Question about simulation of light scattering by particles much larger than the wavelength

[Thea]

Dear the ADDA Research Team:

following your 2007 publication "The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength", has your research team conducted new numerical simulations on scatterers significantly larger than the wavelength? What is the current size limit for particle calculations using ADDA? I aim to use ADDA to study hexagonal prism particles with a refractive index of 1.3 and a column length of 100 μm (size parameter ≈498.3206) in random orientations(128 α,17 β,and 3 γ). However, computations already become challenging at a column length of 10 μm, taking over two days. In your experience, would simulating 100μm particles be infeasible with current hardware resources?

looking forward to your reply!

Best regards,

Thea

[Maxim Yurkin]

First of all, there are two significantly different problems - particles in fixed orientation or orientation-averaged. I have always been focusing on the fixed orientation, and the benchmarks are for this case. The underlying (very naive) assumption is that if you can simulate single particles, you will be able to do orientation averaging, but much longer (proportional to the number of orientations). While that is practically wrong, it is still simpler than pushing the limit in (x,m) plane as was done in the benchmarks. There the main problem is the number of iterations which grows exponentially near this limit if Im(m) is zero (or very small). This explains why the limit has not changed that much since the 2007 paper that you mentioned. 

There have been a limited progress with using modern DDA formulations (FCD or IGT), playing with iterative solvers and initial guesses for them. See, e.g.,  

Inzhevatkin K.G. and Yurkin M.A. Uniform-over-size approximation of the internal fields for scatterers with low refractive-index contrast, J. Quant. Spectrosc. Radiat. Transfer 277, 107965 (2022). (PDF)

Last week I presented the simulations for size parameter of 1000, see https://www.researchgate.net/publication/393146069_Slides_ELS21-2025_ADDA , but this is a somewhat cheap trick, since the refractive index was up to 1.02. I may be able to increase it to 1.05, but not larger (unless absorption is added). If you are interested in huge, optically soft particles, this issue may be relevant - https://github.com/adda-team/adda/issues/220, although it is far from any practical implementation.

As an intermediate conclusion, this does not help for your ice columns, so even a single orientation of 100 μm particle is completely unreachable. Again, there are some vague ideas here - https://github.com/adda-team/adda/issues/225, but nothing ready to use. Another hope is the recent development of Steven Lanier - see https://github.com/adda-team/adda/issues/244#issuecomment-3019796083 (and the whole issue for background). His code can be very useful for moderate problems, that fit into a single GPU. But again, we are not yet working on implementing this feature in ADDA.

First, ask yourself if you really need such sizes. While they are relevant for atmospheric applications, other methods are much more suitable for that. Specifically, physical optics methods (several variations of them exist) is accurate enough for such sizes and maybe down to size parameter of about 60. For larger particles, the number of orientations also increase a lot, making even physical optics challenging, but still feasible.

Second, if you agree that size limit of 60 or a bit more is sufficient, that would be within the reachable limit of the DDA (already at 2007), but the computational times will still be large due to both large number of orientations and large number of orientations (optimization of the latter was discussed in my reply to your other question). Again, one simulation is completely feasible (although it may take days), but systematic study, e.g., for constructing a database would require a lot of core-hours on a cluster (supercomputer).

Maxim.

[Александр Кононошкин]

Hello! If you need a solution for light scattering on hexoganal ice crystals for exact backscattering, you can easy reach the ScIce-2025 database for optical properties of realistic ice particles of cirrus clouds via https://zenodo.org/records/15144868 or https://scice.konoshonkin.com/

If you need a solution over all scattering directions, I would recomed you to use the physical-optics method, it suits this task better.

Alexander Konoshonkin

понедельник, 30 июня 2025 г. в 10:46:35 UTC+7, Thea:

[Thea]

Dear Prof. Maxim and Prof. Alexander:

Thank you for your prompt reply! I would like to study the scattering characteristics of cloud particles, so such a large particle size range is indeed necessary.

I also intend to introduce Bessel beams to explore the influence of different beams on cloud particles. I wonder whether the physical optics approximation

method supports the introduction of beams other than parallel light. Of course, I will try to explore the implementation of the physical optics approximation method!

