Thanks Prof.Alexandre for your insight explanation and web links .........

Dear Prof.Tomasz , thanks for your inputs , i have already used your software for generating scattering angle vs intensity plot , but i think polar plots cannot be generated using this software , since polar plots will give more precise information on scattering pattern of particle w.r.t different wavelength. At present i was using a software "MiePlot" , using this i can generate pattern for both Rayleigh and Mie scattering. In this software , especially for generating polar plots , intensity of Incident radiation should be given [ W/cm2] . All together i can generate plots for Rayleigh and Mie , but i can only understand the Rayleigh approximation  [ which is well defined in the same website and this relation is used by the software to generate plots ] , but i am unclear that what formulation is used to generate plots for Mie's scattering using this software. Also , if your X>>1 then the software intimates that value is high for Rayleigh and we have to use Mie approximation . Kindly chk this software if you find time and clarify my doubts , your feedback will be highly supportive.......thanks again.

In Mie theory, an incident plane wave is represented by an infinite combination of spherical harmonics. Their amplitudes depend on the polarization and the direction of the incident wave and are given in general case by analytical formulae. The advantage of such representation is in that each such harmonics is scattered as a single spherical outgoing harmonics which amplitude depends on the particle radius and refractive indices and is prescribed by coefficient given by an analytical expression. Since each scattered harmonics propagates independently, the total scattered power is found as the sum of particular powers in all scattered harmonics, the correspondent analytical expressions exist as well.

In principle, it is possible to combine together these three types of expressions and to deliver the scattered power in a closed analytical form but I have never seen such formula anywhere. Moreover, you have to truncate the infinite set of harmonics and look for numerical convergence of obtained solutions.

For more information, I recommend you the following site: http://www.t-matrix.de

Dear Vikram, 20 years ago I've made a Pascal program calculating both components of Mie scattering, it is based directly on Maxwell equations and available on our webpage. It produces active graphs or exports data in the table for excell. Software was validated when I was working in the Institute of Experimental Physics in Vienna, first 5 digits are the same like in the software developed by Prof. W.W. Szymanski and A. Majerowitch.

http://www.biomedlab.ichip.pw.edu.pl/content/view/24/13/lang,english/

Software:

http://www.biomedlab.ichip.pw.edu.pl/content/view/33/8/lang,english/

Just click "Calculation of light scattering"

Best, Tomek

Thanks Prof.Alexandre for your insight explanation and web links .........

Dear Prof.Tomasz , thanks for your inputs , i have already used your software for generating scattering angle vs intensity plot , but i think polar plots cannot be generated using this software , since polar plots will give more precise information on scattering pattern of particle w.r.t different wavelength. At present i was using a software "MiePlot" , using this i can generate pattern for both Rayleigh and Mie scattering. In this software , especially for generating polar plots , intensity of Incident radiation should be given [ W/cm2] . All together i can generate plots for Rayleigh and Mie , but i can only understand the Rayleigh approximation  [ which is well defined in the same website and this relation is used by the software to generate plots ] , but i am unclear that what formulation is used to generate plots for Mie's scattering using this software. Also , if your X>>1 then the software intimates that value is high for Rayleigh and we have to use Mie approximation . Kindly chk this software if you find time and clarify my doubts , your feedback will be highly supportive.......thanks again.

Dear Vikram

Mie Scattering is based on the solution of Maxwell equitation of electromagnetic wave propagation and resonant phenomena inside objects of different dielectric constant, the equitation set was given by Gustav Mie. It is an accurate solution while Rayleigh is just an approximation. The best description of this phenomenon can be found in the book:

Absorption and Scattering of Light by Small Particles, Craig F. Bohren, Donald R. Huffman, Willey, ISBN: 978-0-471-29340-8,

What I can do, I can send You a sourcecode of my software in pascal (Delphi 5, free for universities), You can reuse the main procedure which calculates i1 and i2 (two polarization components) at the given solid angle and given wavelength, particle diameter, dielectric constant (complex). The rest are just reverse recurrence procedures and complex number calculation procedures, since Pascal does not support complex numbers, and the entire graphic interface. You can make any type of plot or integrate it over any solid angle.

