Cloud Computing Simulation Speeds Run on a Laptop; How Photon Design’s EME Revolutionises Photonics Design

In recent years the Finite Difference Time Domain (FDTD) method has become the go-to simulation tool for many engineers simulating photonic components. Where once its requirement for billions of arithmetic operations per simulation was severely limiting, the method now rides the coattails of the AI-GPU revolution marching toward more tolerable runtimes. However, these runtimes can be often beaten even without reliance on taxing and expensive cloud computing by exploring alternative simulation methods.

For decades, Oxford, UK based software vendor Photon Design have pioneered another simulation method, EigenMode Expansion (EME). There are few implementations of the EME method near the standard of Photon Design’s software FIMMPROP and, as such, the industry is littered with costly misconceptions related to simulation accuracy and range of applications which this paper explores and corrects.

When simulating common photonic components, there is no reason why EME and FDTD simulations should disagree, with both methods being rigorous solutions to Maxwell’s equations.  Thanks to results from [1] we can directly compare 3D simulations of a directional coupler demonstrating the startling fact; EME can produce the same results as FDTD orders of magnitude faster.

FDTD Runtimes reported from [1]. Vendor 1 results converged within <5% at 20 cells/ wavelength. Vendor 2 results do not converge within 5% in these data. Photon Design results converged within <1%. Further analysis found on [2].

• With a ~45 minute runtime, an engineer using FDTD finds they can only run 10 simulations in their working day; this could amount to a few set-up simulations to test accuracy (such as those shown above) and a handful of results. Sweeping a single parameter like the directional coupler’s waveguide separation could perhaps be performed overnight.
   
• In contrast the engineer using Photon Design’s FIMMPROP EME can run thousands of simulations in their working day, not only sweeping multiple parameters but also supporting optimisation algorithms to perfect their design while making progress with other tasks.

The option of cloud computing services does allow FDTD to reach comparable simulation times though typically offloading an additional cost to the user renting time on GPU servers – the environmental impact of which is discussed at great lengths in AI circles. For this directional coupler we find the energy consumption to be over 200 times that of EME’s requirement [2].  

In 2023, Photon Design expanded the scope of EME’s applications with an expansion called multi-topology (MT) FIMMPROP [4,5]. Unlike any other EME software, MT-FIMMPROP natively combines multiple simulation regions to build out larger devices such as MZIs and entire 3D ring resonators. Despite their centimeter lengths/ large bounding volumes, EME can still simulate these simulations in seconds.

Figure: 3D Simulation in MT-FIMMPROP – 30um coupled ring resonators.

The simulation runtimes for a 12um radius ring resonator structure are also presented in [1] for the same FDTD vendors. Engineers working on just the CPU version must set aside over 4 hours to complete just one 3D simulation. Vendor 2 writes in their page [3] that “[High-Q micro-ring resonators] are also among the most expensive devices to model with [vendor 2’s] FDTD”. Those able to afford Vendor 2’s “expensive” GPU accelerated FDTD simulations would find a simulation time of just less than 20 minutes.

In comparison, MT-FIMMPROP simulates an even larger 30um radius ring resonator in just 11 seconds.

Even for the relatively small directional coupler, Vendor 2’s FDTD required over 11 trillion calculations. The FDTD method must define full bounding volume of the geometry with hundreds of thousands grid points and propagate the field over tens of thousands of time steps. Because of this:

• Doubling the length of the directional coupler would make simulation run-times 4 times as long.
  This slows the engineer running FDTD on a CPU down to just 3 simulations per day.
   
• Doubling the radius of a ring resonator would make simulation run-times 8 times as long; even the fastest cloud computing results of [1] would have 1 hour runtimes per simulation.

In either of these cases, the simulation runtimes for an engineer using Photon Design’s EME would see little change. To describe propagation through a device with EME, the component is split up into its unique cross sections and modes solved at each. The number of cross sections needed to describe a directional coupler does not change if its length is doubled, nor if a ring resonator is doubled in size.

