SiMM4×4

The SiMM4×4 Program has been developed by Paul Rogers, Tae Dong Kang, Gelu Nita, Roman Basistyy, Michael Kotelyanskii, and Andrei Sirenko at NJIT and Rudolph Technologies.

supported by NSF-MRI DMR-0821224  and DMR-0546985         

e-mail for support and comments:      sirenko@njit.edu 

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To use SiMM4×4 you need to download  SiMM_1.zip or SiMM_1.rar  file. SiMM4×4 can be unzipped to any folder. The recommended location for unzipping is C:\\SiMM\       In this case the default paths for data save/load will work from the start.

Run Application.exe file and have fun (J).

Note: to refresh the calculation use SPACEBAR.   Do not press ENTER every time you change input parameters, just edit the number(s) and move the cursor away from the control field. If you press ENTER, then the Program will try to LOAD a set of input parameters from a binary file.

Requirements:

You need LabVIEW  2010  installed in your computer. If you have earlier LabVIEW versions, upgrade here: https://lumen.ni.com/nicif/us/evallvuser/content.xhtml

If you do not have LabVIEW  or never used LabVIEW, just download free software:

LabVIEW Run-Time Engine 2010

from NI website (requires registration) : http://joule.ni.com/nidu/cds/view/p/id/2087/lang/en

If for some reasons (like Administrator privileges in your own computer) you have problems installing LabVIEW Run-Time Engine 2010 in a default configuration, try to install only the top option in the Installation Menu (see below). Cross the other four and repeat the installation. It should work.

Theory:

The theory of light reflection/transmission in anisotropic magneto-dielectric medium was developed by Berreman and was also described in the book of R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, North-Holland, Amsterdam, 1977. The SiMM4×4 code is based on equations from these References. Interestingly, the SiMM4×4 code describes well the case of the negative refractive index. Recent work of our group in this field is published in ThinSolidFilms-2010.

The input parameters in the model are Eps, Mu, and Rho tensor components that connect E and H vectors with D and B:

 

In contrast to and  tensors, the bi-anisotropic tensors and are less known and their properties require clarification. SiMM4×4  calculates two major additive contributions to Rho and Rho’: the magneto-electric effect and chirality, so that:

 

One can see that the ME contribution is described by the complex tensor Alpha, and chirality is represented by tensor  Ksi  . Both tensors, Ksi  and Alpha, are complex and can have both real and imaginary parts. Accordingly, Rho and Rho’ are  not expected to be the complex-conjugate-transpose for each other.

According to Dzyaloshinskii, the corresponding ME contribution to Rho’ hould be a “transpose” tensor: Alpha’=AlphaT. This requirement follows from the Dzyaloshinsky’s definition of Alpha in the static case:

Although at present  this requirement of Alpha’=AlphaT  for optical frequencies is under debate in the literature, we still use it in the SiMM4×4  calculations. Note that both Alpha and Alpha’ have the same sign of their complex parts, so that the oscillators in both Alpha and Alpha’ should absorb light in the transmission experiments. Tensors Alpha and Alpha’ change sign under space inversion and time inversion operation, remaining unchanged if both operations are applied simultaneously. This property results in the requirement that  Alpha=Alpha’ =0 in materials with the center of inversion or with time-reversal symmetry (see Refs.[11, 12] for more detail). In contrast to Alpha, the chirality term tensor  i*Ksi    has its transpose-complex conjugate counterpart -i*KsiT    that contributes to Rho’. For isotropic materials, Georgieva showed that the chirality parameter Ksi  , which originates from the time derivatives of the electric and magnetic field vector terms in the Maxwell equations, scales proportionally to Omega, which requires its disappearance at zero frequency. In the case of a crystal, we assume that the chirality effect can also have a resonant behavior and should diminish at high frequencies.  

SiMM is designed for users with a general knowledge of MM ellipsometry providing an opportunity to simulate Muller Matrix spectra in anisotropic magneto-dielectric medium. The appropriate experimental technique for studies of magneto-dielectric samples is full-Muller Matrix Ellipsometry. Alternatively, one can measure Rss, Rpp, Rps, and Rsp spectra and compare to the simulation. See recent papers by Mathias Schubert: [1] and [2].

 

By request from the Community of Rotating-Analyzer-Ellipsometry (RAE), an additional simulation option for PSI-DELTA / pseudoEps / n-k is included. However, for magneto-dielectric samples or anisotropic samples with non-zero Rp, and Rsp  these simulations of PSI/DELTA and pseudoEps / n-k  can show unphysical results !!! These simulations are added for illustration purpose only. For example, if you want to simulate the case of a negative index of refraction in anisotropic sample, then MM spectra behave “normally” displaying smooth variation between -1 and 1. However, pseudo-Eps function will have unphysical behavior (negative Eps2) in the frequency range for the negative refractive index. So, for anisotropic samples use the option for PSI-DELTA / pseudoEps / n-k with caution. The meaning of the corresponding simulation is to demonstrate limitations of the traditional RAE approach. If your simulation shows unphysical result (e.g., negative Eps2) just think about using MM ellipsometry instead of RAE.

 

Manual:

The basic package covers Reflection experiments for semi-infinite samples with Lorentz oscillator model. In addition to that we have also developed simulations for thin films in both Reflection and Transmission configurations, included multiple dielectric models (Drude, coupled oscillators, etc), and fit-to-experiment using Levenberg–Marquardt algorithm. It is available through collaboration. Send e-mail to Andrei Sirenko: Sirenko@njit.edu

 

Controls are on the left, Indicators and results of simulations are in the Tabs on the right-hand side. Control buttons are painted yellow (you can change the values), indicators are painted blue (you can only watch these numbers). To refresh the simulation with the new input parameter values just press the SPACE BAR or Up/Down keys of your key-board. Omega-counts indicator shows the progress with the calculations. The refresh rate should be less than ~2 seconds on a modern computer for 500 data points in a spectrum. If it takes too long, decrease the number of data points to 200.

