Lecture 1 (FDTD) -- Introduction

[@Gantics-Antics]

Fantastic Series!! You may find this funny - and I must preface this with stating that I have next to zero knowledge on physics. However I love to program and wanted to see if I could learn a bit about the fundamentals of physics by rendering oscillating fields/waves in 3D. However I foolishly thought that I could achieve this effect merely by overlapping field curvatures along a uniform time domain. As you would expect all I produced was a lumpy field :(! I haven't implemented FDTD to my project, yet I feel pretty confident that I can use your content to make it happen - thank you!

[@empossible1577]

Great!! Let me point you to the official course website. I recommend using it as your main portal because it has the latest version of the notes, links to the latest videos, MATLAB codes, and other resources. empossible.net/academics/emp5304/ Also, if you are willing to pay for an online course, here is a course intended for the complete beginner. It includes everything including MATLAB codes. It is highly visual and very simplified. empossible.thinkific.com/courses/1D-FDTD

[@StewartMNash]

Actually, Artech periodically publishes new "Advances in FDTD Computational Electrodynamics" by Taflove (editor). I plan to get the newest, "Photonics and Nanotechnology," sometime.

[@daohung1112]

Have you worked with photonic crystal fibers by using FDTD?

[@joaopaulocoelho5401]

Hi. Thank you for posting this set of videos. Can you be so kind and explain why in the update equations presented at 5:59, there is a phase difference between H and E? That is, why not H(t+Δt)-H(t)?

[@empossible1577]

Great question! This is just the introduction so don't expect too much until you get into the course. The short answer is that E and H are staggered in time so that the time derivatives can be approximated most accurately with central finite-differences. This will make more sense when it is discussed in more detail in a later lecture. Let me point you to the official course website where you can download the notes, get links to latest version of the videos, and other learning resources. empossible.net/academics/emp5304/ If you are willing to spend some money, there is also an incredible online course for FDTD that is intended for the complete beginner. The first half of the first course is entirely free to see if you like the teaching style. empossible.thinkific.com/collections Hope this helps!

[@joaopaulocoelho5401]

@@empossible1577 Thank you. I will take a look on your course. Best regards from Portugal :)

[@empossible1577]

@@joaopaulocoelho5401 Hello Portugal!! Did you know that we recently translated an introduction to electromagnetics into Portuguese? Here is the link: kzbin.info/www/bejne/hX2XlJSPpt6dq5Y

[@SanchitPEE]

Awesome lectures... loved the way u explain

[@empossible1577]

Thank you!

[@juan-hw]

Hello, I'm trying to simulate a wave impinging a homogeneous lossless dielectric material to calculate transmittance and reflectance, I'd like to have some kind of source similar to that shown in minute 1:32 in the Radar simulation example. I need it windowed, tilted an angle w.r.t. x-axis or y-axis and also of short duration (Gaussian) in order to investigate a wider range of frequencies (wavelengths)- Could you please give me any hint on how this wave is introduced or what it mathematically looks like when it is also spatially dependent? I thank you for your reply and your videos, they have been of much help. Juan

[@empossible1577]

I don't have a whole lot on that type of source, but it is pretty easy to do. Take a look at the notes (not the video) for Lecture 15 "FDFD Extras here": emlab.utep.edu/ee5390cem.htm You will see a section for Gaussian Beam Source. Until I revise the slides, right now it starts on slide 60 in that PDF. This is for finite-difference frequency-domain, but it is not a lot different for FDTD. See what you can do with this. It shows you how to tilt the source, control its width, etc.

