I found that when the Debye theory calculates the far-field scattered light intensity of bubbles, the forward scattered light intensity is quite different from the result calculated by the Mie theory due to the convergence problem, so the expression of the Debye coefficient has been revised. I derived the Debye reflectance and transmittance according to the physical meaning of Debye theory and compared them with Fresnel’s formula. I modified the Debye coefficient expressions for bubbles based on the differences between the Debye reflectance and transmittance from the Fresnel formula. Finally, compared with the far-field scattered light intensity calculated by the original Debye theory, the far-field scattered light intensity calculated based on the modified Debye coefficient can obtain more accurate forward scattered light intensity with fewer sub-waves.
References
[1]
Proust, J., Bedu, F., Gallas, B., Ozerov, I. and Bonod, N. (2016) All-Dielectric Colored Metasurfaces with Silicon Mie Resonators. ACS Nano, 10, 7761-7767. https://doi.org/10.1021/acsnano.6b03207
Van de Hulst, H.C. (1981) Light Scattering by Small Particles. Courier Corporation, Chelmsford, MA.
[4]
Mie, G. (1908) Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Annalen der Physik, 330, 377-445. https://doi.org/10.1002/andp.19083300302
[5]
Gouesbet, G., Maheu, B. and Gréhan, G. (1988) Light Scattering from a Sphere Arbitrarily Located in a Gaussian Beam, Using a Bromwich Formulation. Journal of the Optical Society of America A, 5, 1427-1443. https://doi.org/10.1364/JOSAA.5.001427
[6]
Lock, J.A. (1993) Contribution of High-Order Rainbows to the Scattering of a Gaussian Laser Beam by a Spherical Particle. Journal of the Optical Society of America A, 10, 693-706. https://doi.org/10.1364/JOSAA.10.000693
[7]
Gouesbet, G. and Gréhan, G. (2011) Generalized Lorenz-Mie Theories. Springer, Berlin. https://doi.org/10.1007/978-3-642-17194-9
[8]
Van der Pol, B. and Bremmer, H. (1937) XIII. The Diffraction of Electromagnetic Waves from an Electrical Point Source Round a Finitely Conducting Sphere, with Applications to Badiotelegraphy and the Theory of the Rainbow—Part I. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 24, 141-176. https://doi.org/10.1080/14786443708561897
[9]
Nussenzveig, H.M. (1969) High-Frequency Scattering by a Transparent Sphere. I. Direct Reflection and Transmission. Journal of Mathematical Physics, 10, 82-124. https://doi.org/10.1063/1.1664764
[10]
Nussenzveig, H.M. (1969) High-Frequency Scattering by a Transparent Sphere. II. Theory of the Rainbow and the Glory. Journal of Mathematical Physics, 10, 125-176. https://doi.org/10.1063/1.1664747
[11]
Khare, V. (1976) Short-Wavelength Scattering of Electromagnetic Waves by a Homogeneous Dielectric Sphere. Ph.D. Thesis, University of Rochester, New York.
[12]
Lock, J.A. (1988) Cooperative Effects among Partial Waves in Mie Scattering. Journal of the Optical Society of America A, 5, 2032-2044. https://doi.org/10.1364/JOSAA.5.002032
[13]
Lock, J.A. and Hovenac, E.A. (1991) Internal Caustic Structure of Illuminated Liquid Droplets. Journal of the Optical Society of America A, 8, 1541-1552. https://doi.org/10.1364/JOSAA.8.001541
[14]
Debye, P. (1908) Das elektromagnetische Feldum einen Zylinder und die Theorie des Regenbogens. Physikalische Zeitschrift, 9, 775-778.
[15]
Bohren, C.F. and Huffman, D.R. (2008) Absorption and Scattering of Light by Small Particles. John Wiley & Sons, Hoboken, NJ.
[16]
Gouesbet, G. (2020) Van de Hulst Essay: A Review on Generalized Lorenz-Mie theories with Wow Stories and an Epistemological Discussion. Journal of Quantitative Spectroscopy and Radiative Transfer, 253, Article ID: 107117. https://doi.org/10.1016/j.jqsrt.2020.107117
[17]
Van de Hulst, H.C. (1957) Light Scattering by Small Particles. John Wiley and Sons, New York; Chapman and Hall, London. https://doi.org/10.1063/1.3060205
[18]
Shen, J. and Wang, H. (2010) Calculation of Debye Series Expansion of Light Scattering. Applied Optics, 49, 2422-2428. https://doi.org/10.1364/AO.49.002422
[19]
Yu, H., Shen, J. and Wei, Y. (2008) Geometrical Optics Approximation of Light Scattering by Large Air Bubbles. Particuology, 6, 340-346. https://doi.org/10.1016/j.partic.2008.07.003