 

The conventional geometry of experiment: Z is normal to the sample surface, X is in the plane of the incidence, Y is perpendicular to the plane of incidence.

 

Controls on the left:  

In the dielectric model for Eps, Mu, and Rho tensors one can change for each of the principle axes of the sample (X,Y,Z)

·         The number of Lorentz oscillators, which is the same for Eps and Mu models (can be set to zero). The max number of oscillators is < 30, the oscillator strength can be set to zero if different number of oscillators is needed for Eps and Mu models. For example, if you just want to simulate Eps response for Mu=1, then all Mu-oscillators should have zero oscillator strength. The absolute values of omega's and gamma's are taken for calculations of the tensor components:

 

·         Dielectric tensor components of Eps_inf  and Mu_inf accept real values only. Default value for Eps_inf is 10. Default value for Mu_inf is 1, but it can be changed, of course.

·         The default dispersion values of the off-diagonal elements of the Rho tensor are set to zero. One can add oscillators in Rho by changing the default oscillator strength from zero to a desired value. Note, however, that Rho2 should be less than the product of Eps*Mu for every frequency, but  SiMM4×4 program does not execute this limit condition (!). If you put too much of the oscillator strength in Rho then unphysical values will result in divergence and discontinuity of the MM spectra. Note that Rho diagonal components (symmetric part) is “equivalent” to an additional contribution in Eps, while the off-diagonal part of Rho (asymmetric part of the tensor) is “equivalent” to an additional contribution to Mu. Reality is more complex than this naïve explanation. Magneto-dielectric tensors are well described in Rivera’s paper. But their Alpha tensor is different from the Berreman’s  Rho tensor, so be careful! The Rho-prime part is calculated automatically as shown above, so there is no control for that part of the dielectric model.

 

·         The symmetry of Eps, Mu, and Rho tensors can be different in magneto-dielectric samples. Independent rotation of the Eps,  Mu, and Rho tensors with respect to the measurements frame is possible using the Euler’s table in the left-hand side. The default values are all zeros that correspond to a perfect alignment of the orthorhombic sample (a,b,c axes) with respect to the experiment reference frame (XYZ). Thus, tilt (in deg) of the sample with respect to the experimental (s,p) reference frame  (-180 --- +180 deg) can be controlled for Eps,  Mu, and Rho tensors independently.

 

·         angle of incidence, AOI,:  0 - 90 deg. Normal incidence corresponds to AOI=0.

 

·         Ambient refractive index  can be different from 1 (default value is No=1)

            TABS in the right-hand side:

Note

brief manual

 

Eps Mu

indicators for the dielectric model

 

Rho

indicators for the dielectric model

 

Spectra Eps Mu

Spectra for the three principle axes of Eps and Mu tensors

 

Spectra Rho

Spectra for the three diagonal and three off-diagonal components of the Rho tensor (defaults are zeros)

 

M, Del, R, MM

indicators for the model calculations

 

MM

Muller Matrix spectra

 

Refl

Reflectivity spectra

 

Psi-Delta

Psi-Delta spectra for RAE ellipsometry. Here you may see unphysical results for anisotropic and magneto-electric samples

 

Pseudo

Pseudo dielectric function spectra for RAE ellipsometry. Here you may see unphysical results for anisotropic and magneto-electric samples

 

Errors

Errors of the code. These fields should be empty, but for a certain unphysical input parameter combination, there could be an error. Report them to Sirenko@njit.edu

 

Save

Save data of simulation for MM and for R’s, Psi/Delta, etc. in a 2D ASCII data format that can be opened with Matlab or ORIGIN.

Save data for input parameters in a one-column format. Can be used as an input in our FITTING PROGRAM (available through collaboration)

Quick Save / Load the set of the input parameters in/from a binary file. Useful for quick recovery of the simulation results. Press frequently and use different names to preserve results of your work for different models

 

ExpDat Psi Delt

Here you can open experimental data in 2D column  ASCII format (or results of your previous simulation) and compare to the results of the current simulation.

 To refresh the exp data alternate the controls for the column number for the experimental file or the indicator for the simulated function.

 

ExpDataMM

Here you can open experimental data in 2D column  ASCII format (or results of your previous simulation) and compare to the results of the current simulation.

To refresh the exp data alternate the controls for the column number for the experimental file or the indicator for the simulated function.

 

 

Let’s start using SiMM4×4:

Select “1” for the number of oscillators and have, correspondingly, one electric dipole at 80 cm-1 and one magnetic dipole at 60 cm-1. Press the SPACE BAR of your keyboard to refresh your simulation.

Do not press ENTER every time you change the inputs: the Program will try to LOAD a set of inputs from a binary file (e.g., Parameters1).

In the MM window we will see the 16 spectra with zero off-diagonal components that is normal for orthorhombic symmetry

Now you can save the results of simulation and the input model parameters in this window:

You can “zoom” on the simulation results for each MM component in the Tab shown below. Also, you can load your experimental data or results of the previous simulations. The selection of the column is marked with blue. M11 corresponds to the second column of the input data file (the first one is the “Wavenumber”, of course). The top three lines of the input file is displayed in the window above the graph.

If you do not see numbers that means SiMM4×4 does not recognize the format of the input file, which should be Tab-separated multi-column ASCII with X-axis in the left-hand side column.