Cheng Zhi Huang, Jian Ling, Yuan Fang LI 1 Introduction to light scattering
particles by the Maxwell equation. When the particle size is far smaller than the
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- Diameter (μm) Scattering Intensity
particles by the Maxwell equation. When the particle size is far smaller than the wavelength of the incident light, the electron dipole in the Mie equation plays a leading role and the equation can be simpli fied to the Rayleigh equation. Although the Mie theory could solve light scattering of any size, in light concept description, people still called scattering of molecules or particles (a few nanometers), far smaller than the wavelength of scattered light, as Rayleigh scattering, while large particle scattering that was unsuitable for the Rayleigh scattering theory is called Mie scattering. That is, to say, Mie scattering is suitable for particles whose size are of the same order or larger than light wave, and so Mie scattering is also called particle scattering. Di fferent from scattering intensity distribution of Rayleigh scattering, Mie scat- tering has asymmetric scattering light intensity, where the forward light scattering is larger than the backward light scattering. With the increase of the particle size, the ratio of the forward light scattering intensity and backward light scattering intensity gets increased, and the lobe of forward light scattering increases (Figure 1.8). When a particle is larger than the wavelength, the scattering process has no obvious reliable relationship on the wavelength. 0 0 100 200 300 400 500 600 700 2 4 Diameter (μm) Scattering Intensity 6 8 10 Figure 1.7: The intensity of scattered light of di fferent droplets. The incident wavelength was 633 nm, and scattering angle ( θ) 4°–12°. Data source: http://www.app17.com/tech/infodetail/157035.html. 16 Cheng Zhi Huang, Jian Ling, Yuan Fang Li Brought to you by | University of Iowa Libraries Authenticated Download Date | 1/19/20 3:36 AM 0.13 μm Theoretical value 0.13 μm Experimental value after normalization 2 3 4 5 6 7 8 9 10 68 69 70 71 72 73 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 0.13 μm Theoretical value 0.13 μm Experimental value after normalization 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 Figure 1.8: The light angle distribution of Mie scattering. Data source: http://www.app17.com/tech/infodetail/157035.html Introduction to light scattering 17 Brought to you by | University of Iowa Libraries Authenticated Download Date | 1/19/20 3:36 AM 1.4.2 Features of Mie scattering Compared with Rayleigh scattering, Mie scattering has the following features: (1) The light intensity of Mie scattering is much larger than that of Rayleigh scatter- ing, while its variation with the incident wavelength is not as obvious as that of Rayleigh scattering. (2) With the change of scattering angle, the light intensity of Mie scattering has many maximum and minimum values. When size parameter increases, the number of extremum value also increases. (3) With the increase of scattering particle size, the total energy of Mie scattering increases rapidly, and then it comes to a constant value in vibrating form. (4) When scattering particle size is rather small, Mie scattering can be simpli fied to Rayleigh scattering. With an increase of the particle parameter, the ratio of forward light scattering and backward light scattering increases, and forward light scattering increases. When the particle has a large size, the Mie scattering result is same as that by geometrical optics, namely there is light re flection or di ffraction. In the moderate range of a size parameter, only Mie scattering could obtain the correct result. That is, Mie scattering calculation mode could widely describe scattering features of homogeneous spherical particles of any size. By using the Mie scattering theory, we could well understand why cloud at noon appears white or grey. Scattering particles in the cloud such as water drops or crystals are large enough to the wavelength of sun lights, and so Mie scattering occurs with no obvious relation between the intensity and wavelength of the incident light. The scattered light has the color of sunshine, and so cloud in the sky appears white. If the cloud is too thick, the scattered light is unable to pass through the cloud, and the cloud appears grey or even black to our eyes. It should be noted that Mie scattering in essence is not an independent theory, but solutions of Maxwell equations for a spherical medium. However, as the solution to Maxwell ’s equation is rather complex, the first perfect solution provided by Mie became classic, so this solution algorithm was called the Mie theory. Through Mie theory, people obtained many regular things, for example, rules of scattering related anisotropy coe fficient changing with the relative diameter of medium balls, scatter- ing of complex particles and particle groups. 1.4.3 Lorenz –Mie–Debye scattering In the history of light scattering study, Mie was not the first scientist to formularize electromagnetic scattering. Before him, a German mathematician Rudolf Friedrich Alfred Clebsch (1833 –1872) used the potential energy function to solve the scattering issues of perfectly rigid sphere as a elastic point source, while a Danish mathematician 18 Cheng Zhi Huang, Jian Ling, Yuan Fang Li Brought to you by | University of Iowa Libraries Authenticated Download Date | 1/19/20 3:36 AM and physicist Ludvig Valentin Lorenz (1829 –1891) independently put forward a similar theory in 1890, almost 20 years before the Mie theory. Although Lorenz ’s study was earlier than Mie ’s, his paper was published in Denmark and was less concerned. Comparatively, the Mie theory was drawn wide attention and was further developed, and so the phenomenon is called the Mie scattering theory. In 1908, when Mie put forward a scattering solution to a homogeneous spherical Download 275.97 Kb. Do'stlaringiz bilan baham: |
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