Several works concerning Stokes parameter mea-surements have been done, from the Azzam four-detector photopolarimeter and the division of theamplitude photopolarimeter1,2 to the Nikolova spec-trophotopolarimeter.3,4 All these instruments allowone to perform real-time measurements of the Stokesparameters. They do not require any modulating ormoving optics, and the measurement time is relatedonly to the speed of the detectors and electronics. Inaddition, the instruments based on diffraction grat-ings not only give spectral information but also allowfor operation with a white-light source. Nevertheless,the devices proposed have some limitations anddrawbacks. Some of them1,2 are difficult to align andoften need a complex calibration procedure so thatthe device can identify the polarization state of thelight. In Refs. 2 and 5 where a diffraction grating isused, knowledge of the polarization properties of the
grating require ellipsometric characterization and aparametric model. The device of Nikolova et al.,4 onthe other hand, is based on a diffraction grating madeof a material, an emulsion of AgCl, having intrinsicstability limits.
In this paper we present a photopolarimeter forsimultaneous measurements of the Stokes parame-ters by splitting the light beam to be analyzed intofour beams by means of two diffraction gratings, as inthe scheme of the Nikolova device. The choice of ma-terials for the gratings introduces relevant improve-ments and makes the proposed device free of thedrawbacks mentioned above. The main component ofthe instrument is a polarization grating that has along time stability (more than two years), which doesnot show topographical relief (as tested by atomicforce microscope measurements), that is temperatureindependent in a wide range, and shows a good dif-fraction efficiency. The last property comes from thehigh photoinduced birefringence of the material,6�n � 0.4, that is quite a high value compared withthose reported in the literature.7,8
The second fundamental element is a conventionaltransmission grating recorded by means of an inten-sity holographic technique in a thin film of a pho-topolymer. To avoid anisotropies during the gratingrecording, the interference of two parallel circularlypolarized beams has been used. The gratings are sta-ble for a long time period. The two gratings constitutethe main elements of the device, which also includestwo fixed polarizers and four detectors (photodiodes).
C. Provenzano and G. Cipparrone ([email protected]) arewith the Dipartimento di Fisica and Excellence CentreCEMIF.CAL, Università della Calabria, I-87036, Rende (Cs), It-aly. A Mazzulla is with the Consiglio Nazionale delle Ricerche,Istituto Nazionale per la Fisica della Materia, Laboratory andExcellence Centre CEMIF.CAL, c�o Dipartimento di Fisica Uni-versità della Calabria, I-87036, Rende (Cs), Italy.
Received 16 November 2005; accepted 30 December 2005; posted13 January 2006 (Doc. ID 66080).
The main component of the photopolarimeter is adiffraction grating recorded in a Langmuir–Blodgett film composed by amphiphilic azo-dye mol-ecules and prepared as reported elsewhere.6 Thefilm used in the device consists of 50 monolayers.The grating is recorded using a polarization holo-graphic technique6,9,10: Two Ar-ion �� � 514.5 nm�circularly polarized laser beams (left and righthanded, respectively) with equal intensities and acrossing angle of � � 3.5° impinge on the film placedin the superposition region. In this configuration, theintensity distribution is almost uniform, but the lightis linearly polarized and the polarization directionrotates. The permanent polarization holographicgrating has been recorded at a 200 mW�cm2 lightpower density and 30 s exposure time. A He–Ne laserbeam �� � 633 nm� has been used as a probe toinvestigate the light fields transmitted by the grat-ing. The probe beam does not influence the recordedgratings since the azo-compound film does not absorbit. As expected, one diffracted beam (�1 order) is aleft-circularly polarized wave and is proportional tothe right-hand component of the incident wave, the�1 order is right-circularly polarized and is propor-tional to the left-hand component of the incidentwave, whereas the zero order keeps the same polar-ization state of the incident probe beam.6,10
B. Transmission Grating in a Photopolymer Film
The second grating used in the device has been re-corded in a thin film of a photopolymer. The materialconsists of a prepolymer mixture composed by themonomer dipentaerytrol hydroxy penta acrylate, with10 wt. % N-vinylpyrrolidone, 10�3 M N-phenylgly-cine, and 10�4 M 2,2-dimethoxy-2-phenylacetophe-none.