[@juan-hw]

Hi, thanks for your soon reply. Maybe just to clear my mind a bit up, would it look like a source of the type: fsrc = real(gaussian(x,y)*exp(j*w - k.r)*gaussian(t))? Because then it is not clear for me whether this source satisfies Maxwell's equations in free space. Thanks a lot for your reply in advance. Juan

[@empossible1577]

This Gaussian actually does not satisfy Maxwell's equations exactly. For one, it does not account for divergence of the beam. However, it is close enough and has worked perfectly every time I have tried it. For TF/SF, you only need the field in two planes that are spaced a half cell apart. Your equation for a Gaussian is close enough to a rigorous beam over this distance that you do not have to worry about it. At least, I have never encountered a problems with it.

[@juan-hw]

CEM Lectures Professor thank you very much for your reply. It has been a big help. Thanks a lot for the videos and lecture materials as well. Juan

[@empossible1577]

You are welcome!

[@khashabriGG]

Question: Could somebody please tell me why there is no J (current density) in the upper right curl equation in min 5:30 ? It should be like this ∇ x H = J + eps * d/dt E but is written without J.

[@ifeanyipatrick16]

Because it is assumed to be a source free region I.e j =0

[@skydahe9615]

For small devices, how can we tell if the device is "small" ?

[@empossible1577]

For electromagnetic simulations, size is always relative to wavelength. So a 1 meter device operating at 1 meter wavelength is exactly the same "size" as a 1micrometer device operating at a 1 micrometer wavelength. I would say 10 wavelengths and less is small, but that is rather subjective and depends a lot on the available computational resources.

[@skydahe9615]

@@empossible1577 gotcha! thank you!!

[@lokeshgnanasekar]

This video was really helpful. Thank you so much for this video!!!! Can you please tell me whether FDTD method can simulate SERS effect in MATLAB. If yes, kindly explain how thank you

[@empossible1577]

Yes, absolutely. I recommend referring to the literature as I have not ever simulated SERS. Here are two papers I found on Google Scholar: Zeng, Zheng, Yiyang Liu, and Jianjun Wei. "Recent advances in surface-enhanced raman spectroscopy (SERS): Finite-difference time-domain (FDTD) method for SERS and sensing applications." TrAC Trends in Analytical Chemistry 75 (2016): 162-173. Grimault, A-S., Alexandre Vial, and M. Lamy De la Chapelle. "Modeling of regular gold nanostructures arrays for SERS applications using a 3D FDTD method." Applied Physics B 84.1 (2006): 111-115.

[@lokeshgnanasekar]

@@empossible1577 THANKS YOU SO MUCH!!! I wish you all the very best! In the drawback part of your video you have mention it as FDTD is quite insufficient for resonant devices; SERS is involved in Surface Plasmon Resonance (SPR). Does other methods like Boundary Element Method (BEM), Finite Element Method works well? Please explain, Sir!

[@empossible1577]

@@lokeshgnanasekar SPR is an atomic scale resonance that is handled fine by FDTD. I was talking about simulating devices with wave resonances where the waves bounce around many times. FDTD can still certainly handle these, but the simulation has to run and run and run and run and run ... until the wave leaks completely out of its resonance. As an example, I give a problem in my CEM class to simulate a guided-mode resonance filter. These are essentially just resonant diffraction gratings. FDTD takes around 36 hours to simulate. Another method I teach called finite-difference frequency-domain takes about 12 minutes for the same simulation. The same devices simulated using rigorous coupled-wave analysis takes only a few seconds. This does not mean RCWA is better than FDTD. It only means it is the superior method for that specific device.

[@lokeshgnanasekar]

@@empossible1577 Thank you for the information

[@versatile_gentlemen]

Thanks for offering very helpful tutorials. I don't have any experience of using FDTD yet, therefore I want to ask you couple of things: a) How good FDTD is for simulating Plasmonic structures? b) Can I do Kretschmann configuration using FDTD where the excitation source is Gaussian beam?

[@empossible1577]

FDTD is excellent for plasmonic devices and it is capable of simulating anything. FDTD tends to become less efficient for highly resonant devices. In this case, frequency-domain methods are preferred. FDTD is excellent for very large devices and plasmonic circuits tend to be large.

