One of the best lectures on GMR that I have come across. It was very relevant to my research and helped me in the better understanding of the results that I obtained. Thanks Dr. Raymond.
To couple power from an external wave into a guided mode, at least one diffraction order other than the zero order is necessary. Therefore, the grating cannot be subwavelength to the waveguide. However, it can still be subwavelength to external waves since the refractive index is lower and wavelengths are longer.
@@rajatsharma6256 I am referring to the effective refractive index of the guided mode. If the period of the grating is less than the period of the guided mode, there will be no diffraction into any diffraction orders and guided-mode resonance cannot happen. The effective index of the guided mode must be such that the grating is not subwavelength to it. I am speaking in these terms because the grating can be placed almost anywhere, above the waveguide, below the waveguide, inside the waveguide, combinations of these, etc.
@@rajatsharma6256 This is not a subwavelength grating. The refractive index of SiO2 is around 1.5 so the wavelength inside of the glass is closer to 200 nm. This will give you +/- diffraction orders and guided-mode resonance can occur. Now your substrate needs to be thin enough to be an effective slab waveguide. If it is too thick, it will be leaky for other reasons and you will not get a clean GMR response from it. The now suppose the diffraction grating period was 199 nm. There would be no diffraction orders and guided-mode resonance could not be supported. The energy propagating parallel to the surface are cutoff diffraction orders and decay quickly. Those modes cannot excite a guided wave because their spatial frequency is too high (i.e. they are oscillating too quickly).
@@empossible1577 Thanks. I have some ohter questions, 1. when we use corss-grating, I have x polarized incidence. Do I need to use the grating equation in both directions to calcuate the diffraction, seperately? 2. how to distinguish the TE and TM mode in a waveguide when the incident is a normal incidence (by a cross gating)? 3. will the waguide mode be disturbed by the grating after we adding the grating on the top? thanks.
@@没有巅峰人生永远是上 Regardless of polarization, diffraction will occur in all directions described the grating equation. Polarization just affects how much power couples into each of the diffraction orders. For normal incidence on a flat interface (i.e. no grating), TE and TM have no meaning. When there is a ruled grating, some people define TE and TM relative to the grating vector K. In this case, TE is usually the polarization that has the electric field perpendicular to K. For crossed gratings, I think TE and TM and have no meaning again. If the cross grating is 90 degree symmetric, both polarizations will behave the same anyway. The grating can be placed anywhere and everywhere, as long as it is close enough to the waveguide to be electromagnetically coupled. It could be on the top, on the bottom, inside the waveguide, or any combination of the above. The farther away the grating is from the waveguide, the weaker the coupling and the narrower the resonance will be. As some point, the resonance becomes so week and narrow that it effectively vanishes.
Thank you for excellent lecture on GMR! I have some questions for you. 1. Based on the equation in (09:25), the effective index of the grating consisting of Si should be matched in the case of (29:50). We can get the effective index of Si waveguide without grating, but how could I get the effective index of grating in this case? If I assume the fill factor F is 0.6, is it reasonable to calculate the effective index of the grating to be (0.6 * index of Si waveguide) + (0.4 * 0 ) because there is no guided mode in the region of (1-F)? 2. Is it also reasonable to consider the GMR condition as a condition for grating coupling? 3. Is it safe to think the condition for GMR, resonance in spectrum in RCWA, and grating coupling? In addition, where does the guided mode is confined in the case of (23:09)? In this configuration, how could I design GMR for the guided mode to be confined in the grating layer and what is the design principles?
I hope I understand your questions correctly. Here my answers… 1. I would not think of this as the effective index of the grating. Instead, think of it as the effective index of the guided mode. This is an important distinction because some GMRs have the grating away from the slab waveguide. Calculating the effective index requires a simulation very similar to how photonic bands are calculated. The guided mode is a Bloch wave in a periodic structure. A weighted average like you suggest may get you close, but the guided mode extends outside of the grating layer to experience air and the silica substrate. There is a guided mode in the regions where there is no silicon. That is because the guided mode is a Bloch wave in a periodic structure. 2. Yes! A grating coupler and a GMR are the exact same device, just used in different ways. In fact, I have designed grating couplers and I always start that design by first designing a GMR. That only requires a single unit cell and is a fast simulation. Grating couplers also tend to involve apodization, curved gratings, and other things that go beyond the typical GMR. 3. Yes, the frequency of the GMR resonance is the very same frequency that grating would be used for grating coupling. 4. (23:09) In this case, the mode is mostly confined to the eps2 region, but it still overlaps the grating. It really is best to think of the guided mode as a Bloch wave in periodic structure. Hope this helps!
