frequency dependent coding
I need a reference about frequency dependent FDTD
in which both epsilon and mu are frequency dependent
in most of papers which I've found, mu is not frequency dependent
please help me
The reason that they do not mention this in papers is that exactly
the same methods can be used (just switch E and H and also epsilon and mu).
For example if you use the ADE method then you add a polarization current to the
E-fields. If you also have frequency dependent H then you would also have to add
a magnetic polarization current.
Basically FDTD is symmetric in E and H if you add a magnetic conductivity. So anything
you can handle for the electric field you can also handle for the magnetic field or both.
I know that FDTD is symmetric but when both epsilon and mu become frequency dependent formulation will be complex
I want this case
Can you explain what you mean by that. I assume you do not mean that you have complex
permittivity or permeability. It sounds as if you mean that you *must* run FDTD with complex
E and H fields. I don't see why this should be necessary but since I usually only deal with
materials with constant permeabilty that does not mean much.
When you say "complex" do you mean numbers with real and imaginary parts or do you mean the formulation is difficult? If you are thinking mu and eps are complex in the sense of having real and imaginary parts, you are probably thinking of these from a frequency-domain perspective. FDTD is a time-domain method so the dispersive behavior of mu and eps is due to a time-domain "ringing" response. If you Fourier transform this response to an impulse excitation, you will get the complex mu and eps. In the time-domain, you are essentially convolving the time-domain impulse response with the E and H fields so there are no complex numbers. The impulse response is purely real.
Just to be complete, the only time I have seen or used complex numbers in FDTD is when computing photonic band diagrams or implementing some periodic boundary conditions. I want to say I've seen them used for some absorbing boundary conditions, but I can't be sure about that. Almost always, complex numbers in the frequency-domain become purely real numbers when Maxwell's equations are expressed in the time-domain the time-domain.
-Tip
hello
I mean I want to simulate amedia in which both mu and epsilon is frequency dependent(drude model)
I said formulation is difficult
I want a refrence for this case
I think iyami said it well. Just take a formulation for dispersive eps, then exchange eps for mu, and E for H, and you will have the formulation for dispersive mu. When you write your code implement both formulations at the same time.
Are you going to simulate the actual structures (split ring resonator or whatever) that gives you the negative mu and eps? If so, I am skeptical you need the dispersive mu feature. Most materials have negligible magnetic response and the structure itself will automatically produce the "effective" magnetic response. If you are not doing this and modeling the negative index material as an effective medium of if you are actually incorporating materials with a magnetic response, I can understand why you need this.
Anyway, attached are some references that may help you, but they are taking the effective medium approach.
-Tip
dear rrumpf
it is simple
I want to write a FDTD code in which both mu and epsilon are frequency dependent because I want to model a metamaterial media by FDTD
I apologize, but I may be writing too quickly and confusing you.
In meta-materials, special structures typically composed of metals are arranged so as to give rise to effective mu and eps material properties. Based on this, two types of FDTD models can be constructed to model devices made of meta-materials. (1) The most rigorous approach is to actually build into your model the actual structures themselves giving rise to the effective eps and mu values. (2) The second is an effective medium approach where you do not incorporate the actual structures giving you your effective mu and eps values. Instead, you treat the meta-material just like any other homogeneous material, but use dispersive models for mu and eps.
For approach (1), you probably only need a Drude model for the metals. The mu properties will naturally arise because you are simulating the structure that provides the effective magnetic material response. In this approach, you only need to dispersive models to describe the actual materials you are using, not the "artificial" mu and eps values the meta-material will give you. These will naturally arise in your model.
For approach (2), you will need the dispersive model for your effective mu and eps and I have provided you two papers that show how to do this.
Hopefully this helps. If not, can anyone else help this person?
-Tip
seems here there are many people who can help in metamaterial simulation. Currently i am trying to simulate a left handed metamaterial which can show negative refractive index . before i go to do something more specific can anyone help me by explaining the procedure of simulating metamaterial in fullwave(rsoft)?
do anyone have any tutorial on metamaterial simulation using fullwave? i am not sure that whether fullwave can extract transmission and reflection parameters of the material.
i am not clear about using the PML boundary in left and right .and PEC/PMC boundary condition in up and down.
please help me.