[@jszhouxy]

Thanks for the series lectures on FDTD, I am curious, in order to reduce computational cost in steady state 3D FDTD simulation, is it possible to start FDTD iteration from a initial guess where fields are computed from a simplified model with certain approximation?

[@empossible1577]

In principle yes, but that initial guess must be a rigorous solution to Maxwell's equations.

[@thgmansur]

May I ask why some lectures are not visible, for instance Lecture 21. Thanks for the awesome, informative lectures!!

[@empossible1577]

Thank you! I am glad they are helping you! I have removed some lectures because they provide MATLAB codes that give away answers for classes I am teaching. In other cases, the lectures have been improved and replaced with newer and better lectures. I recommend accessing the course through the website. You can download the latest version of the notes, get links to the latest lectures, get links to MATLAB implementations, and much more. empossible.net/academics/emp5304/

[@andrewkeshishian5711]

hey whats your name by chance?

[@crunchtime901]

Hello, your website is very resourceful. I am currently writing a dissertation and FDTD is the method I am using. Can you please post any recent tutorials or work done? I remember you telling me that you had revised a lot of your work, if I'm not mistaken. I really need help with PML and dispersive material and writing the code for each. Help doc HELP!!!!

[@empossible1577]

The official course website is at the link below. It has links to these KZbin lectures in addition to the latest version of the electronic notes that you are looking for. It also has some tools to help you develop you own FDTD codes. emlab.utep.edu/ee5390fdtd.htm

[@crunchtime901]

Thank you so much.

[@masterburgn]

hi really nice vid! what can i cite in my thesis, if i used this videos (slides) as one of my literature? thanks

[@empossible1577]

I actually have no idea! You could perhaps point to the official course website here: emlab.utep.edu/ee5390fdtd.htm

[@masterburgn]

thank u, thats enough ;)

[@varunsaxena6823]

Sir, can you share with us the radar example through a series of video lectures that you talk about in lecture 1, how you go about simulating it though matlab.

[@empossible1577]

varun saxena I may consider doing that in the future, but I do not have any immediate plans to add that series of videos. I think if you work through the course materials, you will have a pretty good understanding about how to do that.

[@varunsaxena6823]

Thank you. I will go through the course material and get back if i need clarifications to get that problem going.

[@deeptiiap6848]

Please guide me in finding the answer of: how can we relate backscattering and reflection in FDTD??

[@empossible1577]

If I understand your question correctly, reflection and back scattering are the same thing. Transmission and forward scattering, however, are different. The easiest way to think of this is that scattering has the source removed. If you are simulating just empty space, you will get 0% reflection, 0% back scattering, 100% transmission, and 0% forward scattering. Empty space does not scatter. Now if you simulate a big metal wall you will get 100% reflection, 100% back scattering, 0% transmission, and 100% forward scattering. Why 100% forward scattering? You will need to scatter a wave in the forward direction that is 180 degrees out of phase with the source so that the two will interfere and cancel so that no waves end up travelling in the forward direction. See Lecture 24 on the course website at the link below. It covers scattering analysis, but it is an advanced topic and you will need to learn more FDTD before being able to understand it fully. Unfortunately, I do not yet have a video recorded for this lecture. It is only the notes. emlab.utep.edu/ee5390fdtd.htm Hope this helps!

[@deeptiiap6848]

thank u sir for ur reply..... My question is what is the relation between back scattering/forward scattering (i.e.angular light scattering spectrum which is far field) and diffraction field (i.e. DHM) from a microparticle in FDTD??

[@empossible1577]

Very sorry, but I do not understand your question. Perhaps another person reading this can help us out here.

[@deeptiiap6848]

Thank u sir...... Can u help me in knowing what is the relation between transmission and forward scattering, as u mentioned that it is different?? As I am simulating for 1 micrometer bead.

