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the optical hall effect ( ohe ) is a physical phenomenon , which describes transverse and longitudinal magnetic field - induced birefringence , caused by the non - reciprocal magneto - optic response of electric charge carriers . the term ohe is used in analogy to the classic , electrical hall effect@xcite , since the electrical hall effect and certain cases of ohe observation can be explained by extensions of the classic drude model for the transport of electrons in matter ( metals).@xcite for the ohe , drude s classic model is extended by a magnetic field and frequency dependency , describing the electron s momentum under the influence of the lorentz force . as a result an antisymmetric contribution is added to the dielectric tensor @xmath3 , whose sign depends on the type of the free charge carrier ( electron , hole ) . the non - vanishing off - diagonal elements of the dielectric tensor reflect the magneto - optic birefringence , which lead to conversion of _ p_-polarized into _ s_-polarized electromagnetic waves , and vice versa . the ohe can be quantified in terms of the mueller matrix , which characterizes the transformation of an electromagnetic wave s polarization state.@xcite experimentally the mueller matrix is measured by generalized ellipsometry ( ge).@xcite during a ge measurement different polarization states of the incident light are prepared and their change upon reflection from or transmission through a sample is determined . an ohe instrument conducts ge measurements on samples in high , quasi - static magnetic fields , and detects the magnetic field induced changes of the mueller matrix.@xcite though several instruments with partial ohe instrument characteristics were described in the literature , most instruments did not fulfill all criteria for an ohe instrument . nederpel and martens developed in 1985 a single wavelength  ( 444  nm ) magneto - optical ellipsometer for the visible spectral range , but the instrument provided only low magnetic fields ( @xmath4  mt).@xcite in 2003 erne _ _ presented a magneto - polarimetry instrument ( @xmath5  t ) for the mid - infrared spectral range  ( spectral lines of co@xmath6 laser)@xcite , and in 2004 padilla _ et  al . _ developed a terahertz - visible ( 6 to 20000  @xmath0 ) magneto - reflectance and -transmittance instrument ( @xmath7  t)@xcite . while both instruments provide high magnetic fields , and contain polarizers and photo - elastic - modulators , these instruments were not designed to record mueller matrix data ( ge ) . the full @xmath2  mueller matrix in the terahertz - mid - infrared spectral range ( 20 to 4000  @xmath0 ) can be measured by an instrument described in 2013 by stanislavchuk _ et  al._,@xcite but here the instrument is not designed for experiments with the sample in magnetic fields .    the first full ohe instrument developed in 2006 by hofmann _ et  al . _ for the far - infrared ( fir ) spectral range ( 30 to 650  @xmath0 ) provided magnetic fields up to @xmath8  t and allowed sample temperatures between @xmath9  k and room temperature.@xcite this first ohe instrument has since been successfully used to determine free charge carrier properties@xcite , including effective mass parameters for a variety of material systems.@xcite later , ohe experiments were conducted in the terahertz ( thz ) spectral range,@xcite but were limited to room temperature and low magnetic fields .@xcite since the magnitude of the ohe depends on the magnetic field strength , higher magnetic fields facilitate the detection of the ohe . furthermore , the sensitivity to the ohe is greatly enhanced by phonon mode coupling,@xcite surface guided waves@xcite and fabry - prot interferences.@xcite since these effects appear from the thz to the mid - infrared ( mir ) spectral range , depending on the structure and material of the sample , it is necessary to extend the spectral range covered by ohe instrumentation . an ohe instrument for the mir , for example , can detect the magneto - optic response of free charge carriers enhanced by phonon modes present in the spectral range above 600 @xmath0 , which applies to many substrate materials , _ e.g. _ , sic,@xcite al@xmath6o@xmath10,@xcite or gan,@xcite as well as to many materials used for thin films , _ e.g. _ , iii - v nitride semiconductors al@xmath11ga@xmath12n,@xcite al@xmath11in@xmath12n@xcite or in@xmath11ga@xmath12n@xcite . in addition , inter - landau - level transitions can be studied in the mir spectral range@xcite with a mir ohe instrument.@xcite the extension to the thz spectral range enables the detection of the ohe in samples with low carrier concentrations.@xcite furthermore , the strongest magneto - optic response can be observed at the cyclotron resonance frequency , which typically lies in the microwave / thz spectral range for moderate magnetic fields ( few tesla ) and effective mass values comparable to the free electron mass .    in this article , we present an ohe instrument , covering an ultra wide spectral range from 3  @xmath0 to 7000  @xmath0 ( 0.1210  thz or 0.4870  mev ) , which combines mir , fir and thz magneto - optic generalized ellipsometry in a single instrument . this integrated mir , fir and thz ohe instrument incorporates a commercially available , closed cycle refrigerated , superconducting 8  tesla magnet - cryostat sub - system , with four optical ports , providing sample temperatures between @xmath13  k and room temperature . the ellipsometer sub - systems were built in - house and operate in the rotating - analyzer configuration , capable of determining the normalized upper @xmath14 block of the sample mueller matrix . the operation of the integrated mir , fir and thz ohe instrument is demonstrated by three sample systems . combined experimental data from the mir , fir and thz spectral range of a single epitaxial graphene sample , grown on a 6__h__-sic substrate by thermal decomposition , are shown . the mir ohe data of the same epitaxial graphene sample is used to demonstrate the operation of the mir ellipsometer sub - system of the integrated mir , fir and thz ohe instrument,@xcite over the full available magnetic field range of the instrument . the magneto - optic response of free charge carriers and quantum mechanical inter - landau - level transitions is observed , and their polarization selection rules obtained therefrom are briefly discussed . a te - doped , n - type gaas substrate serves as a model system for the fir spectral range of the fir / thz ellipsometer sub - system . the ohe signal originating from conduction band electrons in a bulk material is discussed , and the concentration , mobility , and effective mass of the conduction band electrons is determined . finally , ohe data from an algan / gan high electron mobility transistor structure ( hemt ) from the thz spectral range of the fir / thz ellipsometer sub - system is presented and analyzed.@xcite the data was recorded at different temperatures between @xmath15  k and room temperature , representing the full sample temperature range of the instrument . the manuscript is organized as follows , in section  [ sec : theory ] dielectric and magneto - optic dielectric tensors are introduced , a brief theoretical overview on mueller matrices and ge data - acquisition is given , and general ge data analysis procedures are introduced . section  [ sec : experimental setup ] gives a detailed description of the experimental setup , while in section  [ sec : acq - anal ] data acquisition and data analysis procedures for ohe data are discussed . examples of experimental results , demonstrating the operation of the integrated mir , fir and thz ohe instrument , are presented and discussed in section  [ sec : samplesystems ] , which is followed by a short summary in section  [ sec : summary ] . the evaluation of physical relevant parameters from the ohe requires the experimental observation and quantification of the ohe , and a physical model to analyze ohe data . experimentally , the ohe is quantified in terms of the mueller matrix @xmath16@xcite by employing generalized ellipsometry ( ge ) . the physical model which is used to analyze the observed transverse and longitudinal magneto - optic birefringence of the ohe is based on the magneto - optic dielectric tensor @xmath17 , which is a function of the slowly varying external magnetic field @xmath18 . if , among other parameters , the magneto - optic dielectric tensor of a sample is known , experimental mueller matrices @xmath16 can be modeled from @xmath17 using the relation @xmath19 this relation is in general not invertible analytically , but can be used to determine the magneto - optic dielectric tensor from experimental mueller matrix data through non - linear model regression analysis@xcite . dielectric tensors , mueller matrix calculus , generalized ellipsometry including data acquisition , as well as data analysis will be addressed in this section . the optical response of a sample is here described by the dielectric tensor @xmath20 . if the dielectric tensor of the sample without a magnetic field is given by @xmath21 and the change of the dielectric tensor induced by a magnetic field @xmath18 by @xmath22 , the magneto - optic dielectric tensor describing the ohe , can be expressed as @xmath23 the magneto - optic response of the sample described by @xmath22 usually originates from bound and unbound charge carriers subjected to the magnetic field and is caused by the action of the lorentz force . the magneto - optic response is anisotropic , and non - reciprocal in time.