# Near field radiative energy transfer

#1

I was wondering if anybody could help me with near filed simulation by using FDTD! I have some ideas, but I am not quite sure. I think, first, one source such as Ricker wavelet should be applied, then green functions, GH and GE, should be calculated by G=E/J and finally spectral radiative energy transfer can be calculated.

#2

Hi, @psabbagh !

Could you provide more detail on what you actually want to simulate?

#3

I should add that two planar surfaces are separated by a vacuum gap of 1 um.

#4

Hi Mikhail
Thanks for your response. I want to calculate spectral radiative heat transfer between two planar surfaces such as SiC (emitter at 400K and receiver at 300K).

#5

Did you check this example https://kb.lumerical.com/en/nanophotonic_applications_thermal_emission.html ?

Later, we can figure out what to do.

#6

Thanks so much! I checked this problem. It calculates the absorption of a 2d periodic structure consisting of a tungsten slab and a dielectric slab with a periodic array of holes. This calculation is based on Kirchhoff’s law and has been done for far field radiation. In a near field radiation, emitter and receiver are separated by a vacuum gap distance of 1 um or so. Based on what I have learned from this example, we can set two monitor on very top of receiver (far away from vacuum gap distance) and one inside the vacuum gap between emitter and receiver. The differences of transmission would be absorption by receiver. (however, at very top transmission would be zero and hence absorption would be equal to transmission through monitor inside the vacuum gap). The main problem is that how it is possible to simulate an emitter in for example 1000 K by FDTD. I think, the approach should be different this time. We need to calculate the green function of this system by exciting a dirac delta for instance.(As I have seen from literature) If green function can be calculated, the heat transfer is possible to be measured. However, I am not sure how to calculate the green function of such a system.

#7

Hi,

It is not entirely obvious to me the exact device you are trying to simulation. I would like to understand a little more of it. Can you provide some cartoon or sketch, or publication? It will be best if you can reproduce some published results before you move on to your own design.

The simulation approach can highly depend on the type of device, and the physical results you want to extract. So I wanted to make sure I understand your simulation before providing any specific comments.

#8

Thanks Kchow for your kind response. I have provided some related publications below. They are talking about the numerical calculation of near field radiation by using FDTD and Green’s function.
(1) Otey, Journal of Quantitative Spectroscopy and Radiative Transfer 132(2014) 3-11
(2) Francoeur, Journal of Quantitative Spectroscopy and Radiative Transfer 109 (2008) 280-293
(3) Didari, Journal of Quantitative Spectroscopy and Radiative Transfer146 (2014) 214-226

As you can see, near field radiative heat transfer is calculated by Green’s function. In order to calculate the Green’s function, first the system should be excited by a current density at different locations of “r_prime” inside the emitter and the corresponding electric and magnetic field at location “r” should be calculated to determine magnetic and electric dyadic Green’s function (G_e=E/(iwmuJ), G_m=H/J). I am thinking that this can be done by sweeping a dipole at different locations of the emitter and then LDOS and heat flux can be calculated. Right now, I have two fundamental question.
(1) Siince, you have defined the Green’s function in your website based on dipole moment, I want to make sure that dipole moment = total amplitude
time signal
(2) If someone wants to calculate the Green’s function based on the induced current density, what is an induced current of a dipole. Since, the definition of Green’s function based on dipole moment and current density should be same, I have got J=dP/dt in which J in the current density of a dipole with moment P. Am I right?
Thanks

#9

It looks like it is going to be fairly involved topic so maybe we should break down some items for discussion.

I can imagine that could be different approaches to deal with thermal emission. But I wanted to know more about the type structure you are going to simulate. Then we can focus on the most efficient way on the thermal emission you hope to simulate.

• can you give us an illustration of your structure? periodic, standalone?

• what are the requirements of the simulation? did you want the near field or far field radiation? Did you need the absolute radiated power or you are just working with emission enhancement due to grating layers?

I have seen a couple of different other approaches using the Kirchhoff’s law (like the KB example), or direct white noise simulations. And there are pros and cons for different approaches so I wanted to know more about your particular structure before I give specific comments.

(1) I think this is a yes, in the time domain
(2) I think it will depend on how you depend the term “induced”, you may be able to make use of a reference simulation for subtraction.
(3) I am not too concern about the temperature since you can simple scale it with the Black Body Radiation, like the KB example. I think it is the structure and your simulation goal that will determine the simulation approach.