The cell was assembled putting 8 �m thick Mylarspacers between two glass substrates and gluing withepoxy resin from the outside. The cell was filled withthe above described mixture. Film polymerizationwas induced by means of UV light exposure as in thefollowing description. Two Ar-ion �� � 352 nm� left-circularly polarized laser beams, with equal intensi-ties and a crossing angle of � � 7.2°, impinge on thefilm placed in the superposition region. In this con-figuration the polarization state is everywhere circu-lar, and a deep modulation of the light intensitydistribution occurs. This writing configuration hasbeen chosen to avoid a photoalignment effect and toallow an isotropic growth of the polymer chains. Thegrating is permanently recorded by exposing the filmfor �300 s.
A test of the transmitted beams has been per-formed to verify the correct behavior of the grating,i.e., the requirement that transmitted and diffractedbeams keep the same polarization state of the incom-ing beam, and that their intensities are independentof the polarization state of the incident beams.
The polar plots displayed in Fig. 1 represent thepolarization analysis of the transmitted and dif-fracted beams when the probe is circularly polarized.
3. Operation Principles and Description of the Device
A scheme of the two-grating photopolarimeter (TGP)is shown in Fig. 2. The light beam to be measured (I0)impinges onto the polarization grating (PG), and thefirst diffracted orders I�1 �I1� and I�1 �I2� are detectedby the photodiodes Ph1 and Ph2, respectively. Thetransmitted beam (zero order) is diffracted again by aconventional intensity grating (IG) in which the firstorders �I3 and I4� are collected, after passing throughpolarizers P45° and P0°, by the photodiodes Ph3 andPh4. The four output signals �ii� are sent to an analog-to-digital circuit board of a PC that controls the ex-periment.
The polarization grating PG consists of a perma-nent anisotropic phase grating due only to the pho-toinduced linear birefringence. Such a grating haspeculiar features; the zero-order wave has the samepolarization as the incident one, differing just for anamplitude factor. The �1 order is left-circularly po-larized and is proportional to the right-componentof the incident wave, and the �1 order is right-circularly polarized and is proportional to the leftcomponent of the incident wave. For different po-larization states of the incident beam, only an en-ergy exchange between the two diffracted beams isobserved, the whole efficiency ���1 � ��1� remainingconstant.
Furthermore, the transmitted beam is sent onto theintensity grating where the employed holographictechnique produces an isotropic structure. The polar-ization of this intensity pattern in fact inhibits pho-toaligning processes that could occur in our material.11
The two first-order diffracted waves are the exact re-production of the incident one; i.e., they retain theoriginal polarization properties. In front of each pho-todiode Ph3 and Ph4 is placed a polarizer at angles of45° and 0°, respectively, from the incidence plane,namely, P45° and P0°.
For a particular wavelength, the relationships be-tween the four signals and the Stokes parameters areestablished as follows. The Jones vector of the inci-dent wave is
E � � Ex
Ey exp�i��, (1)
where Ex and Ey are the field components along thex and y axes and � is the phase difference betweenthese components. The measured photosignals arethen
where EL and ER are the left- and right-circularlypolarized waves and ki are the coefficients that de-pend on the diffraction grating efficiency, the po-larizer absorption, and the photodiode sensitivities.Using the Jones formalism, the signals can be writtenas a function of the Stokes parameters3,4:
i1 �S0 � S3
2k1,
i2 �S0 � S3
2k2,
i3 �S0 � S2
2k3,
i4 �S0 � S1
2k4. (3)
Inverting Eqs. (3), the Stokes parameters can be ex-pressed in terms of the measured signal values:
S0 � k1i1 � k2i2,
S1 � 2k4i4 � k1i1 � k2i2,
S2 � 2k3i3 � k1i1 � k2i2,
S3 � k1i1 � k2i2. (4)
To calibrate the TGP, ki coefficients are found for eachwavelength by a preliminary measurement of the sig-nals ii for a p-polarized incident light beam of knownintensity. The ki coefficients are thus given by
Fig. 1. Polarization analyses of the normalized intensities of theincident, transmitted, and diffracted beams: (a) incident (circles)and zero-order (squares) beams, (b) �1 order, and (c) �1 order forcircular incident polarization.