@@empossible1577 I always thank for your kind reply! They are much more than I expected. You are right, it's the guided mode in a periodic structure which have effective index. Thank you so much. And I have one more question for you if it does not bother you. If I want to calculate the effective index of guided mode in (29:50), is it right to calculate the band structure using 2D PWEM as we do in 2D photonic bands? In this case I think I just have to give periodic boundary condition in x direction and no periodicity(Q=1) in z direction(29:50). Do you think it is correct?
@@HCho-xe1cj You will need the periodic BC in the direction the wave is propagating. In the other direction, you can use whatever boundary condition you want because you need to add enough space above and below the GMR that the mode is completely confined and decays to zero. Remember when you solve it this way, you will be making a guess at neff and then calculating frequency. You will need to setup a simple optimization or just experiment manually to guess neff that places the frequency where you want it. It is possible to reformulate the problem so you don't have to do this, but I don't think it is necessary. Not worth the trouble.
@@empossible1577 Thank you so much professor! Supposing I have target wavelength and other parameters except for the period which I want to find out. Here is my strategy for it: 1) Get effective index of the guided mode in the periodic structure and assume appropriate period, 2) Do RCWA, 3) 2D simulation with grating coupler and waveguide, 4) Do 3D simulation. Can I ask your typical simulation process when you are designing a grating coupler?
@@HCho-xe1cj I follow pretty much your same process. I design the GMR first because it is much faster. Many grating couplers are apodised so I might use my GMR simulation to do a parameter sweep so I can accurately apodize the grating.
Other than the journal articles referenced in the lecture notes, there is nothing that I am aware of. The best author in this area is Dr. Robert Magnusson. Search the literature for his name. He is a great person and professor.
Hi, thanks for your awesome lecture. However, I was just wondering if how you did the simulations of GMR filter on slide at 16:19. Using COMSOL and RCWA method, I could not represent that graph. If the graph of that picture is from a paper, could you give me the name of it? I am a student who wants to study this, and thanks again to your great video.
It looks like I was slightly inconsistent when writing the grating equation. The angle phi is the slant of the grating. Usually this is 90 degrees and sin(90) is just 1 and so not written in the equation. This parameter is discussed in a prior video on diffracting gratings. Thanks for pointing this out. I will put it on my "to correct" list.
I edited the notes on the course website to retain the angle phi in all expressions of the grating equation. This way, it does not appear and disappear at random. Incase you are not aware, here is a link to the official course website that has links to the RUclips videos, the latest version of the electronic notes, and other resources. emlab.utep.edu/ee5390em21.htm
Hi, Thank you for this great video, but I have a question. What on resonance the device reverse the background response ? I don't see the physical reason. best regards
The GMR produces a filtering response due to the interference between the waves scattered by the slab and the "leaked" wave. The background transmission and reflection establishes the phase relationship between the fields scattered by the slab. Thus, they interfere differently with the "leaked" wave to produce different transmission and reflection responses. In the end, the GMR acts to reverse whatever the background transmission and reflection is. This is also why the ugliest resonances occur when the background response is around 50%.
I am embarrassed to say that I cannot find the code I used to generate this figure. I will have to rewrite the code and generate a new figure. I also noticed some inconsistent notation used in this part of the lecture (i.e. n1, n2 vs erL and erH). I will fix this as soon as I can. Thank you for pointing this out.
I rewrote my code and played with the numbers until I got as close of a match as I could. I ended up using n1 = 1.0, n2 = 1.4, n3 = 1.2. I "think" I picked these numbers to separate the regions for a better picture, but I don't think they are very realistic. For example, it would be difficult to have a substrate with refractive index 1.2. I will soon update the slides with a more realistic example. Hope this helps!
I updated the lecture notes, but not the recorded lecture with a new Slide 12. See Lecture 11 here: emlab.utep.edu/ee5390em21.htm I show more resonances, the device and all the associated parameters, as well as the equations I used to calculate the regions. Let me know if anything is still unclear or missing.
cool! just one more question, maybe its silly but i don't really get it. so, why don't we see the resonance from the zeroth diffraction order in the graph? I mean we would expect to see only zero diffraction orders when the ratio lo/L is higher than 2 right?
Thanks for the video! I would like to know whats the reason for the very small bump that appears near the resonance for H-mode in slide16? Or whats the reason of the dip that appears very close to the resonance for H-mode in slides19 and 15. Why it does not appear for E-mode?
