the structure into sections that are invariant along the propagation direction; in each section the field is expanded onto a basis of eigenmodes, and the transitions between sections are described by scattering matrices (S-matrix). Unlike BPM, the method accounts for back-reflections and can be much more efficient than direct methods for long structures — particularly when the geometry changes in a limited number of sections. The cost depends among other things on the number of sections, the number of modes included, and how the structure varies.
When: adiabatic tapers, ring resonators, couplers, devices with reflections. Limitation: not very efficient for structures that are highly irregular along the propagation axis — FDTD is appropriate there.
Optiwave provides mode analysis in OptiMode and the propagation tools OptiBPM and OptiFDTD; EME as a method can be realised within specific design flows. It is worth knowing — for many long devices it can be more accurate than BPM and cheaper than FDTD.
When: adiabatic tapers, ring resonators, couplers, devices with reflections. Limitation: not very efficient for structures that are highly irregular along the propagation axis — FDTD is appropriate there.
Optiwave provides mode analysis in OptiMode and the propagation tools OptiBPM and OptiFDTD; EME as a method can be realised within specific design flows. It is worth knowing — for many long devices it can be more accurate than BPM and cheaper than FDTD.
Mode solver (FEM)
It does not propagate the field — it determines the eigenmodes, their propagation constants, and losses in a given waveguide or fiber cross-section. It can provide mode profiles and parameters used as input for propagation methods, including BPM and EME, and is the basis for analysing bend losses, inter-mode coupling, birefringence, and waveguide dispersion.
When: characterising a waveguide before a propagation simulation; designing specialty fibers (polarisation-maintaining, microstructured). Tool: OptiMode; for telecom fibers — OptiFiber.
When: characterising a waveguide before a propagation simulation; designing specialty fibers (polarisation-maintaining, microstructured). Tool: OptiMode; for telecom fibers — OptiFiber.
RCWA — periodic structures
Rigorous Coupled-Wave Analysis (also known as the Fourier Modal Method) expands the field and the material profile into a Fourier series in the plane of periodicity and solves the eigenvalue problem layer by layer. Very efficient for periodic structures: diffraction gratings, sub-wavelength gratings, periodic metasurfaces, photonic-crystal layers.
RCWA is particularly intended for periodic structures; this does not, however, mean a simple split "periodic = RCWA, aperiodic = FDTD" — there are other methods for aperiodic structures too, and FDTD with periodic boundary conditions also computes periodic structures. In the portfolio: fiber gratings (Bragg / FBG and long-period) are modelled by OptiGrating; general periodic structures — OptiFDTD with periodic boundary conditions.
RCWA is particularly intended for periodic structures; this does not, however, mean a simple split "periodic = RCWA, aperiodic = FDTD" — there are other methods for aperiodic structures too, and FDTD with periodic boundary conditions also computes periodic structures. In the portfolio: fiber gratings (Bragg / FBG and long-period) are modelled by OptiGrating; general periodic structures — OptiFDTD with periodic boundary conditions.
Physical and diffraction optics
Selected diffraction methods — the scalar Fresnel–Kirchhoff integral, angular-spectrum propagation, Gaussian Beam Decomposition — describe diffraction and interference on the macro scale without solving the full Maxwell's equations (physical optics also includes non-scalar methods). They form a bridge between ray tracing and electrodynamics: laser-beam propagation, apertures, spot analysis, depth of focus, coupling to a fiber.
When: systems with apertures on the order of thousands of wavelengths, where diffraction matters but FDTD is infeasible. Available among other things as a supplement to ray tracing in OSLO (diffraction PSF/MTF analysis).
When: systems with apertures on the order of thousands of wavelengths, where diffraction matters but FDTD is infeasible. Available among other things as a supplement to ray tracing in OSLO (diffraction PSF/MTF analysis).
