Reproduction of Fig. 11b of A. Egel et al., J. Quant. Spectrosc. Radiat. Transfer 273, 107846 (2021)

[Tanay Paul]

Hi all,

I was trying to reproduce the example 'Field enhancement between two plasmonic nano spheres on a substrate' (Fig. 11) provided in the paper 'SMUTHI: A python package for the simulation of light scattering by multiple particles near or between planar interfaces' by the SMUTHI developers [A. Egel et al., J. Quant. Spectrosc. Radiat. Transfer 273, 107846 (2021)]. The plot I could produce of the electric field in the middle of the gap as a function of wavelength matched in magnitudes with the one given in the paper (Fig. 11b). However, I am not able to produce the hump-like pattern of the plot for smaller particle gaps. Could this happen because of the refractive indices I use for gold? In that case, please let me know what values of refractive indices of gold are required for an exact reproduction of the figure or the source from which I can obtain the same. I used the gold refractive indices given in the paper by P.B. Johnson and R.W. Christy, Phys. Rev. B 6, 4370 (1972).

Thanks and regards,

Tanay Paul.

[Amos Egel]

Dear Tanay,

thank you for your interest in the nano-spheres example from the Smuthi paper. 

The gold refractive index data are from Johnson.

You can inspect the script that we used to produce the Smuthi data and also the FEM reference data here.

Hope this helps to sort out the issue with the deviating results for smaller gaps.

Best regards, Amos

https://gitlab.com/AmosEgel/smuthi/-/tree/master/examples/submitted_to_JQSRT_2021/plasmonic_nano_spheres

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[Tanay Paul]

Many thanks for helping with the example scripts and data. I made two mistakes, and my code could not reproduce the figure perfectly. I did not realize that Si has a frequency-dependent refractive index in the frequency range where we expect resonance of gold, and secondly, I made a wrong choice of n_eff_max. It appears that the results are highly sensitive to the choice of n_eff_max and l_max.

I have another question for you all. I was wondering whether it is possible to extract the transmission and reflection coefficients rather than calculating the transmitted and reflected powers. 

Please let me know if you have any solution.

Best regards,

Tanay.

[Amos Egel]

Dear Tanay,

Reflection and transmission coefficients are a concept that cannot a priori be applied to plane waves scattered by a finite number of particles. (Infinite incoming power versus finite scattered power)

The following approaches have been used to compute reflection and transmission coefficents:

1. Periodic simulations: A plane wave is scattered by an infinite periodic particle collection

2. Beams with finite width: A beam with finite power is scattered by a finite number of particles. The reflected power divided by the incoming power estimates the reflection coefficient. Make sure that the beam width is smaller than the size of the particle aggregate.

3. Plane waves on finite scattering samples: The back-scattering cross section of the aggregate divided by the geometric extent of the aggregate can be used to estimate the reflection coefficient. Care has to be taken with regard to diffraction effects by the aggregate boundary.

Best regards, Amos

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[Tanay Paul]

Dear Amos,

Many thanks for your detailed explanation.

In my last email, I forgot to mention that I am interested in calculating the transmission and reflection coefficients for a 3-layer system where the middle layer has a periodic arrangement of scattering particles. For post-processing purposes, I am using the 'smuthi.periodicboundaries.post_processing' module. I can calculate the transmittance and reflectance from the transmitted, reflected, and incident powers following the steps as demonstrated in the example 'Fifteen periodic spheres in a slab' provided in the SMUTHI documentation. I was hoping to find a way to directly/indirectly calculate the transmission and reflection coefficients, as well, with the help of any SMUTHI post-processing modules.

Thank you again for your time and support. Best regards,

Tanay.

[Dominik Theobald]

Hey Tanay,

 

thanks for the clarification of what you are looking for.

 

The reflection and transmission coefficient you have shared are defined as the amplitude ratio between the transmitted/reflected wave and the incident field. Which is identical to the transmitted/reflected power divided by the intial power (which you already found in the benchmark example "fifteen periodic spheres in a slab).

 

In addition, you mentioned the Fresnel equations that relate the incident wave to its partially transmitted and reflected wave, given a planar interface. These Fresnel equations can be extended to multi-layered planar environments by means of the transfer matrix (and or scattering matrix). For such planar interfaces, both the power ratios and the Fresnel coefficients are identical, as all power is refrected into one direction or reflected into another.

 

Now considering scattering media, an incident wave will be scattered into all possible directions and therefore it would make sense to define the transmission and reflection coefficients as a function of the polar and azimuthal angle. In the special case of infinite periodic arrangements however, light is not scattered in all possible directions, but rather in finite, discrete directions.

 

In Smuthi/periodicboundaries/post_processing you find all tools to evaluate such matrices of transmission/reflection coefficients. E.g. you evaluate the plane wave expansion of transmitted light (https://gitlab.com/AmosEgel/smuthi/-/blob/master/smuthi/periodicboundaries/post_processing.py?ref_type=heads#L218), transform it into a far field expansion (https://gitlab.com/AmosEgel/smuthi/-/blob/master/smuthi/periodicboundaries/post_processing.py?ref_type=heads#L481) and compare the FarField.signal values with the initial wave's power per area (https://gitlab.com/AmosEgel/smuthi/-/blob/master/smuthi/periodicboundaries/post_processing.py?ref_type=heads#L481).

 

The result is a matrix (polar x azimuthal angle) of how much power of the incident wave is scattered into distinct solid angles.

 

I hope this helps.

If you have any further questions please let me know.

 

Best

Dominik

 

 

Gesendet: Sonntag, 16. Juni 2024 um 17:28 Uhr
Von: "Tanay Paul" <tanayp...@gmail.com>
An: "Dominik Theobald" <dominik....@web.de>
Betreff: Re: Re: [Smuthi] Reproduction of Fig. 11b of A. Egel et al., J. Quant. Spectrosc. Radiat. Transfer 273, 107846 (2021)

For a detailed understanding, I would like to draw your attention to the Fresnel Equations, which provide the relations of the reflection and transmission coefficients at an interface between two media with the refractive indices of those media; please look at the attached snapshot.

 

Thank you again for your help.

 

Best regards,

Tanay

 

On Sun, Jun 16, 2024 at 10:19 AM Tanay Paul <tanayp...@gmail.com> wrote:

Dear Dominik,

 

I am attaching herewith a snapshot containing the definitions of the reflection and the transmission coefficients. Please have a look. 

 

Thank you for your kind reply and support.

 

Best regards,

Tanay. 

 

On Sun, Jun 16, 2024 at 2:47 AM Dominik Theobald <dominik....@web.de> wrote:

Hey Tanay,

 

the post-processing routines do not include a routine to directly compute transmission and reflection coefficients. However, all necessary tools should be available.

Could be please share the definition of transmission and reflection coefficients that you are interested in? I'll then have a look how you can evaluate them with the available tools

 

Best
Dominik

 

 

Gesendet: Mittwoch, 12. Juni 2024 um 21:35 Uhr
Von: "Tanay Paul" <tanayp...@gmail.com>
An: "Smuthi" <smu...@googlegroups.com>
Betreff: Re: [Smuthi] Reproduction of Fig. 11b of A. Egel et al., J. Quant. Spectrosc. Radiat. Transfer 273, 107846 (2021)

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