Incident polarization state

Summary:

How to specify an arbitrary polarization state for the incident plane wave in ddscat.par

Incident polarization state

Ya-fei Wang (guest) 22 Aug 2018 07:38

Dear Professor Draine,

I am using DDSCAT 7.3 to calculate the orientationally-averaged values of Q_abs, Q_sca and <cosθ> of randomly-oriented soot aggregates interacting with monochromatic plane waves with specified polarization states. According to User Guide for the Discrete Dipole Approximation Code DDSCAT 7.3, DDSCAT allows the user to specify a general elliptical polarization state for the incident radiation, by specifying the (complex) polarization vector ${\hat e_{01}}$ (see §24). Moreover, if ddscat.par specifies IORTH = 2, the orthonormal polarization state ${\hat e_{02}} = {\hat x_{LF}} \times \hat e_{01}^*$is generated automatically. However, there are some confusing questions on how to specify an arbitrary polarization state for the incident plane wave in ddscat.par as follows:

(1) Assume that the incident plane wave has a specified polarization state represented by the following Jones vector:

(1)

\begin{align} J = \left[ {\begin{array}{*{20}{c}} {{E_{0y}}{e^{{\text{ - }}i{\delta _y}}}} \\ {{E_{0z}}{e^{{\text{ - }}i{\delta _z}}}} \end{array}} \right] \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {J = \frac{1}{{\sqrt {E_{0y}^2 + E_{0z}^2} }}\left[ {\begin{array}{*{20}{c}} {{E_{0y}}} \\ {{E_{0z}}{e^{{\text{ - }}i\delta }}} \end{array}} \right]} \\ {\delta = {\delta _z} - {\delta _y}} \\ {\cos \beta = \frac{{{E_{0y}}}}{{\sqrt {E_{0y}^2 + E_{0z}^2} }}} \\ {s{\text{in}}\beta = \frac{{{E_{0z}}}}{{\sqrt {E_{0y}^2 + E_{0z}^2} }}} \end{array}} \right\} \Rightarrow J = \left[ {\begin{array}{*{20}{c}} {\cos \beta } \\ {s{\text{in}}\beta \cos \delta - is{\text{in}}\beta s{\text{in}}\delta } \end{array}} \right] \end{align}

where E_0y and E_0z are the amplitude of the two components of the electric field vector, while δ_y and δ_z are the phase of the two components of the electric field vector, should we simply set ${\hat e_{01}}$ by specifying (0, 0) (cosβ, 0) (sinβcosδ, - sinβsinδ) in ddscat.par ?

(2) Assume that we simply set ${\hat e_{01}} = {\hat y_{LF}}$ and ${\hat e_{02}} = {\hat z_{LF}}$, and calculate the orientationally-averaged values of Q_abs, Q_sca and <cosθ> in the two orthonormal polarization states, can we calculate the orientationally-averaged values of Q_abs, Q_sca and <cosθ> in an arbitrary incident polarization state, just based on the orientationally-averaged values of Q_abs, Q_sca and <cosθ> in the two orthonormal polarization states ?

(3) In wxxxryyy.avg, there are two lines like this:

	Qext	Qabs	Qsca	g(1)=<cos>	<cos^2>	Qbk	Qpha
JO=1:	9.2037E-01	8.1852E-01	1.0185E-01	7.2936E-02	4.0114E-01	1.0141E-02	5.3381E-01
JO=2:	9.2037E-01	8.1852E-01	1.0185E-01	7.2936E-02	4.0114E-01	1.0141E-02	5.3380E-01

I am wondering if the data in the lines of JO=1 and JO=2 in the red box are the calculation results of Q_abs, Q_sca and <cosθ> in the incident polarization states ${\hat e_{01}}$ and ${\hat e_{02}}$, respectively ?

It is highly appreciated if you would instruct me on these questions, and I am looking forward to your reply.

Sincerely yours
Ya-fei Wang

Re: Incident polarization state

draine 22 Aug 2018 17:13

Dear Ya-fei Wang,

(1) Yes, what you wrote appears to be correct for specifying elliptically polarized e01. If you use IORTH=2, DDSCAT should generate an orthogonal e02 for the second incident state.

(2) Good question. The answer is "No". Think about a chiral target: Even if randomly-oriented, the cross section for absorption or scattering can be different for circularly-polarized than for linearly-polarized light. If you want to calculate the absorption or extinction cross sections, the calculation should use the actual polarization state of interest.

However, for scattering, if you calculate the Mueller scattering matrix S_ij for the desired scattering direction, then you *can* calculate the differential scattering cross section for elliptically-polarized light even if you used linearly-polarized e01 for the DDSCAT calculation. Therefore, you could in principle obtain the integrated scattering cross section Qsca and the anisotropy parameter <cos(theta)> by integrating over many scattering directions. However, this approach requires calculating S_ij for many scattering directions, which is tedious and may be numerically expensive.
If you are interested in total cross sections for polarized light, it is most efficient to calculate Q_abs, Q_sca, and Q_ext by specifying the incident polarization state of interest in ddscat.par

(3) Yes. The numbers written out in wxxxryyy.avg for JO=1 and JO=2 give <Qabs>, <Qsca>, <cos(theta)>, and <cos^2(theta)> for incident polarization states e01 and e02, averaged over the specified target orientations.

So far as I know DDSCAT is correct, but I must stress that testing of the treatment of elliptical polarization has been limited, therefore please remain alert for any results that seem suspicious. You may want to do some simple tests, such as calculating the orientationally-averaged Mueller matrix using linearly-polarized e01, and then repeating the calculation using elliptically-polarized e01. The resulting Mueller matrix S_ij should (ideally) be identical for both cases, but of course the numerically-calculated values of S_ij will differ slightly because of (1) round-off errors and (2) termination of iterative improvmenet when the error tolerance is satisfied.

Unpolarized incident beam

Jennifer Lopez 23 May 2023 10:31

Hello,
I am using DDSCAT 7.3.3 to calculate properties of oriented spheroidal grains. I have seen in the User Guide that a recommended incident polarization state is ê₀₁=ŷ. I am interested in working with an unpolarized incident beam, so I am wondering how I can establish an unpolarized incident beam at the parameters file of DDSCAT.
And, moreover, I do not really understand how, if an specific state of polarization is given for the incident light beam, the linear polarization P of the scattered light for incident unpolarized light (Eq. 90 of the User Guide) is given at the waaarbbbkccc.sca file. If P is calculated with S_ij from the same file, it leads me to think that these S_ij are also calculated with unpolarized incident light.
I look forward to your answer. Thank you.
Regards.