Further, FIMMPROP EME can re-use the simulation results of regions that are identical, effectively halving the computation run-time for the ring (pictured left) and the directional coupler discussed previously. No similar options are available natively in any FDTD.

Taking runtimes head-to-head with FDTD, the results from [1] show FIMMPROP EME to produce rigorous results in a fraction of the time even compared to the full force of cloud computing. The result is not just a less frustrating experience for an engineer but the opportunity for a much more efficient workflow that gets far more from your working week.

[1] Z. Liu, J.Poon, Comparison of Lumerical FDTD and Tidy3D for three-dimensional FDTD simulations of passive silicon photonic components. https://arxiv.org/pdf/2506.16665
[2] Additional information found on this page following references
[3]https://docs.flexcompute.com/projects/photonforge/en/latest/examples/High_Q_Ring_DirectionalCouplerCircuitModel.html
[4] D. Gallagher,  FIMMPROP – an advanced EME framework for modelling waveguide-based photonic components – performance advantages and limitations, CLEO 2026 Symposium on Photonics Modelling and Simulations [https://surl.li/lcgnww]
[5] D. Gallagher, A new approach for integrated simulation and layout of photonic integrated circuits, Photonics North 2025 [https://surli.cc/trhswf]
[6] US Patent 12,026,445

The following section provides justification for figures shown in the above.

Convergence

In Figure 1 we show results from [1] where the simulated transmission of a directional coupler is plotted as a function of the simulation’s convergence parameter. For FDTD, this is the cells per wavelength and for EME we consider the number of modes in this plot. To compare the simulations and their runtimes, we must find the smallest value of the convergence parameter at which the results show agreement with more thorough simulations.

• Photon Design’s EME FIMMPROP converges quickly as shown on figure 1. When a value of 14 modes is selected, the result of the simulation is with 0.2% of when 15 or 13 modes are chosen; agreement to two decimal places.
• For vendor 1 a value of 20 cells per wavelength is considered converged. It has a 3.7% difference with the highest resolution result presented (25 cells per wavelength).
• For vendor 2 the maximum resolution value of 25 cells per wavelength must be considered converged. The result at 20 and 25 cells per wavelength differ by 8.0%, too large a discrepancy to be considered to have converged in this report.

In the additional example of ring resonators, a value of 15 cells per wavelength is acceptable for both vendors.

EME has further convergence parameters such as discretisation of tapering waveguide and mode solver resolution. Values for these parameters have also been chosen to a convergent result.

Energy Consumption
The references below show the max power consumption of different GPU and CPUs used in these simulations. Assuming operation at max power and the runtimes of convergent results, an energy consumption is found.

Such estimates could be improved by contributions from other vendors sharing the power usage of their software directly.

[a] “up to eight NVIDIA L405 GPUs”[1] – Max power consumption: https://www.nvidia.com/en-gb/data-center/l40s/
[b] “AMD 3960X 24 Core” [1] - TDP  - https://www.cpubenchmark.net/cpu.php?cpu=AMD+Ryzen+Threadripper+3960X&id=3617
[c] AMD Ryzen 3700X 8 Core – TDP - https://www.cpubenchmark.net/cpu.php?cpu=AMD+Ryzen+7+3700X&id=3485

Spectral Response from Simulations

EME simulations provide simulation results rigorously at a single wavelength per simulation. FDTD simulations provide a spectral response. This report considers the simulation time for the first result however one may run multiple EME simulations to construct a spectral response and compare the runtime of this sweep to the FDTD runtimes quoted in [1] for a more direct comparison.

Instead of running 'N' simulations to find the results at 'N' different wavelengths, an approximation can be taken with EME such that a wavelength sweep can be taken without full recalculation of mode-lists. Photon Design has implemented such approximations in simulation tool EPIPPROP. It is common place in many of EPIPPROP’s standard examples to use as little as 3 rigorous simulations as ‘seed’ results from which the spectral response can be produced.

Further investigation on the effectiveness of these approximations in EME will be made available.