Fig. 2. Scheme of the TGP. I0, incident beams; I1–I4, diffractedbeams; PG, polarization grating; IG, intensity grating; P0° andP45°, polarizers; Ph1–Ph4, photodiodes; PC, personal computer withacquisition system.
For a He–Ne incident beam, � � 632.8 nm, and theki coefficient values are found to be k1 � 42.57,k2 � 42.57, k3 � 30.92, and k4 � 32.60, within anaccuracy of 0.01. As a consequence, by using the TGP,the ellipticity of an incident light beam can be eval-uated from the simple relation �k1 � k2�:
e � tan�12 arcsin�i2 � i1
i2 � i1��. (6)
Acquiring the four photosignals ii, the set of Stokesparameters of the light beam is calculated. It is
noteworthy that the TGP does not require any waveplates or polarizer prisms, which are used in othermethods to determine the parameters, and as aconsequence it operates at any wavelength in thesame original configuration. The only effect pro-duced by a variation of the light wavelength is achange in the direction of the first-order diffractedbeams. Beam deviation can be easily monitored us-ing a linear array of photodiodes.
For this reason the instrument has been verified tooperate with the Ar-ion laser beam �� � 514.5 nm�. Inthis case the values of the ki coefficients are found tobe k1 � k2 � 17.18, k3 � 72.10, and k4 � 94.44.
4. Experiment
To demonstrate that the TGP can measure the po-larization state of any light beam, a simple test hasbeen performed. A He–Ne laser beam has beenused, followed by a polarizer at a 0° angle from theincidence plane and a quarter-wave plate. The lat-ter is completely rotated (from 0° to 360°) in steps of5°; this rotation generates different polarizationstates: linear, elliptical, and circular. The normal-ized Stokes parameters in this case are written asfollows12:
Fig. 3. Stokes parameters as a function of the quarter-wave plate rotation angle �. Continuous curves are the theory and circles arethe data.
where � is the rotation angle of the wave plate. Fig-ure 3 shows the plots of these quantities as continu-ous curves, and the Stokes parameters measured bythe TGP are represented by circles. As can be seenfrom the graphs, assuming perfect polarizing optics,the agreement between theory and experiment isgood. The maximum error, 2%, occurs in the S1measurement, whereas the average error for all pa-rameters is much less; it is estimated as below 1%.The slight deviations between theory and experimentseem to be systematic errors due to optical componentimperfections; TGP appears to be a powerful tool tocharacterize such imperfections.
To verify measurement repeatability, the time sta-bility of the device has been tested. A single polariza-tion state (p) was monitored over a period of morethan seven hours. A variation within 1% of the meanvalues is found, indicating the successful operation ofthe TGP. The precision achieved is satisfactory; how-ever, it can be improved by low-noise electronics.
Figure 4 represents a run test of the ellipticity e ofthe light beam transmitted by the quarter-wave plateas a function of the rotation angle � of its optical axis.Our device is able to perform this measurement in astraightforward way; in fact, only the diffracted beamsignals from the polarization grating are involved, i1and i2, as from Eq. (6). The data (circles) are com-pared with the theory:
e � tan12 arcsin�sin�2�� . (8)
The ellipticity measurements fit well with the theory,confirming the high reliability of the polarizationgrating.
5. Conclusions
We have reported a photopolarimeter based on twodiffraction gratings recorded by means holographictechniques on thin films of organic materials. Theproper holographic recording geometries, the materialcomposition, and film preparation allowed us to obtaindiffraction properties of the gratings suitable to becombined for a spectropolarimeter extension. The pho-topolarimeter proposed in this work has an extremesimplicity of tuning, is free of modulating or movingparts, and is easy to calibrate. It has been satisfactorilytested for a single wavelength, but it can operate overthe whole visible spectral range. The only requirementis the estimation of the ki coefficients for each wave-length. Four CCD linear arrays can replace the fourphotodiodes to allow for the spectral acquisition of adispersed polychromatic beam. Proper research ofmaterials is required to enlarge the working spectralrange of the device, mainly in the UV range where thedevice could have interesting applications. Only de-tector speed and electronics acquisition processeslimit the rate at which data can be taken by theinstrument; hence it can be useful in real-time mea-surements.
The authors thank L. M. Blinov, S. P. Palto, andS. G. Yudin for useful discussions and for supplyingthe material.
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