Small bump -- I would have to run another simulation to be sure, but I suspect that bump is a second resonance that has not been resolved (not enough frequency points). Sometimes, however, nonphysical resonances can appear in a simulation due to numerical problems. To be be sure, I would resimulate this device in the vicinity of that bump and make sure my simulation was well converged. Dips -- I have observed these dips to be most severe when the background transmission or reflection is not close to 0% or 100% or when the background response has a slope. It really is the natural response of a resonance. It is just that we usually suppress it with symmetry and railing the background transmission and reflection.
How can one determine whether the resonance obtained is a Rayleigh Anomaly (RA) or GMR? In both cases, the light is guided in the plane parallel to the wave vector of the grating. Can RA be present for subwavelength grating ?
I always visualize the fields during a simulation. You will see a big difference between a guided wave and a surface wave. Different people have different definitions of a subwavelength grating. Some define it as a grating with period less than the free space wavelength. In this case you can have RA because inside the grating it may not be subwavelength and diffraction orders can span cutoffs. Others define it as less than a wavelength everywhere. In this case, you cannot have any RA because no diffraction orders can ever exist.
@@empossible1577 Thank you for the reply. Do you have a video where the difference between the fields for a guided wave and a surface wave is shown? Any other references? From the experimental point of view, can one observe this difference by looking at the transmission or reflection spectrum from the grating?
@@rajatsharma6256 I really should not have called them surface waves. A surface wave is a true guided-wave phenomenon and you could actually design a GMR based on surface waves. A diffraction order at cutoff looks like a surface wave, but is not a surface wave because it leaks away. A true surface wave stays guided. Based on this, a diffraction order at cutoff will produce corners in the transmission and reflection response. A guided-mode resonance will produce sharp spikes in the spectral response.
@@rajatsharma6256 Maybe the reflection response is increasing, but then suddenly starts decreasing. It is a sudden change in the slope and/or curvature of the line.
When a wave is incident on a GMR, some of the applied wave is reflected, some is transmitted, and the rest is coupled into a guided mode in the slab. As the mode propagates, it slowly leaks from the guide due to the grating. It is the interference between the leaked wave and the applied wave that leads to the filtering response. It is absolutely possible to couple power into a waveguide. These structures are called grating couplers and are used quite commonly in integrated optics. In fact, grating couplers and GMRs operate on the very same physics.
@@empossible1577 Hello, is it possible to use grating couplers to couple power into a waveguide smaller in size that the wavelength of light you are using? And then perhaps couple it out of the waveguide through some other method to acheive an extremely small spot size? Sorry - I'm very new to optics.
@@dragongirlster Yes, but you need to make sure that the small waveguide still supports a guided mode. If not, the grating coupler cannot force that to happen. The small spot size is more challenging. Grating couplers that do this are called focusing grating couplers, but they cannot focus beyond what an ordinary lens can do. The real limitation is that once the light leaves your device and enters air, it is subject to ordinary diffraction laws.
Great question! The tool we use to simulate devices depends on the type of device we want to simulate. In this lecture, my two favorite techniques are finite-difference frequency-domain (FDFD) and rigorous coupled-wave analysis (RCWA). I teach both of these methods in the course Computational Electromagnetics. Here is a link to that course website which has links to the RUclips videos, the latest version of the notes (lots of improvements and revisions), and tools to help you develop your own codes. emlab.utep.edu/ee5390cem.htm I am aware of the LightTrans suite of tools, but have never used them.
Dear, Prof. Rumpf, I wrote FDFD algorithm using Your lectures. Thank You! Everything seems to be working when I use only one material, but whenever I start using two materials (for example the structure as in Your slide 22), I am starting to get illogical results: R>100%, resonance doubled etc... I definitely set nmax to maximum refractive index and used quite high spatial resolution. Any advice of where I should look for problem?
I have only seen that when using a collocated grid, not a Yee grid. Assuming that is not your problem, there is a mistake somewhere in your code. I will guess it is hiding in your calculations of transmission and reflection. Do the fields look correct or do they also look crazy?
@@empossible1577 The fields look quite good, nothing crazy going on there. When calculation indicate R and T > 100 %, it is not a lot, just few percent, in some cases 150 %, so I am not sure if the fields would show me something... Since I checked the functions calcpml2d and yeeder2d according to Your recommendations (I got the confirmation), I assume I do not have to check them for errors? I will overview the code again for errors, I am just surprised that when modeling glass gratings everything is correct (checked with FDTD) :)
@@tomastolenis6023 Can you figure out any patters, like is it always R or T that is wrong? Is the answer always wrong when the transmission region is something other than vacuum? etc.