Thank you very much for your help, which has given great support to my study!

Best regards,

Thea

[Alexander Konoshonkin]

Apologies for the delayed response, I was on a business trip.

Let me break this question into two parts:

1. In principle, the physical optics method can handle Bessel beams under some assumptions. However, none of the existing computer implementations of this method can currently process it.

 2. In real-world applications, the cross-sectional size of a laser beam is typically much larger than the particles in cirrus clouds. This is because the lidar’s light travels a long distance (several kilometers) before reaching the cloud. Thus, in practice, any irregularities in the laser light are much larger than the ice crystals, allowing the assumption of a plane-parallel wave for each particle.

 Due to point 2, nobody implements point 1.

 

Additionally, as I know, real Bessel beams cannot propagate very far, while physical optics is only valid for the far zone (far field). Therefore, using physical optics for light scattering at distances of a few centimeters (or meters) is generally inconsistent.

 You can provide more specific details about your problem so we can offer better assistance.

Best regards,

Alexander

среда, 2 июля 2025 г. в 16:29:05 UTC+7, Thea:

[Thea]

Dear Prof. Alexander,

Hope this email finds you well! First off, sorry for my extremely late reply as I just saw your message. Your earlier detailed explanation was really insightful and helpful!

Actually, we aim to apply Bessel vortex beams in lidar if possible. Theoretically, an ideal Bessel beam can propagate infinitely, and the non-diffracting and self-healing properties of Bessel vortex beams might help address beam diffusion issues. Of course, there are still huge challenges in getting Bessel beams to propagate over several kilometers. So, for now, we want to start with some basic research and discussions on Bessel vortex beams.

My research focuses on the interaction between Bessel vortex beams and cloud particles, as well as studying their scattering characteristics. I'll prioritize the ideal Bessel beam, though Bessel Gaussian beams are also under consideration.

Meanwhile, I have some questions about your first point, what exactly do the "assumptions" refer to? And could you explain what "none of the existing computer implementations of this method can currently process it" means? I'd be really grateful for your answers.

Additionally, I am still in the learning stage. If there is any imprecision in the above descriptions, you are more than welcome to point it out and discuss it.

Looking forward to your response.

Best regards,

Thea

[Maxim Yurkin]

Thea, let me try to answer this to keep the discussion going. In my understanding, any beam (including the Bessel ones)
can be considered as a superposition of plane waves. So one of the solutions is to simulate each of the component
independently and then add them coherently (i.e., for field amplitudes). I guess, no physical-optics code can do it
naively, so one has to develop some script for it. Moreover, the existing codes probably do not produce the field
amplitudes in the standard output - it is available inside, but some modifications to the code will be required to
extract it.

On the one hand, that will require efforts for implementation and, even after that is done, it will be definitely not
efficient in terms of computer time. On the other hand, it is worth thinking more about the practically feasible
parameters of such beams (for atmospheric applications) before going in this direction. While extremely long-propagating
Bessel beams are, in principle, possible they will not differ from a plane wave on a size scale of a single particle. In
other words, the plane-wave decomposition will have a very narrow weighting function around the main propagation
direction. Then for simulation of cloud response, it would be sufficient to consider that various particles sense
different local intensity of the beam, but each single-particle response is well-described by plane-wave scattering.

Maxim.

[Thea]

Dear Prof. Maxim,

Thank you very much for your explanation. Due to my insufficient knowledge reserve, it took me some time to digest and think, so I am replying to you now.

You mentioned in the email that Bessel beams can be approximately simulated through plane wave decomposition, and the response of a single particle can be described by plane wave scattering. However, I have a question that I hope to discuss with you: The central spot size of high-order Bessel beams (such as the diameter of the first bright ring) is usually on the micrometer or even sub-micrometer scale (the values of the spot radius varying with the order n and half-cone angle α are shown in the attachment). In contrast, the size range of cloud particles is relatively wide (e.g., 0.1–100 micrometers). If we choose the order n=3, the spot size is likely to be smaller than the particle size. In this case, the particle may cover both the bright and dark ring regions of the beam. Will the significant difference in incident light intensity on different parts of the particle lead to the failure of the plane wave approximation?

