Pvψv 、ζ v are Bessel functions.Pvψv’(mpα)ψv(α)–mpψv(mpα)ψv’(α)ψv’(mpα) ζ v(α)–mpψv(mpα) ζ v’(α)mpψv’(mpα)ψv(α)–ψv(mpα)ψv’(α)mpψv’(mpα) ζ v(α)–ψv(mpα) ζ v’(α)1(cosθ)1(cosθ)dPv+bv1(cosθ)Pvsinθdθ+a vbvsinθ1(cosθ)1(cosθ)+a vsinθdθ1(cosθ)ψv’(mpα)ψv(α)–mpψv(mpα)ψv’(α)sinθψv’(mpα) ζ v(α)–mpψv(mpα) ζ v’(α)1(cosθ) is a Legendre polynomial, and1(cosθ)dθ2(i1+i2)λ02(i1+i2)8π28π22222888+8Pvψv 、ζ v are Bessel functions.mpψv’(mpα)ψv(α)–ψv(mpα)ψv’(α)mpψv’(mpα) ζ v(α)–ψv(mpα) ζ v’(α)i2=Pv1(cosθ)dθv = 1Σi1 =v = 1Σi1 =v = 1Σv = 1Σi2=a v =The complexity that lies in the resonance between particles and lightThe core theme of my research while I was a university student was air pollution and meteorological phenomena. It was during that time that I learned about Rion’s particle counters and was introduced to the Mie scattering theory, which was the principle behind its measurement method. A lot of my work since then has involved this theory.The theory of Mie scattering is based on electromagnetism, which explains the phenomenon wherein incident light on a particle induces dipole oscillations in the atoms or molecules making up the particle, thereby emitting light. When the particle size is close to the wavelength of light, numerous dipole oscillations having different phases occur, resulting in a complex light scattering phenomenon called Mie resonance. My initial work upon joining Rion involved creating a program to compute this physical phenomenon. I confirmed that the program's calculation results matched prior research, proving the method highly valuable for developing subsequent particle counter models. This success has been a solid anchor in my career.Tohoku University on the measurement of particle contamination in semiconductor dry processes, and we succeeded in measuring particles in specific material gases using the light scattering phenomena. We also applied the results to measuring particles generated in the gas phase within reactors during the plasma deposition and etching processes, which were both cutting-edge technologies at the time.Then I became intrigued particles generated in plasma. I wanted to find out more about their behavior, so I began a collaborated research project with Kyushu University on the remote measurement of particles generated and suspended within plasma. We developed a remote particle sizing method using Mie scattering theory to analyze scattered light intensity ratios from multi-wavelength light with differing polarization planes.This study was primarily modeled on the deposition of amorphous silicon (α-Si) using plasma. The α-Si has a light absorption in the visible light band, and the light absorption can be expressed using the complex refractive index. But the precise value of this refractive The general formula for Mie scattering express-es the intensity of scattered light as a function of angle θ, thereby allowing the determination of scattered light distribution as an exact solution based on wavelength, particle size, and refractive index.* *Since 1989, I have taken part in collaborative research with an explanation of the Mie scattering theory, which remains the foundation of my research from start to finish, in the appendix.project entitled “Development of a Real-Time Measurement Device for Determining Actual Kaoru KondoSenior Advisor of the Development Department, Particle Counter Division. Joined Rion in 1981. Since joining the company, he focused on the develop-ment of particle counters over many years in the Engineering Department. He assumed his current position in 2018. He earned his doctorate in engineering from Hiroshima University in 2003.* *From 2016, I participated in a national research Article by Kaoru KondoA Column by Rion’s Staff on Their Obsession with ScienceTheory of Mie ScatteringNo. 010The Theory of Mie ScatteringRion is supported by many science-loving and math-loving staff members.In this series, our science-minded staff members write about their enthusiasm for their respective fields of interest. In Part 10, a veteran researcher recounts his expe-rience exploring the theory of Mie scattering—the theory that explains, among other phenomena associated with light, why clouds appear white.index remained unclear. On the other hand, experiments showed that particles generated in the gas phase in the plasma experienced rapid growth in particle size.We performed experiments to measure the changes in scattered light intensity with particle growth while varying the wavelength and polarization planes of the light. We then performed fitting explorations for the theoretical calculation values to find the particle refractive index that matched the observed changes in pattern. In this way, we were able to estimate the complex refractive index of the α-Si particles.With these results in hand, I embarked on a new collaborative research with Hiroshima University. I compiled and published the results of this research that elucidated the behavior of particles in a plasma reactor and established a method for particle measurement, which allowed me to obtain my doctoral degree. In the paper, I included Particle Size and Refractive Index in Flow Fields.”We developed a method for calculating particle refractive index in flow fields: first, measure Brownian motion momentum to find the diffusion coefficient-equivalent size(i.e., the actual particle size); then substitute this size and measured light scattering intensity into the inverse scattering formula. This appears to be the world's first real-time approach for such measurements. Regardless of whether the particle's light absorption stems from dipole vibration resonance or from plasmon resonance induced by the vibration of free electrons, it is possible to obtain a numerical solution using the Mie scattering theory based on classical electromagnetism, which I am quite familiar with. However, this solution method alone may not sufficiently explain the fundamentals of the phenomenon. Currently, research is ongoing to solve Mie scattering theory based on quantum optics. This approach seeks to grasp the scattering phenomena and the significance of complex refractive indices from a quantum physics perspective. The explanations of the phenomena presented in these studies are so fascinating—lately, I find myself wanting to stay a little longer with research on Mie scattering.b v =2v+1v(v+1)2v+1v(v+1)b v =a v =a v1(cosθ) is a Legendre polynomial, andb va v2v+1v(v+1)Pvb v2v+1v(v+1)dPvI (θ) =λ0EPILOGUE SCIENCE, SCIENCE ! dPvdPv20Because We’re Science and Math LoversI (θ) =
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