@@tomastolenis6023 By fields looking crazy, I was asking when you get 150% reflection, do the fields really look this strong? Whether they do or not gives a clue about what might be wrong.
@@empossible1577 Dear, Prof. Rumpf, sorry for the late response. At the moment I can not even get back to the state where I thought my modelling was correct :) Now even conservation of energy does not add up. Fields look ok, nothing crazy is going on, even if I observe resonance effect. It definitely might be that R and T calculations are wrong, but if that would be the only problem, then the doubling of the resonances would not appear... I think I have to just sit longer to this method, all that "sparsing" and transforming matrixes to the arrays got me confused at the moment and I maybe after I will understand every line of the code I will find my mistake :)
There are two ways I may have used those words because there are two simultaneous mechanisms happening that produce a guided-mode resonances. First is diffraction from a grating. There must be at least one diffraction order, other than the zero-order mode. Second, there must be a waveguide. If modes in the waveguide are all "cutoff," then there will be no GMR. If the diffraction orders from the grating are all "cutoff," then there will be no GMR.
There are other ways to produce filtering, but grating diffraction is needed almost by definition for guided-mode resonance. I am not sure how else you could couple into a guided mode. With that said, there are surface waves with coupling mechanisms other than gratings can be be used to create a similar effect. In fact, this response is how people confirm they have excited a surface waves. See Lecture 7b here: empossible.net/academics/emp6303/
Thank you for the fast reply. Really very helpful. I have another question. What parameters decide the qualtiy of GMR? In particular, how will the thickness, duty cycle (fill factor) and refractive index of the material that make a set of discontinuos arrays effect GMR?
@@samirsingh148 Not sure what you mean by quality. I might interpret that has a GMR that has excellent contrast between on and off resonance. The main thing for this is to ensure either very low reflection or very high reflection without the grating in place. A mediocre background response leads to crazy resonances. From here, controlling the width of the resonance is all about the strength of the grating. The stronger the grating, the wider the resonance up to a point. The grating can be made stronger by increasing contrast or moving it closer or into the waveguide. This is actually more useful for making the resonances narrower by weakening the grating. A better way to make them broadband is to engineer multiple resonances that cooperate to give an overall broad response.
Dear Sir, Thank you very much for such a great lecture. I have a small question can you kindly provide the research paper the Square cross grating and hexagonal grating whose reflectance curve is shown in lecture 11 slide 32. Thank you sir once again.
I don't think I got these devices from the literature. I think I just made them up for the picture. I really should have included the specs of the devices to reproduce the results, but I did not. Is there something special about these devices? If not, there should be plenty of similar devices in the literature you can practice with.
Thank you, sir, for the prompt response I was designing 2D GMR filter. I use CrystlWave (PhotonD) tool for stimulation. I want to design a Hexagonal crossed grating to filter for wavelength 600 nm. Hence, I want to try simulating the structure in the slide 32. Also, it would be extremely helpful if you can make a lecture for designing and optimizing 2D GMR filter. Thank you once again.
You can design a hexagonal GMR just like 1D GMRs. First, design a stack of homogeneous layers that give you the background response you want. Second, introduce a grating somewhere such that the effective index in the grating layer gives the refractive index of the design from the first step. You can use effective medium theory or you can just perform a parameter sweep for size cylinder vs background response and pick the cylinder size that is best. Third, adjust the period of the grating until you see a resonance where you want it, probably in the middle of the background response.
One of the best lectures on GMR that I have come across. It was very relevant to my research and helped me in the better understanding of the results that I obtained. Thanks Dr. Raymond.
Thank you!! There is a lot I still want to do with this lecture when I get time.
Thanks for your great video! helped me a lot.
Great to hear!
These are very good lectures.
To couple power from an external wave into a guided mode, at least one diffraction order other than the zero order is necessary. Therefore, the grating cannot be subwavelength to the waveguide. However, it can still be subwavelength to external waves since the refractive index is lower and wavelengths are longer.
@@rajatsharma6256 I am referring to the effective refractive index of the guided mode. If the period of the grating is less than the period of the guided mode, there will be no diffraction into any diffraction orders and guided-mode resonance cannot happen. The effective index of the guided mode must be such that the grating is not subwavelength to it. I am speaking in these terms because the grating can be placed almost anywhere, above the waveguide, below the waveguide, inside the waveguide, combinations of these, etc.
