Thank you! Don't forget to visit the official course website where you can download the latest version of the notes and other resources. emlab.utep.edu/ee5390em21.htm
First, I should let you know you are watching an older video that has been replaced with a considerably improved series of videos. I recommend accessing all of the material through the course website so you will always have links to the latest versions of notes, videos, and other learning resources. Look under Diffraction Gratings in Topic 4 here: empossible.net/academics/21cem/ It is actually hard to find good learning materials on diffraction gratings. To help this a little bit, I added some discussion to a book I recently wrote on the finite-difference frequency-domain method. In this book, Chapter 2 reviews many topics in electromagnetics. Pages 56-62 cover theory of diffraction gratings and calculating diffraction efficiencies for both ruled gratings and crossed gratings. Simulation and analysis of a sawtooth diffraction grating is given in Chapter 8. Here is a link to the book website if you want to learn more: empossible.net/fdfdbook/ Hope this helps!
"Thank you for your nice lectures. I have a question about fabricating a cross-grating with only four diffraction orders/modes, excluding the zero order or DC term mode. Specifically, I want to create two modes with orders +1 and -1 along the x-axis and two modes with orders +1 and -1 along the y-axis. Do you suggest using the GS algorithm to accomplish this?"
If you do this, you will have 8 diffraction orders, excluding the zero-order mode. Is this what you want or do you really just want four diffraction orders? If you are only concerned about getting the diffraction orders and not so much controlling the in any other way, just using the grating equation to calculate the correct period is all you need. You could perhaps do a simple parameter sweep of grating depth to help balance the power in each of the diffraction orders. If you want to get more sophisticated, you can consider GS, genetic, particle swarm, or just multiple parameter sweeps.
@@empossible1577 Thanks for your reply. I want 8 diffraction orders but do not want zero order. How can I convert it directly into GDS for e-beam fabrication?
@@sandeepchamoli6849 Well, first you need to produce the design. Any variety of algorithms will work, but I would try a simple parameter sweep of grating depth and see where that zeros out the diffraction efficiency of the zero order. It may get a little more complicated if you want to also control the diffraction efficiency of the other diffraction orders. I have limited experience with GDS so I may not be of much help. As I recall, it is a script language that defines primitive shapes. Maybe you can write your own code? For some reason, I am thinking you generate isocontours in MATLAB and then export those paths into GDS? I am really getting outside of what I know here.
What purpose would it serve (if any) to have both outputs of an optical beam splitter then fed into as two inputs to a transmission diffraction grating? The diffraction grating has two outputs used. What's the point of doing that?
Hmmm.. I am not completely sure. Maybe to split the beam four different ways with some differences between the beams? Some beam splitters can also manipulate polarization, performing filtering, etc.
Thanks for the video, I am wondering if you have a video about phase conjugation? what happens if a diffraction grating can produce phase conjugation of the incoming wave
I have a question regarding diffraction in reflection region. what kind of grating can have both backward and forward diffraction. Considring that it is a low order grating. does it depend on reflectence of the surface?
+Leila Mazaheri If you etch a grating into glass, it will have both forward and backward diffraction because it is partially transmissive. In fact, I would say this is the most common case. You would need something like a metal grating to prevent forward diffraction.
Many thanks for your videos. But I have a question on slide 31. In this page, considering a p-polarized wave (E-vector parallel to x-y plane), the norm. incident wave with wave vector points to y direction indicating the zero-Ey components; however, the sum of the diffracted waves(..., -2, -1, 0, +1, +2, ...) in your figure indicate the non-zero Ey components. At the interface, the boundary condition could not be satisfied with a zero-Ey (incidence) and non-zero Ey (diffracted waves). Thus, the diffraction does not exit.
The waves shown are only the POSSIBLE directions for waves to propagate. This slide says nothing about how much power will reside in each of those diffraction orders. In fact, if the reflected waves are ignored (that complicates the boundary condition problem a bit), there will be only the zero-order mode on the transmitted side in order to satisfy boundary conditions with the applied wave. As that zero-order mode propagates into the grating, power will gradually be coupled into the other diffraction orders.
