Single mode and multimode ridgewaveguide laser




I am simulating a ridgewaveguide laser layer structure to analyse its TE modes. In my simulation I am facing some of these problems

  1. I have calculted modes and the mode with largest effective index (3.366492) is ‘1’ which is fundamental TE mode? But when I select fundamental mode then I get a mode with second largest neff, that is 3.36643. Can I please know the my fundamental mode TE is not the one with highest neff?

  2. Mode should be confined under the ridge in ‘active’ layer but what I see from ‘YZ profile monitor’ is a mode that is not confined under the RWG, but its at the position of pink arrow of mode source. How can I know is this mode confined in a right layer?

  3. If I select fundamenal TE mode source, I get ‘-0.281168’ T_backward (from mode expansion monitor), but if I launch more modes then T_backward in fundamental mode changes. Isn’t T_backward in fundamental mode should remain same if I launch other modes?

  4. Finally, is there any way I can confirm that my RWG is fundamental TE mode?

  5. Is there any way I can confirm that my ridgewaveguide is a fundamental TE mode.


Here is my simulation GaAs_RWG.lms (702.2 KB)


Hi @nouman.zia

  1. The first mode is TM mode. When the TE polarization factor is zero, it means that the mode is TM polarized.

2,3,4,5. The green cross in your simulation is placed outside the varFDTD region. Please place it on top of waveguide to make sure that simulation is set properly and check the injected mode from the effective index tab. Blue crosses can be outside the varFDTD region, but green cross should be located on top of waveguide.

4,5: If the fundamental mode is injected I expect it will be propagated over the waveguide. You can use profile monitors to check and make sure that proper mode is propagated. I believe the confusion is caused because the green cross was located outside varFDTD and you were injecting proper mode.

Please rerun the modified simulations and keep me updated if you had further questions.

Please limit your post to one question so that we can address it properly before moving on the next question.


Thank you @bkhanaliloo!
Problem still exists in injecting the right mode. I have attached a modiifed simulation with green cross on the top of RWGGaAs_RWG.lms (512.1 KB)


Hi @nouman.zia

The plot shows the effective index as a function of z in the waveguide:

As you can see, the p_active object has the highest material index. Is this intended? I was expecting the ridge waveguide to have the highest effective index.

As a result there are many different supported modes. Here are some of the interesting modes:

The mode has to be properly selected. Once you confirm the mode, we can study its propagation in the waveguide.


Hi @bkhanaliloo,
Thanks for feedback!
Yes p_active should have high index becuase it confines the mode in vertical direction, whereas a ridge waveguide provides mode confinement in horizontal direction - that eventually confines the mode below the RWG and in p_active layer.
I have updated my design and now it looks better gaas_rwg.lms (748.4 KB). I did some changes in the refractive index.
My next issue is the different effective indexes of fundamental TE modes obtained from ‘Eigen mode solver for mode source’ and ‘Eigen mode solver for slab modes’ windowa . Do you have any thoughts why these two windwos give me different results and what is different between these two mode analysis results?

I have also calculated fundamental TE mode from FDE solver, for same structue, and it looks different from varFDTD gaas_rwg_FDE.lms (338.3 KB)


Hi @nouman.zia

The varFDTD works by collapsing a 3D geometry into 2D. Thus the effective index of the mode will be different in the z-direction (obtained from Effective index tab in varFDTD) and y-direction (obtained from mode source). Please note that the calculations in both cases use 1D FDE solver.

The results will be also different from a 2D FDE solver that you obtained with FDE solver. You can obtain the same results as above if you use 1D FDE solver by selecting 1D solver type from General settings of FDE:


Thanks @bkhanaliloo!
I optimizing my ridge waveguide for fundamental TE00 mode, so other higher order modes should not be present. I believe if I have optimized my geometry for TE00 mode in 2D FDE then it should be TE00 mode in varFDTD. The design I shared with you is already optimized using 2d FDE, but when I bring this to varFDTD, I see some heigher order modes along y/z-direction.

I can also see this mode propagating in the waveguide (below). But the effective index shown by mode expansion monitor belongs to some other mode (maybe TE00). Is this possible to confirm which mode eventully propagates in the waveguide simulation?


Hi @nouman.zia

I selected the fundamental mode in varFDTD and below are the E intensity results that I obtained from profile monitors:


I am also attaching the simulation file for your review:
GaAs_RWG_BK.lms (537.4 KB)

It is important to make sure that you are selecting the correct mode in varFDTD and Mode source.

Please elaborate on your inquiry if you had any further questions. Another option would be to sun simulations in FDTD or start with some simpler design in varFDTD.


Thanks @bkhanaliloo,

I went for a simple design of a Si RWG in varFDTD. Out of curiosity I did compare the effective indexes from varFDTD with FDE 1D X, and the results are quite different. varFDTD: taper_width_sweep_var_FDTD.lms (465.2 KB)
FDE:taper_width_sweep.lms (239.7 KB).
Btw, is there any guide on lumerical KB where I can find the role of 1D and 2D FDE, and mode solvers in varFDTD?
I have understanding of these parameters but I don’t know how they are used in lumerical.


Hi @nouman.zia

Sorry for a late reply. We had a long weekend here.

One inconsistency between the simulation files was that the FDE background index should be 1.

Regarding comparing 1D FDE and varFDTD: I assume you were comparing the 1D Y:X prop FDE with results from source object in varFDTD?

As I explained above, varFDTD works by collapsing a 3D geometry into 2D. The effective index results (obtained for collapsed geometry) thus would be different than the FDE where it looks at material index at each location. For example, see the plots below for effective index in the y-direction where they have different min and max values:

varFDTD effective index:

1D FDE index:

If you want to learn more about the governing equations, please visit the solver physics section in the links below:

You can also watch the first part of the EDU courses on FDE and varFDTD to learn more about how the algorithm works.


Thank you @bkhanaliloo,
Everything looks fine by now! Now my next step was to angle the waveguide in FDTD and measure reflection of a mode. It looks that mode profile becomes really poor infront of mode source and even poor after the mode source (reflected field). Seems mode is not confined in the waveguide after reflection. Also I am not sure where to place my exp. monitor to get the right reflection, as its value changes with the location of monitors.
Mesh accuracy is kept to save simulation time. My orignal dimensions are even much larger.


Hi @nouman.zia

Sorry for a late reply. Can you please share your simulation file for a review?

In general, injected light must satisfy total internal reflection (TIR) if you want to have confined modes. Otherwise you will loose the power after a few reflections from the edge of the waveguide. Please visit the link below where we discussed the light propagation in angled waveguides:
What is the corresponding angle of incidence for guided modes in a waveguide?


Thank you!
Attached is the lms file.tilted_RWG.lms (543.9 KB)


Hi @nouman.zia

My colleague @gbaethge is working on this case and will provide you a response once he has further information:
Simulation tool and geometry

Thanks for your patience.