Respected Sir,
DDA solution for polarization considering a gold nanorod shows an interesting pattern. The well-documented pattern (i.e. maximum @90°and minimum @180°) was obtained when the transverse wavelength was considered and beta, theta, and phi were set to zero. Using the same settings, the polarization patterns obtained for the longitudinal wavelength show patterns which deviate from their physical picture.
Please suggest the required modification that I need to make for obtaining the correct polarization pattern.
Thanks and regards,
Hirak
Dear Hirak,
Insufficient information to be able to comment on this. Size, aspect ratio, wavelength, orientation…?. What version of DDSCAT are you using? Did DDSCAT claim to meet the error tolerance?
Also: DDSCAT does not work well when the dielectric function is very large, so you may not be able to calculate for gold in the
infrared.
Respected Prof. Draine,
Sorry for the extremely late reply.
Regarding the questionnaire, I am using DDSCAT (version 7.3) with which I need to compute the scattering matrices of gold nanorods having some different aspect ratio from 300 nm to 1000 nm wavelength regime with 5 nm shift. The length regime was considered from 20 nm to 80 nm possessing suitable increase in aspect ratio perceived in fabrication configurations.
Initially, for a 20 nm long nanorod having a diameter of 10 nm, I have considered the CYLNDRCAP module to model the system with 2 nm spacing in dipoles. The size parameter was set to
'CYLNDRCAP' = CSHAPE*9 shape directive
10 5 2 0.0 0.0 = shape parameters 1 - 7
For longitudinal polarization along the axis of the nanorod, I set the parameters
' Specify Target Rotations '
0. 0. 1 = BETAMI, BETAMX, NBETA (beta=rotation around a1)
90. 90. 1 = THETMI, THETMX, NTHETA (theta=angle between a1 and k)
0. 0. 1 = PHIMIN, PHIMAX, NPHI (phi=rotation angle of a1 around k)
For transverse polarization along the diameter of the nanorod, I set the parameters
' Specify Target Rotations '
0. 0. 1 = BETAMI, BETAMX, NBETA (beta=rotation around a1)
0. 0. 1 = THETMI, THETMX, NTHETA (theta=angle between a1 and k)
0. 0. 1 = PHIMIN, PHIMAX, NPHI (phi=rotation angle of a1 around k)
which yields contradictory results for polarization; I have got maximum polarization for transverse polarization at 90o and for longitudinal polarization condition the pattern is quite complex and doesn't match with the experimental data. Am I doing right? Please suggest me. If I need to produce details for the parameterization, please intimate me.
I wish to add the whole parameter file as an attachment, but couldn't find the way to attach those.
Thank you,
Yours sincerely,
Hirak
From what you wrote, the cylinder length is 10d, and the diameter is 5d, but I can't tell how you are setting the value of d, wavelength, and refractive index.
To set d, you need to specify the value of aeff = radius of equal volume sphere.
For this geometry, aeff = [(3/16)*D^2*L + (1/8)D^3]^{1/3}.
If you want D=20nm and L=20nm, then aeff=13.57 nm
You must also set the value of the wavelength and refractive index. Are you sure you are specifying these correctly?
I would also suggest that you repeat your calculation using a very mild refractive index (e.g., m=1.1+0.01i) just
to check that you get reasonable results for this case. Gold at 1000nm has a very large refractive index that
may pose numerical difficulties.
Also, you are using a very modest number of dipoles. DDSCAT can easily do this problem with a smaller value of d, which you can set by changing shape parameters 1 and 2 to, say, 32 16
Respected Prof. Draine,
Thank you very much for such a helpful and insightful reply.
I have set the volume of a nanorod as a function of their aspect ratio ( here, L/D) so that the dipole distance remains constant for a group of calculations. I have used the "au_evap" file for dielectric function and wavelength range was fixed from 0.3 um to 1 um.
I will repeat the calculation suggested by you, Sir.
Were the configurations for the target orientation right? Please let me know.