@@empossible1577 Many thanks for your quick reply. Sorry for bothering you, but I can't understand " As that zero-order mode propagates into the grating, power will gradually be coupled into the other diffraction orders." Could you please give more explanation about it? Another question comes from slide 15, the second figure "Subwavelength Grating". In this case (no higher-order reflection), as you said, the tilted blue arrows just show the POSSIBILITY of diffraction. Indeed, there is only zero-order transmitted wave (to satisfy the boundary condition). Is that right?
@@jiyaoyu9073 The diffraction orders are just possible directions that waves can propagate. At the very top of the grating, only the zero-order mode has any power in it. If there were power in any of the other diffraction orders, the boundary conditions to the incident plane wave could not be satisfied. As that zero-order propagates into the grating, power is gradually coupled into the higher-order modes. This can happen in a quarter wavelength or so. In that figure in "subwavelength gratings," there is only one diffraction order, but the reason is not boundary conditions. There is only one diffraction order (the zero order mode) because the period of the grating is too short to support any higher-order diffraction modes.
@@empossible1577 Many thanks for your reply. I think I could understand a bit of the "gradually coupling". But in the second question, I mentioned the second figure but not the first figure in slide 15. In this case, the condition of "effective wavelength in incident plane > grating period > effective wavelength in the grating" is satisfied. In my understanding, the grating period is larger than the wavelength in the grating, the diffraction could appear. For a infinite etched grating (grating depth is infinite, but not the grating length), the boundary condition on the top interface is not satisfied only between the incident waves and higher-order diffracted waves, i.e. always only zero-transmitted waves exist. But for a finite etched grating, the boundary could be satisfied between the incident wave and higher order diffracted waves and "reflected waves". These "reflected waves" means the reflected waves by the bottom interface of the grating, but not the top interface of the grating.
@@jiyaoyu9073 The waves in a diffraction grating are more complicated than I think can be visualized. First, you have the reflected diffraction orders that contribute to the boundary conditions allowing for some power to be in the higher-order diffracted modes, even at first. The grating also acts like a Fabry-Perot cavity complicating things even more. The picture I painted was an overly simplified one to help you understand. Finite gratings are even more complicated because they are not infinitely periodic and the field changes at bit at the edges of the grating. Take a look at Slide 22 in Lecture 15 here: emlab.utep.edu/ee5390cem.htm
Thanks for your great videos! I have a question regarding slide 12. Why doesn't kx_i=kx_m? That is what I would expect from phase matching at the interface.
+Zoé-Lise Deck-Léger By kx_i are you talking about kx_inc? The incident wave is a uniform plane wave. The grating has the effect of inducing a periodic fluctuation in the amplitude of that plane wave. This really is no longer a plane wave and as this lecture shows it is actually the sum of a bunch of plane waves propagating at different angles. The interference of all these planes waves combines to reconstruct the fluctuations.
Why is the dielectric function in slide 10 a sinusoidal grating but not other periodic function? I mean later you mentioned that the wave is periodic and is a sum of a bunch of waves, but you did not mention it like in slide 10. Is it just a possible function of dielectric you give as a example and Is it depend on permittivity profile? Thanks a lot
When it comes to the grating equation and calculating the direction of the diffraction orders, the only thing that matters is the period of the grating. Therefore, expressing the grating as a simple sinusoid is very convenient and makes the math easy. Don't read more into this than simply conveying the period. The actual pattern of the grating controls how much power gets coupled into each of the diffraction orders, not the direction of the diffraction orders. In this case, approximating the gratings as a sinusoid would not work because that does not convey the pattern of the grating. Hope this helps!
Thank you for your lecture. But I have a question about the proof in Slide 13 ' the grating eqation' in video. Why do you use period over sin(phi) to take place of the x component of period? I can't understand it.
As most grating figures in this video are showing top view of the gratings, I would like to know if each incident light wave vector and transmitted/reflected wavevectors have perpendicular in plane and out of plan directions, respectively? and is each diffraction order arrow attributed with a plane like shown in slide 15? also in slide 16, how do you usually define n(avg)? is it the transmission/reflection medium refractive index? Thank you.
