Periodic grating modelling. Transmission and Reflection Spectrum

[Natalia Rebrova]

Hi,

Following this example https://optiwave.com/optifdtd-manuals/fdtd-transmission-and-reflection-spectrum-from-grating-unit-cell/ I am trying to model my grating.
I have several questions.
1) If I want to model lossy material can I just put negative imaginary part in refractive index of material or only models like Lorentz_Drude models are supported?
2) Can FDTD use the substrate as the output medium, i.e. ignore there’s anything below?
3) Option “normalize with”. What it does normalize to?

Best regards,
Natalia rebrova

[davcm]

Hello Natalia,
1) Yes, it is enough to just put the imaginary part in the refractive index of the material.
2) Don’t understand your question, sorry about my low comprehension.
3) When you’re watching your reflected or transmited spectrum normalized in an Observation line, it wants to say that for each wavelength of the simulation, Optiwave mesures the amplitude of its signal. Then divides the reflected or transmited amplitude for the one that the input wave have in this exact wavelength. And, if you add both of the normalized signals you will find that (more or less) they sum 1. But, in case you’re in an Observation point, you have to obtain the data from ‘save data button’ and then make the sqare of them to obtain the (more or less again) result given in the observation area. Of course, after the normalization of the input signal (you can erase the crystal structure and then divide one by one the differnt lambdas). I’ve done it and it fits.

I hope I was helpfull.

Regards,

David.

[Natalia Rebrova]

Hello, David.

Thank you very much for your answer it is very helpful.
About normalization on observation line. What got me confused is that sometimes I get values larger than one after normalization.

Best regards,
Natalia

[Damian Marek]

Hi,

I’ll just add a bit of info:

1) Yes, if your spectrum is small enough such that the refractive index changes very little with respect to wavelength you can use an imaginary index of refraction. However, if you want to include dispersion effects you need to make sure that your material follows the Kramers – Kronig relation:

http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations

2) Sure, you can place observation points and areas wherever you feel appropriate. We just include the option of a substrate and cladding because MANY devices are fabricated in the same way. You can change the material for AIR both both section to simulate free space if you feel like it.

Cheers

[Natalia Rebrova]

Dear Damian,

Thank you for the answer.
About the substrate what I meant is the situation on the attached pictures. I am getting different reflection spectra depending on the thickness of SrF2 layer. If I model the same situation say in ricwaa it wouldn’t be the case.
I thought may be it’s possible to modify initial conditions in a way that the lower side of the substrate is considered infinite?

Best regards,
Natalia Rebrova

[Damian Marek]

In FDTD methods there are no infinite boundary conditions, at least not yet in OptiFDTD. However, it is possible to perform a far field expansion.

A couple things may be happening and I say either the field is changing because you are still in the near field regime, so the waves are interfering with each other or maybe there is a problem with the boundaries. In your case I’m guessing you are using a combination of periodic and absorbing boundary conditions.

Could you attach your FDTD project file so I can take a look?

Regards

[Natalia Rebrova]

Hi, Damian,

I attached my file.
Basically, what I need to calculate is reflection coefficients over 7.5 – 12.5 mu.

Thank you for your help.

Best regards,
Natalia

[Damian Marek]

Hi,

For you long wavelength I would increase the z domain and place the grating at the center, try 20 um.

Also the DFT spectrum you specified wasn’t reflected by the simulation parameters. I think it was set to something like 0.4 to 0.8 um, so I changed it to 7.5 um to 12.5 um. Note: As a time domain approach you can solve for the frequency response in one simulation, however the Gaussian time pulse that is injected into the system should be centered at your frequency of interest, so that there are sufficient power levels to calculate the spectrum accurately.

Try out the attached project file, you may need to make some modifications to increase the accuracy.

[Natalia Rebrova]

Dear Damian,

I can’t open the file cause my version is 32 bit. Could you please save the file in other format, our describe what to change.
In particular I can’t find where do I set these
Also the DFT spectrum you specified wasn’t reflected by the simulation parameters. I think it was set to something like 0.4 to 0.8 um, so I changed it to 7.5 um to 12.5 um.
I don’t see any wavelength changes in simulation parameters dialog.

Thank you very much for your help.

[Damian Marek]

Yes I made a mistake sorry. The DFT can be set after the simulation for the 32 bit version so it is fine. I did however, increase the length of the domain. I also placed a observation plane to make sure the domain was large enough and I believe it is as there is not a lot of power at the edges.

[Natalia Rebrova]

Thanks again for help.
I tried to run your file. And it still shows normalized power more than one.
I also played with distances and it seems that the spectrum is different depending on where I put the input field plane. Why is that?

[Damian Marek]

Ah ok, I am also getting some strange results. I think the domain needs to be expanded even further lengthwise because of the large wavelength, although I am not positive. Do you have an similar article or paper you are trying to reproduce? Having results that should be expected can help a lot when troubleshooting.

Thanks

[Natalia Rebrova]

I have ricwaa calculations. I’m comparing against them. See the plot attached

[Natalia Rebrova]

I think I found the problem. It was insufficient timesteps number for this size.

[harkiranjeet kaur]

Hi Natalia, is your problem of getting dft normalized output greater than one solved? because i am facing the same issue while simulating photonic crystal circuit.
Can you help?

Regards

[Natalia Rebrova]

Hi Harkiranjeet,

It is still larger but marginally, like 1.00005 so I guess this is just computational errors piling up and this can be ignored.

What helped me to solve the issue was 2 things. First I enlarged a bit the free space between the grating and input line. My dimensions are 7 microns device and 20 microns free space. Second, I increased the number of time steps there was insufficient number of them. I had 10000 and 60000 or 100000 solved the issue.

Hope this helps,
Natalia

[Dr. Subhashish Tiwari]

Hello Natalia !

I want to design and simulate a Long period grating with OptiFdtd. Have you done the same.

[Natalia Rebrova]

No, sorry, I haven’t tried that one

[Dr. Subhashish Tiwari]

Alright.

[sumeet kumar]

Hi folks

I was trying to calculate transmittance and reflectance of a sawtooth grating. Details of problem are height = 1 cm and distance between two consecutive teeth = 1.5 cm; Permittivity of material = 9; center frequency = 10 GHz. I set up the problem in the OptiFDTD too. But after running for sufficient time steps, I could not get sum of reflectance and transmittence equal to 1. In fact their values are of the order of 10^(-2). Also it seems like wave was not propagating in the direction in which I set it to.

Please go through the OptiFDTD file and suggest me to do possible modifications.

[Author]

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