@xcite thus , the corresponding magneto - optic contributions @xmath24 and @xmath25 to the permittivity tensor @xmath26 , where @xmath27 is the @xmath1 identity matrix , originate from the interaction of right- and left - handed circularly polarized light with the sample , respectively.@xcite without loss of generality , if the magnetic field @xmath18 is pointing in the _ z_-direction , the polarization vector can be described by arranging the electric fields in their circularly polarized eigensystem by @xmath28 , where @xmath29 is the imaginary unit.@xcite transforming @xmath30 back into the laboratory system the change of the dielectric tensor induced by the magnetic field takes the form:@xcite is not part of the magneto - optic dielectric tensor @xmath22 since it is already incorporated in the non - magnetic part of the dielectric tensor @xmath21 . ] @xmath31 note , under field inversion @xmath32 , the polarizabilities for left- and right - handed circularly polarized light interchange . @xmath22 is only diagonal if @xmath33 , and otherwise is non - diagonal with anti - symmetric off diagonal elements . charged carriers , subject to a slowly varying magnetic field obey the classical newtonian equation of motion ( lorentz - drude model)@xcite @xmath34 where @xmath35 , @xmath36 , @xmath37 , @xmath38 and @xmath39 represent the effective mass tensor , the electric charge , the mobility tensor , the spatial coordinate of the charged carrier and the eigenfrequency of the undamped system without external excitation and magnetic field , respectively . for a time harmonic electromagnetic plane wave with an electric field @xmath40 with angular frequency @xmath41 , the time derivative of the spatial coordinate of the charge carrier is @xmath42 , where @xmath43 is the velocity of the charge carrier . with the current density @xmath44 eq . ( [ eqn : fcc - newton ] ) reads @xmath45\;,\ ] ] where @xmath46 is the charge carrier density . with the levi - cevita - symbol @xmath47 , the conductivity tensor @xmath48 , the dielectric constant @xmath49 , and using and the dielectric tensor for charge carriers subject to the external magnetic field @xmath18 can be expressed as @xmath50^{-1}\;.\ ] ]    [ [ sec : phonondf ] ] polar lattice vibrations ( lorentz oscillator ) + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +    for isotopic effective mass tensors the cyclotron frequency @xmath51 can be defined . for the mass of the vibrating atoms of polar lattice vibrations , the cyclotron frequency is several orders of magnitude smaller than for effective electron masses , and can be neglected for the magnetic fields and spectral ranges discussed in this paper . therefore , the dielectric tensor of polar lattice vibrations @xmath52 can be approximated using eq . ( [ eqn : fulldrude ] ) with @xmath53 . when assuming isotropic effective mass and mobility tensors , the result is a simple harmonic oscillator function with lorentzian - type broadening.@xcite for materials with orthorhombic symmetry and multiple optical excitable lattice vibrations , the dielectric tensor can be diagonalized to @xmath54 where @xmath55 ( @xmath56 ) is given by@xcite @xmath57 where @xmath58 , @xmath59 , @xmath60 , and @xmath61 denote the component of the frequency and the broadening values of the @xmath62 longitudinal optical ( lo ) and transverse optical ( to ) phonon modes , respectively , while the index @xmath63 runs over @xmath64 modes . further details can be found in refs .  , and a detailed discussion of the requirements to the broadening parameters , such as im@xmath65 , in ref .  . [ [ sec : drudedf ] ] free charged carriers ( extended drude model ) + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +    for free charged carriers no restoring force is present and the eigenfrequency of the system is @xmath66 . for isotropic effective mass and conductivity tensors , and magnetic fields aligned along the _ z_-axis eq . ( [ eqn : fulldrude ] ) can be written in the form @xmath67 , with the drude dielectric tensor for @xmath68 @xmath69 where @xmath70 is the plasma frequency , and @xmath71 is the isotropic drude dielectric function . the magneto - optic contribution to the dielectric tensor @xmath72 for isotropic effective masses and conductivities can be expressed , using eq . ( [ eq : llteps ] ) , through polarizability functions for right- and left - handed circularly polarized light @xmath73 where @xmath74 is the isotropic cyclotron frequency . the dielectric tensor @xmath75 describing a series of inter - landau - level transitions can be approximated by a sum of lorentz oscillators . the quantities @xmath76 in eq . ( [ eq : llteps ] ) are then expressed by @xmath77 where @xmath78 , @xmath79 , and @xmath80 are amplitude , transition energy , and broadening parameter of the @xmath81 inter - landau - level transition , respectively , which in general depend on the magnetic field . the phase factor @xmath82 was introduced empirically here to describe the experimentally observed line shapes of all mueller matrix elements . for inter - landau - level transitions in graphite or bi - layer graphene we find @xmath83 , and for inter - landau - level transitions in single layer graphene @xmath84 . note that for @xmath84 , the polarizabilities for left and right handed circularly polarized light are equal , and @xmath75 is diagonal . the real - valued stokes vector @xmath85 has four components , carries the dimension of an intensity , and can quantify any polarization state of plane electromagnetic waves . if expressed in terms of the _ p_- and _ s_-coordinate system , its individual components can be defined by @xmath86 , @xmath87 , @xmath88 , and @xmath89 , with @xmath90 , @xmath91 , @xmath92 , @xmath93 , @xmath94 , and @xmath95 being the intensities for the _ p_- , _ s_- , + 45@xmath96 , -45@xmath96 , right- and left - handed circularly polarized light components , respectively.@xcite    the real - valued @xmath2 mueller matrix @xmath97 describes the change of electromagnetic plane wave properties ( intensity , polarization state ) , expressed by a stokes vector @xmath85 , upon change of the coordinate system or the interaction with a sample , optical element , or any other matter@xcite @xmath98 where @xmath99 and @xmath100 denote the stokes vectors of the electromagnetic plane wave before and after the change of the coordinate system , or an interaction with a sample , respectively . note that all mueller matrix elements of the ge data discussed in this paper , are normalized by the element @xmath101 , therefore @xmath102 and @xmath103 . the mueller matrix can be decomposed in 4 sub - matrices , where the matrix elements of the two off - diagonal - blocks @xmath104 only deviate from zero if _ p_-_s_-polarization mode conversion appears , while the matrix elements in the two on - diagonal - blocks @xmath105 mainly contain information about _ p_-_s_-polarization mode conserving processes . _ p_-_s_-polarization mode conversion is defined as the transfer of energy from the _ p_-polarized channel of an electromagnetic plane wave to the _ s_-polarized channel , or vice versa . polarization mode conversion can appear when the _ p_-_s_-coordinate system is different for @xmath100 and @xmath99 rotation of the coordinate system around the beam path . ] , or when a sample shows birefringence , for example . in particular , polarization mode conversion appears if the dielectric tensor of a sample possesses non - vanishing off - diagonal elements . therefore , in mueller matrix data from optically isotropic samples , ideally all off - diagonal - block elements vanish , while , for example , magneto - optic birefringence can cause non - zero off - diagonal - block elements in the mueller matrix .    