For all 2D pictures, the angle of incidence is in a plane perpendicular to the grating grooves. This is a simplifying case where all diffraction orders lie in the same plane. If this were not the case, it is called conical diffraction and diffraction no longer occurs in a single plane and analysis is a bit more complicated. n_avg is the average refractive index where the diffraction orders are being analyzed. If this is inside the grating, you need the actual average. If it is outside of the grating, then n_avg is simply the refractive index of that region.
I am not sure. I have not seen any books that handle this subject very well. You may want to look at the latest course notes. I have improved many of them quite a bit since I recorded the videos and the new notes may clear some things up for you. Here is a link to the course website: empossible.net/academics/emp6303/
Sir,, thank you for your informative lecture. The portion of the lecture I dont understand is why the 3 splitting wave splits again as they already left the structure unless the z-dimention is large enough.
The splitting happens simultaneously. It is just that the power slowly leaks from the applied wave to the other diffraction orders as the wave propagates through the periodic medium. Once the wave leaves the periodic medium, all of that coupling and splitting is over. Sorry if I confused this point.
Awesome video. I have a question regarding slide 19. Can you explain how do we know for sure that m = +/-1 are going to be the last diffracted mode that will exist?
I think the movies following slide 19 are the best explanation here. The +/- 1 order modes are the first to appear as the grating period is expanded. If you want to prove that to yourself, calculate the angles from the grating equation and you will see that +/- 1 become purely real angles before any higher order modes.
ShiXingDongZhan There is not textbook for these lectures. Over time, I am trying to work more references to the literature into the notes. If there is a specific topic, let me know.
CEM Lectures I am interested in the polarization selectivity of Bragg grating. Intuitively the electric field will parallel to the grating, but is there some straightforward derivation like the way you derive the grating equation? Thanks a lot.
ShiXingDongZhan A Bragg grating is not really polarization sensitive. I think you are asking about the diffraction gratings in this lecture. There is a difference, but I don't think I have laid that out well. In a Bragg grating, the planes of the grating are perpendicular to the direction of the wave. They produce a stop band like a photonic crystal. In a diffraction grating, the wave is applied parallel or at some angle to the grating planes. The grating can then split the applied wave into some number of diffraction orders. To answer you question, a solution to Maxwell's equations is needed to determine the polarization selectivity because you need to know field amplitudes. There may exist some closed form expressions somewhere, but I do not know where. There is a somewhat nice derivation for the effective properties when the grating is subwavelength and not diffracting. Are you interested in polarizers?
Yes, I was referring to the diffraction grating. The derivation of the Grating Equation you gave is very nice and instructive, which is much better that that in many textbook. Actually I am working on some one dimensional DFB laser experimentally, basically a gain medium with a !-D grating. So I'd like to understand the polarization of the resonance wave, if there is nice analytical description of this. Thank you so much for your kindly explanation.
ShiXingDongZhan By resonance wave, are you looking a resonant grating (i.e. a guided-mode resonator)? Otherwise, I do not know how to get quantitative without a simulation. There may be some first-order theories. Do you need an analytical solution or would a simulation suffice?
Many of the notes in the lectures have been revised for mistakes, content, etc. You can get the latest version of the notes from the course website here: emlab.utep.edu/ee5390em21.htm If you still find mistakes, please report them to me!
Thank you for this lecture. I love how you teach electromagnetic, everything's so well explained and easily derived.
Thank you! Don't forget to visit the official course website where you can download the latest version of the notes and other resources.
emlab.utep.edu/ee5390em21.htm
Very good illustration of Gerchberg-Saxton phase retrieval algorithm!
Thank you!
Beautiful content! Such a helpful video!
I love hearing this! Thank you!!!