Thanks and regards,
Hirak
Respected Prof. Draine,
I have found out that longitudinal polarization along a gold nanorod axis ( set at x-axis) in LF can be achieved by setting the theta value ~ 18 0 , and it is independent on phi and beta value. The results obtained from .sca file are mentioned after the text.
I got puzzled . Why 18 0 ?
Sorry to ask you such a silly question but I have tried and spent couple of nights realizing the 3D space.
Please illuminate me.
Yours sincerely,
Hirak
DDSCAT - DDSCAT 7.3.0 [13.05.03]
TARGET - Cyl.prism, NAT= 6385 NFAC= 225 NLAY= 17 asp.ratio= 1.0044
GKDLDR - DDA method
PBCGS2 - CCG method
CYLNDRCAP - shape
6385 = NAT0 = number of dipoles
0.08689122 = d/aeff for this target [d=dipole spacing]
0.002377 = d (physical units)
- physical extent of target volume in Target Frame -—-
-0.039214 0.039214 = xmin,xmax (physical units)
-0.020201 0.020201 = ymin,ymax (physical units)
-0.020201 0.020201 = zmin,zmax (physical units)
AEFF= 0.020156 = effective radius (physical units)
WAVE= 0.624000 = wavelength (in vacuo, physical units)
K*AEFF= 0.275406 = 2*pi*aeff/lambda
NAMBIENT= 1.357000 = refractive index of ambient medium
n= ( 0.1435 , 2.4668), eps.= ( -6.0645 , 0.7078) |m|kd= 0.0591 for subs. 1
TOL= 1.000E-05 = error tolerance for CCG method
( 1.00000 0.00000 0.00000 ) = target axis A1 in Target Frame
( 0.00000 1.00000 0.00000 ) = target axis A2 in Target Frame
NAVG= 248 = (theta,phi) values used in comp. of Qsca,g
( 0.02273 -0.00747 0.00000 ) = k vector (latt. units) in TF
( 0.30362, 0.00000 )( 0.92375, 0.00000 )(-0.23345, 0.00000 )=inc.pol.vec. 1 in TF
( 0.07289, 0.00000 )( 0.22177, 0.00000 )( 0.97237, 0.00000 )=inc.pol.vec. 2 in TF
( 0.95000 0.30362 0.07289 ) = target axis A1 in Lab Frame
(-0.31225 0.92375 0.22177 ) = target axis A2 in Lab Frame
( 0.02393 0.00000 0.00000 ) = k vector (latt. units) in Lab Frame
( 0.00000, 0.00000 )( 1.00000, 0.00000 )( 0.00000, 0.00000 )=inc.pol.vec. 1 in LF
( 0.00000, 0.00000 )(-0.00000, 0.00000 )( 1.00000,-0.00000 )=inc.pol.vec. 2 in LF
BETA = 0.000 = rotation of target around A1
THETA= 18.195 = angle between A1 and k
PHI = 13.500 = rotation of A1 around k
0.5000 = ETASCA = param. controlling # of scatt. dirs used to calculate <cos> etc.
