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# [SOLVED]Materials with losses in FDTD method

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#### FDTD beginner

##### Newbie level 4
Dear all!

Can anybody explain me is there any problems in FDTD method in case of materials with losses?
Do you know any articles or books with theoretical discussion of this topik?

Dear all!

Can anybody explain me is there any problems in FDTD method in case of materials with losses?
Do you know any articles or books with theoretical discussion of this topik?

Any textbook on FDTD (Taflove, Sullivan, Elsherbeni, Kunz&Lubbers, Gedney, Uno,...) discusses conductive materials. There is no problem modelling conductive materials. The modifications are straightforward

Points: 2

### Kirill Zaitsev

Points: 2
Dear iyami!

Thank you very much for your comment!

I quickly look through Taflove and Sullivan and found that they discuss conductive materials in one-dimensional case.
And what if I would like to simulate photonic crystal with woodpile structure that was considered in Taflove's "13.8.1 Photonic Bandgap Structures" but with metalic rods. Do I correctly understand that the only problem is to extent equations for conductive materials to three dimensional case? Maybe it had already been done? Do you know any similar articles or books?

Dear iyami!

Thank you very much for your comment!

I quickly look through Taflove and Sullivan and found that they discuss conductive materials in one-dimensional case.
And what if I would like to simulate photonic crystal with woodpile structure that was considered in Taflove's "13.8.1 Photonic Bandgap Structures" but with metalic rods. Do I correctly understand that the only problem is to extent equations for conductive materials to three dimensional case? Maybe it had already been done? Do you know any similar articles or books?

Section 3 already has the 3d code for conductive materials (section 3.6.3 in the 3rd edition). Whenever your code looks like E(n+1) = c*E + c'*(Del x H) and c != 1 then you are using already conductive materials (c != 1 <==> sigma != 0 <==> material is conductive).

Points: 2

### Kirill Zaitsev

Points: 2
Dear iyami!

Unfortunately, we have only Taflove's 2nd edition in our library.
It would take a lot of time to get this book.
If it is possible, may i ask you to send me section 3.6.3 to my email AnRu1@Yandex.ru

Dear iyami!

Unfortunately, we have only Taflove's 2nd edition in our library.
It would take a lot of time to get this book.
If it is possible, may i ask you to send me section 3.6.3 to my email AnRu1@Yandex.ru

It is the same section in the 2nd edition (starting at p.80)

Points: 2

### Kirill Zaitsev

Points: 2
Dear iyami!

Thank you very much for your help!

I have one more question. What if I would like to investigate photonic crystal with metalic rods in optical frequency band. Do I correctly understand that according to Kramers–Kronig relation material will be frequency dependent in this region? Does FDTD method applicable in this case or I should use one of its modifications?

Dear iyami!

Thank you very much for your help!

I have one more question. What if I would like to investigate photonic crystal with metalic rods in optical frequency band. Do I correctly understand that according to Kramers–Kronig relation material will be frequency dependent in this region? Does FDTD method applicable in this case or I should use one of its modifications?

1) epsilon + sigma for metals are frequency dependent in that region
2) see chapter 9 in Taflove for ways to model dispersive materials
3) if you consider a single frequency at a time and if epsilon >= 1.0 and sigma >= 0.0 standard FDTD can be used

Points: 2

### Kirill Zaitsev

Points: 2
Dear iyami, many thanks for your help!

At this point I don't have new questions.

liliya

Points: 2