Thanks for the answers. Yes I agree the SVD would just push everything to a diagonal matrix and would likely miss some physical effects of the system, and also the degenerate modes.

Hello again Sebastien,

In your paper above, Learning and Avoiding disorder in multimode fibers, my understanding is that you measured the TM in pixel basics. After that it can be converted to the mode basics by multiplying with corresponding theoretically/analytically estimated mode basic matrix (input and output). The resultant TM in mode basics is not diagonal which it should be due to the short and straight MMF. The Deep learning frame work then converted the theoretically estimated mode basics matrix into the realistic one that accounts for the misalignment in the system. Once used with these new basic matrix, the TM in mode basic will become diagonal.

Please correct me if I am wrong but in that case why don't you simply calculate the SVD on the pixel-basic TM, and use the left and right and basic vectors as the realistic modes that include the misalignment instead of Deep learning? The deformation-free principal modes are calculated that way aren't they?

I think the issue with the SVD could be, again please correct me here, that the SV basics vectors are not the true modes of the fiber, and they could miss some modal components of the fiber modes due to the way the DMD pattern excites the modes. In that case the number of significant SVs would be quite less than the number of modes. This should not be the case as the fiber is very short and the loss on all modes would be negligible. By training the theoretically estimated modes with Deep learning using Zerkite polynomials you can assure that all the modes are there being accounted for in the basic vector matrix.

Thanks for enlightening me on this topic. I am learning so please don't the mind the silly questions and self-explanation.

sebastien.popoff wrote:

Hi,

I was told by a professor from Yale

Is it Hui Cao? Doug Stone?

Not sure I understand your point about interferences of pairs of FFT components (and by the way modes do not corresponds to FFT components).
But you can quite easily try numerically to see if it works.
We have a simple simulation code in Python in which you can simulate mode matrices and transmission matrices:
github.com/wavefrontshaping/pyMMF

Yes Hui Cao.

Thanks for the Python code I will check it out. We have a Matlab code that we simulate the effective indices of the fiber, and assuming random coupling to each mode we could also estimate the SVD but we haven't run it for the case of many modes because it is too slow. Our measurement kind of showed the SVs in the vicinity of 2N (with N is the mode number) as well. So I think it is likely the case.

Yeah sorry I wasn't clear. I meant the FFT component corresponds to a pair of modes that interferes with each other. The intensity is the square of summation of all the modes and therefore it could be decomposed into FFT components with each FFT peak corresponding to the interference of 2 modes. I think that when the number of modes become large (~100), there will be many overlapping FFT frequencies because it is basically the difference between the effective indices of 2 modes and the ultimate SVs will average to 2N.

For the case of optical field I can understand that a TM linearly maps the input fields to output fields. Doing an SVD on the TM of a MMF can reveal the steps in which the input field (SLM-pixel vector) is projected onto the fiber mode space, scaling along each mode axis by its SV, and sum up the fiber mode vectors back to the CCD-pixel vector. But intensity is nonlinear which depends on the input fields in a quadratic way so I am struggling with the meaning of an "Intensity TM" and the SVD on such matrix.

Thanks again for your answers, very helpful.

Hi Sebastien,

Thank you very much for your answer.

About the SVD on intensity, it is also my problem that I cannot find any formal discussion of that but I was told by a professor from Yale that should be the case. My (guessed) understanding of its physical meaning is that the left SV vectors mapping to the intensity can be considered as a summation in the Fourier domain with each pair of modes interfering is represented by a FFT frequency. Even though in that case the total number of FFT components would be larger than 2N (with N the number of modes), for large enough N many of the constituent interferences will have overlap FFT components and average to 2N.

But I cannot prove it theoretically yet.

Hi forum members,

Could you please shed some light for me on the measurement of TM, for the case of a multimode fibre?

1. Is it absolutely critical to use a orthorgonal basis in the input? As for the case of a MMF, can I use random patterns as per the paper below. My thinking is along this
2. Use some set of random patterns and measure a TM.
3. Apply SVD on the TM, find SVs (say 98% of the total power)
4. Use a bigger set of random patterns, measure again the TM
5. Apply SVD again, check the SVs... when the number of SVs is stable it indicates that all of the modes has been activated (assuming large NA input)

Can it be done that way? Here the paper they used the random pattern but they just say that 900 patterns is enough.
https://arxiv.org/ftp/arxiv/papers/1806/1806.09315.pdf

1. The TM for a multimode fibre should ideally has the rank of N (number of macro pixel on the SLM)? It is because I think the basic vectors of both left and right singular matrices are the same fibre modes, so that the TM would be an square vector of rank N.

My question is: After obtaining the TM, should I apply SVD on such TM and try to reduce it to a leaner version (less noisy) of the TM before testing the stuffs such as focusing or imaging?

1. I was told that if I do the SVD directly on the intensities obtained from different input (basically not applying the 4-phase or off-axis technique to extract the complex field pattern but just use the intensity vectors as column of the "intensity TM"), the number of SVs will be roughly twice the number of modes. I could not find any paper which actually did this but just wonder if it is something obvious that someone here can give me some light on? For the case of TM matrix measured on the complex field pattern then the number of SVs is the number of modes as shown in this paper
   https://www.osapublishing.org/ol/fulltext.cfm?uri=ol-37-21-4558&id=244834

Thank you very much for your help.

My problem turned out to be with the incident angle. With the angle less than 10 deg the issue was solved. Before I noticed extra brighter spot jump on to the position of the 1st order at phase value above Pi and increase the power at the spot (filtered through a pinhole).

Thanks Sebastien.

I also applied a Sine profile instead of the rectangular one on the SLM, results were the same. Changed the incident angle, did not help. As the SLM came with dual windows AR coating I made sure to change the wavelength to 1550 nm before experiment.

Perhaps I would contact the vendor with my data and see if I did something wrong with the setup, or make up a Michelson interferometer or a reflection setup with polarizer and analyzer to check the phase directly.

Cheers,

A

Hi all,

I am new to SLM so got a Santec SLM-100 with dual windows (visible and 1550 nm). A graduate student has used the visible windows for a while and it seems to work ok. I am now trying to use this for some experiment in the 1550 nm region and want to test to make sure that the SLM is working fine for that wavelength? Atm I made up a simple line grating with a pitch of 60 um (6 pixel) and diffract the zero-order to the 1st order when the grating is On. I then changed the level of phase modulation at all lines (increase the value in the csv file) and observe increasing power at the 1st spot.

My expectation is that the power would gradually increase to a peak at Pi (something between 0 and 1024 values of the pixel), then gradually reduce to near zero when the phase change reaches 2pi (1024). However I have power fluctuating and increasing all the way to nearly 2Pi (1000 value). What did I do wrong here?

Your comments are highly appreciated.

A