Hello philsol: May I ask what meaning is this code or which paper is it from?

[Hd-Edison]

Hello philsol:
May I ask what meaning is this code or which paper is it from? It's in philsol-master/examples/example_KTP_waveguide.ipynb.

      def n_guide(lam):
          A = 2.17954368571 
          B = np.log(2.17954368571 / 1.75292972992) / 0.7
          return A * np.exp(- B * (lam - 0.3)) 

     And thanks for your work.                     Hd-Edison

[philmain28]

Ah yes it might not be clear from the description but it is an algorithm to track a mode over a wide range of wavelengths in a highly multimode structure. To get the full picture look at the cell below. These kind of trick can be quite important for structures like the one shown in

https://github.com/philmain28/philsol/blob/ea0cffa7fe75824b37f664e20b40b1dde0c2facc/examples/Hollow_Core_Fibre.ipynb

Anyway the steps in the algorithm are something like this:

• Calculate n at the extremes of the range
• Come up with a simple fitting function between them
• Use the fit to come up with an accurate initial guess to pass to the eigensolver
• Solve for enough modes that you can be sure you caught the one you are interested it
• Calculate the overlap between modes that are adjacent in wavelength to check you have the mode you are interested in (this is related to the concept of adiabatic taper transition only with wavelength rather than width)

If you plot the refractive index without the sorting you will see the problem which is being solved.

[Hd-Edison]

Thanks for your reply!
I've read [Hollow_Core_Fibre.ipynb], however I am lack of knowledge in this area, so there are still plenty of questions in my mind, so may I ask which book or paper you refered to when you were writting these codes? It will help me a lot, thank you.

[philmain28]

The structure used in that particular notebook has now been published, you can read about it here.

The physics behind them are pretty interesting (and not super well established). They guide using antiresonance effects (like photonic crystal waveguides etc) rather than potential confinement (waves in a box). In general the examples are a mishmash of my research interests (quantum optics) and the people around me at the time (fibre optics). My thesis might give a bit more context or if nothing else give some useful references. I'm not sure there is much published on the computational methods because a lot of this stuff is relatively old hat/not containing enough physics to be interesting. That's kind of the point of phisol because a lot of research groups are using expensive commercial solvers for problems that are relatively straight forward/solved.

If you point me towards the problem you are trying to solve maybe I can be a bit more helpful but some nice (graduate level) texts on all things about waveguides are:

Comprehensive:
snyder and love optical waveguide theory

More general photonics but including waveguides:
gaponenko (more accessible)
joannopoulos

[Hd-Edison]

Thanks for your meticulous reply!
In fact, I'm trying to write some python code that can set a mode source and waveguides, then caculate the E and H field of the light propagation, but I find I'm so lack of knowledge, lol
The book Introduction to Nanophotonics has so many pages, it may takes me hundres of hours to read it, lol
And the information you shared do helped me a lot, thank you again

[Hd-Edison]

Hello, [philmain28]:
Sorry to bother you again, After a month I'm still confused about the codes below, what is the meaning of the number '1.75292972992',
and what is the meaning of the number '0.7', does it means 1 minus 0.3 because the sweep range is 0.3um to 1um?

def n_guide(lam):
A = 2.17954368571
B = np.log(2.17954368571 / 1.75292972992) / 0.7
return A * np.exp(- B * (lam - 0.3))

Because of my poor English reading, I just can't figure it myself.
Thank you Hd-Edison

[philmain28]

Yes you are correct they come from the data points that the fitting function is being drawn through which is something like:

$$(n_{guess}, \lambda ) = (2.18, 0.3), (1.75,1)$$

Then it is just a case of doing the algebra with the exponential fit function

$$n_{guess}= A \exp[-B*(\lambda - \lambda_0)],$$

to find what A, B and $\lambda_0$. $\lambda_0$ is a free parameter and you can set it to whatever you like but if you set it to 0.3 it make the maths easy because the exponent goes to 1. Once you have A you can substitute the other point in and rearrange to get B.

[Hd-Edison]

I wonder what 'B' means?

[philmain28]

Sorry I was playing around with the way the maths is displayed.

[philmain28]

If I get a bit of time at some point I will try and make a demo with more fundamentals in it.

[Hd-Edison]

Thank you for guiding me so patiently and clearing up a big confusion in my mind！😃😃😃