[@deeptiiap6848]

Dear Sir I am also facing one more problem that is: I simulated for 1 micrometer bead in FDTD, now I want to change the radius of bead in sweep so when I am doing sweep for this lets say radius from 0.6 to 1 micrometer, I am not getting any data..... Please guide me....

[@edobuggs]

Really helpful tutorial.. by the way Sir, if i want to simulate an ultrasonic wave transmitted from a curve shaped ultrasonic transducer, is it possible to use this fdtd method? I am still new to this field. thank you

[@empossible1577]

This method can still be used, however, ultrasonic waves involve different physics than electromagnetic waves. You will start with different governing equations and may need something different in your boundary conditions. The basic procedure and techniques will be identical.

[@edobuggs]

First of all, thank you so much for your reply. Oh i see...Sir, could you please give me some details about the governing equations you mentioned above? and since it is ultrasonic, should i still use the maxwell equation as well? thank you.

[@empossible1577]

The governing equations are the fundamental equations that you are solving. In electromagnetics, Maxwell's equations are the governing equations. Unfortunately, I do not have any expertise to offer in ultrasonics. I know that there is an FDTD book by Dennis M. Sullivan which has a chapter devoted to acoustic simulations. Check into this. I am also sure there will be a lot of literature on this subject that you can find with a simple internet search. Good luck!

[@edobuggs]

Okay sir, thank you so much for help. i will start looking for some references about it then. Your channel is amazing.

[@empossible1577]

Thank you!

[@mauorama]

Question: How can I simulate an external magnetic field? I want to simulate wave propagating in an external magnetic field

[@empossible1577]

The easiest way is not to. What would that external field do to effect the wave in the simulation? Would it modify the properties of the material the wave is passing through? If so, just modify the properties of the material to what it would be in the presence of the magnetic field. You can certainly make a more complicated FDTD simulation that accounts for all the physic, but maybe you don't need to do that.

[@MrCuddlyable3]

@@empossible1577 In English the words AFFECT and EFFECT are spelled differently because they mean different things.

[@empossible1577]

@@MrCuddlyable3 Your welcome to a refund. (yes, that mistake was intentional)

[@MrCuddlyable3]

@@empossible1577 Dear Sir. You have just taken part in a social screening test. It was necessary that you were unaware of being tested and that you were free to respond or not respond. A test subject is given a score that depends on how the subject responds to being informed about a grammar mistake. These are the score ranges: 3.0 to 5.0 High ethic level. These people take responsibility for correcting their error (which is possible for them to do in KZbin by clicking to the right of a post on "Edit") and/or apologize genuinely. 0.0 to 3.0 Normal to subnormal ethic level. The person either does not comprehend, "chooses" not to comprehend or "chooses" not to care about their error. -1.0 to 0.0 Self delusory ethic level. The person constructs any excuse for their error rather than accept responsibility. Examples include blaming the error on "just a typo" or "not my fault, a spelling checker did it" and pretending the error was a deliberate joke. Persons below 0.0 do not voluntarily correct their mistake. -2.0 to -1.0 Triggered abreaction. The person expresses emotional tension in a complaint about having been corrected. The overlooked reality is that we don't identify explicitly the person's mistake. -5.0 to -2.0 Antisocial abreaction. The person launches a "justified" attack on the source of correct information. At mild levels the person may use sarcasm and insult. At psychopathic levels -4 to -5 the person exhibits paranoid fantasies such as conspiracy theories about education, and instances of Godwin's Law (insults about grammar "Nazis") are too obvious. No more participation is needed by you EMPossible. Thank you.

[@empossible1577]

@@MrCuddlyable3 So what is my score?

[@crunchtime901]

In the second finite-difference approximation, why did you change the H?

[@empossible1577]

Can you point to a specific slide so that I can be sure about what you are asking?

[@crunchtime901]

In slide 8 when you go to the Theory of FDTD, the electric field finite difference approximation has H with a time step I believe, but the Maxwell's equation just has H. The E in the magnetic field Maxwell's equation and finite-difference approximation stayed the same.