Hi sir,
Thank you for the great lecture series can you please let me know the reference for this diffraction gratings and blazed grating
First, I should let you know you are watching an older video that has been replaced with a considerably improved series of videos. I recommend accessing all of the material through the course website so you will always have links to the latest versions of notes, videos, and other learning resources. Look under Diffraction Gratings in Topic 4 here:
empossible.net/academics/21cem/
It is actually hard to find good learning materials on diffraction gratings. To help this a little bit, I added some discussion to a book I recently wrote on the finite-difference frequency-domain method. In this book, Chapter 2 reviews many topics in electromagnetics. Pages 56-62 cover theory of diffraction gratings and calculating diffraction efficiencies for both ruled gratings and crossed gratings. Simulation and analysis of a sawtooth diffraction grating is given in Chapter 8. Here is a link to the book website if you want to learn more:
empossible.net/fdfdbook/
Hope this helps!
"Thank you for your nice lectures.
I have a question about fabricating a cross-grating with only four diffraction orders/modes, excluding the zero order or DC term mode. Specifically, I want to create two modes with orders +1 and -1 along the x-axis and two modes with orders +1 and -1 along the y-axis. Do you suggest using the GS algorithm to accomplish this?"
If you do this, you will have 8 diffraction orders, excluding the zero-order mode. Is this what you want or do you really just want four diffraction orders?
If you are only concerned about getting the diffraction orders and not so much controlling the in any other way, just using the grating equation to calculate the correct period is all you need. You could perhaps do a simple parameter sweep of grating depth to help balance the power in each of the diffraction orders. If you want to get more sophisticated, you can consider GS, genetic, particle swarm, or just multiple parameter sweeps.
@@empossible1577 Thanks for your reply. I want 8 diffraction orders but do not want zero order. How can I convert it directly into GDS for e-beam fabrication?
@@sandeepchamoli6849 Well, first you need to produce the design. Any variety of algorithms will work, but I would try a simple parameter sweep of grating depth and see where that zeros out the diffraction efficiency of the zero order. It may get a little more complicated if you want to also control the diffraction efficiency of the other diffraction orders.
I have limited experience with GDS so I may not be of much help. As I recall, it is a script language that defines primitive shapes. Maybe you can write your own code? For some reason, I am thinking you generate isocontours in MATLAB and then export those paths into GDS? I am really getting outside of what I know here.
@@empossible1577 Thanks.
True, diffraction efficiency would be an issue.
Great video. Like it.
A bit deep lecture, however very useful! thanks a lot! I found the answer to my question. Thanks a lot!
A bit deep? Sorry! Did you listen to the prior lectures? Maybe there was some background information you were missing.
What purpose would it serve (if any) to have both outputs of an optical beam splitter then fed into as two inputs to a transmission diffraction grating? The diffraction grating has two outputs used. What's the point of doing that?
Hmmm.. I am not completely sure. Maybe to split the beam four different ways with some differences between the beams? Some beam splitters can also manipulate polarization, performing filtering, etc.
Thanks for the video, I am wondering if you have a video about phase conjugation? what happens if a diffraction grating can produce phase conjugation of the incoming wave
+Leila Mazaheri Unfortunately, I do not. Sorry!
I have a question regarding diffraction in reflection region. what kind of grating can have both backward and forward diffraction. Considring that it is a low order grating. does it depend on reflectence of the surface?
+Leila Mazaheri If you etch a grating into glass, it will have both forward and backward diffraction because it is partially transmissive. In fact, I would say this is the most common case. You would need something like a metal grating to prevent forward diffraction.
Many thanks for your videos. But I have a question on slide 31. In this page, considering a p-polarized wave (E-vector parallel to x-y plane), the norm. incident wave with wave vector points to y direction indicating the zero-Ey components; however, the sum of the diffracted waves(..., -2, -1, 0, +1, +2, ...) in your figure indicate the non-zero Ey components. At the interface, the boundary condition could not be satisfied with a zero-Ey (incidence) and non-zero Ey (diffracted waves). Thus, the diffraction does not exit.
