Learning Forum

[Tenyu Aikawa]

Hi all I just need help understanding material loss in my metamaterial. From what I understand, in order to take into account the material loss in my metamaterial a passivity plot as a function of frequency should show how much material loss I am experiencing at every frequency. When I plot a function of the magnitude of the passivity vs frequency the passivity is around 0.99-0.97 which seems quite high... So I am not exactly sure how to interpret this.

Ultimately I want to know the radiation loss that my metamaterial is experiencing. The way that I am calculating this is through the S-parameters (ie the reflection and transmission). Using conservation of energy 1 = S11 + S21. Since there will be some loss due to radiation loss and material loss I will have a total loss. Thus the equation changes to 1 = S11 + S21 + Total_loss. The total loss should be equal to the radiation loss and the material loss. Thus that is why I need to know the material loss in order to calculate the radiation loss.

I have already been able to calculate the total loss which is a small fraction of 1. But if I were to look at the passivity the magnitude is much greater than my total loss. That is why I am confused about how to interpret the magnitude of the passivity when looking at it as a function of frequency.

Plot for passivity:

 

Plot for S-paramters reflection and tranission:

[Aymen Mzoughi]

Understanding material loss in metamaterials can indeed be challenging. The passivity plot you mentioned, which shows values around 0.99-0.97, indicates that your metamaterial is mostly passive over the frequency range you are examining. High passivity values close to 1 suggest that there is very little loss, which might seem contradictory if you are expecting higher losses.

When you calculate the total loss using S-parameters, you are considering both the reflection (S11) and transmission (S21) to account for the energy that is not lost. The total loss you've calculated as a small fraction of 1 is the energy that is neither reflected nor transmitted, which includes both material and radiation losses.

The confusion arises when the passivity is much greater than the total loss. This could be due to several factors, including the possibility that the material losses are indeed very small within the frequency range you are looking at, or there might be an issue with how the passivity is being calculated or interpreted.

To further understand the material loss, you might need to look into the effective material parameters such as the effective permittivity and permeability, which can be extracted from the S-parameters. The effective refractive index and impedance can be calculated, which then allows for the retrieval of the effective permittivity and permeability. However, it's important to note that the extraction process can be challenging due to the multivalued nature of the complex inverse cosine function, and choosing the wrong branch can lead to incorrect results.

[Tenyu Aikawa]

 

Hi thanks for the response! Yes my metamaterial is completely passive, I do not have and active components. From you statement “High passivity values close to 1 suggest that there is very little loss, which might seem contradictory if you are expecting higher losses.”  I am actually expecting low material loss. Here is the full formula for calculating the radiation loss:  1 = (S11)^2 + (S21)^2 + Radiation_loss + Material_loss. If I’m interpreting the material loss as the passivity with values that are ranging from 0.99-0.97, would that not be high loss? You mentioned that “1 suggests that there is very little loss” if that is the case, I am probably interpreting the values incorrectly. If the passivity were subtracted from 1, then these values would be low enough. But if I am interpreting them as a function of my S-parameters they will give a value greater than 1. I have taken the s-parameters and passivity as a function of magnitude when graphing them in HFSS. 

 

Could you maybe clarify this statement a bit more: “High passivity values close to 1 suggest that there is very little loss’ ‘. Also would you by chance know what units the magnitudes for passivity are?