System and circuit simulation
At the highest level of abstraction you do not model the field, but the signal parameters:
- OptiSystem — whole transmission links (WDM/DWDM, coherent, 400G+): power budget, OSNR, BER, Q-factor, dispersion, fiber nonlinear effects, EDFA amplifiers.
- OptiSPICE — simulation of optoelectronic circuits: it combines models of optical and electronic components (lasers, modulators, photodiodes, amplifiers) in a single circuit-level simulation.
When: assessing the performance of the whole system, once the geometry of the individual component is already fixed.
- OptiSystem — whole transmission links (WDM/DWDM, coherent, 400G+): power budget, OSNR, BER, Q-factor, dispersion, fiber nonlinear effects, EDFA amplifiers.
- OptiSPICE — simulation of optoelectronic circuits: it combines models of optical and electronic components (lasers, modulators, photodiodes, amplifiers) in a single circuit-level simulation.
When: assessing the performance of the whole system, once the geometry of the individual component is already fixed.
The hybrid approach and STOP analysis
A complete project usually combines methods:
- component (FDTD / EME) → section or circuit (BPM, OptiSPICE) → system (OptiSystem); each level verifies a different aspect.
- STOP (Structural–Thermal–Optical Performance) — coupling mechanical and thermal simulation (FEM) with optical: stresses and thermal expansion of the mounts can change the geometry of the system and the refractive index, which can lead to a degradation of imaging parameters such as MTF (the analysis may also show that the effect is negligible). Key in aerospace, space, and defence optics.
- CAD integration — RayViz lets you apply optical properties and run ray tracing directly in the SOLIDWORKS environment, and the model can then be passed to TracePro for a full analysis.
- component (FDTD / EME) → section or circuit (BPM, OptiSPICE) → system (OptiSystem); each level verifies a different aspect.
- STOP (Structural–Thermal–Optical Performance) — coupling mechanical and thermal simulation (FEM) with optical: stresses and thermal expansion of the mounts can change the geometry of the system and the refractive index, which can lead to a degradation of imaging parameters such as MTF (the analysis may also show that the effect is negligible). Key in aerospace, space, and defence optics.
- CAD integration — RayViz lets you apply optical properties and run ray tracing directly in the SOLIDWORKS environment, and the model can then be passed to TracePro for a full analysis.
Quick cheat sheet
| Task / phenomenon | Typical scale | Method | Tool |
|---|---|---|---|
| Imaging, aberrations, MTF | mm–cm | sequential ray tracing | OSLO; also TracePro (Sequence Editor) |
| Illumination, stray light, optical efficiency | mm and larger | non-sequential ray tracing (Monte Carlo) | TracePro |
| Nanostructure, metasurface, photonic crystal | nm–µm | FDTD | OptiFDTD; OptiOmega (GPU, 3D) |
| Long waveguide, coupler, taper, MMI | µm–mm | BPM | OptiBPM |
| Taper / resonator with reflections, long device | µm–mm | EME (+ mode solver) | OptiMode + OptiBPM / OptiFDTD |
| Modes, bend losses, waveguide dispersion | µm | mode solver (FEM) | OptiMode, OptiFiber |
| Diffraction grating, periodic metasurface | nm–µm | RCWA / FDTD | OptiFDTD |
| Fiber grating (FBG, long-period) | µm–mm | fiber-grating analysis | OptiGrating |
| Laser-beam propagation, macro diffraction | mm–cm | physical / diffraction optics | OSLO (diffraction analysis) |
| Transmission link (DWDM, 400G) | system level | system simulation | OptiSystem |
| Optoelectronic circuit | circuit level | circuit-level simulation | OptiSPICE |
How to choose the method and the tool
Step by step — the scale of the system, the goal (imaging / illumination / transmission), the design stage, CAD integration, and the licensing model — we set out in a separate guide → How to choose optical simulation software?. If you are not sure where the boundary between methods runs for your system, describe the problem to us — we will point to the method and the package.