The waves shown are only the POSSIBLE directions for waves to propagate. This slide says nothing about how much power will reside in each of those diffraction orders. In fact, if the reflected waves are ignored (that complicates the boundary condition problem a bit), there will be only the zero-order mode on the transmitted side in order to satisfy boundary conditions with the applied wave. As that zero-order mode propagates into the grating, power will gradually be coupled into the other diffraction orders.
@@empossible1577 Many thanks for your quick reply. Sorry for bothering you, but I can't understand " As that zero-order mode propagates into the grating, power will gradually be coupled into the other diffraction orders." Could you please give more explanation about it? Another question comes from slide 15, the second figure "Subwavelength Grating". In this case (no higher-order reflection), as you said, the tilted blue arrows just show the POSSIBILITY of diffraction. Indeed, there is only zero-order transmitted wave (to satisfy the boundary condition). Is that right?
@@jiyaoyu9073 The diffraction orders are just possible directions that waves can propagate. At the very top of the grating, only the zero-order mode has any power in it. If there were power in any of the other diffraction orders, the boundary conditions to the incident plane wave could not be satisfied. As that zero-order propagates into the grating, power is gradually coupled into the higher-order modes. This can happen in a quarter wavelength or so.
In that figure in "subwavelength gratings," there is only one diffraction order, but the reason is not boundary conditions. There is only one diffraction order (the zero order mode) because the period of the grating is too short to support any higher-order diffraction modes.
@@empossible1577
Many thanks for your reply. I think I could understand a bit of the "gradually coupling". But in the second question, I mentioned the second figure but not the first figure in slide 15. In this case, the condition of "effective wavelength in incident plane > grating period > effective wavelength in the grating" is satisfied. In my understanding, the grating period is larger than the wavelength in the grating, the diffraction could appear. For a infinite etched grating (grating depth is infinite, but not the grating length), the boundary condition on the top interface is not satisfied only between the incident waves and higher-order diffracted waves, i.e. always only zero-transmitted waves exist. But for a finite etched grating, the boundary could be satisfied between the incident wave and higher order diffracted waves and "reflected waves". These "reflected waves" means the reflected waves by the bottom interface of the grating, but not the top interface of the grating.
@@jiyaoyu9073 The waves in a diffraction grating are more complicated than I think can be visualized. First, you have the reflected diffraction orders that contribute to the boundary conditions allowing for some power to be in the higher-order diffracted modes, even at first. The grating also acts like a Fabry-Perot cavity complicating things even more. The picture I painted was an overly simplified one to help you understand. Finite gratings are even more complicated because they are not infinitely periodic and the field changes at bit at the edges of the grating. Take a look at Slide 22 in Lecture 15 here:
emlab.utep.edu/ee5390cem.htm
Thanks for your great videos! I have a question regarding slide 12. Why doesn't kx_i=kx_m? That is what I would expect from phase matching at the interface.
+Zoé-Lise Deck-Léger By kx_i are you talking about kx_inc? The incident wave is a uniform plane wave. The grating has the effect of inducing a periodic fluctuation in the amplitude of that plane wave. This really is no longer a plane wave and as this lecture shows it is actually the sum of a bunch of plane waves propagating at different angles. The interference of all these planes waves combines to reconstruct the fluctuations.
Why is the dielectric function in slide 10 a sinusoidal grating but not other periodic function? I mean later you mentioned that the wave is periodic and is a sum of a bunch of waves, but you did not mention it like in slide 10. Is it just a possible function of dielectric you give as a example and Is it depend on permittivity profile? Thanks a lot
When it comes to the grating equation and calculating the direction of the diffraction orders, the only thing that matters is the period of the grating. Therefore, expressing the grating as a simple sinusoid is very convenient and makes the math easy. Don't read more into this than simply conveying the period. The actual pattern of the grating controls how much power gets coupled into each of the diffraction orders, not the direction of the diffraction orders. In this case, approximating the gratings as a sinusoid would not work because that does not convey the pattern of the grating.
Hope this helps!
@@empossible1577 thanks a lot
Thank you for your lecture. But I have a question about the proof in Slide 13 ' the grating eqation' in video. Why do you use period over sin(phi) to take place of the x component of period? I can't understand it.
