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PWE Band Solver Simulation

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(joined November 2018)
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Hello,
In the tutorials, I read that when you include a point defect in your photonic crystal and run the PWE band solver simulation, you should fix the supercell settings so that the supercell includes the defect and the resulting band diagram should include a flat defect band where the original band gap was. However, when I ran my simulation with the supercell including the defect, the resulting band diagram does not include the defect band. Can you help me with this?

The supercell parameters with the defect are saved, and the supercell parameters without the defect are the default parameters.

Thank you so much,
Malik

Responses (25):

  • #50287
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    Malik Javaid
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    Hello,
    In the tutorials, I read that when you include a point defect in your photonic crystal and run the PWE band solver simulation, you should fix the supercell settings so that the supercell includes the defect and the resulting band diagram should include a flat defect band where the original band gap was. However, when I ran my simulation with the supercell including the defect, the resulting band diagram does not include the defect band. Can you help me with this?

    The supercell parameters with the defect are saved, and the supercell parameters without the defect are the default parameters.

    Thank you so much,
    Malik

  • #50293
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    Scott Newman
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    There are two things at play with your simulation and why you are not getting results.

    1) You have mixed up the directions that the lattice vectors A and C represent. You have set your origin to A-3 C-6 when it should be the other way around, A-6 C-3.

    2) There appears to also be an unexpected result in the PWE solver when setting the origin when the position of the crystal is set using the expression fields. Go to your crystal properties and set the position using the offset fields not the expressions.

    Making these two corrections will yield a result with the bandgap and the defect.

  • #50299
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    Malik Javaid
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    I ran the PWE simulation and I received the solutions within the bandgap. However, when I ran the 2D FDTD simulation using a solution as a wavelength parameter, the wave was not propogating through the cavity at all. Do I have the wrong solution, or is there something else at play?

    I’ve attached my design file, along with a screenshot of the PWE simulation output. I chose 0.535 (w/2pic), which is in between band gaps 6 and 7, and converted it to um as my parameter.

  • #50301
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    Scott Newman
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    Malik,

    It would appear that you files did not get attached. Could you please attach them as I am not entirely sure I am following what you are doing in your simulations.

    Scott

  • #50302
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    Malik Javaid
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    Oh I apologize let me reattach them.

  • #50306
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    Scott Newman
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    A couple of points I would give here:

    1) Your PWE results look like it is for a single defect. However, your design uses a L3 cavity. What exactly were you looking for in your PWE calculation? If it was simply the location of the bandgaps you should be doing the calculation over a pure crystal.

    2) The gaps you are working with are well into a dense region of propagating states and gaps between them, it is difficult to sort out what wavelengths should work and which ones should not. This is made worse by this being a PWE result for a cavity which adds cavity modes to the propagating modes.

    3) Typically in photonic crystal designs people work with the larger gaps, this for you would be the gaps from 0.18 to 0.24 (ignoring the resonator state in the middle). At this point I kind of need to ask what your design constraints are? Why did you choose 0.535? Are you able to change your lattice (a) and radius (r) values? scaling r and a to maintain your r/a value of 0.3 while lowering your a would shift the gap from 0.18-0.24 to higher values closer to your operating wavelength of 0.187.

  • #50307
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    Scott Newman
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    Disregard my response before this, it was not as complete as I would like. I am reposting here with some additional information.

    A couple of points I would give here:

    1) Your PWE results look like it is for a single defect. However, your design uses a L3 cavity. What exactly were you looking for in your PWE calculation? If it was simply the location of the bandgaps you should be doing the calculation over a pure crystal.

    2) The gaps you are working with are well into a dense region of propagating states and gaps between them, it is difficult to sort out what wavelengths should work and which ones should not. This is made worse by this being a PWE result for a cavity which adds cavity modes to the propagating modes.

    3) When designing this kind of a system you want your operating wavelength to be within a bandgap and correspond to a state introduced by your cavity. It is too difficult to tell which is which in the region in which you have chosen to work. For example changing your defect to the L1 you originally asked about and setting your operating wavelength to 4.718um which is the defect state at w/2pic of 0.211 gives the results in the attached image.

