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**FIMMPROP is typically much faster and more accurate than FDTD and BPM for a wide range of devices.**

FIMMPROP is the propagation simulation option for the FIMMWAVE base module. It is a highly innovative tool for simulating 2D and 3D propagation phenomena in waveguides based on the EME (EigenMode Expansion) method, permitting the user to analyze a variety of 3D waveguide structures in a rigorous and fully vectorial manner.

- Rigorous Maxwell Equation solver
- Semi analytical, fully vectorial 3D propagation
- Bidirectional algorithm models all internal reflections
- Wide angle simulation
- Design MMIs, periodic structures, tapers and bends FAST!
- Flexible design paradigm

FIMMPROP is an inherently bi-directional tool which takes all internal reflections into account. It is therefore capable of modeling structures such as Bragg gratings or AR coatings, which are not solvable by other methods such as BPM. It can also model devices with strong internal reflections such as waveguides terminated by a tilted or straight facet. In addition FIMMPROP is also a true "wide angle" algorithm compared to "wide angle BPM" which can model light travelling at a wide angle only if all the light is travelling close to that same angle.

FIMMPROP is a great tool for the thinking optics designer since it provides not only a transmission efficiency result, but the mode analysis approach gives you a deep insight into what is going on inside the device, often giving invaluable hints about how to improve the structure. Furthermore, the flexible design interface makes it very easy to model complicated systems, which may include bends, couplers, mode converters etc. FIMMPROP can also model tilted joins, facets and free space regions, e.g. for waveguide-gap-fibre simulations.

The ease of use and the speed of the calculations make FIMMPROP the ideal tool for designing a wide range of sophisticated structures and moreover, the use of semi analytical modal methods permits calculations to achieve high accuracy even for complicated structures.

PC: x86+x64: Win2000/XP/Vista/7, 1GB RAM, 2GHz or better recommended.

FIMMPROP is based on the EME (EigenMode Expansion) method which enables the fields to be calculated using fast semi analytical methods and the nature of the calculations allow the propagation to be treated in a fully bi-directional manner making FIMMPROP capable of modeling structures which are insolvable by other methods such as BPM.

The EME technique has been well established in photonics for some time. In essence it is a very simple technique which starts with a definition of an eigenmode of a waveguide.

This very simple z-dependence is the key to enabling EME to solve long slowly varying structures quickly and efficiently.

Boundaries surrounding the structure create a discrete set of “radiation modes,” therefore in a typical waveguide, there are a few guided modes (which propagate without loss along the waveguide), and some radiation modes (which carry optical power away from the waveguide). The guided and discretized radiation modes together form a complete basis set – in other words we can express any solution of Maxwell’s Equations in the region of the waveguide in terms of a superposition of the forward and backward propagating modes:

where the Em and Hm terms are for the electric and magnetic field profiles of the mth mode, bm is its propagation constant, and the C terms are the amplitudes of the mode in the +z and –z directions.

Assuming an infinite sum, this set of equations is an exact solution of Maxwell’s Equations in a linear medium. In practice we can truncate the sum to a finite basis set and still maintain high accuracy. The size of the set needed will depend on the problem, with more modes needed to model light travelling at a large angle to z.

The above describes the technique for analyzing only z-invariant structures. At a join between two waveguides continuity conditions for the fields allow us to deduce a relationship between the coefficients of the form:

where SJ is a scattering matrix for the join. The scattering matrix expresses the fields travelling away from the join in terms of the fields incident on the join. A complete set of modes permits to write a scattering matrix for any component.

These few equations immediately illustrate some useful features of EME:

- EME is fully bi-directional; in fact it can be made omni-directional if sufficient modes are used.
- EME is a fully vectorial algorithm, making no approximations about the light polarization.
- EME is a rigorous solution to Maxwell's Equations; the main approximation being the finite number of modes.
- Propagation along the length of a z-invariant section is near-instantaneous. i.e. the calculation time is independent of the length of the device.
- The scattering matrix approach means that you solve the problem for all inputs simultaneously, so you can for example get the response for both TE and TM polarizations in one go.
- If you alter the structure, the routine needs only to recalculate the elements that have changed.
- It allows efficient modeling of periodic or repeating structures since one can evaluate the s-matrix of one period and then re-use.

Parameter Scanners: Much attention has been paid to efficiency, so that when any parameter of the structure is changed, only the minimum amount of recalculation is done. To exploit this fact FIMMPROP comes with a scanner which allows you to vary the structure parameters continuously. This provides a quick and intuitive graphical way of optimizing your structure, slashing the design cycle in a way unachievable using other numerical methods.

