# a problem: overlap with two definitions of Gaussian beam

#1

There are two kinds of Gaussian beam definition in lumerical: fully vectorial beam and scalar beam.
In my caculation, the overlap between a waveguide mode and a gaussian beam with MFD=6um has different values using two different definitions of gaussian beam.

For the scalar beam, the parameters are set as. The overlap is 93.12%.

However, for the vectorial beam, the overlap is 77.64% which is smaller.
The parameters are
Here, NA=21.55/(6Pi)=0.16646

Would anyone like to explain the differences between these two definitions? When to use the scalar beam or the vectorial beam?

#2

Dear @baiyanfei

When the beam waist radius is comparable with wavelength, thin lens approach is more precise:
From KB page under Beam Options:

TIP: selecting the beam option When the beam waist radius is several times larger than the wavelength used, scalar approximation option should be selected. When the beam waist radius is roughly on the same order as the wavelength, the thin lens option should be used.

We expect that the results of two approaches to converge when beam waist is few time bigger than wavelength. However I was not expecting to see such a big difference. Can you please upload your simulation file for a review?

Thanks

#3

edge coupler_test.lms (242.8 KB)

The simulation model is based on the page https://kb.lumerical.com/en/pic_passive_edge_couplers_initial_eme.html
The overlap between mode 6 and the Gaussian beam is calculated. However, using two kinds of Gaussian beam would get different values. The MFD of Gaussian beam is set as 6 um.

#4

Dear @baiyanfei

Two different values for overlap analysis using two different Gaussian beam comes from the shape of Gaussian beam (as we discussed). I took a look at the literature (the link for some of them is provided here) and looks like you need a very big waist size compared to wavelength for the scalar approximation to work. In your case since they are comparable, using vector analysis should be the right approach which means that the overlap value of ~77% is the correct value.

Thanks

#5

Dear @bkhanaliloo,

I have plotted the Ey and |E|^2 for the two situations.
For vectorial Gaussian beam, the mode field of Ey is . It seems there are some mode distributions beyond the central region.
Ey of scalar Gaussian beam is . The mode is concencrated in the central region. I try to use the Gaussian beam to simulate a fiber mode and calculate the modefield overlap with waveguide mode. As seen from the figure, there are some mode distributions out of the central region for the vectorial case. I think the scalar beam might be the right choice.

The intensity distribution of the vectorial case is ,.
The intensity of the scalar case is
The beam diameter of the vectorial case is larger as seen in the figure. However, I use the same parameters definition for the two cases. The parameters for the vectorial case are
The parameters for the scalar case are

Are all these parameter settings right?

Thank you very much!

#6

Dear @baiyanfei

Thank you for the plots. I noticed them when I was working on your case. My understanding is that the vectorial approach is more rigorous.

When you use thins lens approach, software assumes that a collimated beam with radius bigger then lens in shined on the lens. Since this beam is bigger than lens, it is diffracted on the edge of the lens and thus creates artefacts and some field distribution outside the central hole. This is the main reason that while you expect to get similar results based on your settings, you are seeing some discrepancy. Please note that this is a realistic demonstration of the physical setup and is what you expect to see experimentally.

Also, it is important to note that we can simulate cases where lens is bigger than beam as is explained here:
https://kb.lumerical.com/en/index.html?ref_sim_obj_sources_plane_waves_and_beam.html

In summary, scalar approach might give you a theoretical result but will not be an indication of a real experimental setup and is a good estimation when your waist size is at least an order of magnitude bigger than your wavelength.

How to set the beam diameter and lens diameter when using fully vectorial gaussian beam?
#7

@bkhanaliloo Thanks again for your kind help!

#8

@bkhanaliloo
If the gaussian beam is generated from the fiber and is lauched into the waveguide directly without passing a lens, is the scalar gaussian beam more accurate to the real physical configuration?

#9

Dear @baiyanfei

Gaussian beam is meant to be used if you know the lens NA (or beam waist) in your experimental setup. Obviously, if you know the injected beam profile of the fiber, you can make some assumptions to create this mode using Gaussian beam.

However, the more sophisticated approach is to simulate the exact experimental setup i.e. build the fiber and then inject the mode of interest using a mode source. I have prepared you a very simple file to show you the idea but you can modify the geometry so that it matches with the fiber used in real setup.

InjectionFromFiber.fsp (809.6 KB)

Grating coupler example uses this approach:
https://kb.lumerical.com/en/index.html?pic_passive_grating_coupler_2d.html

Please let me know if you had further questions.
Thanks