@@rajatsharma6256 This is not a subwavelength grating. The refractive index of SiO2 is around 1.5 so the wavelength inside of the glass is closer to 200 nm. This will give you +/- diffraction orders and guided-mode resonance can occur. Now your substrate needs to be thin enough to be an effective slab waveguide. If it is too thick, it will be leaky for other reasons and you will not get a clean GMR response from it.
The now suppose the diffraction grating period was 199 nm. There would be no diffraction orders and guided-mode resonance could not be supported. The energy propagating parallel to the surface are cutoff diffraction orders and decay quickly. Those modes cannot excite a guided wave because their spatial frequency is too high (i.e. they are oscillating too quickly).
thank very much for the excellent lecture. could I ask where I can find the parameters for slide 18?
Unfortunately, that data is long gone after a Ryuk attack at my university. I an unable to tell you.
@@empossible1577 Thanks. I have some ohter questions, 1. when we use corss-grating, I have x polarized incidence. Do I need to use the grating equation in both directions to calcuate the diffraction, seperately? 2. how to distinguish the TE and TM mode in a waveguide when the incident is a normal incidence (by a cross gating)? 3. will the waguide mode be disturbed by the grating after we adding the grating on the top?
thanks.
@@没有巅峰人生永远是上 Regardless of polarization, diffraction will occur in all directions described the grating equation. Polarization just affects how much power couples into each of the diffraction orders.
For normal incidence on a flat interface (i.e. no grating), TE and TM have no meaning. When there is a ruled grating, some people define TE and TM relative to the grating vector K. In this case, TE is usually the polarization that has the electric field perpendicular to K. For crossed gratings, I think TE and TM and have no meaning again. If the cross grating is 90 degree symmetric, both polarizations will behave the same anyway.
The grating can be placed anywhere and everywhere, as long as it is close enough to the waveguide to be electromagnetically coupled. It could be on the top, on the bottom, inside the waveguide, or any combination of the above. The farther away the grating is from the waveguide, the weaker the coupling and the narrower the resonance will be. As some point, the resonance becomes so week and narrow that it effectively vanishes.
Thank you for excellent lecture on GMR! I have some questions for you.
1. Based on the equation in (09:25), the effective index of the grating consisting of Si should be matched in the case of (29:50). We can get the effective index of Si waveguide without grating, but how could I get the effective index of grating in this case? If I assume the fill factor F is 0.6, is it reasonable to calculate the effective index of the grating to be (0.6 * index of Si waveguide) + (0.4 * 0 ) because there is no guided mode in the region of (1-F)?
2. Is it also reasonable to consider the GMR condition as a condition for grating coupling?
3. Is it safe to think the condition for GMR, resonance in spectrum in RCWA, and grating coupling?
In addition, where does the guided mode is confined in the case of (23:09)? In this configuration, how could I design GMR for the guided mode to be confined in the grating layer and what is the design principles?
I hope I understand your questions correctly. Here my answers…
1. I would not think of this as the effective index of the grating. Instead, think of it as the effective index of the guided mode. This is an important distinction because some GMRs have the grating away from the slab waveguide. Calculating the effective index requires a simulation very similar to how photonic bands are calculated. The guided mode is a Bloch wave in a periodic structure. A weighted average like you suggest may get you close, but the guided mode extends outside of the grating layer to experience air and the silica substrate. There is a guided mode in the regions where there is no silicon. That is because the guided mode is a Bloch wave in a periodic structure.
2. Yes! A grating coupler and a GMR are the exact same device, just used in different ways. In fact, I have designed grating couplers and I always start that design by first designing a GMR. That only requires a single unit cell and is a fast simulation. Grating couplers also tend to involve apodization, curved gratings, and other things that go beyond the typical GMR.
3. Yes, the frequency of the GMR resonance is the very same frequency that grating would be used for grating coupling.
4. (23:09) In this case, the mode is mostly confined to the eps2 region, but it still overlaps the grating. It really is best to think of the guided mode as a Bloch wave in periodic structure.
Hope this helps!
@@empossible1577 I always thank for your kind reply! They are much more than I expected. You are right, it's the guided mode in a periodic structure which have effective index. Thank you so much. And I have one more question for you if it does not bother you.
If I want to calculate the effective index of guided mode in (29:50), is it right to calculate the band structure using 2D PWEM as we do in 2D photonic bands? In this case I think I just have to give periodic boundary condition in x direction and no periodicity(Q=1) in z direction(29:50). Do you think it is correct?