#10

Thanks Kchow for your kind response. I have been working on this problem during these days and I think you are right. I need to break down this problem. This is the main question. “how it can be possible to calculate the near field radiative heat transfer by using dyadic Green’s function”. This is a huge question. Let me ask you step by step some questions in each post and I would be grateful if you could help me out.
First question:
It indicates that electric Green’s function is G_mn=E(m)/(iwmu0J(n)) and magnetic Green’s function is G_mn=H(m)/J(n) in which J(n) is the current density along n direction(x,y, or z) at the excitation location “r_prime” and E and H are the fields along m direction(x,y, or z) at the location “r”. Hence, equations 5 and 6 provide electric and magnetic matrices Green’s functions at location “r” due to excitation at location “r_prime” with 9 components(G_xx,G_xy,G_xz;G_yx,G_yy,G_yz;G_zx,G_zy,G_zz). For instance, electric G_xy is E(x)/(iwmu0J(y)) and and magnetic G_xy is H(x)/J(y).
The script file, dipole_gf.lsf, indicates how one can define electric Green’s function at the location of a dipole source due to excitation of itself.
Please put a point “frequency domain field and power” monitor exactly at the location of the dipole.
In the script, Ez_w (=czt(Ez,t,2pif)*(t(2)-t(1))) is exactly the same as Ez in the raw data of point “frequency domain field and power” monitor.
My first question is that:
what is the differences between Ez in raw data section and the result section of point monitor. They are different. Which one is really the Fourier transform of electric field. Please note that in the Lumerical script, Ez_w is exactly the same as Ez in the raw data of point monitor that has been used to define the electric Green’s function at the location of dipole. I am asking this question because later, It is needed to calculate the Green’s function at a location different from the dipole location. In this case, one point monitor should be placed at that place to record E_w and H_w to use in defining the electric and magnetic Green’s functions. However, I am curious why this field should be E in the raw data section and not in the result section of point monitor. What is the differences between these two fields. Thanks so much for your time and help.
What about H field. This is my second question after your response.
Thanks

#11

My next question is about the magnetic Green’s function as it needs to be calculated for the near field thermal radiation. I have set a TimeMonitor at the location of dipole (the same example in “https://kb.lumerical.com/en/nanophotonic_applications_greens_function_and_ldos.html”) and tried to take the Fourier transform of the magnetic field. Later, I should be able to calculate the magnetic Green’s function via Gm_ij=H(i)epsilon_r/(-1iwP).Please note that Gm_ij=H(i)epsilon_r/(-1iwP)=H(i)/J(j) if we assume that J=-1iwP and epsilon_r=1. I have added my commands to main script file. Here are my commands:

f=getdata(“trans_box”,“f”);
eps_r=1;
Hz = pinch(getdata(“monitor_Time”,“Hz”));
t2 = getdata(“monitor_Time”,“t”);
Hz_w = czt(Hz,t2,2pif)*(t2(2)-t2(1));

# get the field from the source for Greens function Calculation

moment = getnamed(“source1”,“total amplitude”);
m = momentgetdata(“source1”,“time_signal”);
ts = getdata(“source1”,“time”);
m_w = czt(m,ts,2
pif)(ts(2)-ts(1));
w = 2pif;
Gm_zz=(Hz_w)eps_r/(-1iw*m_w);

I was hoping that I could get Im(Gm_zz)=w/(6pic0) as it should be in the vacuum. However, I was not successful. I would be grateful if you can also help me how to define a correct magnetic Green’s function as well. Thanks so much!

#12

Sorry for the late response, I was sick last week so did not get to look at your questions on time.

I have looked at the paper and I realized that the author actually stated a method to simulate such effect with an FDTD based simulator, see equation 36. That is to introduce a white noise term K(t) to represent the randomness. I think this would be a relatively easier approach compared to the Green’s function method that may introduce a lot of complications. You can refer to ref 47-49 on that paper to see more publications how people used this direct approach to model thermal simulation. This is the direct white noise approach I mentioned earlier. However, this approach should have statistical error associated with it.

On the other hand, I think you can also consider using a dipole (at multiple locations) to represent the thermal emission by a hot object. This approach will be similar to our OLED examples. Although the OLED device emit light based on a different mechanism, I think it is worth-noting that it is possible to address the randomly emitted light caused by OLED devices using the dipole source. So I think it should be also possible to address the thermal effects that you are hoping to simulate. If you would like to address the temperature of the hot object, you can always normalize the results with the Black Body Radiation. And this approach should be less associated with statistical error.

In any case, I think the above two approaches (white noise, or using dipole source similar to our OLED applications) should be reasonable to model the effect you described. I would suggest the OLED approach to start with since we already have some existing examples. If you have questions or concern regarding the OLED approach, we can discuss that. If will be nice to know the exact end results that you are looking for.

I would encourage you to take a look at the two approached that I recommended before jumping into the Green’s function complications. If we find that at the end necessary to use Green’s function, I am happy to continue the conversation that way.

Near Field Thermal EMission calculation