In addition, such plane wave approximated beams may still retain some characteristics of their initial beam modes in terms of energy distribution and other properties. I want to see what happens when these characteristics interact with particles. I came across a study on the propagation characteristics of vortex beams in hazy environments: Chenge Shi, Lixin Guo, Mingjian Cheng, Martin PJ Lavery, and Songhua Liu, "Aerosol scattering of vortex beams transmission in hazy atmosphere," Opt. Express 28, 28072-28084 (2020) , which also seems to involve far-field scattering. What I want to do is similar research.

By the way, I plan to reduce the range of particle sizes for calculation, and use ADDA to call Bessel beams to calculate as large particles as possible (currently, I can only calculate particles with a maximum length Dmax=10μm, and cannot achieve the calculation for 15μm) to initially observe the relationship between Bessel beams and particles.

In addition, I am currently learning to use ADDA to call different types of Bessel beams to interact with particles. For example, when selecting order n=3, half-cone angle α=10°, wavelength of 0.532 μm, and the column length of the hexagonal prism particle is 2 μm, I found that the phase function P11 of different Bessel beam types differs by almost an order of magnitude, and P22, which characterizes the depolarization ratio, is also different. This phenomenon is very interesting. Do you know the underlying principle?

Thank you again for your reply, which has given me a lot to think about and has been very helpful to me!

Best regards,
Thea

[Thea]

Sorry, I forgot to attach the file.

[Maxim Yurkin]

You mentioned in the email that Bessel beams can be approximately simulated through plane wave decomposition, and the response of a single particle can be described by plane wave scattering. However, I have a question that I hope to discuss with you: The central spot size of high-order Bessel beams (such as the diameter of the first bright ring) is usually on the micrometer or even sub-micrometer scale (the values of the spot radius varying with the order n and half-cone angle α are shown in the attachment). In contrast, the size range of cloud particles is relatively wide (e.g., 0.1–100 micrometers). If we choose the order n=3, the spot size is likely to be smaller than the particle size. In this case, the particle may cover both the bright and dark ring regions of the beam. Will the significant difference in incident light intensity on different parts of the particle lead to the failure of the plane wave approximation?

There is definitely a significant difference between plane wave and sufficiently focused Bessel beam. Still, any Bessel beam can be represented by a superposition of plane waves, but then the field rather than intensities need to be summed from each plane-wave contribution.

In addition, such plane wave approximated beams may still retain some characteristics of their initial beam modes in terms of energy distribution and other properties. I want to see what happens when these characteristics interact with particles. I came across a study on the propagation characteristics of vortex beams in hazy environments: Chenge Shi, Lixin Guo, Mingjian Cheng, Martin PJ Lavery, and Songhua Liu, "Aerosol scattering of vortex beams transmission in hazy atmosphere," Opt. Express 28, 28072-28084 (2020) , which also seems to involve far-field scattering. What I want to do is similar research.

Yes, it is possible to simulate a lot of things, but practical considerations are very different for table-top experiments (here you can have almost any Bessel beams) and lidar applications. In the latter case, even alpha = 1 deg is unrealistically large. That is the main question that was asked to you in the discussion above.

In addition, I am currently learning to use ADDA to call different types of Bessel beams to interact with particles. For example, when selecting order n=3, half-cone angle α=10°, wavelength of 0.532 μm, and the column length of the hexagonal prism particle is 2 μm, I found that the phase function P11 of different Bessel beam types differs by almost an order of magnitude, and P22, which characterizes the depolarization ratio, is also different. This phenomenon is very interesting. Do you know the underlying principle?

Some simple features, like reduced forward scattering for P11, can be easily interpreted (due to the reduced intensity on the beam axis). But I can't provide any guidance for P22 behavior. Note also that generalization of Mueller matrix definition to Bessel beams is somewhat ambiguous, as discussed in our paper (Glukhova & Yurkin 2022). It is reasonable and reproducible, but measuring, e.g., P22 is not easy. Specifically, some standard configuration for measuring P22 for plane wave incidence will, most probably, not be directly suitable for Bessel beams. So, before discussing the behavior of some simulated quantities, it is important to link them to potential experimental configurations.

Maxim.