@@HCho-xe1cj You will need the periodic BC in the direction the wave is propagating. In the other direction, you can use whatever boundary condition you want because you need to add enough space above and below the GMR that the mode is completely confined and decays to zero.
Remember when you solve it this way, you will be making a guess at neff and then calculating frequency. You will need to setup a simple optimization or just experiment manually to guess neff that places the frequency where you want it. It is possible to reformulate the problem so you don't have to do this, but I don't think it is necessary. Not worth the trouble.
@@empossible1577 Thank you so much professor!
Supposing I have target wavelength and other parameters except for the period which I want to find out. Here is my strategy for it: 1) Get effective index of the guided mode in the periodic structure and assume appropriate period, 2) Do RCWA, 3) 2D simulation with grating coupler and waveguide, 4) Do 3D simulation.
Can I ask your typical simulation process when you are designing a grating coupler?
@@HCho-xe1cj I follow pretty much your same process. I design the GMR first because it is much faster. Many grating couplers are apodised so I might use my GMR simulation to do a parameter sweep so I can accurately apodize the grating.
Hi, the lecture was very helpful. Thank you! I would like to know the reference materials for this lecture
Other than the journal articles referenced in the lecture notes, there is nothing that I am aware of. The best author in this area is Dr. Robert Magnusson. Search the literature for his name. He is a great person and professor.
Hi, thanks for your awesome lecture.
However, I was just wondering if how you did the simulations of GMR filter on slide at 16:19.
Using COMSOL and RCWA method, I could not represent that graph.
If the graph of that picture is from a paper, could you give me the name of it?
I am a student who wants to study this, and thanks again to your great video.
+성장운 This is not from a paper. In this device, the substrate material is taken to infinity (infinite half space). Did you put that in your model?
Thanks for a kind comment. I did solved my problem which was due to my wrong code manipulation.
Again thank you!
Thanks for the explanation, What is angle phi in slide 11 ?
It looks like I was slightly inconsistent when writing the grating equation. The angle phi is the slant of the grating. Usually this is 90 degrees and sin(90) is just 1 and so not written in the equation. This parameter is discussed in a prior video on diffracting gratings.
Thanks for pointing this out. I will put it on my "to correct" list.
I edited the notes on the course website to retain the angle phi in all expressions of the grating equation. This way, it does not appear and disappear at random. Incase you are not aware, here is a link to the official course website that has links to the RUclips videos, the latest version of the electronic notes, and other resources.
emlab.utep.edu/ee5390em21.htm
Thank you @Raymond Rumpf
Do you know any good tool that simulates multi-layer patterned structures?
Hi, Thank you for this great video, but I have a question. What on resonance the device reverse the background response ? I don't see the physical reason.
best regards
The GMR produces a filtering response due to the interference between the waves scattered by the slab and the "leaked" wave. The background transmission and reflection establishes the phase relationship between the fields scattered by the slab. Thus, they interfere differently with the "leaked" wave to produce different transmission and reflection responses. In the end, the GMR acts to reverse whatever the background transmission and reflection is. This is also why the ugliest resonances occur when the background response is around 50%.
Thanks for the video! Nice explanation. What are the refractive indices that you use to plot the regions of resonance?
I am embarrassed to say that I cannot find the code I used to generate this figure. I will have to rewrite the code and generate a new figure. I also noticed some inconsistent notation used in this part of the lecture (i.e. n1, n2 vs erL and erH). I will fix this as soon as I can. Thank you for pointing this out.
I rewrote my code and played with the numbers until I got as close of a match as I could. I ended up using n1 = 1.0, n2 = 1.4, n3 = 1.2. I "think" I picked these numbers to separate the regions for a better picture, but I don't think they are very realistic. For example, it would be difficult to have a substrate with refractive index 1.2. I will soon update the slides with a more realistic example. Hope this helps!
I updated the lecture notes, but not the recorded lecture with a new Slide 12. See Lecture 11 here:
emlab.utep.edu/ee5390em21.htm
I show more resonances, the device and all the associated parameters, as well as the equations I used to calculate the regions. Let me know if anything is still unclear or missing.
CEM Lectures Yes it does! Thanks a lot!
cool! just one more question, maybe its silly but i don't really get it. so, why don't we see the resonance from the zeroth diffraction order in the graph? I mean we would expect to see only zero diffraction orders when the ratio lo/L is higher than 2 right?
Thanks for the video! I would like to know whats the reason for the very small bump that appears near the resonance for H-mode in slide16? Or whats the reason of the dip that appears very close to the resonance for H-mode in slides19 and 15. Why it does not appear for E-mode?