here , we define ohe data as mueller matrix data from an ohe experiment [ eq . ( [ eqn : mm - df ] ) ] with magnetic field @xmath106 @xmath107 furthermore , we define the derived ohe datasets @xmath108 as difference data between the mueller matrix datasets , measured at the magnetic field @xmath106 and the corresponding zero field dataset @xmath109 where @xmath110 is the mueller matrix of the zero field experiment and @xmath111 is the magnetic field induced change of the mueller matrix . this form of presentation is in particular advantageous in case the magnetic field causes only small changes in the mueller matrix , and provides improved sensitivity to magnetic field dependent model parameters during data analysis . another form of presentation for derived ohe data is @xmath112 which can be used to inspect symmetry properties of magneto - optic mueller matrix data , and can help to improve the sensitivity to magnetic field dependent model parameters during data analysis . rotating element ellipsometers can be classified into two categories:@xcite ( i ) rotating analyzer ellipsometers ( rae)@xcite in polarizer - sample - rotating - analyzer ( @xmath113 ) or rotating - polarizer - sample - analyzer ( @xmath114 ) configuration , capable to measure the upper left @xmath1 block of the mueller matrix ; ( ii ) rotating compensators ellipsometers ( rce)@xcite in polarizer - sample - rotating - compensator - analyzer ( @xmath115 ) or polarizer - rotating - compensator - sample - analyzer ( @xmath116 ) configuration , capable to measure the upper left @xmath117 or @xmath118 block of the mueller matrix , respectively . the mueller matrices of a polarizer  @xmath119 , analyzer  @xmath120 , compensator  @xmath121 with phase shift @xmath122 , coordinate rotation along beam path  @xmath123 by an angle @xmath124 , and of the sample  @xmath97 are given by @xmath125{\(-\)}\sin \delta\\          \hspace{8pt}0&\hspace{17pt}0&\hspace{10pt}\sin \delta&\hspace{7pt}\cos \delta      \end{bmatrix}\;,\\      & \mathbf{r}\left(\theta\right )      & = \ \ \      & \begin{bmatrix }          \hspace{8pt}1&\hspace{6pt}0                          & \hspace{-12pt}0                                                                 & \hspace{1pt}0&\hspace{5pt } { } \\ \hspace{8pt}0&\hspace{4pt}\cos 2\theta_j     & \hspace{-1pt}\sin 2\theta_j                                     & \hspace{1pt}0&\hspace{5pt } { } \\ \hspace{8pt}0&\hspace{-2pt}\scalebox{0.6}[1.0]{\(-\)}\hspace{1pt}\sin 2\theta_j              & \hspace{-1pt}\cos 2\theta _          j                        & \hspace{1pt}0&\hspace{5pt } { } \\          \hspace{8pt}0&\hspace{7pt}0                          & \hspace{-12pt}0                                                                 & \hspace{1pt}1&\hspace{5pt } { }       \end{bmatrix}\;,\\      & \mathbf{m }      & = \ \ \      & \begin{bmatrix }          \hspace{3pt}m_{11}&\hspace{4pt}m_{12}&\hspace{4pt}m_{13}&\hspace{4pt}m_{14}&\hspace{-2pt } { }   \\          \hspace{3pt}m_{21}&\hspace{4pt}m_{22}&\hspace{4pt}m_{23}&\hspace{4pt}m_{24}&\hspace{-2pt } { }   \\          \hspace{3pt}m_{31}&\hspace{4pt}m_{22}&\hspace{4pt}m_{33}&\hspace{4pt}m_{34}&\hspace{-2pt } { }   \\          \hspace{3pt}m_{41}&\hspace{4pt}m_{42}&\hspace{4pt}m_{43}&\hspace{4pt}m_{44}&\hspace{-2pt } { }       \end{bmatrix}\ ; , \end{aligned}\ ] ] respectively . execution of the matrix multiplication characteristic for the corresponding ellipsometer type@xcite shows that , due to the rotation of optical elements , the measured intensity at the detector is typically sinusoidal . fourier analysis of the detector signal provides fourier coefficients , which are used to determine the mueller matrix of the sample ( see sec . [ sec : ohe - acq ] ) . ellipsometry is an indirect experimental technique . therefore , in general , ellipsometric data analysis invokes model calculations to determine physical parameters in dielectric tensors or the thickness of layers , for instance.@xcite sequences of homogeneous layers with smooth and parallel interfaces are assumed in order to calculate the propagation of light through a layered sample , by the 4@xmath1264 matrix formalism.@xcite to best match the generated data with experimental results , parameters with significance are varied and mueller matrix data is calculated for all spectral data points , angles of incidence and magnetic fields . during the mean square error ( mse ) regression , the generated mueller matrix data @xmath127 is compared with the experimental mueller matrix data @xmath128 and their match is quantified by the mse @xmath129 where @xmath130 , @xmath131 and @xmath132 denotes the total number of data points , the total number of parameters varied during the non - linear regression process , and the standard deviation of @xmath128 , obtained during the experiment , respectively . for fast convergence of the mse regression , the levenberg - marquardt fitting algorithm is used.@xcite the mse regression is interrupted when the decrease in the mse is smaller than a set threshold and the determined parameters are considered as best model parameters . the sensitivity and possible correlation of the varied parameters is checked and , if necessary , the model is changed and the process is repeated.@xcite figure  [ fig : cad - overview ] shows ( side view ) the integrated mir , fir and thz ohe instrument with its four sub - systems : ( a ) the mir ellipsometer sub - system , ( b ) the fir / thz ellipsometer sub - system , ( c ) the magneto - cryostat sub - system , and ( d ) the magneto - cryostat transfer sub - system . in order to utilize the magneto - cryostat sub - system with the mir or the fir / thz ellipsometer sub - system the magneto - cryostat transfer sub - system was installed . the integrated mir , fir and thz ohe instrument contains multiple light sources and detectors , and covers a spectral range from 3  @xmath0 to 7000  @xmath0 ( 0.1210  thz or 0.4870  mev ) . both ellipsometer sub - systems can be operated without the magneto - cryostat sub - system , in a variable angle of incidence ellipsometry mode ( @xmath133 ) . figure  [ fig:2dsetup ] shows a schematic overview ( top view ) of all major components in the integrated mir , fir and thz ohe instrument .      the upper part of fig . [ fig:2dsetup ] shows a schematic drawing ( top view ) of the optical configuration of the mir sub - system of the integrated mir , fir and thz ohe instrument . the mir ellipsometer sub - system is composed of ( i ) the mir source unit , ( ii ) the polarization state preparation unit , ( iii ) the mir goniometer unit , and ( iv ) the polarization state detection unit . to minimize absorption due to water vapor , the complete beam path of the mir ellipsometer sub - system is purged with dried air.@xcite due to the high magnetic stray - fields ( see fig .  [ fig : cad ] ) , all opto - mechanical components in the polarization state preparation and detection units were designed and manufactured without ferromagnetic materials ( with exception of the stepper motors ) . the mir source unit of the mir ellipsometer sub - system is a bruker vertex 70 fourier - transform - infrared spectrometer ( fig . [ fig:2dsetup ] : mir - ftir ) with a silicon carbide globar light source ( spectral range 5807000  @xmath0 ) . after being collimated , the light beam passes the interferometer ( potassium bromide ( kbr ) beam splitter ) , is reflected by a plane mirror , and exits the mir source unit . the beam enters the polarization state preparation unit . inside the polarization state preparation unit the beam passes a beam steering plane mirror assembly  ( m@xmath134 ) , a source selection and beam focusing assembly  ( r@xmath134 ) and a rotation stage assembly  ( p@xmath134-b@xmath134-st@xmath134 ) , respectively . the beam steering plane mirror assembly  ( m@xmath134 ) is composed of an opto - mechanic mount and a plane first surface gold mirror@xcite . the source selection and beam focusing assembly  ( r@xmath134 ) comprises two sub - assemblies ( detailed drawing : fig . [ fig : beamlift ] a ) , the rotatable plane mirror sub - assembly ( stepper motor , axis extension , mechanic mount for axis extension , opto - mechanic mount for mirror , plane first surface gold mirror@xcite ) and the beam focusing off - axis paraboloid stage sub - assembly ( opto - mechanic mount for paraboloid , gold surface @xmath135 off - axis paraboloid with an effective focal length of @xmath136  mm is the distance between the focal point and the center of the off - axis paraboloid mirror . for 90@xmath137 off - axis paraboloids the effective focal length is twice the focal length @xmath138 . ] ) , which focuses the beam onto the sample position . the focused beam then reaches the rotation stage assembly  ( p@xmath134-b@xmath134-st@xmath134 ) which has a nominal angular resolution of 0.045@xmath96 . the rotation stage assembly ( detailed drawing : fig . [ fig : beamlift ] b ) contains a krs-5 substrate based wire grid polarizer  ( p@xmath134 ) , which is mounted in a hollow tube , which is fitted into two polymer bearings with glass balls , which are held by an aluminum block . a 48-tooth polymer gear is mounted to the hollow tube , and is connected via a kevlar timing belt  ( b@xmath134 ) to a 12-tooth polymer gear on a stainless steel shaft ( gear ratio :  1:4 ) , leading to the stepper motor  ( st@xmath134 ) . after passing the rotation stage assembly , the polarized and focused beam leaves the polarization state preparation unit . the beam is then reflected by , or transmitted through the sample  ( s@xmath134 ) . the sample can be mounted on a sample holder , attached to the mir goniometer unit  ( g@xmath134 ) ( commercially available 2-circle goniometer 415 , huber diffraktionstechnik ) , or inside the magneto - cryostat sub - system  ( m1 ) . if the magneto - cryostat sub - system is used , reflection type measurements can only be conducted at a @xmath139 angle of incidence . a detailed description of the magneto - cryostat sub - system , its sample mount , and the optical window configuration is given in section  ( [ sec : magnet ] ) . the beam then enters the polarization state detection unit , which is mounted to the rotatable arm of the mir goniometer unit  ( g@xmath134 ) . the polarization state detection unit contains a rotation stage assembly  ( a@xmath134-b@xmath6-st@xmath6 ) , a beam collimation and detector selection assembly  ( r@xmath6 ) , and three beam focusing / detection assemblies  ( o@xmath134-mct , o@xmath6-dtgs@xmath134 and o@xmath10-b@xmath134 ) . the rotation stage assembly  ( a@xmath134-b@xmath6-st@xmath6 ) is equivalent to the one in the