32Bit Software TM and TE labels wrong way round

[Yameng Cao]

I am trying to reproduce the dispersion diagram, for an H1 defect in a rod photonic crystal lattice, lattice constant a = 1, rod radius r =0.2a, refractive index n=3.5. A TM mode should be confined, with resonant frequency within the bandgap.

Using OptiFDTD’s 32bit simulation software, Plane Wave Expansion method, to calculate a 5×5 supercell containing the H1 defect, The correct dispersion and corresponding resonance frequency for TM mode can only be found by calculating the TE trace in OptiFDTD, and vice versa for TE.

Is this because I have defined something incorrectly? Or is it an actual bug in the software? If it’s bug does it also apply to every other instance where one has to select TM or TE for simulation? For instance 2D and 3D FDTD simulations and also the E(x,y,z) and H(x,y,z) field amplitudes? Are all instances of electric field and magnetic field labels the wrong way round in 32 bit software?

Thank you.

[Damian Marek]

Yameng,

I think this comes from different conventions for defining TE and TM modes. In OptiFDTD, the convention is:

TE : Hx, Ey, Hz
TM : Ex, Hy, Ez

whereas a very popular photonic crystal reference book “Photonic Crystals Molding The Flow of Light” uses the convention:

TE : Ex, Ey, Hz
TM : Hx, Hy, Ez

[Yameng Cao]

Thank you, though I do not understand why you take this convention, why not call electrical field components Ex, Ey and Ez and magnetic with Hx Hy and Hz? Do you know where in that book is the convention explained?

Yameng

[Damian Marek]

The difference comes from different dimensions used in 2D calculations and different ways of defining the transverse plane. In our formulation of 2d-FDTD the dimensions are x and z and from that the fields can be decomposed into the two groups I gave above. However, usually a 2D simulation will propagate along z, and so the transverse fields are defined as along x and y.

In the photonic crystal book I referenced they define a 2D dimension as x and y and the transverse plane to also be x and y, so therefore they will have different fields for the TE and TM and in fact there TM fields correspond to our TE fields. I understand this is confusing! Maybe looking at our reference below and the formulation of the FDTD equations will help.

NOTE: The E and H still stand for electric and magnetic field, however the two types of polarizations are mixed up with different field components.

FDTD Basics

Please let me know if you have any questions!

[Yameng Cao]

I understand this now, thank you!

[Author]

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