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version (56 KB) by Jan Schäfer
Solve the scattering of electromagnetic radiation by a sphere or multiple cylinders.


Updated 04 Jan 2016

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MatScat is a MATLAB package which contains different solutions for the
scattering of electromagnetic radiation by a sphere (Mie theory) or an
infinite circular cylinder. Most of the code has been developed during my PhD
work [3]. The multiple cylinder near field solution has been implemented
afterwards and has been presented in a seperate publication [4].
Make sure that the root folder and the folders '/bessel', '/expcoeff' and
'/util' are in the Matlab-Path. The files in '/test' can be run to check if
everything works fine.

The functions to start the calculation can be found in the root folder.
These are:

calccyl.m - calculate the far field solution for a single (stratified) cylinder
calccyl_nf.m - calculate the near field solution for a single (stratified) cylinder
calccyl_multi.m - calculate the far field solution for multiple cylinders
calccyl_multi_nf.m - calculate the near field solution for multiple cylinders
calcmie.m - calculate the far field solution for a single (stratified) sphere
calcmie_nf.m - calculate the near field solution for a single (stratified) sphere


If you use these functions in your research work please cite my work [3,4].
Please also cite the theoretical work underlying my implementation which is:
calccyl, calccyl_nf, calcmie and calcmie_nf are implemented based on [1].
calccyl_multi and calccyl_multi_nf are implemented based on [2,4].
The stratified cylinder/sphere solution is implemented based on [1,5].

[1] Bohren, C. F. and Huffman, D. R., Absorption and scattering of light by
small particles, Wiley-Interscience, New York, 1998.

[2] Lee, S.-C., Dependent scattering of an obliquely incident plane wave by a
collection of parallel cylinders. J. Appl. Phys. 68(10), 1990.

[3] Schäfer, J.-P.,Implementierung und Anwendung analytischer und numerischer
Verfahren zur Lösung der Maxwellgleichungen für die Untersuchung der
Lichtausbreitung in biologischem Gewebe, PhD thesis, Univerität Ulm, 2011,

[4] Schäfer, J. and Lee, S.-C. and Kienle, A,, Calculation of the near
fields for the scattering of electromagnetic waves by multiple infinite
cylinders at perpendicular incidence, J. Quant. Spectrosc. Radiat. Trans.
113(16), 2012.

[5] Kerker, M., The scattering of light and other electromagnetic
radiation, Academic Press, 1969

If you have questions or remarks about the MatScat package or if you find any
bugs in the code please send an email to jan.schaefer(at)

Take a look at my website at

Have fun!

Copyright 2012 Jan Schäfer, Institut für Lasertechnologien (ILM)
Author: Jan Schäfer (jan.patrick.schaefer(at)
Organization: Institut für Lasertechnologien in der Medizin und Meßtechnik an
der Universität Ulm (

Cite As

Jan Schäfer (2020). MatScat (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (24)

Edwin Beller

Mark Molenaar

Mark Molenaar

Homa Bayat

shuai wang

Refet Ali YALCIN

Thank you for sharing this code with us.

The codes in asmcyl.m should change. The present form in v 1.4 is this; = 4/k*(abs(bnp(1)).^2 + 2*sum(abs(bnp(2:end)).^2)); = 4/k*(abs(ann(1)).^2 + 2*sum(abs(ann(2:end)).^2));

it should be like this: = 4/k*(abs(bnp(1)).^2 + 2*sum(abs(bnp(2:end)).^2+abs(anp(2:end)).^2)); = 4/k*(abs(ann(1)).^2 + 2*sum(abs(ann(2:end)).^2+abs(bnn(2:end)).^2));

Zhihao Wu

Dear Jan Schäfer, thank you for your excellent work and it helps a lot in my graduation project. However, I found there is a small mistake in the calculation of scattering coefficient a extinction coefficient. in the file 'assmie.m'. The error happens on the 44th and 45th row, where the corrected code should be 'C.ext = 2/x^2*sum(n2.*real(an + bn));' and ' = 2/x^2*sum(n2.*(abs(an).^2 + abs(bn).^2));'. And don't forget to import variable x given by 'x=k*r' in 'calcmie.m' into 'asmmie.m' before running the modified code. I modified the code on my PC and verified the result by comparing the one given by online mie theory calculator found on '' and the result can match with the modification aforementioned applied.
Best regards!

kim yu

Thank you. It's a great help to me.This code is very interesting.

Xiaoxuan Liang

Dear Dr. Schäfer, thanks for sharing your code in the public domain. With its clarity, simplicity, it helps me a lot understanding the Mie code! Well done!

