Home Forums FDTD PWE Band Solver Simulation

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    • #50287
      Malik Javaid
      Participant

      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
      Scott Newman
      Moderator

      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
      Malik Javaid
      Participant

      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
      Scott Newman
      Moderator

      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
      Malik Javaid
      Participant

      Oh I apologize let me reattach them.

    • #50306
      Scott Newman
      Moderator

      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
      Scott Newman
      Moderator

      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.

      Attachments:
    • #50309
      Malik Javaid
      Participant

      I don’t see an attached image. Could you please reattach it?

    • #50311
      Scott Newman
      Moderator

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

    • #50312
      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
      Scott Newman
      Moderator

      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
      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
      Scott Newman
      Moderator

      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
      Malik Javaid
      Participant

      What do you mean by centered at the waveguide with the correct width? How do you find the correct center and width?

    • #50424
      Scott Newman
      Moderator

      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

    • #50432
      Malik Javaid
      Participant

      I found the transmission spectrum attached, but when I run the FDTD simulation with the peak power in the graph, 4.508 um, the results don’t match what I found in the graph.

    • #50438
      Scott Newman
      Moderator

      I would need to see your reference as well as your design file to comment.

      Scott

    • #50439
      Malik Javaid
      Participant

      Oh I thought I had attached them, I guess they didn’t attach.

    • #50476
      Scott Newman
      Moderator

      Is that transmission spectrum in fact obtained for the structure without the waveguides and resonator?

      To be entirely honest, looking at the structure I am not entirely certain I know what you are in fact trying to accomplish with this structure. Why the need for the resonator with the waveguides? They are so close you will get coupling through evanescent fields whether you have resonance or not.

      Do you have a reference for what you are trying to setup?

    • #50477
      Malik Javaid
      Participant

      https://www.photonics.com/a63226/All-Optical_Logic_Gates_Show_Promise_for_Optical

      This article is the reference I am using. I am trying to replicate what they have built, except instead of using one input waveguide, I am planning on using two with different intensities so that the waveguide with the greater intensity light is able to control the other waveguide’s light using nonlinear properties. This article is also supported by the book you had referred to me, Photonic Crystals: Modeling the Flow of Light, on pages 214-218 and by the screenshot I have attached to this post which I had posted before. This screenshot is on page 197 of the book.

      Here is the link to the book in case you need it:
      http://ab-initio.mit.edu/book/photonic-crystals-book.pdf

      Also, the transmission spectrum I have attached above is in fact for the structure with the resonator and waveguides.

    • #50479
      Malik Javaid
      Participant

      I apologize, I attached the wrong file. Here is the correct one.

    • #50483
      Scott Newman
      Moderator

      If that transmission spectrum is for the structure with the waveguides then a source of 4.5um corresponds to a region of minimal transmission, you would need to use a wavelength that corresponds to one of the spikes in the transmission.

    • #50485
      Malik Javaid
      Participant

      I ran the simulation again with a source of 4.5um and I received the graph shown where the peak is 4.055um. I then ran the simulation once again with a source of 4.055um and I received a transmission graph different than the one I had gotten before. Why is this the case?

    • #50495
      Scott Newman
      Moderator

      The mesh resolution in your design file is set to auto which sets it to 1/10 the central wavelength of your source in the highest refractive index material. You are running at a fairly low resolution so changes in the resolution could result in different simulation results.

    • #50545
      Malik Javaid
      Participant

      I ran the simulation at the lower mesh size, as you said, but the results I received were similar to the results shown above.

      I also read that increasing the amount of PMLs in the simulation could reduce error, however, that also did not yield accurate results for me. Can you help me find other ways to decrease the error in the graph and get accurate results?

    • #50580
      Scott Newman
      Moderator

      This is a design issue that you need to work through. I will look at it if I get a chance but this is up to you.

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