Small bump -- I would have to run another simulation to be sure, but I suspect that bump is a second resonance that has not been resolved (not enough frequency points). Sometimes, however, nonphysical resonances can appear in a simulation due to numerical problems. To be be sure, I would resimulate this device in the vicinity of that bump and make sure my simulation was well converged.
Dips -- I have observed these dips to be most severe when the background transmission or reflection is not close to 0% or 100% or when the background response has a slope. It really is the natural response of a resonance. It is just that we usually suppress it with symmetry and railing the background transmission and reflection.
Thanks for the explanation.
How can one determine whether the resonance obtained is a Rayleigh Anomaly (RA) or GMR? In both cases, the light is guided in the plane parallel to the wave vector of the grating. Can RA be present for subwavelength grating ?
I always visualize the fields during a simulation. You will see a big difference between a guided wave and a surface wave.
Different people have different definitions of a subwavelength grating. Some define it as a grating with period less than the free space wavelength. In this case you can have RA because inside the grating it may not be subwavelength and diffraction orders can span cutoffs. Others define it as less than a wavelength everywhere. In this case, you cannot have any RA because no diffraction orders can ever exist.
@@empossible1577 Thank you for the reply. Do you have a video where the difference between the fields for a guided wave and a surface wave is shown? Any other references? From the experimental point of view, can one observe this difference by looking at the transmission or reflection spectrum from the grating?
@@rajatsharma6256 I really should not have called them surface waves. A surface wave is a true guided-wave phenomenon and you could actually design a GMR based on surface waves. A diffraction order at cutoff looks like a surface wave, but is not a surface wave because it leaks away. A true surface wave stays guided. Based on this, a diffraction order at cutoff will produce corners in the transmission and reflection response. A guided-mode resonance will produce sharp spikes in the spectral response.
@@empossible1577 Thank you for the response but what do you mean by corners in transmission/reflection spectra?
@@rajatsharma6256 Maybe the reflection response is increasing, but then suddenly starts decreasing. It is a sudden change in the slope and/or curvature of the line.
Hi, what is the unit of distances d1 and d2 (") on the slide 26 ? thank you.
In English units, the " symbol means inches and the ' means feet. In this case, d1 and d2 are in inches.
Thank you.
:-)
Sorry, I have another question. Can we have surface mode instead of transmitted or reflected modes? And, is it possible to couple it to the waveguide?
When a wave is incident on a GMR, some of the applied wave is reflected, some is transmitted, and the rest is coupled into a guided mode in the slab. As the mode propagates, it slowly leaks from the guide due to the grating. It is the interference between the leaked wave and the applied wave that leads to the filtering response.
It is absolutely possible to couple power into a waveguide. These structures are called grating couplers and are used quite commonly in integrated optics. In fact, grating couplers and GMRs operate on the very same physics.
Thanks for reply
@@empossible1577 Hello, is it possible to use grating couplers to couple power into a waveguide smaller in size that the wavelength of light you are using? And then perhaps couple it out of the waveguide through some other method to acheive an extremely small spot size? Sorry - I'm very new to optics.
@@dragongirlster Yes, but you need to make sure that the small waveguide still supports a guided mode. If not, the grating coupler cannot force that to happen. The small spot size is more challenging. Grating couplers that do this are called focusing grating couplers, but they cannot focus beyond what an ordinary lens can do. The real limitation is that once the light leaves your device and enters air, it is subject to ordinary diffraction laws.
Hi, I have another question. How do you do simulations? Do you know LightTrans VirtualLab 5 software? Thank you.
Great question! The tool we use to simulate devices depends on the type of device we want to simulate. In this lecture, my two favorite techniques are finite-difference frequency-domain (FDFD) and rigorous coupled-wave analysis (RCWA). I teach both of these methods in the course Computational Electromagnetics. Here is a link to that course website which has links to the RUclips videos, the latest version of the notes (lots of improvements and revisions), and tools to help you develop your own codes.
emlab.utep.edu/ee5390cem.htm
I am aware of the LightTrans suite of tools, but have never used them.
Thank you for your help.
Dear, Prof. Rumpf, I wrote FDFD algorithm using Your lectures. Thank You! Everything seems to be working when I use only one material, but whenever I start using two materials (for example the structure as in Your slide 22), I am starting to get illogical results: R>100%, resonance doubled etc... I definitely set nmax to maximum refractive index and used quite high spatial resolution. Any advice of where I should look for problem?