Because the final equation is in terms of the period, not the period along the x-axis. The sin(phi) converts between the two.
As most grating figures in this video are showing top view of the gratings, I would like to know if each incident light wave vector and transmitted/reflected wavevectors have perpendicular in plane and out of plan directions, respectively? and is each diffraction order arrow attributed with a plane like shown in slide 15? also in slide 16, how do you usually define n(avg)? is it the transmission/reflection medium refractive index? Thank you.
For all 2D pictures, the angle of incidence is in a plane perpendicular to the grating grooves. This is a simplifying case where all diffraction orders lie in the same plane. If this were not the case, it is called conical diffraction and diffraction no longer occurs in a single plane and analysis is a bit more complicated.
n_avg is the average refractive index where the diffraction orders are being analyzed. If this is inside the grating, you need the actual average. If it is outside of the grating, then n_avg is simply the refractive index of that region.
which book i prefer for this lecture to understand
I am not sure. I have not seen any books that handle this subject very well. You may want to look at the latest course notes. I have improved many of them quite a bit since I recorded the videos and the new notes may clear some things up for you. Here is a link to the course website:
empossible.net/academics/emp6303/
Sir,, thank you for your informative lecture. The portion of the lecture I dont understand is why the 3 splitting wave splits again as they already left the structure unless the z-dimention is large enough.
The splitting happens simultaneously. It is just that the power slowly leaks from the applied wave to the other diffraction orders as the wave propagates through the periodic medium. Once the wave leaves the periodic medium, all of that coupling and splitting is over. Sorry if I confused this point.
Awesome video. I have a question regarding slide 19. Can you explain how do we know for sure that m = +/-1 are going to be the last diffracted mode that will exist?
I think the movies following slide 19 are the best explanation here. The +/- 1 order modes are the first to appear as the grating period is expanded. If you want to prove that to yourself, calculate the angles from the grating equation and you will see that +/- 1 become purely real angles before any higher order modes.
Thanks a lot for uploading this video. What is the reference textbook for these lectures?
ShiXingDongZhan There is not textbook for these lectures. Over time, I am trying to work more references to the literature into the notes. If there is a specific topic, let me know.
CEM Lectures I am interested in the polarization selectivity of Bragg grating. Intuitively the electric field will parallel to the grating, but is there some straightforward derivation like the way you derive the grating equation? Thanks a lot.
ShiXingDongZhan A Bragg grating is not really polarization sensitive. I think you are asking about the diffraction gratings in this lecture. There is a difference, but I don't think I have laid that out well. In a Bragg grating, the planes of the grating are perpendicular to the direction of the wave. They produce a stop band like a photonic crystal. In a diffraction grating, the wave is applied parallel or at some angle to the grating planes. The grating can then split the applied wave into some number of diffraction orders.
To answer you question, a solution to Maxwell's equations is needed to determine the polarization selectivity because you need to know field amplitudes. There may exist some closed form expressions somewhere, but I do not know where. There is a somewhat nice derivation for the effective properties when the grating is subwavelength and not diffracting. Are you interested in polarizers?
Yes, I was referring to the diffraction grating. The derivation of the Grating Equation you gave is very nice and instructive, which is much better that that in many textbook. Actually I am working on some one dimensional DFB laser experimentally, basically a gain medium with a !-D grating. So I'd like to understand the polarization of the resonance wave, if there is nice analytical description of this. Thank you so much for your kindly explanation.
ShiXingDongZhan By resonance wave, are you looking a resonant grating (i.e. a guided-mode resonator)? Otherwise, I do not know how to get quantitative without a simulation. There may be some first-order theories. Do you need an analytical solution or would a simulation suffice?
Who is the speaker? It sounds a lot like David Wilcock...
lot of mistakes, did you check your presentation?
Many of the notes in the lectures have been revised for mistakes, content, etc. You can get the latest version of the notes from the course website here:
emlab.utep.edu/ee5390em21.htm
If you still find mistakes, please report them to me!
sir please reply its really urgent
Replied.