Qext Qabs Qsca g(1)=<cos> <cos^2> Qbk Qpha
JO=1: 1.6468E+00 1.3128E+00 3.3396E-01 1.7513E-03 2.3078E-01 5.9597E-03 5.7771E-01
JO=2: 2.7998E-01 2.3300E-01 4.6979E-02 1.1112E-02 3.3016E-01 3.4188E-03 7.5858E-01
mean: 9.6337E-01 7.7289E-01 1.9047E-01 2.9057E-03 2.4304E-01 4.6893E-03 6.6814E-01
Qpol= 1.3668E+00 dQpha= -1.8087E-01
Qsca*g(1) Qsca*g(2) Qsca*g(3) iter mxiter Nsca
JO=1: 5.8488E-04 -2.3407E-04 4.2185E-05 99 10000 248
JO=2: 5.2201E-04 2.1309E-04 -4.7081E-05 106 10000 248
mean: 5.5344E-04 -1.0490E-05 -2.4484E-06
Mueller matrix elements for selected scattering directions in Target Frame
theta phi Pol. S_11 S_12 S_21 S_22 S_31 S_41 S_34 S_43
0.00 0.00 0.05336 8.2200E-04 -3.9079E-05 -4.386E-05 7.324E-04 2.765E-10 -5.275E-11 2.206E-07 -1.965E-07
10.00 0.00 0.10003 9.6275E-04 8.5808E-05 9.631E-05 8.578E-04 -7.130E-10 -4.075E-10 -4.875E-04 4.343E-04
20.00 0.00 0.35199 1.3385E-03 4.1977E-04 4.711E-04 1.193E-03 5.239E-10 -1.164E-10 -9.614E-04 8.567E-04
30.00 0.00 0.54439 1.9058E-03 9.2442E-04 1.037E-03 1.698E-03 -6.694E-10 4.075E-10 -1.408E-03 1.254E-03
40.00 0.00 0.66563 2.5985E-03 1.5411E-03 1.730E-03 2.315E-03 4.511E-10 1.426E-09 -1.813E-03 1.615E-03
50.00 0.00 0.73951 3.3343E-03 2.1970E-03 2.466E-03 2.971E-03 -4.366E-10 -1.222E-09 -2.163E-03 1.927E-03
60.00 0.00 0.78458 4.0244E-03 2.8133E-03 3.157E-03 3.586E-03 -6.476E-10 0.000E+00 -2.447E-03 2.180E-03
70.00 0.00 0.81160 4.5838E-03 3.3147E-03 3.720E-03 4.084E-03 -1.615E-09 2.910E-10 -2.653E-03 2.363E-03
80.00 0.00 0.82635 4.9422E-03 3.6388E-03 4.084E-03 4.404E-03 -5.311E-10 -2.095E-09 -2.773E-03 2.471E-03
90.00 0.00 0.83165 5.0536E-03 3.7448E-03 4.203E-03 4.503E-03 -6.476E-10 2.212E-09 -2.805E-03 2.499E-03
100.00 0.00 0.82837 4.9027E-03 3.6186E-03 4.061E-03 4.368E-03 -1.062E-09 -8.731E-10 -2.746E-03 2.447E-03
110.00 0.00 0.81571 4.5073E-03 3.2759E-03 3.677E-03 4.016E-03 -8.549E-10 -6.403E-10 -2.602E-03 2.318E-03
120.00 0.00 0.79086 3.9158E-03 2.7594E-03 3.097E-03 3.489E-03 -8.440E-10 -1.164E-09 -2.378E-03 2.119E-03
130.00 0.00 0.74787 3.2013E-03 2.1332E-03 2.394E-03 2.852E-03 -4.075E-10 4.948E-10 -2.086E-03 1.858E-03
140.00 0.00 0.67522 2.4509E-03 1.4745E-03 1.655E-03 2.184E-03 -8.949E-10 1.310E-09 -1.735E-03 1.546E-03
150.00 0.00 0.55206 1.7554E-03 8.6345E-04 9.691E-04 1.564E-03 -8.731E-11 -1.892E-09 -1.340E-03 1.194E-03
160.00 0.00 0.34991 1.1979E-03 3.7346E-04 4.191E-04 1.067E-03 -5.384E-10 2.183E-10 -9.111E-04 8.118E-04
170.00 0.00 0.08337 8.4419E-04 6.2705E-05 7.038E-05 7.522E-04 -3.056E-10 -1.455E-10 -4.608E-04 4.105E-04
180.00 0.00 0.04916 7.3574E-04 -3.2226E-05 -3.617E-05 6.555E-04 -2.910E-11 6.912E-11 1.673E-07 -1.491E-07
190.00 0.00 0.12656 8.8517E-04 9.9820E-05 1.120E-04 7.887E-04 -1.164E-10 -4.366E-11 4.610E-04 -4.108E-04