I have only seen that when using a collocated grid, not a Yee grid. Assuming that is not your problem, there is a mistake somewhere in your code. I will guess it is hiding in your calculations of transmission and reflection. Do the fields look correct or do they also look crazy?
@@empossible1577 The fields look quite good, nothing crazy going on there. When calculation indicate R and T > 100 %, it is not a lot, just few percent, in some cases 150 %, so I am not sure if the fields would show me something... Since I checked the functions calcpml2d and yeeder2d according to Your recommendations (I got the confirmation), I assume I do not have to check them for errors? I will overview the code again for errors, I am just surprised that when modeling glass gratings everything is correct (checked with FDTD) :)
@@tomastolenis6023 Can you figure out any patters, like is it always R or T that is wrong? Is the answer always wrong when the transmission region is something other than vacuum? etc.
@@tomastolenis6023 By fields looking crazy, I was asking when you get 150% reflection, do the fields really look this strong? Whether they do or not gives a clue about what might be wrong.
@@empossible1577 Dear, Prof. Rumpf, sorry for the late response. At the moment I can not even get back to the state where I thought my modelling was correct :) Now even conservation of energy does not add up. Fields look ok, nothing crazy is going on, even if I observe resonance effect. It definitely might be that R and T calculations are wrong, but if that would be the only problem, then the doubling of the resonances would not appear... I think I have to just sit longer to this method, all that "sparsing" and transforming matrixes to the arrays got me confused at the moment and I maybe after I will understand every line of the code I will find my mistake :)
What does it mean for GMR mode to be cutoff? Does waveguiding happens in this case?
There are two ways I may have used those words because there are two simultaneous mechanisms happening that produce a guided-mode resonances. First is diffraction from a grating. There must be at least one diffraction order, other than the zero-order mode. Second, there must be a waveguide. If modes in the waveguide are all "cutoff," then there will be no GMR. If the diffraction orders from the grating are all "cutoff," then there will be no GMR.
Is diffraction a necessary requirement for guided mode resonance or there can be other ways also of having guided mode resonsnces?
There are other ways to produce filtering, but grating diffraction is needed almost by definition for guided-mode resonance. I am not sure how else you could couple into a guided mode.
With that said, there are surface waves with coupling mechanisms other than gratings can be be used to create a similar effect. In fact, this response is how people confirm they have excited a surface waves. See Lecture 7b here:
empossible.net/academics/emp6303/
Thank you for the fast reply. Really very helpful. I have another question. What parameters decide the qualtiy of GMR? In particular, how will the thickness, duty cycle (fill factor) and refractive index of the material that make a set of discontinuos arrays effect GMR?
@@samirsingh148 Not sure what you mean by quality. I might interpret that has a GMR that has excellent contrast between on and off resonance. The main thing for this is to ensure either very low reflection or very high reflection without the grating in place. A mediocre background response leads to crazy resonances.
From here, controlling the width of the resonance is all about the strength of the grating. The stronger the grating, the wider the resonance up to a point. The grating can be made stronger by increasing contrast or moving it closer or into the waveguide. This is actually more useful for making the resonances narrower by weakening the grating. A better way to make them broadband is to engineer multiple resonances that cooperate to give an overall broad response.
Dear Sir,
Thank you very much for such a great lecture.
I have a small question can you kindly provide the research paper the Square cross grating and hexagonal grating whose reflectance curve is shown in lecture 11 slide 32. Thank you sir once again.
I don't think I got these devices from the literature. I think I just made them up for the picture. I really should have included the specs of the devices to reproduce the results, but I did not. Is there something special about these devices? If not, there should be plenty of similar devices in the literature you can practice with.
Thank you, sir, for the prompt response I was designing 2D GMR filter. I use CrystlWave (PhotonD) tool for stimulation. I want to design a Hexagonal crossed grating to filter for wavelength 600 nm. Hence, I want to try simulating the structure in the slide 32. Also, it would be extremely helpful if you can make a lecture for designing and optimizing 2D GMR filter. Thank you once again.
You can design a hexagonal GMR just like 1D GMRs. First, design a stack of homogeneous layers that give you the background response you want. Second, introduce a grating somewhere such that the effective index in the grating layer gives the refractive index of the design from the first step. You can use effective medium theory or you can just perform a parameter sweep for size cylinder vs background response and pick the cylinder size that is best. Third, adjust the period of the grating until you see a resonance where you want it, probably in the middle of the background response.
I would do that sir! Thank you, sir!