# Suitable method for simulation of in-fiber interferometer

I am trying to simulate an optic-fiber sensor (in-fiber interferometer) to study its respond to temperature. The method I am using is finite-difference time-domain (FDTD), and I come out with a large memory usage problem. The wavelength of the light source centered at 1.55μm while the optical fiber has diameter of 125μm and the length of it is set to order of 10-3m. This make the number of cells become very large.

After that I had tried to reduce the length by 1/62.5 which the memory usage drop to a more reasonable value (7.8Gb) but the result become weird, in which the amplitude of the signal at point of interest is higher than the source (I don't know why).

I found that many people are using beam propagation method (BPM) instead of FDTD. Is FDTD suitable for this case (with some modification on the model) which the wavelength is much much smaller than the geometry, or is there another method which is more suitable to compute?

The structure of the sensor: SMF - single mode fiber (core diameter: 9μm); MMF - multimode fiber (core diameter: 105μm)

• Welcome to SciComp.SE. Your question can have more detail, e.g., what is the setup of your interferometer? Is there any need of 3D modelling or can it be translated to 2D? Also, you can describe better the problems you are facing. – nicoguaro Mar 17 '16 at 0:28
• @ocramz's answer is good. These fiber diameters sound like cladding - is the light mostly confined to a smaller core? (single mode or "few mode"?) or is this really completely multimode - using the full diameter? Usually in fiber interferometry you need single or few mode propagation to get interference which is measurable and easily interpreted. In that case, can you just solve for the single or few transverse modes that are in play as a 2D problem? – uhoh Mar 18 '16 at 18:09
• Actually I don't know how to model it into 2D, and the simulation I just using the commercial FDTD software which I don't need to program. – Wesley Mar 21 '16 at 3:53

A fiber Bragg grating is periodic (for a while), so perhaps you could simulate a single period of it and therefore impose the Bloch condition on the solution in the propagation direction. The mpb code written by the "ab initio" MIT group is made exactly to extract the propagation diagram (frequency vs wavenumber) of periodic structures.
To sum up, both the paraxial and the periodic-coefficient settings are approximations. I'd suggest you get acquainted with mpb (it is a linux code though) since it lets you simulate a single period of the FBG with high resolution, and repeat the analysis for various values of the refractive index contrast.