200.00 0.00 0.39033 1.2751E-03 4.4345E-04 4.977E-04 1.136E-03 -4.075E-10 -3.638E-10 9.111E-04 -8.118E-04
210.00 0.00 0.57830 1.8599E-03 9.5834E-04 1.076E-03 1.657E-03 8.877E-10 8.731E-11 1.339E-03 -1.193E-03
220.00 0.00 0.69135 2.5707E-03 1.5835E-03 1.777E-03 2.290E-03 7.567E-10 -2.328E-10 1.735E-03 -1.545E-03
230.00 0.00 0.75801 3.3226E-03 2.2441E-03 2.519E-03 2.960E-03 5.239E-10 3.783E-10 2.084E-03 -1.857E-03
240.00 0.00 0.79742 4.0251E-03 2.8599E-03 3.210E-03 3.586E-03 1.062E-09 -8.149E-10 2.376E-03 -2.117E-03
250.00 0.00 0.81999 4.5926E-03 3.3554E-03 3.766E-03 4.092E-03 4.584E-10 -2.328E-10 2.599E-03 -2.316E-03
260.00 0.00 0.83104 4.9555E-03 3.6694E-03 4.118E-03 4.415E-03 8.949E-10 2.037E-09 2.743E-03 -2.444E-03
270.00 0.00 0.83303 5.0696E-03 3.7629E-03 4.223E-03 4.517E-03 5.020E-10 1.339E-09 2.802E-03 -2.496E-03
280.00 0.00 0.82650 4.9219E-03 3.6246E-03 4.068E-03 4.385E-03 1.019E-09 5.821E-11 2.771E-03 -2.469E-03
290.00 0.00 0.81035 4.5320E-03 3.2722E-03 3.672E-03 4.038E-03 6.512E-10 9.895E-10 2.650E-03 -2.361E-03
300.00 0.00 0.78145 3.9496E-03 2.7500E-03 3.086E-03 3.519E-03 8.004E-10 8.731E-10 2.445E-03 -2.178E-03
310.00 0.00 0.73355 3.2472E-03 2.1223E-03 2.382E-03 2.893E-03 7.421E-10 -6.403E-10 2.162E-03 -1.926E-03
320.00 0.00 0.65506 2.5107E-03 1.4654E-03 1.645E-03 2.237E-03 5.966E-10 4.948E-10 1.812E-03 -1.615E-03
330.00 0.00 0.52635 1.8286E-03 8.5757E-04 9.625E-04 1.629E-03 3.783E-10 -4.657E-10 1.408E-03 -1.254E-03
340.00 0.00 0.32422 1.2812E-03 3.7012E-04 4.154E-04 1.142E-03 -4.366E-11 -1.164E-10 9.615E-04 -8.567E-04
350.00 0.00 0.07151 9.3236E-04 5.9410E-05 6.668E-05 8.307E-04 1.601E-10 -4.366E-11 4.878E-04 -4.346E-04
360.00 0.00 0.05336 8.2200E-04 -3.9079E-05 -4.386E-05 7.324E-04 3.201E-10 -7.822E-11 2.201E-07 -1.961E-07
I'm not certain what you mean by "longitudinal polarizaiton", but I suppose that you want the electric field to be parallel to the nanorod axis.
With the ddscat.par file that you provided, the cylinder axis will be along the x axis in the Target Frame (TF). If you want the incident electric field to be along this direction, then you have to rotate the target in the Lab Frame (LF) by 90deg. Simply set Theta to 90 by changing the appropriate lines in ddscat.par to read
' Prescribe Target Rotations '
0.00 0.00 1 = BETAMI, BETAMX, NBETA (beta=rotation around a1)
90.00 90.00 1 = THETMI, THETMX, NTHETA (theta=angle between a1 and k)
0.00 0.00 1 = PHIMIN, PHIMAX, NPHI (phi=rotation angle of a1 around k)
With this setting, incident polarization state JP=1 will correspond to incident E along the cylinder axis.
Respected Prof. Draine,
Thank you for your elaborated answer. Now I can see it and can be able to play with it.
Wishing Merry Christmas and Happy New Year, 2018 to you and family.
Thanks and regards,
Hirak
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