polarization state preparation unit  ( p@xmath134-b@xmath134-st@xmath134 , fig . [ fig : beamlift ] b ) , but in the polarization state detection unit the krs-5 substrate based wire grid polarizer serves as the analyzer  ( a@xmath134 ) of the mir ellipsometer sub - system . the beam collimation and detector selection assembly  ( r@xmath6 ) is composed of two sub - assemblies : the rotatable plane mirror sub - assembly and the collimating off - axis paraboloid stage sub - assembly ( gold surface @xmath135 off - axis paraboloid , @xmath136  mm ) . both sub - assemblies are equivalent to the source selection and beam focusing assembly in the polarization state preparation unit ( fig . [ fig : beamlift ] a ) , but are used in reverse order to first collimate and then redirect the beam to one of the three beam focusing / detection assemblies using the rotatable mirror@xcite . each beam focusing / detection assembly contains a beam focusing off - axis paraboloid stage sub - assembly and a detector sub - assembly . all detector sub - assemblies contain an opto - mechanic mount and a detector . the beam focusing off - axis paraboloid stage sub - assemblies  ( o@xmath140 ) are composed of an opto - mechanic mount and a 90@xmath137 off - axis paraboloid with an uncoated gold surface . the focal lengths of the off - axis paraboloids are matched to the corresponding detector . the off - axis paraboloids  ( o@xmath141 , o@xmath142 ) for the liquid nitrogen cooled hgcdte - detector sub - assembly  ( mct ) and the pyroelectric , solid state deuterated triglycine sulfate detector sub - assembly  ( dtgs@xmath141 ) , each have an effective focal length of 38  mm ( 1.5  in ) . the off - axis paraboloid  o@xmath143 for the liquid helium cooled bolometer detector sub - assembly  ( b@xmath141)@xcite has an effective focal length of 190.5  mm ( 7.5  in ) . the signal of the used detector is fed back into the mir - ftir - spectrometer to record interferograms . for more information on the data acquisition and processing see section  [ sec : data analysis ] .      the lower part of fig . [ fig:2dsetup ] shows a schematic drawing ( top view ) of the optical configuration of the fir / thz ellipsometer sub - system of the integrated mir , fir and thz ohe instrument . the fir / thz ellipsometer sub - system can be divided in five units : ( i ) the fir source unit , ( ii ) the thz source unit , ( iii ) the polarization state preparation unit , ( iv ) the fir / thz goniometer unit , and ( v ) the polarization state detection unit . for measurements in the fir spectral range , the fir / thz ellipsometer sub - system is operated in analyzer - step mode,@xcite while for measurements in the thz spectral range the fir / thz ellipsometer sub - system is operated in continuously rotating analyzer mode . to minimize absorption due to water vapor , the complete beam path of the fir / thz ellipsometer sub - system can be purged with dried air.@xcite due to the high magnetic stray - fields ( see fig .  [ fig : cad ] ) , all opto - mechanical components in the thz source unit , polarization state preparation unit and polarization state detection unit were designed and manufactured without ferromagnetic materials ( with exception of the stepper motors and the thz source ) . the fir source unit of the fir / thz ellipsometer sub - system is a bruker vertex v-70 ftir - spectrometer  ( fig . [ fig:2dsetup ] : fir - ftir ) . the spectrometer is equipped with a silicon beam splitter but otherwise identical to the spectrometer used as mir source unit in the mir ellipsometer sub - system . + the thz source unit comprises five assemblies : the thz source and thz - beam collimation assembly  ( fig . [ fig:2dsetup ] : bwo - o@xmath144 ) , the optical chopper assembly  ( ch ) , the beam steering plane mirror assembly  ( m@xmath143 ) , polarization state rotator assembly  ( pr - b@xmath143-st@xmath143 ) , and the beam steering plane mirror assembly  ( m@xmath144 ) . the thz source and thz - beam collimation assembly contains a thz source sub - assembly and a thz - beam collimating off - axis paraboloid stage sub - assembly . the thz source sub - assembly is composed of an opto - mechanic mount and the backward wave oscillator  ( bwo ) thz source ( microtech ) . the bwo source emits thz radiation with a high brilliance ( bandwidth @xmath1452  mhz ) and a high output power ( @xmath1450.10.01  w ) . the thz radiation is almost perfectly linearly polarized and the orientation of the polarization is fixed in space . the base frequency range of the bwo is 107177  ghz , which can be converted to higher frequency bands using gaas schottky diode frequency multipliers . the spectral range accessible by the bwo can be expanded to 220350  ghz ( @xmath146 multiplier ) , 330525  ghz ( @xmath147 multiplier ) , 6501040  ghz ( @xmath146 and @xmath147 multiplier ) and 9801580  ghz ( double @xmath147 multiplier ) . for further details on the bwo based thz source and thz ellipsometry are given in ref .   and references therein . the thz radiation from the bwo is collimated by the thz - beam collimating off - axis paraboloid stage sub - assembly , composed of an opto - mechanic mount and a 90@xmath137 off - axis paraboloid  ( o@xmath144 ) with an uncoated gold surface and an effective focal length @xmath148  mm . the thz - beam then reaches the optical chopper assembly  ( ch ) , which contains an opto - mechanic mount and a 3 bladed optical chopper , driven by a linear motor . the 3 bladed optical chopper is rotated with a frequency of @xmath149  hz , resulting in a optical chopping frequency of @xmath150  hz , which is close to the optimal frequency response of the golay cell detector ( @xmath151  1215  hz ) . after interaction with thz - beam steering plane mirror assembly  ( m@xmath143 ) ( opto - mechanic mount and plane first surface gold mirror@xcite ) , the thz - beam is redirected to the polarization state rotator assembly  ( pr ) . the polarization state rotator assembly ( fig . [ fig : pr ] ) is an odd - bounce image rotation system.@xcite the polarization state rotator is designed to rotate the polarization state of an incoming electromagnetic beam azimuthally in a non - deviating , non - displacing fashion ( with respect to the incoming electromagnetic beam direction ) , and is used to pre - align the polarization direction of the thz - beam with the polarizing axis of the wire - grid polarizer in the polarization state preparation unit . the polarization state rotator assembly is composed of a stepper motor  ( st@xmath10 ) with a 12-tooth polymer gear , which is connected to a 48-tooth polymer gear ( gear ratio :  1:4 ) via a kevlar timing belt  ( b@xmath10 ) , rotating a peek cage  ( pr ) which contains three opto - mechanic mounts with plane first surface gold mirrors@xcite ( rotation axis parallel to the incoming and outgoing thz - beam ) . after reflection on a thz - beam steering plane mirror assembly  ( m@xmath144 ) ( opto - mechanic mount and plane first surface gold mirror@xcite ) , the thz - beam leaves the thz source unit . +    the polarization state preparation unit contains four assemblies : a fir - beam steering plane mirror assembly  ( m@xmath152 ) , a thz - beam steering plane mirror assembly  ( m@xmath153 ) , a source selection and beam focusing assembly  ( r@xmath143 ) , and a rotation stage assembly  ( p@xmath142-b@xmath144-st@xmath144 ) . the fir- and thz - beam steering plane mirror assemblies  ( m@xmath154 ) are identical and both are composed of an opto - mechanic mount and a plane first surface gold mirror.@xcite the plane first surface gold mirrors redirect , depending on the spectral range the fir / thz ellipsometer sub - system is operated in , the fir- or thz - beam to the source selection and beam focusing assembly . the source selection and beam focusing assembly  ( r@xmath143 ) comprises two sub - assemblies , the rotatable plane mirror sub - assembly and the beam focusing off - axis paraboloid stage sub - assembly , which are equivalent to those in the source selection and beam focusing assembly in the polarization state preparation unit of the mir ellipsometer sub - system ( fig . [ fig : beamlift ] a ) . depending on the orientation of the plane first surface gold mirror@xcite in the rotatable plane mirror sub - assembly , either the fir- or thz beam is directed to beam focusing off - axis paraboloid stage sub - assembly ( gold surface @xmath135 off - axis paraboloid , @xmath136  mm ) . the focused beam is then routed through the rotation stage assembly , which contains two polyethylene substrate based wire - grid polarizers  ( p@xmath142 ) , but is otherwise identical to the rotation stage assembly in the polarization state preparation unit of the mir ellipsometer sub - system ( fig . [ fig : beamlift ] b ) . the beam then leaves the polarization state preparation unit . the beam is then reflected by , or transmitted through the sample  ( s@xmath142 ) . the sample can be mounted on a sample holder , attached to the fir / thz goniometer unit  ( g@xmath142 ) ( commercially available , 2-circle goniometer 415 , huber diffraktionstechnik ) , or inside the magneto - cryostat sub - system  ( m2 ) . if the magneto - cryostat sub - system is used , reflection type measurements can only be conducted at @xmath139 angle of incidence . a detailed description