Re: Cloaking
I understand what you mean.
I did the simulation above also in TE and in TM plane wave module, I know that both of them work in the same way in the 2D case. I have just tried the hybrid mode :D
Following your suggestion, I'll try exponential-like mapping :D
I'm really trying to find a sistematic way to refine the mesh in order to get stable results (in particular, the same results varying the frequency....)
I can access the papers you have mentioned, I'll give a look to them.
Cheers
I am not very familiar with cloaking but have some interest. My opinion is that most of the work based on Pendry is unachievable because we can not avoid two limitations for material, which both permittivity and permeability are required to approach 0 or infinite. At both limitations, it is easy find the solutions for Maxwell equations are odd and hence it makes no sence to discuss the scattering intensity depending on the parameters. Anyway how can we get a material with 0 or infinite permeability or permittivity .
On the other hand, from experimental viewpoint, how to get a continuous permittivity and permeability. Even we get, from the wavelength lamda point, how do you know permeability or permittivity is continuous or discrete. For most cases,
permeability or permittivity is discrete (such as its value can not changed with increasing its volume).
So, I believe Prof U. Leonhardt is correct: one can never completely hide from wave, but can from rays.
Hi qqqooo!
I think perhaps I didn't get precisely what you were saying but probably I got the point. I like your questions.
First: for the 2D cylinder case the cloaking formula gives 0 and infinite values of eps and mu, while for the 3D sphere case it is 'only' 0 - there is no infinity. Even for the 2D cylinder, it is possible to find a way to make a cloak which needs to have 'only' 0 and not infinity. If you don't believe me, I can give you an example, but I would like to receive a beer in return:)
Therefore, we got rid of the infinity problem.
Second: How do we get a material with zero permittivity and permeability?
Not easily but it is possible - you 'just' have to hit some resonance. This is exactly how metamaterials operate. The only problem is that in nature we don't have these 0s appearing at the same place because the magnetic resonances are at much lower frequencies than electric resonances.
Example: use the phonon resonance in SiC to get zero values of the permittivity in the infrared.
The point here is something else: you can't expect these to have EXACTLY zero values - as anything in nature it always goes a bit up or down. And it is not a problem unless the phenomenon which you are interested in shows singular behaviour in the point in which case you have to be really carefull.
For cloaks, these 0s (don't worry about infinities - it's the same) ARE SINGULAR therefore we have to be carefull. Therefore, calculations on how does the scattering depend on parameters have a lot of sense. (I did a lot of those so don't tell me it was meaningless :)
Third: how we get continuous parameters?
Ok, I guess this is not a serious question - you answered yourself. If we control the material structure on a scale much (factor >10) smaller than lambda_effective ('wavelength' in that medium), we can make a material which is seen by the wave as if it were homogeneous. There is no problem making a 'continuously' changing value of eps or mu - it will appear to be homogenous if the discrete layers are thin enough.
Fourth: Can we really get continuous parameters? (or, is this limit of thin layers singular in a similar manner like the 0s of cloak parameters?)
Yes, we can get. It is possible to show that most of the scattering from cloaks is always going to come from the problem with 0s - the fact that eps and mu are not continuously changing has a negligible impact. In other words, the physics is not singular as you are approaching the zero thickness limit of the discrete layers.
Fifth: Can we make these values for eps and mu the same? (ie overlap zeros etc)
That is, presently, the biggest problem when the actual implementation is considered. The thing with the 0s is a fundamental limitation. Any consideration of the implementation problems is just to be superimposed to that.
I think it is pointless for me to discuss whether a cloak can be made. I did calculations saying precisely what happens if the parameters are such and such. If an expert says to me: 'this cannot be nearly done in the next 10 years', I have to accept that.
To decide whether something can or cannot be done we would have to agree on what do we mean by 'can be done'.
If I say that I will become infinitely rich when I get older, you would say that is meaningless because there is no such thing as infinity. But if I explain you that by that I mean that I can get more money than any previously given amount, you would have to agree that it probable (though, unfortunately, the probability is very low if the amount is in millions) and therefore possible.
So, if I say (it's actually Pendry who says it) that a cloak is possible meaning that the scattering cross-section can be reduced below any previously given value, you will have to agree because I will show you the formulas and the scatt. cross section reaching zero asymptotically.
As for whether there is an upper limit for how rich I could get - clearly there is since there is only a finite amount of money in the world. Though, there is really a lot of money, so I wouldn't be really concerned about that. The issue I really need to be concerned about is how to get even that finite amount.
Similarly - presently there is some upper limit for what can be done with metamaterials. In 2 years, it will shift. More so in 10 years. We have to investigate the thing in more detail if we are to give estimates of what can or cannot be done.
No one said that the scattering cross section has to be exactly zero. Also, no one mentioned things like launching single photons in a highly controlled environment to investigate whether the cloak is really perfect (I mean the QED thery). It's clearly not. But hey!, lets look at the bright side - the Christmas is coming.
Regards
Hi, goran1901
Thanks for your quite excellent response. Yes I notice in Pendry's paper, no 0 or infinite cases. But I notice all later simulations or experiment by Dr. D Schurig involved in 0 or infinite. Could you give me some paper that do not involved in 0 or infinite. But not simulation results, because in the simulation when you set permittivity or permeability anisotropy larger than 1E5 (for example exx=uxx=1, eyy=uyy=10000), you can find the strong "cloaking" effect.
Everyone is welcome to put forward your ideas about cloaking. I am sure it is an opening question either for experiments or theory.
I would like to simulate a scattering problem where the amplitude of the incident plane wave is modulated by a signal which is time dependent.
Does anyone know how to simulate the impulse response in the electromagnetic module of COMSOL?
Thanks.
im newer in anisotropic concept plz tell me what should i do first!
regards
In your reply: Even for the 2D cylinder, it is possible to find a way to make a cloak which needs to have 'only' 0 and not infinity.
Do u mean this by a simplified cloak?
hi iaia
can u help me to find some example of cloaking by using comsol