## Photonics

#### Efficiency and power normalization for the monitor perpendicular position to the source

• Infinite
Subscriber
• Guilin Sun
Ansys Employee
For linear materials, the normalization is to the source spectrum, please refer https://support.lumerical.com/hc/en-us/articles/360034394234-Understanding-frequency-domain-CW-normalization
Suppose the source amplitude is A0 (default it is 1 V/m). Since the injection is a pulse, so different wavelength will have different intensity, which is the source spectrum. To remove the frequency dependency, just divide the frequency-domain data with the source spectrum as shown in the above page. Such normalization means all the wavelengths would have injected amplitude of A0.
Once source amplitude is normalized, intensity is normalized. However, due to complicated interaction of light with matter, such normalization does not mean the maximum is 1. For example, the interference maximum intensity can be 4 when to plane waves interfere. In some devices, the field enhancement can be thousands of orders to A0^2. However, the normalized power should be smaller than or equal to 1.
Power is normalized to the source power. Please refer https://support.lumerical.com/hc/en-us/articles/360034925313-sourcepower-Script-command
Efficiency is usually defined by users.

The frequency-domain monitors do the above normalization.

• Infinite
Subscriber
Usually in the DFT monitor when I see pure reflection that is the monitor plane is parallel to source injection plane the efficiency is smaller that 1 (less than 100%), but the screen shot I gave here for side YZ DFT monitor is showing almost 800% efficiency at 900 nm wavelength. So is this both 'source top XY monitor' and 'side YZ monitor' result consistent?
Also for power absorption analysis group if I calculate the power injected by incident plane wave by the (p = - 0.5 w *abs(E^2) *ima(permittivity) then I got something say 10^15 order/ per unit area for a particular wavelength, but the analysis group shows power absorbed about 10^21 order per unit area, (if I take one slice of area from volume) Is that also consistence? where E= 1 V/m, and area is 2.14*10^-13 m^2.
Finally could you please show me an example file for the plane wave is injected from the source and passing through a structure and I can calculate the normalized power that is going through all the 3 monitors (reflection and transmission parallel to the source and side transmission perpendicular to the source).
Thank you so much.

• Guilin Sun
Ansys Employee
Hi´╝îtransmission can be be meaningful when the DFT monitor is in parallel to the source plane for periodic structure with Periodic BCs. The YZ monitor can monitor E fields but not the transmission. In theory, if this YZ monitor is exactly on the periodic BC, it should record zero transmission. In your case XY monitor gives correct transmission only. xz and yz monitors are not for transmission calculation. They are only helpful if you want to know where the fields are strong.
Power equals the integration of Poyinting_vector dot plane_normal , please refer this https://support.lumerical.com/hc/en-us/articles/360034405354-transmission-Script-command
The analysis group gives you the power density, not the power except T_total. Only after integration along x,y and z then can you get the power. Since you are using analysis group, please refer this solar example https://support.lumerical.com/hc/en-us/articles/360042156874-Plasmonic-solar-cell-at-normal-and-oblique-incidence
In general, if you only have interest in transmission/reflection, just use Power DFT monitor, not the analysis group, which is less accurate than the power monitor along, since the analysis group has additional interpolation and integration which could introduce errors.

• Infinite
Subscriber
Hello Gun, Thank you for quick response.
Well this is a plasmonic structure and I am using Block BC. And obviously for a lot of simulations based on what type of structure I have as for nanoantenna the Side monitor are not giving zero intensity.
My main goal is to understand and calculate how much power and efficiency is going to the side way towards the dielectric layer.
Is there any way Lumerical package can do that please?
Thank you
• Guilin Sun
Ansys Employee
non-zero transmission is because the monitor is not on the Bloch Boundary. In physics power cannot just go in one direction on the sides that are periodic when periodic BCs are used. Bloch BC is a generalized periodic BC.
For your purpose, you may need to check the slab mode using FDE instead of using power monitor in FDTD. I would suggest that you consider the physics carefully.
• Infinite
Subscriber
Hello I have checked a lots of simulations with many varying conditions, with various nanoantenna geometry, and different metals.
The YZ monitor is placed exactly at the Block boundary (block bc in x and y direction and pml in z direction).
As I mentioned earlier depending on the geometry of the nanoantenna sometime the YZ monitor efficiency of transmission shows zero sometime not zero at all. Even if I put the YZ monitor inside the boundary there are values of transmission efficiency.
If there is an inconsistency with physics of the simulation result then how can we rely on the Lumerical result?
Could you please help me with a simulation set up for slab mode Using FDE where say there is some nanoantenna over a dielectric, over the metal layer?
Thank you
• Guilin Sun
Ansys Employee
FDTD is a discrete method, and all the 6 field components are interleaved in space. Periodic BCs mean infinite number of periods, no beginning point no ending point, just like a "circle".So if there is power travelling along one direction where the power goes in periodic BCs? This is the physics from my intuition. What do you think? Bloch BCs need special treatment to apply additional phase on the exact
Yee Mesh, something could be "unphysical" for example in theory the periodic BC is a plane however in the discrete world it is not a single plane. In addition, what is the size of the monitor on the XZ and YZ plane? do they pass across the source? if so, it is not a surprise since source has a grey area where the fields are unphysical also in order to have the source propagate in one direction but not the other direction.
In the forum and Knowledge Base as well as the App examples, we show how to use the software normally in a common way. If users want to explore some other extra ordinary, it is ok however it will be out of the scope of this forum. On the other hand,
If you want to analyze the mode properties of such device please refer FDE examples online. This OLED example might be helpful in particular for your case https://support.lumerical.com/hc/en-us/articles/360042713113-Mode-analysis-of-an-OLED-layer-structure

• Infinite
Subscriber

Hello Gsun Hope it's not too late to reply.
Well regarding Source position , it is plane wave source at 700 nm above the structure and the YZ-side monitor is placed at 0 to -300 nm on Z-axes. Can I take it granted that this DFT (side monitors) shows the E-field values that only pass through on the monitor surface area?
The attached Picture shows the variation of efficiency for from top, side and Pabs (Pabs is covering only the volume of the dielectric).
It seems if even the E-field value this side monitors can provide they can not provide the transmission efficiency correctly because there is no way they can be weighted by source injected power in perpendicular plane. So can I trust the magnitude of E-field values from the side monitors at least? while the E-field enhanced by 800%.
What is the best option of simulating the propagating surface wave from this type of Nano resonator structure please?
Thank you
• Guilin Sun
Ansys Employee
You can trust the data from the monitor, with 800% enhanced. Local electric field enhancement can be engineered to arbitrary value, such as 1e6 or even higher. This is the field, not the power, where power is conserved no larger than the incidence.
Please do not measure the transmission of the monitor on the periodic axis since it is not measurable in experiment.
In addition, we can say how much power passes a surface, but not for the fields, as the fields are local, spatially exist. Fields and power are not the same concepts. Again, the net power to the periodic BCs is ZERO, otherwise it violates the physics.
If you want to simulate the surface wave propagation, you will need to set up the device long enough along the propagation direction. However, never apply for the periodic BC in that direction. This can be another interesting topic, please have a new post if you have questions.