of the magneto - cryostat sub - system , its sample mount , and the optical window configuration is given in section  [ sec : magnet ] . the beam then enters the polarization state detection unit , which comprises a rotation stage assembly  ( a@xmath142-b@xmath153-st@xmath153 ) , a beam collimation and detector selection assembly  ( r@xmath144 ) , and three beam focusing / detection assemblies  ( m@xmath155-o@xmath153-g , o@xmath152-dtgs@xmath142 and o@xmath155-b@xmath142 ) . the beam is routed through the rotation stage assembly for the analyzer of the fir / thz ellipsometer sub - system , which contains two polyethylene substrate based wire - grid polarizers  ( a@xmath142 ) , but is otherwise identical to the rotation stage assembly in the polarization state detection unit of the mir ellipsometer sub - system ( fig . [ fig : beamlift ] b ) . the rotation stage assembly for the analyzer of the fir / thz ellipsometer sub - system can be operated in step mode for fir measurements@xcite or in continuous rotation mode for thz measurements . the beam is then collimated ( gold surface @xmath135 off - axis paraboloid , @xmath136  mm ) and redirected to the selected detector by the beam collimation and detector selection assembly  ( r@xmath144 ) , identical to the beam collimation and detector selection assembly in the polarization state detection unit of the mir ellipsometer sub - system ( fig . [ fig : beamlift ] a ) . the beam focusing and golay - cell - detector assembly  ( m@xmath155-o@xmath153-g ) contains a beam steering plane mirror sub - assembly  ( m@xmath155 ) ( opto - mechanic mount , plane first surface gold mirror@xcite ) , a beam focusing off - axis paraboloid stage sub - assembly  ( o@xmath153 ) ( opto - mechanic mount , gold surface @xmath135 off - axis paraboloid , @xmath156  mm ) , and a golay - cell detector sub - assembly  ( g ) ( opto - mechanic mount , golay - cell detector ) . the beam focusing and dtgs detector assembly  ( o@xmath152-dtgs@xmath142 ) comprises a beam focusing off - axis paraboloid stage sub - assembly  ( o@xmath152 ) ( opto - mechanic mount , gold surface @xmath135 off - axis paraboloid , @xmath157  mm ) , and a solid state deuterated triglycine sulfate detector sub - assembly  ( dtgs@xmath142 ) ( opto - mechanic mount , bruker vertex v-70 dtgs detector ) . alternatively , the beam focusing and bolometer detector assembly  ( o@xmath155-b@xmath142 ) , composed of a beam focusing off - axis paraboloid stage sub - assembly  ( o@xmath155 ) ( opto - mechanic mount , gold surface @xmath135 off - axis paraboloid , @xmath158  mm ) and the bolometer detector sub - assembly  ( b@xmath142 ) ( opto - mechanic mount ; commercially available , liquid helium cooled bolometer detector , infrared laboratories inc . ) , can be used . for thz measurements the bolometer or the golay cell detector can be chosen , while for fir measurements only the bolometer or the dtgs detector provide frequency responses fast enough to record interferograms . the central piece of equipment of the integrated mir , fir and thz ohe instrument is the commercially available , superconducting , closed cycle magneto - cryostat sub - system ( 7t - spectromagpt , oxford instruments ) with four optical ports ( fig . [ fig : cad ] ) . the design of the integrated mir , fir and thz ohe instrument allows the usage of the magneto - cryostat sub - system with the mir and the fir / thz ellipsometer sub - system by employing the magneto - cryostat transfer sub - system . the magneto - cryostat sub - system can be subdivided into the magnet head , the primary cooling cycle , the secondary cooling cycle , the sample holder and the optical windows . the magnet head contains two magnet coils , which are mounted around the sample position and are fabricated in a split - coil pair design . in a spherical volume of 10  mm diameter around the sample , magnetic fields up to @xmath159  t with an inhomogeneity of less than 0.3  % can be achieved . the magnetic field can be reversed and points towards one of the optical windows . therefore , for reflection type ohe measurements , the magnetic field lies within the plane of incidence and forms an angle of @xmath160 with the sample normal . this leads to a magnetic field component @xmath161 perpendicular to the sample surface . the primary cooling cycle comprises a pulse tube cooler ( srp-082 , shi cryogenics ) , high pressure helium lines and a helium compressor ( f-70 , sumitomo heavy industries ) . ultra - high - purity helium  ( uhp - he ) gas at high pressure is provided by the helium compressor , and guided by a high pressure helium line to the pulse tube cooler . the pulse tube cooler is thermally coupled to the superconducting magnet coils and allows to cool the magnet coils to temperatures of @xmath162  k. the pulse tube cooler also pre - cools the uhp - he in the secondary cooling cycle . the uhp - he gas is then guided back to the helium compressor by a high pressure helium line , and is reused . the secondary cooling cycle uses uhp - he gas to cool the sample . the uhp - he gas in the closed cycle , is circulated by an oil - free , dry scroll pump ( xds-10 , edwards ) . when the sample is at base temperature , the uhp - he gas leaves the outlet of the scroll pump at a pressure of @xmath145  0.5  bar , and is pumped through a zeolite and a liquid nitrogen trap , in order to extract possible contaminants leaking into the closed cycle . the uhp - he gas then passes a distiller spiral , which is thermally coupled to the pulse tube cooler ( primary cooling cycle ) , and condenses the uhp - he gas into liquid helium ( lhe ) . the lhe flow is controlled by a needle valve , and the lhe is then injected into a heat exchanger . the heat exchanger is attached to the double - walled , hollow variable temperature inset ( vti ) cryostat ( fig . [ fig : sampleholder ] ) . finally , the scroll pump reduces the gas pressure above the lhe to 1.5 - 3  mbar and thereby cools the vti to a minimal temperature of @xmath13  k. the sample is thermally coupled to the vti by a static exchange gas ( uhp - he ) . a resistive heater allows to warm the sample up to room temperature , without bringing the temperature of the superconducting magnet coils above the critical temperature .    the sample holder of the magneto - cryostat sub - system ( fig . [ fig : sampleholder ] ) can hold up to two samples at a time . if two samples are mounted the optimal sample size is , while the maximum sample size is ( only one sample can be mounted ) . the sample position is adjustable in the vertical direction ( @xmath163  mm ) and rotationally around the vertical axis of the vti by 360@xmath137 ( angle of incidence alignment ) . all other degrees of freedom necessary for sample alignment ( linear motion , rotation , tip / tilt ) can only be accessed by moving the sample together with the magneto - cryostat sub - system . the magneto - cryostat sub - system can be moved parallel to the incoming beam , using the magneto - cryostat transfer sub - system . the alignment perpendicular to the incoming beam and the rotational alignment of the magneto - cryostat sub - system is achieved by sliding the magneto - cryostat sub - system in the magneto - cryostat holding frame of the magneto - cryostat transfer sub - system ( see sec .  [ sec : magnet_transfer ] ) . four screws in the same magneto - cryostat holding frame of the magneto - cryostat transfer sub - system are used for tip / tilt alignment . after successful alignment , in order to minimize motion , the magneto - cryostat sub - system is clamped to the magneto - cryostat holding frame of the magneto - cryostat transfer sub - system . when the light beam is routed through the magnet head , it passes a set of exterior and interior optical windows . for measurements in the fir / thz spectral range , the exterior optical windows are made of 0.27  mm thick homo - polypropylene films , while for the mir spectral range potassium bromide ( kbr ) windows are used . all four exterior windows are purged on the exterior side with dried air , to prevent condensation of moisture from the ambient air . the exterior optical windows of the magnet can be exchanged and arranged for both transmission- and reflection - type measurements . the latter window configuration allows reflection - type measurements over the full spectral range of the ohe instrument , by simply moving the magneto - cryostat between the ellipsometer sub - systems without warming up the superconducting coils or the sample . the interior four optical windows on the vti are made of polished diamond , grown by chemical vapor deposition ( cvd ) , with a thickness of 0.35  mm , a diameter of 14  mm and an average surface roughness of @xmath164  nm ( arithmetic average ) . to reduce fabry - prot interferences in the interior optical windows the interior windows were wedged by an angle of @xmath1450.5@xmath137 . the interior windows were glued into stainless steel window frames by a cryogenic two component epoxy , leaving a clear aperture of @xmath14512  mm ( see cutout in fig .  [ fig : sampleholder ] ) .    