    4) Typically in photonic crystal designs people work with the larger gaps, this for you would be the gaps from 0.18 to 0.24 (ignoring the resonator state in the middle). At this point I kind of need to ask what your design constraints are? Why did you choose 0.535? Are you able to change your lattice (a) and radius (r) values? scaling r and a to maintain your r/a value of 0.3 while lowering your a would shift the gap from 0.18-0.24 to higher values closer to your operating wavelength of 0.187.

    • This reply was modified 2 months, 4 weeks ago by  Scott Newman.
    Attachments:
  • #50309
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    Malik Javaid
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    I don’t see an attached image. Could you please reattach it?

  • #50311
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    Scott Newman
    Participant

    I have edited my previous comment, you will find the image there.

  • #50312
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    Malik Javaid
    Participant

    I understand what you are trying to say, and I will use the larger band gap for my design. Is my assumption correct that the defect bands within the original bandgap are the wavelengths which will resonate in the cavity? Which means the wavelengths not in the defect bands but still in the bandgap will not resonate in the cavity but will propogate through the linear waveguide?

    Also, in one of my references, it talks of a resonance condition of a cavity, which is the wavelength which will resonate in the cavity and not escape the cavity. What I am trying to do is find this resonance condition so that if I introduce a linear waveguide right after the cavity, the light will not propogate into the waveguide due to the resonance condition. I ran the PWE simulation because I assumed the defect bands would correspond to the resonance condition, but after reading your comments I am not so sure anymore. Is it possible to simulate this condition, and if so, how?

    I attached an image of what I mean when I say resonance condition.

  • #50314
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    Scott Newman
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    The reference you are linking to is fundamentally correct but it is a much simpler situation. Fundamentally what you have is a structure (photonic crystal) that does not allow propagation (band gaps) for specific wavelengths. This means that if you introduce a defect that has a resonant wavelength that is within the bandgap then light can exist within the cavity but cannot propagate outside of it due to the band gap. The location of the cavity/defect state (there is no band) is the location of a resonance, so at w/2pic of 2.11 you have a resonance, i.e. the resonant condition is met.

    This is why your simulation did not work. What you likely chose was in fact a propagating band that existed between two separate band gaps and not a cavity state that existed in a band gap.

    Also you are looking at finding cavity states using a structure with a single defect and then use that value in a structure with a L3 defect. The L3 defect will have a different resonant wavelength as it is longer, recall that a cavity length corresponds to the resonant wavelength. If you are going to use an L3 defect then use the PWEM on that structure and not the single defect.

    As for the structure you are proposing, if the waveguide is within the evanescent region of the cavity and you excite the cavity then the light would enter the waveguide at resonance, I am uncertain why you think it would not.

    I strongly encourage you to refresh yourself on the fundamentals of photonic crystals and designing structures within them. An excellent first stop is the book “Photonic Crystals: Molding the Flow of Light” by Joannopoulos, Meade, and Winn. If you can, get the second edition as I found it to have more information.

  • #50315
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    Malik Javaid
    Participant

    Thank you so much for recommending the book. I consulted it, and I realized what I was looking for. I was not looking for the PWE simulation, but instead I was looking for a transmission spectrum, where it shows at which frequency the mode will propogate in the cavity. Is it possible to simulate this in the software?

  • #50381
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    Scott Newman
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    To setup the simulation to obtain the transmission spectrum simply setup an input plane across the waveguide, setup a Gaussian distribution centered at the waveguide with roughly the correct width. The source should be a pulse to give you broadband response. Then you setup an observation point or observation line (I am assuming you are still working in 2D) and when the simulation is done look at the data from the observer in the frequency spectrum.

    Keep in mind you will need to tell OptiFDTD Analyzer that you want the results from the observer normalized to the source.

    Scott

  • #50417
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    Malik Javaid
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    What do you mean by centered at the waveguide with the correct width? How do you find the correct center and width?

  • #50424
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    Scott Newman
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    Malik,

    You make the design, you know the location of the waveguide so set the center of the source to match the location of your waveguide. For width, either use a rectangular field larger than the waveguide or perhaps a Gaussian that is roughly the size of the waveguide. Again you built the design and therefore know that the waveguide is roughly the width of the lattice constant.

    Scott

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