If You want it, just send me an email.

Regards, Tomek

Thanks Prof.Tomasz for your valuable information and patience for clarifications , i will email surely if there is any requirement regarding source code.

Hello Vikram,

I did some experimental work in calculating the scattering intensity of both nanometer and micrometer range particles, followed by comparison with theoretical plots generated by the softwares easily available in websites. Mie theory gives appreciable results for quite larger particles (having size parameter comparable to the wavelength of incident light). This is because the theory cannot accommodate well for very small particles, especially particles approximately 1/10th of λ , which is the wavelength of the incident light . Try to go through the link [Lecler, S. Light scattering by sub-micrometric particles, PhD thesis, Louis Pasteur University – Strasbourg I, 2005]. This fact was validated by our experiments as well. So I think for particles below the size of nearly 60 nm Mie theory will not give good results. In that case you need to apply some other theories. Check this software too ScatLab light scattering software, http://www.scatlab.org/. And polar and azimuthal part hardly causes any difference for spherical particles. 

Thanks Sanchita for the web link , as i have mentioned already that i was using Mie plot software at present , you can check this link , i have downloaded Scatlab software as per your instructions , i find a bit difficulty in using this software [scatlab] compared to the one in philiplaven , i request you to try the software mentioned given in above link , in that software i can load many parameters and i could calculate both Rayleigh and Mie in the same software . PFA , i have attached some screenshots for few calculation for your reference , kindly chk this software and give your opinion on how this software is useful compared to Scatlab.

Hello everyone. I have a problem here. I have measured the absorbance of 20 nm gold nanoparticles in water. Now i want to find the scattering and absorption part at 365 nm wavelength. Can someone pls advice on this. Can i use Mie Plot software to do this (how an i incorporate the absorbance value that i measured)

Not sure what the problems are here.  MiePlot works very well for me (Mie?!).  It's a powerful program, so reading the Help files does actually help.. A Polar plot can be seen only in the Intensity versus Scattering pull down menu then enabling 'View-Polar Plot'.  Use 0.02 um for 20 nm (effectively Rayleigh anyway).  In terms of Mie then the real and imaginary parts of the particle RI and the medium are needed.  For Au at @ 632.8 nm these are RI = 0.196 - 3.26i.  It's the relative refractive index of particle to medium that's key and this is not the same as the absorbance of a solution - the peak of absorption, of course, governs the color.  Many gold sols are purple but the color can also be yellowish too dependent on size (and shape).

I disagree that Mie can't deal with particles as small as 20 or 60 nm.  There are just fewer terms needed here.  Try this for a primer:

February 25th, 2014The life of Gustav Mie and the development of the Lorenz-Mie solution to Maxwell’s  equations http://tinyurl.com/mt97tp3

More entertainment in (shows the link between real and imaginary parts of the RI):

August 11th 2011 Optical properties of the three forms of titanium dioxide

http://tinyurl.com/pbgf9hj

Thanks Dr.Alan F Rawle for the explanation and link of the webinar.

Dear Prof.Tomasz ;

I would like to thank for your software. But I would like to know the equations of i1 and i2,please.

thank you.

Hi Vikram S Raghavan , just thought you might also like to know that there is a Windows Mie calculator available for free from Malvern. [ https://www.materials-talks.com/blog/2015/03/09/how-to-get-the-latest-software-for-the-zetasizer-nano/ - once installed go to Tools-Calculator] It plots intensity versus size, and you can enter parameters for gold, scattering angle, wave length, etc. Advanced graph options are available with Ctrl-Shift-right-click, for example export as "text" for plotting in external program. Attached is a screen shot example for 90 degrees, 633nm wave length, and colloidal gold refractive index and absorption, in water.