in general , optical windows affect experimental ellipsometry data , especially if the optical window material is birefringent . therefore all optical windows were characterized by transmission ge on a commercial mir ellipsometer ( j.a.woollam co. , inc . ) . no birefringence was observed in the mir spectral range . nevertheless , through mounting of the optical windows , and in particular through stress due to the vacuum in the magneto - cryostat sub - system , strain induced birefringence can not be completely excluded and therefore window effects are included in the analysis of the ohe data ( see sec . [ sec : ohe - analysis ] ) .      the magneto - cryostat transfer sub - system ( fig . [ fig : cad - overview ] ) contains the magneto - cryostat transfer frame , the mir source unit frame and the fir / thz source unit frame . the magneto - cryostat transfer frame comprises the magneto - cryostat transfer assembly , the mir goniometer unit platform assembly and fir / thz goniometer unit platform assembly . the magneto - cryostat transfer assembly is built from alumina extrusions . the grooves of the alumina extrusions are used as guides for a teflon roll based rail sub - assembly . on top of the teflon roll based rail sub - assembly the magneto - cryostat holding frame ( black alumina extrusions in fig . [ fig : cad - overview ] and [ fig : cad ] ) is mounted , which is used for alignment purposes ( see sec . [ sec : magnet ] ) . the mir and fir / thz goniometer unit platform assemblies are mounted into the magneto - cryostat transfer frame and are platforms for the mir and fir / thz goniometer unit of the ellipsometer sub - systems . the mir and fir / thz source unit frames are built from alumina extrusions , equipped with a 19-inch rack mounting system , and provide platforms for the source units of the mir and fir / thz ellipsometer sub - systems , respectively . all spectroscopic ellipsometer sub - systems of the integrated mir , fir and thz ohe instrument are operated in a @xmath113 configuration , capable to measure the upper left @xmath1 block of the mueller matrix . note that this does not affect the ability to determine certain sample properties related to anisotropy , which can be obtained from the off - diagonal - block elements @xmath165 , @xmath166 , @xmath167 and @xmath168 . for rotating - analyzer based ellipsometers with lossless and ideal polarizing optical elements , the stokes vector of a beam of light at the detector @xmath169 can be described within the mueller matrix formalism by@xcite @xmath170 where @xmath171 is the stokes vector of the light leaving the source , and @xmath119 , @xmath120 , @xmath172 and @xmath97 are the mueller matrices of a polarizer , analyzer , coordinate rotation by the angle @xmath173 ( polarizer : @xmath174 ; analyzer : @xmath175 ) and sample , respectively . if the analyzer is rotated with a constant angular frequency @xmath176 , and both , light source and detector exhibit no polarization dependency , _ e.g. _ the source emits unpolarized light with intensity @xmath177 and the detector is only sensitive to the total intensity @xmath178 , and @xmath179 the ratio of these quantities is @xmath180\ ; ,      \end{split}\ ] ] with the time harmonic fourier coefficients @xmath181 individual mueller matrix elements @xmath182 are determined from fourier coefficients measured at different polarizer orientations @xmath183 on the input side ( see subroutine mueller matrix regression in fig . [ fig : flow_aqu ] ) . the complete sequence of operations executed by the ohe instrument during the ge and ohe data acquisition is summarized in fig . [ fig : flow_aqu ] . since the intensity of light at the detector and the fourier coefficients ( employed to determine the mueller matrix elements ) depend on the absolute angular positions of all rotating optical elements [ eq .  ( [ eqn : fouriercoef ] ) and ( [ eqn : ncsparameter ] ) ] , the knowledge of these absolute angular positions is crucial for the operation of every ellipsometer . furthermore , all spectroscopic ellipsometers have to account for non - ideal polarization characteristics of sources and detectors , as well as commonly present non - idealities of mir and fir optical elements ( such as polarizers ) , in their calibration routine . the absolute positions of the optical components used in the ohe instrument , with respect to the _ p_- and _ s_-coordinate system ( the _ s_-axis is parallel to the goniometer axis , the _ p_-axis is perpendicular to the beam ) , as well as the non - idealities of the optical elements are carefully calibrated prior to the ohe data acquisition . all ellipsometers sub - systems are calibrated prior to the experiments .      during ohe data analysis , additional non - idealities , not included in the ellipsometer calibration , introduced by the magneto - cryostat sub - system have to be considered . in particular , three effects are considered : ( i ) in- and - out - of - plane anisotropy in the optical window@xcite , ( ii ) changes in the alignment of mirrors and/or off - axis paraboloids in the polarization state preparation and detection units due to magnetic forces on ferromagnetic components ( ellipsometric coordinate system change ) , and ( iii ) imperfect sample alignment ( ellipsometric coordinate system and angle - of - incidence change ) . in order to account for sample misalignment in the model based data analysis described in section  [ sec : data analysis ] , the angle of incidence and the sample tilt angle are included as model parameters . in order to model the combined non - idealities due to strain induced birefringence in the optical windows and minute changes in the alignment of optical elements on the input ( output ) side , an additional mueller matrix @xmath184 ( @xmath185 ) was included in the model based data analysis ( sec . [ sec : data analysis ] ) . the mueller matrices @xmath184 and @xmath185 are assumed to have no dispersion ( wavelength independent ) . the best - model mueller matrix @xmath186 , used for mse regression as described in section  [ sec : data analysis ] reads @xmath187 where @xmath188 represents the sample mueller matrix calculated by the @xmath2 matrix formalism . of the in- and output matrices @xmath189 and @xmath190 is smaller then 0.02 over the full magnetic field range . ]    for the analysis of ohe data , two strategies may be used exploiting either model - free or model - based approaches . model free analysis provides semi - quantitative results , by studying trends in amplitudes or spectral positions of features in ohe or derived ohe data vs. the magnitude of the magnetic field @xmath191 . the model free analysis can provide insight into the symmetry properties of magneto - optic dielectric tensors,@xcite and an example for the model free analysis of derived ohe data @xmath192 vs. @xmath191 is given in section  [ sec : graphene ] for the case of epitaxial graphene . the model - based data analysis approach provides more quantitative parameters than the model - free data analysis approach , and can be used to determine model parameters such as the free charge carrier concentration or the effective mass parameters . during the data analysis the ge , ohe and derived ohe datasets are analyzed simultaneously to determine physical model parameters of @xmath193 and @xmath194 by a single , consistent optical model ( fig . [ fig : flow ] ) . * in the first step , @xmath110 ( ge data obtained at @xmath68  t ) is analyzed only . during the analysis , all model parameters _ independent _ of the magnetic field , such as those describing , for example , the polar lattice resonances or layer thickness are varied until the calculated data match the measured data as closely as possible . * in the second step , ohe data @xmath195 for @xmath196  t is included in the analysis , and all model parameters _ dependent _ on the magnetic field , such as , for example , effective mass or inter - landau - level transition parameters are varied . in addition , derived ohe data @xmath108 and/or @xmath197 can be included into the simultaneously analyzed dataset . these derived ohe datasets do not increase the amount of information collected during the experiment , but help ( _ a _ ) to visualize magnetic field induced changes , and ( _ b _ ) improve the sensitivity to magnetic - field dependent model parameters during ohe data analysis . t , as for example in case of inter - landau - level transitions in epitaxial graphene , discussed in section  [ sec : graphene ] . ] the parameters determined in the first analysis step are used as starting values for the second analysis step and are varied if necessary . note that an optical model , describing the ge dataset ( @xmath68  t ) sufficiently well , might not be capable to describe the complete dataset including ohe and/or derived ohe data correctly . if necessary the optical model has to be adjusted , and the data analysis procedure has to be repeated . additional information on the data analysis strategies can be found in ref .  . in this section , experimental data from the integrated mir , fir and thz ohe instrument is presented . first , a combined dataset of derived ohe data from the mir , fir and thz spectral range from 7.5  @xmath0 to 4000@xmath198 ( 0.22120  thz or 0.9500  mev ) , and a magnetic field of @xmath1994  t , for an epitaxial graphene sample grown on 6__h__-sic is shown ( fig . [ fig : full_range ] ) . in the spectral range below approximately 500 - 600  @xmath0 the experimental data reveals an ohe signal enhanced by fabry - prot interferences in the 6__h__-sic . an ohe signal , enhanced by coupling with the 6__h__-sic phonon mode , is observed near 1000  @xmath0 . furthermore , between 500 and 4000  @xmath0 inter - landau - level transitions in single layer graphene are observed in the on - diagonal block elements of the mueller matrix .    