A new generic optimization tool KALLISTOS is now available, capable of automatically improving the characteristics of any FIMMPROP component by altering its dimensions and refractive indices.

From this…. ….to this within in minutes.

In this simulation the fundamental mode is injected from the left into a GaAsP Multi Mode Interference coupler. This device has length of around 1000um and is a high refractive index structure. Using FIMMPROP, an accurate 3D Calculation on a 2.8GHz PC takes about 10 seconds!! In comparison FDTD methods would take many hours, and BPM would perhaps not be accurate due to the high refractive index contrast.

In this example the output varies with the length of the middle section. The eigenmodes of each section are calculated during the first simulation. When we vary the length of any section these eigenmodes are still valid and therefore any recalculation is an instantaneous operation. This feature alone makes possible design operations which with other propagation methods, such as BPM, FDTD would require unrealistic lengths of time.

Therefore it was possible to obtain a graph of Transmission vs MMI box length with 1000 data points in just 10 seconds or so. It can be easily seen that the optimal length is around 440um.

Imagine how long 1000 x 3D simulations of this high index structure take using BPM or FDTD software.

FIMMPROP is ideal for designing continuously varying structures such Y-junctions and tapers where typically the designer’s objective is near-adiabatic performance. Exploiting these near-adiabatic properties with semi-analytic routines, the program is able to determine how long a structure must be to achieve adiabatic coupling much more rapidly than traditional optical propagation techniques. Moreover, tapers can be modeled with arbitrarily wide angles and high refractive index step, since FIMMPROP makes no approximations in Maxwell's equations.

The following example of an SOI mode convertor shows that FIMMPROP can handle high index structures quickly and accurately. The vectorial nature of the EME algorithm also allows study of polarization dependence which can be significant in these cases.

Reference: “*Low loss mode size converter from 0.3um square Si wire waveguides to singlemode fibres*”. T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, & H. Morita, NTT Telecommunications Energy Laboratories ELECTRONICS LETTERS Vol. 38 No.25

Top: TE Polarization (Side View), Bottom: TM Polarization (Side View)

The above results show that the TE and the TM responses are quite different. The TM mode is guided in the Si core much longer than the TE case. The Scattering Matrices show that the transmission values for TE (99.4 %) and TM (96.0%) are slightly different too. Only a vectorial algorithm such as EME is able to provide this critical information.

Calculation time for this 3D 600um SOI mode convertor on a 2.8GHz PC is approx. 10 minutes.

FIMMPROP also gives the user more information than just transmission/reflection efficiency. For example FIMMPROP can readily show information about the coupling between the modes inside the structure. Other more numerical methods such as BPM or FDTD do not have access to this information and yet this information can be critical for the designer who needs to understand not only how the design performs but why.

Above: Power in the modes as a function of Z

The above shows the results of a 6mm long tapered fiber simulation. The graph shows the mode coupling between the modes inside the fiber as the core and cladding diameter changes. The red line shows the power in the fundamental mode, it can be easily seen that from Z = 2mm there is significant power coupling between the fundamental mode to multiple cladding modes reducing the core output power at the end of the fiber to less than 30%.

Calculation time for this 3D simulation of the 6mm fiber taper on a 2.8GHz PC is approx. 15 minutes.

**A small sample of publications using results from FIMMPROP**

"*Compact and highly-efficient polarization independent vertical resonant couplers for active-passive monolithic integration*" - M. Galarza, D. Van Thourhout, R. Baets, M. Lopez-Amo. Optics Express, vol. 16(12) 2008 , pp.8350-8358

"*Compact and low loss silicon-on-insulator rib waveguide 90° bend*" - Yusheng Qian, Seunghyun Kim, Jiguo Song, Gregory P. Nordin and Jianhua Jiang. Optics Express, Vol. 14, No. 13, June 2006, pp. 6020-6028

"*Design of modulation-doped SiGe/Si optical modulator integrated in a submicrometer silicon-on-insulator waveguide*" - Delphine Marris, Eric Cassan, Laurent Vivien, Daniel Pascal, Alain Koster, Suzanne Laval. Optical Engineering, Vol.44(8), 084001, August 2005

"*All-Optical Efficient Wavelength Conversion Using Silicon Photonic WIre Waveguide*" - K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji and S. Itabashi. IEEE Photonics Technology Letters, Vol. 18, No. 9, pp. 1046-1048, May 2006

"*Hollow-Core Waveguides and 2-D Waveguide Arrays for Integrated Optics of Gases and Liquids*" - Holger Schmidt, Dongliang Yin, John P. Barber, Aaron R. Hawkins. IEEE Journal of Selected Topics in Quantum Electonics, V11, No. 2, March/April 2005

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