[@empossible1577]

Are you talking about why I am defining E(t) but then H(t+dt/2)? That is a deeper subject that I cover in a later lecture. The short story is that every term in a finite-difference equation has to exist at the same point in time and space. When you approximate the time derivative as (E(t+dt) - E(t))/dt, that term actually exists at time t+dt/2. We choose the H fields to exist at these half time steps to resolve this issue. All of this covered in more detail in a later lecture. So no worries if that does not make sense now.

[@crunchtime901]

CEM Lectures that makes perfectly good sense now. Thanks so much man!

[@mikefredd3390]

That is my question as well at 5.20. I'll suspend my curiosity until you discribe it later.

[@rayvertti]

Where were you 8 years ago??? :(

[@empossible1577]

Ha ha. Eight years ago, I was getting ready to make these videos!

[@rayvertti]

@@empossible1577 These are great. Thorough and well explained. Wish these videos were up in my masters thesis' days :).

[@PhysicsKeeBuniyaad]

Sir please upload a detail video of me wave simulation on an aeroplane that you show little bit here in this video

[@empossible1577]

Sorry. That picture is borrowed from the internet. I do not have that simulation. BTW, simulating waves interacting with airplanes is a very large and intense simulation that usually requires a very powerful computer with lots of memory, or a cluster.

[@PhysicsKeeBuniyaad]

@@empossible1577 its ok and thank you sir for your reply.

[@PhysicsKeeBuniyaad]

@@empossible1577 one more thing i want to know.. i'm getting issue when a plane wave incident on a sphere and plot the scattered field and total field in 3d fdtd . i don't understand what is happening ...

[@empossible1577]

​@@PhysicsKeeBuniyaad Is there a problem with your simulation or you just do not understand the electromagnetics? If it is the theory you are confused about, do some reading on "mie scattering."

[@moaazsherif5236]

I am so excited to start this course =D , what are the prerequisites needed for this course ??

[@empossible1577]

Some familiarity with programming in MATLAB (or Octave) is absolutely needed. Otherwise differential equations and basic electromagnetics. That is pretty much it. Let me point you to the course website which has links to the lecture videos, you can download the latest version of the notes (many revisions and improvements), as well as other resources to help you. emlab.utep.edu/ee5390fdtd.htm Enjoy!!!!

[@moaazsherif5236]

thanks sir for replying ^_^ I was wondering if this method( FDTD )is related to the method of transmission line matrix (TLM)? if so what is the difference between the two? ^_^ thanks in advance .

[@empossible1577]

I would not say the methods are related, but in the end they are very similar in their implementation and properties. I have never coded TLM so I cannot comment too much on its benefits over FDTD. I think there are many more resources available to learn and implement FDTD than there is for TLM. FDTD discretizes Maxwell's equations that evolvethe fields over time. In contrast, the TLM method approximates waves and materials as a large 3D circuit and evolves the currents/voltages over time. This might be more intuitive for some to learn. I am guessing here, but it may be that you can get away with larger cell size in TLM than you can in FDTD. It may also be that TLM is more easily hybridized with circuits and circuit models. Depending on what you want to simulate, I would probably recommend sticking with FDTD. Hope this helps!

[@moaazsherif5236]

CEM Lectures thanks a lot for making it clear 😊

[@benouatasabdelwahab1026]

..showing the FDTD code will be helpful ..

[@empossible1577]

Benouatas Abdelwahab See my previous reply. Folks new to FDTD are not ready to see code at this stage.

[@benouatasabdelwahab1026]

..useful computer code will be appreciated..

[@empossible1577]

Benouatas Abdelwahab Full FDTD codes are provided in later lectures. There is still a lot to learn before you can understand the code at this stage including why the field components are staggered, how to handle the staggering, how to incorporate sources, handling the boundary conditions, calculating transmission and reflection, etc.