then derived ohe data from the individual mir , fir and thz spectral ranges of the integrated mir , fir and thz ohe instrument , and the corresponding best - model calculated data are shown exemplarily . we present results from ohe experiments on an epitaxial graphene sample grown on 6__h__-sic , a te doped n - type gaas substrate and an algan / gan high electron mobility transistor structure  ( hemt ) , representing the mir , fir , and thz spectral range of the integrated mir , fir and thz ohe instrument , respectively . the selected experimental datasets demonstrate the full spectral , magnetic field and temperature range of the integrated mir , fir and thz ohe instrument , as well as analysis strategies . effects from free charge carriers in bulk and in two dimensional confinement as well as quantum mechanical effects ( inter - landau - level transitions ) are observed and discussed . exemplarily , epitaxial graphene on 6__h__-sic was investigated to demonstrate the mir ellipsometer sub - system of the ohe instrument  ( sec . [ sec : mir ] ) . the epitaxial graphene sample was grown in an argon atmosphere at 1400  @xmath96c , by sublimating si from the polar _ c_-face ( 000@xmath200 ) of a semi - insulating 6__h__-sic substrate . from previous measurements on c - face 4__h__-sic @xcite , the number of graphene layers is estimated to be 10 - 20 . further details on growth conditions are beyond the scope of this manuscript , and can be found in ref .  . the ohe experiment was conducted at an angle of incidence of @xmath201  =  45@xmath96 , while the magnetic field was aligned along the reflected beam . experimental data was recorded in the spectral range from 600 to 4000  @xmath0 with a spectral resolution of 1  @xmath0 , using the hgcdte detector , while the sample was kept at a temperature of @xmath15  k.    figure  [ fig : graphene1 ] shows derived ohe data @xmath192 ( green , dotted line ) for @xmath159  t ( effective field parallel to sample normal @xmath202  t ) and results from best model calculations ( red , solid line ) . the model free analysis approach provides valuable information . the ohe data shows several resonances , which can be divided in three groups : a peak near @xmath203  @xmath0 labeled fcc ( triangles , pink ) , a set of features labeled ll@xmath204 ( rectangles , blue ) and a set of peaks labeled ll@xmath205 ( diamonds , orange ) . while the resonances labeled fcc and ll@xmath204 are present in all mueller matrix elements , the features labeled ll@xmath205 are only present in the on - diagonal - block elements of the mueller matrix . since non - vanishing off - diagonal - block elements in the mueller matrix are inherently tied to non - vanishing off - diagonal elements in the underlying dielectric tensor , the dielectric tensor has to be diagonal @xmath206 . furthermore , the magneto - optic contributions of ll@xmath205 to the permittivity tensor in its representation for circularly polarized light [ eq . ( [ eq : llteps ] ) ] must satisfy @xmath33 . in other words , the physical processes leading to the fingerprints labeled ll@xmath205 are polarization conserving - while the processes leading to fcc and ll@xmath204 are polarization mixing ( polarization selection rules ) .    the origin of the individual processes can be determined by field - dependent measurements . figure  [ fig : graphene2 ]  ( c ) displays the magnetic field dependence of a representative on - diagonal - block mueller matrix element @xmath207 of the derived ohe dataset for @xmath208 in @xmath209 increments ( the corresponding representative off - diagonal - block mueller matrix element is omitted here and the interested reader is referred to ref .  ) . at a first glance it can be noted that the resonance labeled fcc increases in amplitude while its spectral position is not affected . this indicates that the resonance labeled fcc is the sic phonon mode ( best model parameter : @xmath210 , , , , , , , , , , and ) enhanced , magneto - optic fingerprint from free charge carriers . in contrast , the spectral positions of the resonances labeled ll@xmath205 shift to higher energies and their amplitudes increase with increasing magnetic field strength . a detailed analysis of the peaks reveals a @xmath211-dependence of their spectral positions , indicative for inter - landau - level transitions in the dirac - type band structure of single - layer graphene with the fermi level close to the charge neutrality point  @xcite . landau level energies in single layered graphene are given by @xmath212 with @xmath213 , where @xmath214 is the average velocity of dirac fermions in graphene . optical selection rules for transitions between levels @xmath215 and @xmath46 demand @xmath216 . the fermi velocity is determined as @xmath217 m/s , in very good agreement with refs .  . the analysis of the magnetic field dependence of the resonances labeled ll@xmath204 reveals their origin from the bi - layer branch of inter - landau - level transitions in aba - stacked ( bernal ) multi - layered graphene . inter - landau - level transitions from bi - layer and tri - layer graphene were identified . for further details the interested reader is referred to ref .  . the _ n_-type gaas substrate investigated here , was moderately doped with tellurium ( @xmath218  @xmath219 ) and is opaque to fir radiation . all measurements were conducted at an angle of incidence of @xmath139 , while the magnetic field was parallel to the reflected beam . figure  [ fig : gaas_8 t ] shows experimental data from the fir spectral range ( 50650 @xmath0 ) obtained at a sample temperature of @xmath220  k. the sub - figures  ( a ) and ( b ) display ge data ( @xmath68  t ) and derived ohe data @xmath221 for @xmath159  t , respectively . without magnetic field , gaas is optically isotropic , i.e. , for @xmath68  t all off - diagonal - block elements ( @xmath165 , @xmath166 , @xmath167 , and @xmath168 ) in ( a ) are zero . in contrast , due to the underlying magneto - optic dielectric tensor symmetry , all on - diagonal - block elements in ( b ) are zero , indicating the anti - symmetry of the off - diagonal elements of the dielectric tensor , as well as their sign change under field inversion . note that for a bulk material and a field orientation that is not perpendicular to the sample surface , all off - diagonal elements of the dielectric tensor are different from zero . this also leads to the asymmetry between corresponding mueller matrix elements with interchanged indices ( @xmath222 and @xmath223 ) . the optical model for the gaas substrate consists of a single , semi - infinite layer which contains two contributions , the optical response of polar lattice vibrations and free charge carriers described by the drude model . due to the crystal symmetry of gaas , the dielectric tensor for the lattice vibration [ eq .  ( [ eqn : phonon2 ] ) and ( [ substrate ] ) ] has identical diagonal elements , _ e.g. _ @xmath224 and possesses only one to - lo resonance in the fir spectral range . best model parameter for the lattice vibrations were determined as @xmath225 , @xmath226  @xmath0 , @xmath227  @xmath0 and @xmath228  @xmath0 . the model parameters for the free - charge - carrier contribution @xmath229  @xmath219 , @xmath230  @xmath231/vs and @xmath232  m@xmath233 are in good agreement with results in previous publications.@xcite      the hemt structure investigated here , was grown on a semi - insulating 4__h__-sic substrate by metal - organic chemical vapor deposition at temperatures of 1050  @xmath137c.@xcite first , a nominally 100  nm thick aln nucleation layer was grown , followed by a 1800  nm thick gan buffer and a 20  nm thick al@xmath234ga@xmath235n electron barrier layer . figure  [ fig : hemt ] displays the temperature dependence of non - vanishing off - diagonal - block mueller matrix elements of derived ohe data @xmath236 and @xmath237 for @xmath238  t in the spectral range from 0.22 to 0.32  thz . the experimental ohe data is depicted as dotted lines  ( green ) , while best - model calculated ohe data is plotted as solid lines  ( red ) for different temperatures between 1.5  k and 300  k. the observed ohe is caused by free charge carriers in the high mobility channel of the hemt structure , which is enhanced by the fabry - prot interference in the @xmath239  @xmath240 m thick sic substrate . the optical model is composed of a sic substrate layer , a aln nucleation layer , a gan buffer layer , a layer for the gan hemt channel and a algan layer . the thickness of the gan hemt layer was set to @xmath241  nm and not varied during data analysis . the hemt layer thickness was used to calculate the sheet charge density @xmath242 , where @xmath243 is the bulk charge density . derived thz ohe data was analyzed simultaneously with ge data recorded with a commercial mir ellipsometer.