However I got a problem in understanding the near-field enhancement result. By executing the file test_calcmie_nf.m, I got the Poynting amplitude (intensity) in the x-y plain, for lamda = 800nm and R_np = 50 nm. By normalizing the intensity to the incident intensity, which I calculated from the formula E0^2*n_m/Z0=3.53e-3. Here, E0 is the incident E-field in x polarization direction, n_m is the refractive index in water and Z0 is the wave impedance in vacuum. After doing so, I have a maximum near-field enhancement about 1.3, which is far below the value of 20 calculated from this source: Tejerina (2014), "Nanosphere Optics Lab Field Simulator,“, DOI: 10.4231/D3FF3M064. I'm thinking where comes the discrepancy... I check the codes. Everything seems O.K.

Looking forward to your reply.


Uni Luebeck

yingying qiao

an excellent working, thanks very much!


This is absolutely a 5 star work!
I haven't used it yet , but the code style is really fascinating!

roy nicolas

Junard Landingin

This help me a lot in my research. Thank you very much.

Sina Talebi



My apologies, I had a mistake in my code! Please ignore my comment in August 2014, the bessel functions are properly calculated.

Konstantin Ladutenko

It seems to be a bug in expcoeff_mie( x, m, conv ) using Octave

x = 0.0010000
xix =

Columns 1 through 3:

3.3333e-07 - 1.0000e+03i 2.6645e-10 - 3.0000e+06i

the second order differs from wolfram alpha SphericalHankelH1[2, 0.001]*0.001 = 6.66667 × 10^-11 -3.00000 × 10^6 i

imanol uria

Hi Jan,

I´m a student and I´m using your programmes. They´re fantastics! I have one question: I´m plotting the maps of the near field for a single sphere, and I want to plot not the total |E| but |E|/|Eincoming|. I can´t find the value of Eincoming in the programmes, if you can help me...

Thank you for your attention!

M Santos

Can anybody explain this? (in test_calcmie). What is fctr?

%% Differential scattering cross sections
fctr = 2/pi/C.k;
dCsdOp = fctr*squeeze(abs(S(1,1,:).^2)); % parallel
dCsdOn = fctr*squeeze(abs(S(2,2,:).^2)); % perpendicular
dCsdO = 0.5*(dCsdOp + dCsdOn); % unpolarized


I believe the derivatives of the Ricatti-Bessel functions are implemented incorrectly. When differentiating by parts, the sqrt(pi/(2x)) term on the spherical bessel functions is left out when dbesselj is called.



I downloaded and extract this code and when I tried to run the tests from the test directory, I have got the following messages:

>> test_calccyl
Undefined function 'dbesselj' for input arguments of type 'double'.

Error in expcoeff_cyl (line 47)
djneta = dbesselj(n, eta);

Error in calccyl (line 91)
[anp, ann, bnp, bnn] = expcoeff_cyl(x, m, zeta, 1, conv);

Error in test_calccyl (line 30)
[T, C, ang] = calccyl(dia/2., ns, nm, lambda, nang, zeta);

>> test_calccyl_multi
Undefined function 'dbesselj' for input arguments of type 'double'.

Error in expcoeff_cyl (line 47)
djneta = dbesselj(n, eta);

Error in calccyl (line 91)
[anp, ann, bnp, bnn] = expcoeff_cyl(x, m, zeta, 1, conv);

Error in test_calccyl_multi (line 25)
[ Ts, Cs, angs ] = calccyl( dia/2., ns, nm, lambda, nang);

Undefined function 'calccyl_nf' for input arguments of type 'double'.

Error in test_calccyl_nf (line 45)
[Ep, En, Hp, Hn, Sp, Sn, T, C, ang] = calccyl_nf(dia/2., ns, nm, ...

>> test_calccyl_nf_multi
Undefined function 'calccyl_nf' for input arguments of type 'double'.

Error in test_calccyl_nf_multi (line 53)
[ Ep1, En1, Hp1, Hn1, Sp1, Sn1, T1, C1, ang1] = calccyl_nf( dia/2., ...

>> test_calcmie
Undefined function 'calcmie' for input arguments of type 'double'.

Error in test_calcmie (line 30)
[S, C, ang] = calcmie(rad, ns, nm, lambda, nang, ...

>> test_calcmie_nf
Undefined function 'calcmie_nf' for input arguments of type 'double'.

Error in test_calcmie_nf (line 49)
[E, H, P, S, C, ang] = calcmie_nf(dia/2., ns, nm, ...

Is anything that I have to update?


Thank you for the submission. While I don't want go through the theory behind I want to make myselft sure about the interpretation of the results for the near field solution. Light is incident upon the particle from the z direction, the particle is placed in [0,0,0], right?

So if I want to obtain solution of the Efield in the plane behind the sphere with radius 25um, I have to set all values of zf to 25 um (file test_calcmie_nf.m). Is this correct?

Thank you in advance.

MATLAB Release Compatibility
Created with R2011b
Compatible with any release
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