@xcite during model based ohe data analysis the parameters for the sheet charge density @xmath244 , the mobility @xmath240 and the effective mass parameter @xmath245 were determined . the sheet carrier density was found to be constant within the error limits at a value of @xmath246  @xmath247 for all temperatures . the mobility and the effective mass parameters were determined as @xmath248 ( @xmath249 ) and @xmath250  @xmath231/vs ( @xmath251  @xmath231/vs ) at @xmath15  k ( @xmath220  k ) , where @xmath252 is the mass of the free electron . further details are omitted here and the interested reader is referred to an in depth discussion in ref .  . in this article , we have given an overview over theoretical and experimental aspects of the ohe , and have successfully demonstrated the operation of an integrated mir , fir and thz optical hall effect instrument . two in - house built ellipsometers sub - systems , operating in the rotating - analyzer configuration , were employed to determine the upper @xmath1 block of the normalized mueller matrix in an ultra wide spectral range from 3  @xmath0 to 7000  @xmath0 ( 0.1210  thz or 0.4870  mev ) . different aspects of the integrated mir , fir and thz optical hall effect instrument , such as the cryogen - free , superconducting 8  tesla magneto - cryostat sub - system , and the optical setup of the integrated mir , fir and thz optical hall effect instrument , as well as the data acquisition and data analysis strategies were discussed in detail . for demonstration purposes of the operation of the integrated mir , fir and thz optical hall effect instrument in the mir , fir and thz spectral range , three sample systems were studied : an epitaxial graphene sample ( mir ) , a gaas substrate ( fir ) and a algan / gan hemt structure ( thz ) . the presented data covered the full magnetic field range ( @xmath253  t ) and temperature range ( @xmath254  k ) of the system . we have demonstrated that the integrated mir , fir and thz optical hall effect instrument can be used to determine the parameters of free charge carriers in bulk , and in two - dimensional confinement . furthermore , it was shown that the integrated mir , fir and thz optical hall effect instrument is capable to investigate the symmetry properties of magneto - optic , dielectric tensors of quantized systems , and was able to determine the polarization selection rules of inter - landau - level transitions . the integrated mir , fir and thz optical hall effect instrument has a wide range of applications , from determining free charge carrier properties contact - free , over the access to free charge carrier properties in buried layers , to magneto - optic quantum phenomena , polarization selection rules , to symmetry properties of magneto - optic dielectric tensors . this work was supported by the army research office ( d. woolard , contract no . w911nf-09-c-0097 ) , the national science foundation ( grant nos . mrsec dmr-0820521 , dmr-0907475 , eps-1004094 ) , with primary support under mri dmr-0922937 , the university of nebraska - lincoln , the j.a . woollam foundation and the j.a . wollam company . the authors thank dr . gaskill and his workgroup at the u.s . naval research laboratory , washington dc for providing epitaxial graphene samples . the authors would like to acknowledge dr . v.  darakchieva and dr . e.  jansen and their workgroups at the university of linkping , sweden for providing the hemt structure samples . thanks to c.  rice , c.  briley , s.  m.  slone and a.  boosalis for their help building and testing mechanical and electrical components . special thanks to the instruments shop at the department of physics at unl , and in particular to l.  marquart for his invaluable advice . 102ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12  & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty @noop * * ,   ( ) @noop * * ,   ( ) link:\doibase 10.1002/andp.19003060312 [ * * ,   ( ) ] @noop _ _  ( ,  ,  ) @noop _ _  ( , ,  ) @noop * * ,   ( ) @noop * * ,   ( ) @noop * * ,   ( ) @noop * * , ( ) in  @noop _ _ ,  ( ,  ,  )  pp .   and ,  eds . , @noop _ _ ( ,  ,  ) @noop _ _ , , vol . ( ,  ,  ) @noop * * ,   ( ) \doibase    http://dx.doi.org/10.1063/1.1138206 [ * * ,   ( ) ] \doibase http://dx.doi.org/10.1063/1.1619582 [ * * ,   ( ) ] \doibase    http://dx.doi.org/10.1063/1.1805252 [ * * ,   ( ) ] \doibase    http://dx.doi.org/10.1063/1.4789495 [ * * ,   ( ) ] link:\doibase    10.1063/1.2209968 [ * * ,   ( ) ] @noop * * ,   ( ) @noop * * , ( ) link:\doibase 10.1063/1.1578162 [ * * ,   ( ) ] @noop * * ,   ( ) \doibase http://dx.doi.org/10.1016/j.tsf.2003.11.215 [ * * ,   ( ) ] link:\doibase 10.1063/1.4772625 [ * * ,   ( ) ] link:\doibase    10.1002/pssc.200565467 [ * * ,   ( ) ] link:\doibase    10.1063/1.2168258 [ * * ,   ( ) ] link:\doibase 10.1063/1.2735669 [ * * ,   ( ) ] link:\doibase    10.1007/s11664 - 008 - 0385 - 8 [ * * ,   ( ) ] @noop * * ,   ( ) @noop * * ,   ( ) @noop * * ,   ( ) @noop * * ,   ( ) link:\doibase    10.1063/1.3556617 [ * * ,   ( ) ] \doibase http://dx.doi.org/10.1557/opl.2013.811 [ * * ( ) , http://dx.doi.org/10.1557/opl.2013.811 ] \doibase    http://dx.doi.org/10.1063/1.4833195 [ * * , ( ) ] link:\doibase    10.1063/1.4765351 [ * * ,   ( ) ] @noop * * ,   ( ) link:\doibase    10.1103/physrevlett.111.077402 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.61.8187 [ * * ,   ( ) ] link:\doibase    10.1103/physrevb.62.7365 [ * * ,   ( ) ] @noop * * ,   ( ) @noop * * ,   ( ) link:\doibase 10.1103/physrevlett.20.1292 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.86.155409 [ * * ,   ( ) ] http://0-search.ebscohost.com.library.unl.edu/login.aspx?direct=true&db=inh&an=10096425&site=ehost-live&scope=site [ * * ,   ( ) ] http://0-search.ebscohost.com.library.unl.edu/login.aspx?direct=true&db=inh&an=9600466&site=ehost-live&scope=site [ * * ,   ( ) ] @noop _ _  ( ,  ,  ) @noop _ _ ,  optical engineering - marcel dekker  ( ,  ) ,  ed . , @noop _ _ ,  vol . ( ,  , ) @noop _ _ ( ,  , ) @noop * * ,   ( ) @noop _ _ ( ,  ,  ) in  @noop _ _ ,  ( ,  ,  ) @noop _ _  ( ,  ,  ) @noop * * ,   ( ) @noop * * ,   ( ) @noop * * ,   ( ) link:\doibase 10.1103/physrevb.66.195204 [ * * ,   ( ) ] @noop _ _  ( , ,  ) \doibase http://dx.doi.org/10.1016/0039-6028(80)90297-6 [ * * ,   ( ) ] link:\doibase 10.1063/1.1141417 [ * * ,   ( ) ] @noop * * ,   ( ) @noop * * ,   ( ) link:\doibase 10.1364/josa.66.000949 [ * * , ( ) ] link:\doibase 10.1364/josa.68.001519 [ * * , ( ) ] @noop * * ,   ( ) @noop _ _  ( ,  ) @noop * * ,   ( ) @noop * * ,   ( ) @noop * * ,   ( ) @noop * * ,   ( ) @noop * * ,   ( ) @noop `` , ''   ( ) http://www.google.de/patents/download/methods_for_uncorrelated_evaluation_of_p.pdf?id=daieaaaaebaj&output=pdf&sig=acfu3u3it9tbri83bleybiqov23nj6awpa [ `` , ''  ] ( ) link:\doibase 10.1364/josaa.5.000773 [ * * ,   ( ) ] link:\doibase    10.1063/1.4732159 [ * * ,   ( ) ] link:\doibase    10.1063/1.3442903 [ * * ,   ( ) ] link:\doibase    10.1103/physrevlett.97.266405 [ * * ,   ( ) ] link:\doibase    10.1103/physrevb.83.125302 [ * * ,   ( ) ] link:\doibase    10.1103/physrevlett.102.166401 [ * * ,   ( ) ] link:\doibase 10.1103/physrevlett.100.087403 [ * * ,   ( ) ] link:\doibase    10.1103/physrevlett.107.216603 [ * * ,   ( ) ] link:\doibase    10.1103/physrevlett.101.267601 [ * * ,   ( ) ] http://stacks.iop.org/0022-3719/12/i=12/a=014 [ * * ,   ( ) ] link:\doibase 10.1063/1.331665 [ * * ,   ( ) ] \doibase http://dx.doi.org/10.1016/j.jcrysgro.2009.01.045 [ * * ,   ( ) ] \doibase http://dx.doi.org/10.1016/j.jcrysgro.2006.10.242 [ * * ,   ( ) ]
we report on the development of the first integrated mid - infrared , far - infrared and terahertz optical hall effect instrument , covering an ultra wide spectral range from 3  @xmath0 to 7000  @xmath0 ( 0.1210  thz or 0.4870  mev ) . 
 the instrument comprises four sub - systems , where the magneto - cryostat - transfer sub - system enables the usage of the magneto - cryostat sub - system with the mid - infrared ellipsometer sub - system , and the far - infrared / terahertz ellipsometer sub - system . 
 both ellipsometer sub - systems can be used as variable angle - of - incidence spectroscopic ellipsometers in reflection or transmission mode , and are equipped with multiple light sources and detectors . 
 the ellipsometer sub - systems are operated in polarizer - sample - rotating - analyzer configuration granting access to the upper left @xmath1 block of the normalized @xmath2 mueller matrix . 
 the closed cycle magneto - cryostat sub - system provides sample temperatures between room temperature and 1.4  k and magnetic fields up to 8  t , enabling the detection of transverse and longitudinal magnetic field - induced birefringence . 
 we discuss theoretical background and practical realization of the integrated mid - infrared , far - infrared and terahertz optical hall effect instrument , as well as acquisition of optical hall effect data and the corresponding model analysis procedures . 
 exemplarily , epitaxial graphene grown on 6__h__-sic , a tellurium doped bulk gaas sample and an algan / gan high electron mobility transistor structure are investigated . 
 the selected experimental datasets display the full spectral , magnetic field and temperature range of the instrument and demonstrate data analysis strategies . 
 effects from free charge carriers in two dimensional confinement and in a volume material , as well as quantum mechanical effects ( inter - landau - level transitions ) are observed and discussed exemplarily .